FACULTY OF ELECTRICAL ENGINEERINGEINDHOVEN UNIVERSITY OF TECHNOLOGY

Telecommunications Division

Modelling and Simulation of IndoorRadio Channels in the mm-Wave Frequency Band

by G.J.A.P. Vervuurt

Graduation Thesis

PeriodMentors

Supervisor

: March 1992 - January 1993: Ir. P.F.M. Smulders

Dr. Ir. M.H.A.J. Herben: Prof. Dr. Ir. G. Brussaard

The Faculty of Electrical Engineering of the Eindhoven University of Technology doesnot accept any responsibility for the contents of trainee and graduation reports

Summary

Over the last few years a lot of research has been done into indoor radio communication.Indoor radio communication systems in future office environments provide true mobilitywithin the building. Furthermore, it offers the flexibility of changing or creating commu­nication services in existing buildings without the need for expensive, time-consumingrewiring. Spectral space necessary for Broadband-ISDN is only available at mm-wavefrequencies. An additional advantage of these freqencies is the strong atmosphericattenuation which makes frequency re-use possible over very short distances. A disadvan­tage of these frequencies is the multipath dispersion which limits the maximum achievabledata rate.

Recently, wideband measurements of indoor radio channels at mm-wave frequencies(using omnidirectional biconical hom antennas) have been performed at the EindhovenUniversity of Technology. The measurement results show typical average power delayprofiles in different indoor environments. In this report, a rule of thumb for the averagerms delay spread (a parameter characterizing the multipath dispersion) is derived withhelp of these typical average power delay profiles. The rule of thumb is a simpleexpression depending solely on the slope of the average power delay profile which ischaracterized by 'Y.

A model to predict the value and attain insight in the behaviour of the slope parameter 'Yis proposed. According to this model, the slope parameter 'Y depends first of all on theaverage number of reflections as function of time. This number can be calculated forevery single wall and is determined by the room dimensions and the beamwidth of thecentrally placed biconical hom antenna. Second, the slope parameter 'Y depends on theaverage reflection coefficient. This coefficient can be calculated for every single wall andis independent of the polarization of the electric field and incident angle. Validation of themodel with measurements shows that correct values of the average reflection coefficientare scarce but necessary to predict the correct value of 'Y.

The rule of thumb predicts low values (only a few ns) of the average rms delay spread ifhighly directive antennas are used. A study of the influence of antenna setup and antennadirectivity on an indoor radio channel is presented in this report. The influence ofantennas is tested with a simulation programme based on Geometrical Optics. Threedifferent antenna setups (in a low and highly reflective room) are considered: A setupwith identical smooth walled pyramidal horns at both base and remote station, a setupwith a biconical hom at the base and a pyramidal hom at the remote station, and finally asetup with identical biconical horns at base and remote station.

The simulation results for the setup with identical pyramidal horns show excellentperformance in a line-of-sight situation if the antennas are pointed exactly towards eachother. If the direct path between remote and base station is blocked or if the antennas arenot pointed exactly towards each other, a severe performance degradation can beobserved. The same effects can be observed for the setup with only one pyramidal hornplaced on the remote. The results for the setup with identical biconical horns show thatblockage of the direct path does not deteriorate the channel performance significantly,especially for biconical horns with a high directivity. Furthermore, a uniform coverage ofreceived power, giving fair access to every user in the room, can be achieved with thisantenna setup.

Contents

1 Introduction -1-

2 Characterization of the Indoor Radio Channel -3-2.1 The Power Delay Profile -3-2.2 Autocorrelation of the Frequency Response -5-

3 Rule of Thumb for the Average Rms Delay Spread -7-3.1 An Analytical Expression for the Average Rms Delay Spread -7-

3.1.1 The OBS channel -8-3.1.2 The LOS channel -11-

3.2 An Analytical Expression for 'Y -15-3.2.1 Decay of Power in a Superstructure -15-3.2.2 The Average Number of Reflections for an Isotropic Antenna -16-3.2.3 The Average Number of Reflections for a Biconical Hom

Antenna -19-3.2.4 The Average Reflection Coefficient -21-3.2.5 'Y for Centrally Placed Isotropic Antennas -27-3.2.6 'Y for Centrally Placed Biconical Hom Antennas -30-3.2.7 Comparison of 'Y with Measurements -31-

3.3 Validation of the Rule of Thumb for (J -33-3.3.1 Comparison of the Rule of thumb with Measurements -33-3.3.2 Comparison of the Rule of thumb with Simulations -34-

3.4 Concluding Remarks on the Rule of Thumb for (J -35-

4 Simulation of Antenna Effects on a mm-Wave Indoor Radio Link -36-4.1 The Used Antennas -36-

4.1.1 Smooth Walled Pyramidal Hom Antenna -36-4.1.2 The Biconical Hom Antenna -40-

4.2 The Software used for Simulation -42-4.2.1 De~riptionoftheSoftware -42-4.2.2 Validation of the Software -43-

4.3 Simulation Configurations -45-4.4 Simulation Results -47-

4.4.1 Simulation Results in the Low Reflective Room -47-4.4.2 Simulation Results in the Highly Reflective Room -53-

4.5 Concluding Remarks on the Simulations -59-

5 Conclusions and Recommendations -61-

6 References -62-

Appendices

Appendix A: Derivation of an Analytical Expression for the Average RIns DelaySpread -Al-

Appendix B: The Number of Reflections in a Room as Function of Time for aBiconical Hom Antenna -Bl-

Appendix C: Dimensions of the Measurement Environments -C1-

Appendix D: Error Consideration for Formulas (3.16) and (3.17) -Dl-

Appendix E: Implementation of Pyramidal Hom Antennas -El-

Appendix F: Simulation Results Presented in Scatterplots -Fl-

1 Introduction

The use of indoor radio communication, e.g. within office buildings, hospitals, televisionstudios, conference centres, etc., is an attractive proposition. It would free the users fromcords tying them to particular locations and offer true mobility within the building, whichis often convenient Qap-top computers, television cameras) or even necessary. Furthermo­re, it would provide the flexibility of changing or creating various communicationservices in existing buildings without the need for expensive, time-consuming rewiring.

The present generation of indoor radio systems is primarily designed for speech and lowdate rate services and cannot provide real time services such as high speed data transferand video distribution, as suggested for the Broadband Integrated Services DigitalNetwork (B-ISDN). Therefore, current research and development activities in the field ofindoor radio are directed towards a large increase of transmission capacity per user. Atarget solution would be a radio network with a capacity of several hundreds of Mbit/s.This high capacity demands a spectral space which is only available in the mm-wavefrequency bands ranging from 30 GHz to 300 GHz. Radio waves in this frequency bandssuffer from high inverse square free space attenuation and attenuation of walls within abuilding. Therefore, single room communication will be an obvious choice. Especially thefrequency band around 58 GHz is an interesting band with respect to frequency re-use,because of the high attenuation due to atmospheric oxygen of about 15 dB/km.

An indoor radio channel can be characterized by multipath dispersion and fading. Topredict the channel characteristics in a particular room, a deterministic model, based ongeometrical optics, has been developed at the Eindhoven University of Technology(EUT). Furthermore, a statistical model, based on a limited number of measurements, hasbeen proposed. Both measurements and models show that the position of the remotestation does not affect the channel performance significantly, at least if omnidirectionalantennas are used at remote and base station. This implies that the indoor radio channel ofa particular room can be described by an average performance. Average performance isexpressed by the average rms delay spread, characterizing the multipath nature, andaverage received signal power.

The average rms delay spread depends highly on the dimensions of a room, reflectionproperties of walls and antennas applied in a room. A rule of thumb predicting theaverage rms delay spread would be of great value; time-consuming calculations with thedeterministic model could be avoided and the statistical model, based on a limited numberof measurements, could be made extendable to other environments. In this report, a ruleof thumb for the average rms delay spread is proposed.

If highly directive antennas are used instead of omnidirectional antennas, the spatialchannel behaviour is in general not uniform and the channel characteristics can hardly bedescribed by an average rms delay spread or average received power. Highly directiveantennas can, however, increase the channel performance significantly if the direct raybetween remote and base station is not blocked by a person and/or an object. A study ofthe possibilities of highly directive antennas in an indoor radio channel will be presentedin this report.

-1-

In Chapter 2 the parameters which characterize the indoor radio channel will be presen­ted. Next, a rule of thumb which predicts the average rms delay spread as function of theroom dimensions and reflectivity of walls is discussed in Chapter 3. The rule of thumb isbased on the measurements performed at the EUT. In Chapter 4 the influence of antennadirectivity of pyramidal horns and omnidirectional biconical horns is discussed. Also, theinfluence of antenna setup in a low and highly reflective room is considered.

-2-

2 Characterization of the Indoor Radio Channel

The indoor radio channel consists of a transmitting and receiving antenna positioned inthe same room. Electromagnetic power will not only travel via a direct path fromtransmitter to receiver, but also via indirect paths due to reflections of the EM wavesagainst walls and objects within a room. The indoor radio channel is therefore a multipathchannel. Multipath dispersion causes a single transmitted pulse to be received as a train ofattenuated and delayed pulses. This time domain spreading of the impulse response candegrade the performance of the channel seriously, because it increases the Inter SymbolInterference (lSI). In this chapter the parameters which describe the multipath dispersionare defined.

2.1 The Power Delay Profile

The indoor radio channel is actually a bandpass filter around a central frequency Ie (in ourcase 58 GHz), with a frequency response V(f). The channel is defined by its equivalentcomplex lowpass frequency response H(f) according to

Inverse Fourier Transform of (2.1) yields

v(t) = 2Re(h(t)eiu)

(2.1)

(2.2)

in which h(t) denotes the Inverse Fourier Transform of H(f) and is called the equivalentcomplex lowpass impulse response.

The channel is represented by multiple paths or rays having real positive gains {all}'propagation delays {Til}' and associated phase shifts {Oil}' where n denotes the path index;in principle, n extends from 0 to oa. For a multipath radio channel h(t) is given by [18]

~ "8h(t) = L.J alit! 'O(t-TII

)

/I

where 0(') is the Dirac delta function.

(2.3)

Because of the motion of people and/or objects in the room, the parameters {all}' {Til}and {Oil} are time-varying parameters. However, since motion speed is low compared to

1

any useful data rates, these parameters can be treated as virtually time-invariant functionsand the channel can be assumed to be quasi-stationary.

The total power received from a transmitted delta-pulse of strength 1 at a particular timet, originates from all delayed pulses with Til equal to t. The total received power asfunction of excess time is called the power delay profile. It is defined as [18]

-3-

p(t) I:! I h(t) 12 (2.4)

From the power delay profIle as defmed in expression (2.4), an important propagationparameter which characterizes the indoor radio channel can be derived. This parameter iscalled the root-mean-square (rms) delay spread (also known as the normalized secondmoment of the power delay profIle) and is defined as

where

q = 1,2

(2.5)

(2.6)

Note, that for continuous profiles the summations over n change into integral expressions.

The rms delay spread is an important parameter for estimating the maximum possible datarate along the channel. In [21] it has been shown that transmission with acceptableirreducible bit-error-rate (the bit-error-rate due to the delay spread alone) is possible if(JIT. ::s; 0.2 (with T. the symbol time), in case there are no special measures taken at thereceiver to combat lSI.

The denominator in (2.6) is commonly called the normalized total received power G sothat

(2.7)

The normalized total received power is also an important parameter characterizing theindoor radio channel. The parameter can be used for estimating the signal to noise ratio inan indoor radio communication system and is important for determining the radiocoverage, that is signal level, throughout a particular room. Note, that for continuousprofiles the summation of (2.7) changes into an integral expression.

In fact, the power delay profile p(t) is not only a function of time but also of thepositioning of antennas. The antenna mounted at the base station is located at a fixedposition in the room. The antenna mounted at the remote station, however, is located at arandom position in the room, so

p(t) =p(t,k) (2.8)

where k represents the position of the remote station in a room. The overall radio channelcharacteristics of a single room can best be described by an average power delay profile.This average power delay profile is expressed by

-4-

NP (t) ~ ! L p(t,k)

av - N 1-1 G(k)(2.9)

where N denotes the number of positions in a room. Each proftle is thus normalized withits own G(k). This is done for the reason that no individual profIle can dominate in theaverage proftle. The time axes of the individual profiles are aligned in such way that allline-of-sight rays are located at zero seconds delay. A typical example of a measuredaverage power delay profile is given in figure 2.1.

Average Power Delay ProfileCorTf;luter room

0

-10

~-20

III-30

~

~ -40

-50

~o

0.00 100.00 200.00

time (ns)

300.00 400.00

Figure 2.1: Measured average power delay profile in the 57-59 GHz band with twoidentical biconical hom antennas

The normalized second moment can be determined from the average power delay profile.That parameter is then called the average rms delay spread. The normalized total receivedpower can also be determined from the average power delay profile. This is called theaverage normalized total received power.

2.2 Autocorrelation of Frequency Response

In the time domain, the data rate limitations can be characterized by the rms delay spread.The data rate is limited by the frequency selectivity which is reflected by deep nulls in thechannel frequency response at certain frequencies.

A measure of the similarity or frequency coherence of the channel is given by the 3-dBwidth of the magnitude of the complex autocorrelation function of the frequency response.The magnitude of the complex autocorrelation function for the radio channel at position kis expressed as:

-5-

IR(.<1,f,k) I = J IH(f,k)· H· (f+.<1,f,k) Id/-ClD

(2.10)

Measurements [22] performed in the frequency domain (the 0.9-1.1 GHz band) show thatthe 3-dB width of I R(4f,k) I is inversely proportional to the rms delay spread asexpected.

Measurements performed at the EUT in the 57-59 band show typical autocorrelationfunctions as presented in figure 2.2a and 2.2b. Figure 2.2a shows the autocorrelationfunction for the antenna setup with two identical biconical hom antennas. The biconicalhom antennas exhibit an omnidirectional radiation pattern in the azimuth plane. Figure2.2b shows the autocorrelation function for the antenna setup with a circular hom antennaat the remote station and a biconica1 hom antenna at the base station.

Autocorrelation of Frequency ResponseReception Room (f026ol)

Autocorrelation of Frequency ResponseReception Room (f026hl)

0,-------------------,

-3

[ij' -63

-9tr

-12

-15

400 800 1200 1600 2000 400 800 1200 1600 2000

6. f [MHz]

(a)

/":,f [MHz]

(b)

Figure 2.2: Magnitude of complex autocorrelation function o/frequency response.(a) biconical-biconical hom setup (b) biconical-circular hom setup

The autocorrelation is actually an even function around zero with I R(.<1f O,k) I = 0dB. Obviously, the autocorrelation function crosses the dotted -3-dB line more than once.This implies that a unique 3-dB width can not be specified. Further investigation has to bedone to find out whether the 3-dB width of the autocorrelation can be a useful parameterin the 57-59 GHz band.

-6-

3 Rule of Thumb for the Average Rms Delay Spread

In Chapter 2 we discussed some important characteristics of a 58 GHz broadband indoorradio channel. Especially the power delay profile and the rms delay spread are crucialcharacteristics for they determine the irreducible bit rate. It is possible to describe thesecharacteristics with models. Especially deterministic models based on Geometrical Optics,and statistical models have extensively been described for broadband indoor radiochannels. Simulation programs, using the deterministic model [2][12], show a rather goodprediction of the channel characteristics. However, the simulations are time-eonsuming.The statistical models presented by Saleh and Valenzuela [19] and by Smulders andWagemans [3], are based on measurements which have been performed in a limitednumber of indoor areas.

The main interest of the study in this chapter is to find a simple analytical expression, arule of thumb, that characterizes the broadband indoor radio channel. With help of thisrule of thumb we want to gain insight in the characteristics of the indoor radio channeland even predict rms delay spread.

The measured propagation characteristics were very similar for different positions of theremote station in one room, but differed considerably from room to room. Therefore, werestrict ourselfs to a rule of thumb predicting the average rms delay spread of a room.

3.1 An Analytical Expression for the Average Rms Delay Spread

The average rms delay spread gives a good impression of the average performance of anindoor radio link. As described in Chapter 2, it can be derived from the average powerdelay profile. The main goal of this section is to attain insight in the dependence of theindoor environment on the average rms delay spread. We present a simple, yet useful,model of the (spatial) average power delay profile. With this model it is possible to obtainan analytical expression for the average rms delay spread.

While describing the model, one can distinguish between two situations, Le. the line-of­sight (LOS) channel, where a direct path exists between transmitter and receiver, and theobstructed line-of-sight (OBS) channel, where the direct path between transmitter andreceiver is blocked. The OBS channel will be examined first.

-7-

3.1.1 The OBS Channel

The model presented here is based on a number of measurements performed at the EUT,[3]. Practically all the measurements concerned LOS channels. To evaluate the OBSchannels the LOS path data points were mathematically removed from the time domainimpulse response. This is justified by experiments; the LOS ray disappeared completely ifit was blocked by a piece of absorber.

The measured average power delay profiles all show the same shape (see also figure 2.1);a constant level part up to t = 71 = 50 ns followed by a linear decreasing function downto the noise floor (in case a dB-scale is assumed). The level part in the average powerdelay profile is caused by antenna gain compensation of free-space losses [6], (identicalbiconical horns were used). This level part is therefore likely to be absent if (near)isotropic antennas are used.

For the linear decreasing part, the logarithm of received power can thus be modelled as alinear fit according to

(3.1)

Linear fitting of the measured average power delay profiles based on a minimum meansquare error (MMSE) criterion yields values for the slope parameter B between -0.06 and-0.3 dB/ns.

The solution for Pav(t) on a linear scale yields

-(t-"Jpav(t) = C'e-"- (3.2)

(3.3)

where 'Y is the time constant of the exponentially decreasing function and thus a measurefor the slope of the linearly decreasing part of the average power delay profile. C is aconstant and equals 1()A'10. The relation between 'Y and B is obtained by substitutingequation (3.2) in (3.1)

-10'Y = BlnlO

Notice that 'Y is expressed in ns; the steeper the slope of the average power delay profilethe smaller the value of 'Y. Typical values for 'Y measured at the EUT lie between 15 and75 ns.

Summarizing, the average power delay profile of a OBS channel can be modelled withthree parameters, i.e. the constant power level A = 1010gC at the start, the time constant71 for the duration of the constant level part, and finally the time constant 'Y which is ameasure for the slope of the linear decreasing part. Figure 3.1 shows a continuousfunction modelling the average power delay profile, based on these three parameters. Thiscontinuous function enables us to derive an analytical expression for the average rmsdelay spread.

-8-

DoL---~--------:==;=to 1:1

• t

Figure 3.1: Modelling the average power delay profile (OBS channel)

In chapter 2 we defined the average rms delay spread parameter (J for a discrete profile.For continuous profiles the summations change into integral expressions and (J can bedefined as

where

!PGv(t) • t iJ dt

(ttJ) =----00!Pav(t)dt

q = 1,2

(3.4)

(3.5)

An analytical expression for the spread can now be gathered from (3.4), (3.5) and finally(3.2). The calculation is presented in appendix A. The solution is given below:

(3.6)

Evidently, (J depends on only two parameters, Le. T1 and 'Y. The expression, however,does not appear very elegant and gives little insight. To gain some insight in the influenceof the parameters 'Y and T1, the spread can best be represented by a three-dimensionalperspective plot.

-9-

Figure 3.2: The average rms delay spread versus 7] and 'Y

As we can see in the figure above, the spread is mainly determined by 'Y and to a lesserextend by 71. The following plots show some cross-cuts of the three-dimensionalperspective plot at 71 = constant and 'Y = constant, respectively.

Average Rms Delay Spread Average Rms Delay Spread

120,---------------, 120,-----------------.

100

80 ••.•..•••••.•.•••...••..••.•••.••...•

--------------------

00 20 40 60 80 100

't I (ns)

---- y --- y = .... y = -y =1Srs SO rs 75 ns Ons

20 -------------------------

40

,.....,(fl

S60

o

20 40 60 80 100

"i ens)---- 1:1 = -- 1:1 = •.•. 1: 1 = - 1:1 =

2Srs SOns 7Sns on5

40

80

100

,.....,(fl

S 60b

Figure 3.3: Average rms delay spread vs 'Y (7]=constant) and vs 7] ('Y=constant)

In spite of the complexity of the function for the average rms delay spread (3.6), theaverage rms delay spread is approximated, as a rule of thumb, by the simple model:

q('Y) ., 9(1 + I)10

(3.7)

This expression is derived by fitting the curve of expression (3.6) for 71 =50 ns within theinterval 0< 'Y < lOOns. Note, that we have chosen the rule of thumb to be independent of

-10-

TI' This has two reasons: first of all, a change in TI will result only in a small change ofu, especially for high values of 'Y. Secondly, the average power delay profIles, measuredin various indoor environments at the EDT, showed all a constant level part up to aboutTI=50 ns.

Naturally, approximating expression (3.6) with the simple model of (3.7) will introducesome errors. Figure 3.4 shows u according to (3.6) minus u according to (3.7).

o

Figure 3.4: The average rms delay spread according to (3.6) minus theaverage rms delay spread according to (3. 7)

It can be observed in the plot above that a large deviation is found for small 'Y and largeTI' This, however, are no typical practical values. Practical values of 'Yare found to rangefrom 15 to 75 ns and TI is about 50 ns. For these values the error amounts up to 2 ns.

As mentioned before, the constant level part at the beginning of the average power delayprofIle, present if biconical horns are applied, is missing if isotropic antennas are used.This means that TI =0. According to expression (3.6), the average rms delay spread for aOBS channel then equals 'Y!

3.1.2 The illS Channel

The model for the LOS channel is based also on the number of measurements performedat the E.U.T. The average power delay profile looks the same as in the OBS case inaddition with a LOS ray present at t=O. According to the measurement data, the powerof the LOS ray exceeds the constant level part with 5-15 dB if biconical horns areapplied.

In our model, we will define the LOS ray as a delta function at t=O with strength D. The

-11-

solution for PaltJ on a linear scale now yields:

Do(t) 1=0

pav(l) = C 0< 1< T1-(t-.,.,)

C·e .,T1 < 1~ 00

(3.8)

The average power delay profile of a LOS channel can be modelled with four parameters,Le. the power D of the LOS delta function, the constant power level C at the beginning,the time constant Tl for the duration of the constant level part, and fmally the slopeparameter 'Y. Figure 3.5 shows the model for the average power delay profile, based onthese four parameters.

Figure 3.5: Modelling the average power delay profile (LOS channel)

Again we use expression (3.4) and (3.5), together with (3.8), to derive an analyticalexpression for the average rms delay spread. Note that PaltJ in the numerator of (3.5) ismultiplied with 1. Thus, the delta function of the LOS ray will have no influence on thenumerator. The delta function will have only influence on the total received power in thedenominator of (3.5). The calculation of a for the LOS case is presented in appendix A.The final expression for a yields

Notice, for D/C=O the expression for the OBS channel appears again. For a LOSchannel, a depends on three parameters, i.e. Th 'Yand the difference in power of the LOSray and the constant level part, (D - C) in dB, or Die on a linear scale. The influence ofthese three parameters can best be represented by a three-dimensional perspective plot.

-12-

o

Figure 3.6: Average rms delay spread/or a LOS and OBS channel (15 dB offset)

Figure 3.6 shows the rms delay spread for the OBS channel and the LOS channel, bothrepresented by a wireframe grid. The wireframe grid for the LOS channel is plotted for aLOS ray exceeding the constant level part with 15 dB (according to the measurementdata). The two wireframe grids in figure 3.6 cross each other. For small Tl we see that (J

is largest for the OBS channel while for large Tl the opposite takes place. The differencesin (J between the OBS channel and the LOS channel are minor, at least for a LOS rayexceeding the constant level part with IS dB. For a LOS ray exceeding the constant levelpart with only 5 dB (not depicted here), the two wireframe grids completely cover eachother and the average rms delay spread is the same for both OBS and LOS channels.

In literature, the effect of blocking the direct path between two biconica1 horn antennashas also been discussed. According to Smulders and Wagemans [10], blockage of thedirect path does not necessarily have to imply that (J has to increase. Both increases anddecreases are observed. Uhteenmili [5] reported (for 1.8-1.9 GHz) a small decrease of (J

in highly reflective rooms, while in low reflective rooms (J tends to increase if the directpath is blocked.

If highly directive antennas are applied in the measurement setup, e.g. 25 dBi pyramidalhorns, the LOS ray can exceed the constant level part up to 40 dB. This can be verifiedwith simulations. The effect of this LOS dominance is demonstrated by the next plot.

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Figure 3. 7: Average rms delay spread for a LOS and OBS channel (40 dB offset)

Comparing figure 3.7 with 3.6, it is obvious that the average rms delay spread can bereduced if highly directive antennas are applied. This reduction in spread is also reportedin literature by Uhteenmaki, [5]. This researcher finds values for highly directiveantennas which are reduced to about one tenth of the values which were obtained forbiconical hom antennas. Lahteenmaki reported also that blockage of the direct path causesthe rms delay spread for highly directive antennas to increase significantly, which agreeswith our results shown in figure 3.7.

Summarizing, if the average power delay profile is modelled with an analytical function,the average rms delay spread can be written as function of three parameters. First of all,the duration of the constant level part, Til and second, the slope parameter 'Y. In case of aLOS channel, a third parameter becomes important: the difference in power between theLOS ray and the constant level part.For biconical and isotropic antennas, the LOS ray is not dominant. This implies that thedifferences in rms delay spread between the LOS and OBS channel are not significant andboth slight increases and decreases of the spread are observed. For highly directiveantennas, the LOS ray may be dominant and an increase of the average rms delay spreadwill be observed for the OBS channel.

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3.2 An Analytical Expression for "y

We now know that the slope parameter 'Y has significant influence on the average nnsdelay spread. In other words, 'Y is an important parameter, characterizing the overallperformance of the indoor radio channel. In this section we present an engineering model,based on Geometrical-Optics, to derive an analytical expression for 'Y.

The model, which we present, is extendable to other environments. Input parameter of themodel is the superstructure of the environment. With superstructure we mean thedimensions of a room and the reflection properties of its walls, floor and ceiling. Noattention will be paid on further details in the room such as furniture, desks, computersystems, etc. In fact, this means that we only regard empty rooms.

3.2.1 Decay of Power in a Superstructure

Assume an empty room with both transmitter and receiver in it. The walls, floor andceiling are smooth. According to the Geometrical-Optics model there is the direct path(line-of-sight) between receiver and transmitter, but also many paths reflecting once ormore. The room is in fact a multipath environment. First of all, the direct ray will arriveat the receiver. Later on, rays reflecting once or more will arrive, depending on time andthe dimensions of the room. The received power of the ray depends first of all on thepropagation distance and second on the reflection coefficient of the separate walls, floorand ceiling. So, assuming the Geometrical-Optics model, the decay of power in a roomcan be expressed as

p(r) - J:.. 77R(r? (3.10)r2

r : Propagation distance (m)77 : Power reflection coefficientR(r) : Number of reflections as function of propagation distance

The faktor .,.-2 in (3.10) represents the inverse free-space loss. The propagation distance isrelated with time t via the velocity of light c. Formula (3.10) is the foundation of ourmodel. By converting it to a logaritmic scale and taking the derative to r, the slope B canbe found. The slope parameter 'Y can then be derived from B with help of (3.3):

-10 -10 1'Y = = -----:-:-::-=:'--;-:~ = -:--------

R·lnl0 clnlOd(lOlogp(r» c[2 _ln77.dR(T)]dr T dr

(3.11)

Evidently, we need to know the number of reflections in a room and the reflectioncoefficient to determine the value of 'Y. The first will be discussed in section 3.2.2 and3.2.3. The second in section 3.2.4.

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3.2.2 The Average Number of Reflections for an Isotropic Antenna

Assume for a moment a two-dimensional room. Both transmit antenna, which is mountedat the centrally placed base station, and receive antenna, which is mounted at the remotestation, are present in this room. The dimensions of the room are a and b, as depicted infigure 3.8a. The walls are numbered 1 to 4.Assume the direction of an excited ray with the horizontal positive x-axis is cPo The rayreflects 3 times before being received by the receiver as can be seen in figure 3.Sa. Thelength of its path is described with r.

2

2

( a :>

1

2

2

- ---- - .....,......---- ..... ...../ "-

l~'-

'"/ \/ , \

I \

{ '"'\.,<I> \

I ~> \I ------- -------- ---.\.--- --_.I T I\ I\ J

\ /\

f'\. /1,

/'-, /..... -- ...--..... _- -------

(aJ

3 4 3 4

(bJ

3 4 3 4

Figure 3.8: a) path ofa possible ray; b) folding out the path of the ray

Each cell in the grid of figure 3.8b represents the room in figure 3.8a. The walls arenumbered similar as the walls in the room of figure 3.8a. When folding out the path ofthe propagated ray one can determine with help of the grid the number of reflections foreach wall. These reflections are in the figure represented with fat dots. The exact numberof reflections for this ray can be formulated with help of the figure:

-16-

Rj(r,</» =

t

/

1 rsincPrune - + --4 2b

trune 3 + Ir sincP I4 2b

(3.12)

(3.13)

trune

trune

3 rcoscP- +4 2a.!. + I rcos</> I4 2a

'I" < q, < 'I"-2 2'I" < q, < 3'1"2 2

(3.14)

R!<r,</» = truneI~ +

trune - +4

rcoscP 12aI rcos</> I

2a

'1"<..1..<'1"2-'f'-2

'I" ~ q, < 3'1"2 -2

(3.15)

The subscript i in R/(r,q,J refers to the wall as defined in figure 3.8. The expression"trunc" is defined as rounding a real value to the nearest lowest positive integer value.Truncation makes the variable R/(r,q,J to a discrete variable. As we can see fromprevious expressions, the number of reflections at a certain wall is composed of twoterms; a constant term (1,4 or ~), and a term depending on the propagation distance and</>. For a large number of reflections, both the small constant term and the truncation willhave negligible influence on the slope parameter 'Y. (See also appendix D for an errorconsideration). We thus can approximate previous expressions with the next continuousfunctions.

(3.16)

(3.17)

If we assume a centrally placed isotropic antenna, rays will not only leave the antenna inone direction, but uniform in all directions. The circle in figure 3.8b thus represents all

-17-

rays excited by a centrally placed isotropic antenna and propagated over a certain distancer. The average number of reflections after a propagation distance r can be determined byaveraging over q,:

2...

R (r) = ~(r) = _1 f I rsinq, Idq, = ...!......1 2'1" t 2b 'l"b

2...

R (r) = R (r) = _I f I rcosq, Idq, = ...!......3 4 2'1" t 2a 'I"a

(3.18)

(3.19)

The previous expressions only validate for a two-dimensional room. We can easily extendthe expressions for a three-dimensional room with help of figure 3.9. The walls, floor andceiling are numbered and the dimensions and angles are defined.

wall c

wall f

wall 4

2x

z r

Figure 3.9: Definition ofdimensions, walls and angles in a room

When counting the number of reflections in X-, y- and z-direction, respectively andintegrating over the solid angle, the average number of reflections for an isotropic anten­na, placed centrally, can be expressed by:

Rc(r) = Rj.r) = ~ J I rcosO IdO = ..!.-4'1" 0=4... 2h 4h

-18-

(3.20)

(3.21)

(3.22)

3.2.3 The Average Number of Reflections for a BiconicalHom Antenna

Until now, the average number of reflections as function of propagation distance isdetermined while assuming a centrally placed isotropic antenna. In this section we willregard the average number of reflections for a (simplified) centrally placed biconical homantenna. The biconica1 hom antenna is omnidirectional in the azimuth plane and has acertain beamwidth in the elevation plane as shown in figure 3.10.

<P=o

e....-e ......n.2

-+- +O _l_ 1\

2

azimuth elevation

Figure 3.10: Simplified normalized radiation pattern ofbiconical hom antenna

Instead of integrating over a solid angle 0 = 4'lr, we now must integrate over a solidangle OQllt. This calculation is described in appendix B. The results are shown below:

Rbi,1(r) = Rbi,2(r)r8Q11t rcos8Q11t 0 < 8

anl< 'lr (3.23)= +

2 'lrb sin8anl 2'lrb 2"

Rbi 3(r) = Rbi i r)r8Q11t rcos8

anl 0 < 8anl

< 'lr (3.24)= +, , 2 'lra sin8tlIIl 2'lra 2

Rbi,c(r) = Rb;jr)rsin8

anl 0 < 8anl< 'lr (3.25)=

4h 2

where 8tl11l is the antenna beamwidth divided by 2. Substituting 8Q11t = lh'lr in previousexpressions yields the average number of reflections for an isotropic antenna while 8anl =oyields the expressions for the two-dimensional case.

Some typical values are presented in figure 3.11. The figure shows the number ofreflection at t = 400 ns (r = 120 m) as function of 8anl for two different rooms. Thedimensions of the rooms are tabulated in appendix C. The corridor has the dimensions

-19-

2.43 m * 44.68 m * 3.12 m. Room EH 11.21 has the dimensions 11.30 m * 7.30 m *3.07m.

Average ,...... of ReflectionsCorridor

Average No" of ReflectionsRoom EH 11.21

10 W ~ ~ ~ ~ ro ~ ~

90M (cIe9'...)

- 1(1-400 ne) ---- R(1-4OO ..) - -1(1-400 ..)_ 1,2 .01 3.4 1100'.....

o

e

10,-------------=----.........-.1 ,,/'"i e ",,,,,/

i r-//~----J1 4 /

---~---------------------------------2/0/

2

o ~=::::;:::=:::;::=:i:::::::::::;:==~:::o=::::::1o 10 W ~ ~ ~ ~ ro ~ ~

9cri (cIe9'...)

- 1(1-400 ...) ---. 1(1-400 ne) - - «(1-400 ftI)_ 1.2 wei 3.4 lloor"*""

1I==~-----------.M -------------------------- _

J 12u 10..:I e1 e: 4

Figure 3.11: Average number of reflections in a roomfor biconical hom antenna

Notice, the number of reflections at floor and ceiling are affected a lot by the radiationpattern of the biconical hom antenna. Rays, excited by a biconical hom with a beamwidthof roughly 30 degrees, have experienced at t = 400 ns an average number of reflectionsof about 42 in the Corridor; 1 reflection at wall 1 and 2; 15 reflections at wall 3 and 4; 5reflections at floor and ceiling. In case of an isotropic antenna «(Jut = 90°) we can countabout 44 reflections; 1 reflection at wall 1 and 2; 12 reflections at wall 3 and 4; 9reflections at floor and ceiling.

-20-

3.2.4 The Average Reflection Coefficient

Now that we have determined the average number of reflections, we only need to knowthe reflection coefficient to complete our expression for 'Y. The average number ofreflections in a room can be split up for every single wall, floor and ceiling. We thereforeneed to have knowledge of the reflection properties of every single wall, floor andceiling.

The reflection coefficient of a wall is not a constant but depends on both the angle of theincident wave and the state of polarisation of the electric field. In deriving a rule ofthumb for 'Y, it would be a very complex task to incorporate a reflection coefficientdepending on the polarisation of the electric field and incident angle. Therefore, we willdefine an average reflection coefficient in this section which is independent of thepolarisation of the electric field and incident angle. Note, that we are looking for anaverage reflection coefficient characterizing a single wall and not for an average reflectioncoefficient characterizing a complete room!

Figure 3.12 shows an incident wave, reflecting at a perfectly smooth wall. Here, iidenotes the normal vector of the wall. OJ denotes the angle of incidence and Or the angle ofreflectance. E,j and E,r denote the electric field vectors of the incident, respectively,reflected wave.

-" : -rE' : E

3~: wall

Figure 3.12: Incident ray on a wall

The incident ray and normal vector ii determine the plane of incidence. In case theelectric field vector is perpendicular to the plane of incidence, we speak: of perpendicularstate of polarisation. In case the electric field vector is parallel to the plane of incidence,we speak: of parallel state of polarisation. In figure 3.12, the polarisation of the electricfield is parallel.

In general, the polarisation of the electric field is not solely perpendicular or parallel.However, the perpendicular and parallel state of polarisation are orthogonal and thus, anygiven electric field vector can be decomposed in a perpendicular part, indicated by E.L'and a parallel part, indicated by EI' as depicted in figure 3.13a:

-21-

exIL-- ----';~ E.L

lEi! cos(a)

(a) (b)

Figure 3.13: Electricfield of (a) incident and (b) reflected wave in a vector diagram

Here, (X denotes the angle of polarisation of the incident wave.

The reflection coefficients for the perpendicular and parallel part differ from each other.For non-conducting materials the reflection coefficients can be expressed as [17]

__E_~ = cosO, - JEr - sin20,

Ei.l cosOj

+ JEr

- sin20j

(3.26)

= ercosOj - Jer - sin20j

e cosO. + ./e - sin20.r J V r J

(3.27)

where Er represents the relative dielectric constant. Actually, the relative dielectricconstant consists of a real and imaginary part. The imaginary part represents theconductance of the material. Until now, not much research has been done on theconductance of materials. Therefore, we will neglect this imaginary part and presumepure dielectric materials that exhibit a relative dielectric constant with just a real part.

As stated, expressions (3.26) and (3.27) hold for infinite surfaces and an incident planewave. In general it is allowed to use the coefficients for finite objects and walls if half ofthe first Fresnel zone is smaller than the dimensions of the objects and walls, since thisarea effectively contributes to the reflection of the wave.

It is clear now that the reflection coefficient of a wall depends on both the angle OJ of theincident wave, the polarisation of the electric field vector, given by (x, and the relative

-22-

dielectric constant. Averaging of the reflection coefficent must lead to a reflectioncoefficient which is independent of both 0i and ex.First of all, averaging, for a wave with arbitrary incident angle 0i' takes place over theangle of polarisation ex. With help of figure 3.13b we can derive the magnitude of thereflected electric field. Adding the reflected electric field vectors for perpendicular andparallel state of polarisation yields:

The reflection coefficient (without regarding the sign) is defined as

R(Oi,ex,i) = I Er(~"ex,fr) I = V(R1.(O"fr)oCOS(ex))2 + (R.(Oi,fr)oSin(CX))2EJ(O"ex)

The average can be found by integrating R(Oi,CX1Er) over ex:

(3.29)

(3.30)

There is no analytical solution for this integral but it can be reduced to a complete ellipticintegral of the second order in the Legendre normal form, [1]. Reduction leads to thefollowing series representation:

(3.31)

where

2 R1. 2(Oi,Er) - R.2(O"fr)k = ---=----=---R 1.2(Oi,fr)

(3.32)

The reflection coefficient now only depends on the incident angle and the relativedielectric constant. Figure 3.14 shows the reflection coefficient R(Oi,fr) for wooden doors(Er = 20.5). We can distinguish the reflection coefficient for parallel state of polarisation,given by R.(Oi,fr), and the reflection coefficient for perpendicular state of polarisation,given by R 1. (Oi,fr). Between these curves we find the reflection coefficient R(Obfr) whichis averaged over the angle of polarisation.

-23-

Reflectionwooden doors of reception room

1.00

0.80

0.60a::

0.40

0.20

0.000 10 20 30 40 50 60 70 80 90

8; (degrees)

- parallelpol.

----- perpend. --- overagepol.

Figure 3.14: Typical example ofangle dependence of reflection coefficient

The next step in deriving an average reflection coefficient is integrating over the incidentangle OJ:

,..'!

Rav(er) = ; rR(Oj,e,)dOj(3.33)

Formula (3.33) represents the average amplitude reflection coefficient. The averagepower reflection coefficient finally follows simply by squaring the average amplitudereflection coefficient:

(3.34)

Indeed, the resulting average (power) reflection coefficient is independent of incidentangle and state of polarisation. However, it is still a complex task to calculate an averagereflection coefficient for a certain dielectric constant and this, in fact, is not veryfavourable for a rule of thumb which must be simple in usage.The next figure shows a plot of the average reflection coefficient as function of therelative dielectric constant.

-24-

A verage ref lect io n coeff ic ie ntvs. relative dielectric constant

.~.· . . .· . . .· . . .· ... .

1.00

0.90

0.80

0.70

1l av0.60

0.50

0.40

0.30

0.20

0.10~0.001

I I I

~..· .. ... ..· ...

10

~ ~ ~ v---.. . . .. . . ..~ ... .. . .. . .

.~.. .. . .

100

Figure 3.15: Average power reflection coefficient versus relativedielectric constant for non-conducting materials

The average reflection coefficient is plotted for values of €r ranging from 1 to 250. Thecomplex calculations lead, as can be observed in the plot, to a relation between theaverage reflection coefficient and the relative dielectric constant which can be approxima­ted very closely with a linear function. This linear function is given by

flay = 0.3Iog€r (3.35)

The error which is made by this linear approximation is 5 percent at most in the range of€r = (1.01,800).

We will now have a look at some practical values of flav in table 3.1. The fust columnshows some materials for which flav is calculated. The second column shows the (power)reflection coefficients for zero incident angle, flo. These values are obtained frommeasurements performed at the EUT and the COST project group 231 report, [3] [20]. Inthe third column, the relative dielectric constant €r is listed. These values are directlydetermined with help of (3.26) and (3.27). In the fourth column, the exact values of theaverage reflection coefficient, according to (3.34), are tabulated. The last column finallyshows the average reflection coefficient calculated with help of formula (3.35).

-25-

Table 3.1: Average reflection coefficient at 58 GHzfor several different materials.

flo f r flav,exact flav

Reception Room

Windows 0.05 2.5 0.12 0.12

Wooden doors 0.41 20.5 0.41 0.39

Wooden panels 0.16 5.5 0.22 0.22

I.ecture Room I

Wooden lathing 0.05 2.6 0.12 0.12

IRoom EH 11.21 IConcrete waIls 0.64 81 0.59 0.57

Cost 231 TD(92)50

Glass (4mm) 0.72 152 0.67 0.65

Plaster on Concrete 0.31 12.6 0.34 0.33

Concrete slab (40 mm) 0.38 18.2 0.39 0.38

If we compare the values of f r (calculated with (3.26» with values reported in literature,it can be observed that values of flr=152 or flr=81 are extremely high and probably notcorrect. This can be explained by the fact that conductivity of the materials is assumed tobe negligible. Furthermore, multiple reflection at materials with a multi-layer structure isnot considered; although high values of the reflection coefficient may be measured in thiscase, it does not necessarily imply a high value of fir.

Note the different values for glass, reported by the COST project group, and for thewindows, measured at the EUT. This can be explained by the fact that not only the kindof material is important but merely the specific construction (thickness, metalization,thermopane, etc.) of the wall or windows.

-26-

3.2.5 l' for Centrally Placed Isotropic Antennas

In section 3.2.1 we stated that the power decay in a room depends on the propagationdistance (inverse free-space loss), the average reflection coefficient and the averagenumber of reflections as function of the propagation distance. In section 3.2.2 and 3.2.3we derived an average number of reflections per wall. This number turned out to beproportional to the propagation distance. In section 3.2.4 we derived an average reflectioncoefficient per wall, independent of incident angle and polarisation. Obviously, both theaverage reflection coefficient and the average number of reflections can be determined forevery single wall in the room, Le. the floor, the ceiling and four side-walls. This enablesus to formulate the decay of power, as defined in expression (3.10), more accurately. Ona linear scale, the decay of power yields

p(r) =D. 1 • R.(r'). R.(r'). Rs(r). R.(r). R.(r'). Rjr')""'2 7Jav,l 7Jav,2 7Jav,3 7Jav,4 7Jav,c 7JavJr

(3.36)

where D is a constant. Every wall is represented with an average reflection coefficient7J.v,i and an average number of reflections Rlr). If the decay of power is expressed in dBvalues, expression (3.36) changes into

[1 R.(r') R.(r') R.(r) R.(r') R.(r') Rjr) ]

10l0gp(r) = lOlog D· r2

• 7Jav,l • 7JQv,2 • 7Jav,3 • 7Jav,4 • 7Jav,c • 7JQvJ

[r r r ]= 10 10gD - 2logr + -log7JQV 17Jav 2 + -log7JQv 37Jav 4 + -log7JavJ7Jav c

4b "4a " 4h '(3.37)

The slope B' (in dB/m), necessary to calculate 'Y, can be determined next by taking thederative:

(3.38)+ _l_ln7J 7J + ~ln7J 7J + 1 ln7J 7J ]4b QV,l QV,2 4a av,3 QV,4 4h QvJ QV,C

=

B' = ~ (lOlogp(r»dr

10 [ 2lnlO r

Note that the slope still depends on the propagation distance c.q. time which is caused bythe inverse square free-space loss. Especially for small r there is a strong dependence.The strong r-dependence near zero is, in fact, in contradiction with the measurementsperformed at the T.U.E. The measured average power delay profile showed a constantlevel up to about t = 50 ns followed by a linear decreasing function down to the noisefloor. The slope B' of formula 3.38 has therefore no meaning for small r and ananalytical expression for 'Y can not be derived for this part of the power delay profile.

For large r, the dependence is negligible. Neglecting the r-dependence enables us tocalculate the time constant 'Y since the power decay then is an exponential decreasing

-27-

function. With (3.3) it follows that

-10 -10'Y = Bln10 = B' cln10

The slope parameter 'Y in case of an isotropic transmit antenna then yields

-4'Y=-~----------------:-

c [ ~ ln~fi.l~fi.2 + ~ In~fi~~fi.' + ~ ln~fiJ~fi"']

(3.39)

(3.40)

This analytical expression for 'Y only depends on the superstructure of the room and givesus some important insight: walls with low reflectivity have great influence. If, forexample, a wall has a reflection coefficient of approximately zero, 'Y will go to zero, evenif the other walls are made of metal. This implies that according to (3.40), rooms witha low value of 'Y need only have one wall with excellent absorbing qualities.Furthermore, walls perpendicular on the shortest dimension of the room (often the floorand ceiling) are weighted stronger than the other walls in the room. Thus, if floor orceiling have low reflectivity, they will mainly determine the slope 'Y in case of anisotropic transmit antenna.

A value for'Y can easily be calculated with formula (3.40) if the superstructure is known.This value, however, may not be correct because the rule of thumb is derived whileassuming r going to infinity. The measured average power delay profiles showed only alinear decay in the interval t = (50,400) ns and only in this interval the slope can becharacterized by a single 'Y. (This interval is determined by the antenna gain compensationat the left side and the noise floor at the right side). Values of'Y that are comparable withpractical values can therefore only be determined for the interval of t, ranging from 50 nsto 400 ns, where, according to (3.36), still a small r-dependence exists.

Figure 3.16 shows the power decay, according to (3.36), in four different rooms. Thesmall r-dependence becomes clear in this figure and the power decay functions can easilybe approximated with linear functions. Linear curve fitting can be used yielding correlati­on factors higher than 99%. With formula 3.3 the value of 'Y can finally be calculatedfrom the slope B.

-28-

Power DecayIsotropic Antenno

0,------------,

-20

- Corridor

----- Compute,.Room

--- Ledur.Room

• • •• RaceptlonRoom

••-_.-- warat cn_.ltuaUon

-120 L.-----'-_...........---'_---L-_~_____"~---'

50 100 150 200 250 300 350 400

time (ns)

Figure 3.16: Power decay in several different rooms

Also shown in figure 3.16 is the worst case situation in which each wall in a room hasexcellent reflection properties, Le. 'Iav,i = 1. For this case, expression (3.36) can bereduced to a simple expression in which the decay of power is only determined by theinverse free-space loss. Curve fitting in the interval of t = 50 to 400 ns then yields amaximum value of 'Y = 96 ns. So, according to our model, the value of 'Y can neverexceed 96 ns!

In section 3.1.1 we mentioned that for isotropic antennas the average power delay proflledoes not exhibit a constant level part at the beginning of the profile (Tl = 0) implying thatthe average rms delay spread equals 'Y. Evidently, for isotropic antennas our model for 'Ypredicts a maximum value of u = 'Y = 96 ns!

-29-

3.2.6 'Y for Centrally Placed Biconical Hom Antennas

In the previous chapter, we studied 'Y for isotropic antennas. It followed that a practicalvalue of 'Y could be found by a linear curve fit of the power decay function, expressed in(3.36), in the interval t = 50 to 400 ns. This section will be used to investigate theinfluence of the radiation pattern (in elevation plane) of biconical hom antennas.

For the biconical hom antenna the average number of reflections changes, especially atfloor and ceiling. With help of the results of section 3.2.3 the power decay can be definedas

p(r)1 R...(r) R..;>(r) R..,.<r) R....(r) R..",(r) R.,}.r)

""2 • 71av:l • f]av,2 • 71av,3 • 71av.4 • f]av,c • f]av,{r

(3.41)

where Rbi.lr) is the average number of reflections at wall i as defined in section 3.2.3.

Figure 3.17 shows the power decay for various beamwidths (in the elevation plane) of thebiconical hom antenna in two different rooms.

-18

Power DecayComputer Room

or------------..,

-2~r----

t -48 - --.----.""='=='=~~JI: -----__

~ -72

-III

-120 '-----L_--L.._....L__"""'""__--'_----'-_-'

50 100 1!10 200 250 300 3 ~o ~OO

lIme (no)

- 8ant = ---- 8ant = -_. 8ant = .. , 8ant =

5 • 15' 45 . 90 •

1J

Power DecayLecture Room

0.-----------------,-2~

~~~~.

~~~;..:....~ ....

-'20 L..----L_~_....L__"""'""_____'''''''''___=__-'

50 100 1!I0 200 250 300 3~0 ~OO

lime (fto)

- 8ant = ,---. 8ant = - - 8ant = . •• 8ant =5 • 15 . 45 • 90 .

Figure 3.17: Power decay for several antenna beamwidths

The differences between the various slopes in a room are minor but remarkable is that anisotropic transmit antenna in the computer room produces the steepest slope while anisotropic antenna in the lecture room produces the least steepest slope! This can beexplained as follows; the biconical hom causes a small increase in number of reflectionsat the side-walls and a decrease in number of reflections at the floor and ceiling (seesection 3.2.3). The computer room has relative highly reflective side walls and here, theinfluence of the decrease in number of reflections at floor and ceiling is largest. Lessnumber of reflections as function of time imply a less steep slope. The lecture room hasrelative low reflective side-walls and here the influence of the increase in number ofreflections at the side-walls is largest, causing a steeper slope.

Note, that although the slope remains practically unchanged, the average rms delay spreadu need not to be unchanged! Different antenna beamwidths can affect the constant levelpart of the average power delay profile and the LOS dominance and so influence thespread u.

-30-

3.2.7 Comparison of 'Y with Measurements

Measurements of 'Y (applying biconica1 horns with a 9 degrees beamwidth in elevation)have been performed in eight different rooms at the TUB. Five of these rooms can moreor less be described by a simple rectangular shaPe. For these rooms we will validate ourmodel for 'Y with the measurements.

Every wall, floor and ceiling in the five different rooms can be described by an averagereflection coefficient, represented by 71.v,i' These are tabulated in table 3.2. Few wallshave known average reflection coefficients, (see also table 3.1). Most walls, however,have unknown reflection properties and so we have to estimate the value of the averagereflection coefficient; these values are followed by a question-mark. For some walls wetried more than one reflection coefficient. For those walls, an extra row is added. Thefirst column after the reflection coefficients shows the values of 'Y, according to ourmodel, with a biconica1 hom antenna that exhibits a beamwidth of 10 degrees. The valuesare, as explained before, acquired with linear curve fitting of the power decay function(3.41) in the interval t = 50 to 400 ns. The second column after the reflection coeffi­cients shows the values of 'Y acquired with curve fittings of the expression for theisotropic antenna (3.36). In the final column the measured values of'Y are listed.

Table 3.2: Reflection properties o/walls, 'Y retrieved with curvejitting and 'Yretrieved with measurements.

'1...,1'1 ...,2 '1..,3 'lav.4 'lav,r 'lav,. 'Y (ns) 'Y (ns) "(Ii (ns)

10° hie iso measured

Corridor 0.671 47 360.67? 0.67? 0.9 0.9 1.0 75

0.8? 48 42

Computerroom 0.67? 53 460.9 0.9 0.9 0.8? 1.0 47

0.12? 27 27

Lectureroom 0.67? 14 160.12 0.12 0.12 0.8? 1.0 16

0.33? 13 15

Room EH 11.21 0.67? 31 300.59 0.59 0.59 0.8? 1.0 2S

0.12? 21 23

Receptionroom 0.8? 21 230.22 0.22 0.12? 0.41 1.0 35

0.9? 21 24

As can be seen, reflection proPerties are estimated for most walls. ESPecially for lowreflective walls this can result in very diverse values of 'Y. This makes our model difficultto use if no exact values of the reflection coefficient are present. Reflection measurementsof all the walls are therefore necessary to test the correctness of the model.

-31-

The table also shows the influence of the radiation pattern (in elevation plane) of abiconica1 hom antenna. It can be concluded that the changes are minor if the reflectioncoefficients of the floor and ceiling are higher than the reflection coefficients of the side­walls. The expression for isotropic antennas (3.36) may therefore be used instead of themore complex expression for biconical antennas (3.41). If the reflection coefficients offloor and ceiling are about the same as those of the side-walls, then changes of 11 ns canbe observed in the highly reflective corridor and changes of 7 ns in the computer room.So, for these rooms the expression for biconical horns (3.41) needs to be used.

-32-

3.3 Validation of the Rule of Thumb for q

3.3.1 Comparison of the Rule of Thumb with Measurements

In section 3.1 a rule of thumb for the average rms delay spread has been derived. Thisrule of thumb depends solely on the slope parameter 'Y which extensively has beendiscussed in section 3.2. In this section, a comparison will be made between the averagerms delay spread values measured at the EUT and the values obtained with the rule ofthumb.

The rule of thumb is, first of all, used for values of 'Y measured in five different rooms atthe EUT. In the second column of table 3.3 the measured values of 'Y are listed. The thirdcolumn shows the average rms delay spread values obtained with the rule of thumb.These values can finally be compared with the values measured at the EUT, listed in thefourth column of table 3.3.Table 3.4 shows values of 'Y in the second column that are obtained with the modeldiscussed in section 3.2 (see also table 3.2 in the previous section). The values of'Y listedin table 3.4 are the values of table 3.2 lying closest to the measured values of 'Y. Thethird column shows the values of the average rms delay spread obtained with the rule ofthumb. The final column shows again the measured average rms delay spread values.

Table 3.3: Results rule of thumbfor measured 'Y

Room 'Y (ns) (1 (ns) (1 (ns)measured measured

Corridor 75 n 70

Computer 47 51 44room

Lecture 16 23 22room

RoomER 25 32 2911.21

Reception 35 41 44room

Table 3.4: Results rule of thumbfor calculated 'Y

Room 'Y (ns) (1 (ns) (1 (ns)measured

Corridor 48 52 70

Computer 53 57 44room

Lecture 16 23 22room

RoomER 23 30 2911.21

Reception 24 31 44room

One can observe in table 3.3 that the values obtained with the rule of thumb are in closeagreement with the measured values of u. This makes the rule of thumb as expressed in(3.7) an adequate description of reality. If we take a look at table 3.4, a difference of 18ns between the calculated and measured value of u can be observed in the corridor. Thereception room and computer room show differences of 13 ns. Obviously, the differencesare caused by incorrect values of 'Y. Correct values of 'Y (implying correct values of theaverage reflection coefficient) are thus a necessity to make adequate use of the rule ofthumb.

-33-

3.3.2 Comparison of the Rule of Thumb with Simulations

A simulation programme based on Geometrical Optics has been used to simulate anaverage power delay profile. The simulation programme is extensively described in [2]and also in chapter 4 the programme briefly will be discussed.An average power delay profJle is simulated for two rooms with equal dimensions; arectangular room with six highly reflective walls, and a room with five highly reflectivewalls and one absorbing wall (1Jav=O.OOl). According to (3.36), a low reflective wall in aroom can lead to extremely low values of 'Y.Isotropic antennas are applied at the remote and base station. To generate an averagepower delay profile, the remote station is positioned at 24 different locations, more orless uniformly distributed over the room. The dimensions of the two rooms are 24 x 12 x4.5 m3

• Figure 3.18 shows the average power delay profiles in both rooms.

Average power delay profileRoom with 6 highly reflective wolls

Power Delay ProfileRoom with 1 absorbing wall

10

0

m -10

~

'" -200E

'"~ -30

-4-0

4-00300200100

10,---------------,

o

-50 L--__-'-----'------UJ"-'­

o

-4-0

go -20E

'"~ -30

m -10~

time (ns) time (ns)

Figure 3.1&: Av PDP for room with 6highly reflective walls

Figure 3.18b: Av PDP for room with 5 highlyreflective and 1 absorbing wall

The average rms delay spread is calculated for the profiles above. In the room with sixhighly reflective walls an average rms delay spread of 39 ns is found. In the room withone absorbing wall an average rms delay spread of 27 ns is found.

According to section 3.1, the average rms delay spread equals 'Y if isotropic antennas areused. If we apply our rule of thumb to the rooms described above, we find a value of(/=27 ns in the room with 6 highly reflective walls and a value of (/= 18 ns in the roomwith one absorbing wall. Evidently, this is not predicted by the simulations; the values of(/ found with the simulation programme differ from the values found with the rule ofthumb (in both rooms).The error is probably be caused by the formulation of expression (3.36). It is thereforerecommended to try other constructions as well in which the parameters, averagereflection coefficient and average number of reflections per wall are used.

-34-

3.4 Concluding Remarks on the Rule of Thumb for (1

In this chapter we discussed a model for the average rms delay spread based on a numberof average power delay profiles measured (with identical biconical horns) at the EUT. Ananalytical expression for the average rms delay spread is derived for ORS and LOSchannels. It is shown that for indoor radio links in which the LOS ray is not dominant(e.g. if the applied antennas at remote and base station are biconical horns), the expressi­on for the LOS channel can well be approximated with the more simple expression for theOBS channel. This results in a simple rule of thumb for the average rms delay spreaddepending only on the slope parameter 'Y of the average power delay profile. For theisotropic antenna setup a constant level part up to Tl (at the beginning of the averagepower delay profile) is missing and for this setup the average rms delay spread equals theslope parameter 'Y.

A model for the slope parameter 'Y is presented next in this chapter. This model is basedon Geometrical Optics and does therefore not regard frequency dependence. In the model,only one centrally placed antenna is included and only rectangular indoor environmentsare considered. According to this model, the decay of the average power delay profile isnot perfectly linear but can very well be approximated with a linear function (consistentwith the measurements), yielding a single value for 'Y. Exact knowledge of the reflectionproperties of walls is necessary for validation with measurements and adequate usage ofthe model in arbitrary indoor environments. This knowledge, however, is scarce forexisting materials. Actual measurements of reflection coefficients are recommended.Looking at the worst case value of 'Y, an interesting conclusions can be made. The worstcase value of 'Y, i.e. the largest possible value of'Y according to our model, occurs if eachwall in the room exhibits an average reflection coefficient of 1 (as is the case with roomswith significant metallic partitions). The power decay function is then solely determinedby the inverse square free-space loss, yielding a worst case value of 'Y = 96 ns.

Simulations show results that differ significantly from the results obtained with the powerdecay function. However, to gain insight in the slope parameter 'Y, the model shows gooduse. It can be concluded that the value of 'Y can be influenced with the superstructure of aroom or more precisely by:

- The reflectivity of a wall. A relative low reflectivity of just one wall in a roomwill decrease the value of 'Y significantly.- The dimensions of the room. Two opposite walls on a relative short distance willsuffer a large average number of reflections. This implies a fast decay of powerand thus a small value of 'Y.- The radiation pattern of the centrally placed antenna. Walls on which theradiated power of an antenna is directed will have more influence than other walls.

These rules may help to construct a wideband indoor radio link if a low value of 'Y ispreferred.

-35-

4 Simulation of Antenna Effects on a mm.-Wave Indoor Radio Link

The antennas used in an indoor environment can have considerable influence on theperformance of a mm-wave indoor radio link. The influence of antennas on an indoorradio link can be tested with a simulation programme. The simulation programme used isdeveloped at the EUT and makes use of Geometrical Optics. The programme calculatesthe power delay profile, the rms delay spread and the normalized total received powerbeing performance measures for an indoor radio link.

Simulations have been performed with two different kind of antennas: directive antennas(pyramidal hom antennas) and omnidirectional biconical hom antennas. Analysis anddesign of these antennas is discussed in the next section. In section 4.2 the simulationsoftware is described and in section 4.3 the simulation configurations are presented.Simulations are performed for three different antenna setups in a low reflective room andin a highly reflective room. A presentation of the results is given in section 4.4 andfmally, in section 4.5, some concluding remarks are presented.

4.1 The Antennas

The antennas used in the simulations are smooth walled pyramidal hom antennas andbiconical hom antennas. The pyramidal horns provide high gain, low VSWR, relativelywide bandwidth, low weight and are rather easy to construct. As an additional side-benefitthe measured antenna properties closely approach the theoretical. The biconical hornsexhibit a radiation pattern in such way that fair access to every user in an indoor radiochannel is provided.

4.1.1 Smooth Walled Pyramidal Hom Antenna

In this section the analysis of a smooth walled pyramidal hom will briefly be discussed.The analysis is based on aperture integration (E-field model) and has extensively beendescribed in [4] and [11]. To test the influence of antennas on an indoor radio channel,six pyramidal hom antennas are designed. The design procedure is implemented insoftware written by Sletten, [11].

The pyramidal hom shown in figure 4.1 can be considered as a taper section between thefeeding rectangular waveguide and an opening aperture with cross-sectional dimensions toaccomodate a mode impedance which approximates that of free-space. The key to solvingaperture antenna problems is to fmd the tangential fields over the aperture. The apertureplane for the pyramidal hom shown in figure 4.1 will be taken to be the xy-plane. Theaperture fields arise from the attached waveguide.

-36-

y" ,,,,, .'

.. : "XI -" II ",,;

~=:_-- ------;·z

Figure 4.1: Design of the smooth walled pyramidal hom antenna

As is usually the case in practice, we will assume that the waveguide carries the dominantTEIO rectangular waveguide mode. The transverse E-field in the waveguide is then givenby [4]

E = E cos('I"x)e -lP,zy 0 a (4.1)

where {3g is the phase constant in the waveguide. The fields arriving at the aperture areessentialy an expanded version of the waveguide fields. However, the phase constantchanges from that in the waveguide, {3g, to the free-space constant, {3, as waves progressdown the hom. Furthermore, the waves arriving at different points in the aperture are notin phase because of different path lenghts. According to [4], the E-field distribution canbe approximated with

(4.2)

inside the aperture and zero elsewhere. r' = xex + yey and is used on the aperture. Theaperture field is linearly polarized in y-direction and the amplitude distribution is, like thatin the waveguide, a cosine taper in the x-direction. The phase dirstribution is oftenreferred to as a quadratic phase error, since the deviation from a uniform phase conditionvaries as the square of the distance from the aperture center. The radiated far-roneelectric field produced by the aperture field is calculated in [4] and is given by

-j(JrEo = j{3_e-(P . sin</» (4.3)

2'1"7 y

-37-

-jIJrE. =iP_e-cos8(Py· cost/»

2'J'"r(4.4)

where r is the distance from the origin in the aperture to a point in the far field. P, is atwo-dimensional Fourier transform of the aperture field, Ell" given by

Py = f f EIp(r') • eiIJr • r' dS's.

(4.5)

where r = xe% + ye, + zez and is used in the far field. Sip is the geometrical aperturesurface.

The radiation pattern of the smooth walled pyramidal horn is now completely determinedfor z > 0 by its geometrical dimensions (A,B,aH,aJ and we can start with the design.The main objective of the design is to determine the geometrical dimensions of the hornthat will produce the desired 3-dB beamwidths in the two main planes: the one containingthe electric field in the aperture (called the E-plane) and the one orthogonal to this (calledthe H-plane). The electric field in the aperture is directed along the y-axis, according toformula 4.2, so the H-plane corresponds to the <1>=0 plane cut and the E-plane to the<1>=90 0 plane cut.

The design procedure is implemented in software [11]. The design is based on aninterpolation of the results obtained from many analyzed horns. Those results are storedin the form of the so-called "universal E and H plane patterns" [4]. The software makesuse of these universal patterns and generates a set of geometrical dimensions (A,B,aH,aJin the corresponding E or H plane producing the desired 3-dB beamwidth.

Not all of the combinations of E and H plane dimensions are possible simultaneously.This is due to an additional restriction: the realizability restriction. This condition is aconsequence of the fact that the distance from the aperture center to the intersection planewith the input waveguide must be equal in both planes. It implies that

(4.6)

which can easily be verified with figure 4.1. C is a constant and a and b are the inputwaveguide dimensions (known a priori in the design).

The software then proceeds as follows. It selects a universal E-plane pattern producingthe desired 3-dB beamwidth and gets the corresponding dimensions, B and aB. Then, Ciscalculated and relation (4.6) can be used to generate a function between A and aH for theH-plane. We will have a realizable hom if this curve does intersect with a universal H­plane pattern producing the desired 3-dB curve in the H-plane.This procedure can be repeated for several other (B,ap) producing a number of possiblegeometrical horn configurations with the desired 3-dB beamwidth in E and H plane.

-38-

To investigate antenna effects on an indoor radio channel we designed six 58 GHzpyramidal horns. Geometrical dimensions, 3-dB beamwidth and directivity of the designedhorns are tabulated below. The dimensions a and b of the attached waveguide are 4.775mm and 2.388 mm, respectively.

Table 4.1: Geometrical dimensions ofseveral pyramidal horns

3-dBBW 3-dB BW A B aR ae DH-plane E-plane

(degrees) (degrees) (mm) (mm) (degrees) (degrees) (dBi)

60 10 5.64 26.40 0.68 4.49 17.4

60 20 5.46 12.70 3.51 9.00 14.1

60 30 5.65 8.70 11.31 13.56 12.5

60 60 5.21 4.25 0.00 27.36 9.1

30 30 11.67 26.06 10.22 22.45 16.2

10 10 36.53 26.40 7.07 4.49 25.1

The calculated antenna radiation patterns are based on (the E-field model) apertureintegration. This method is adequate in the main beam region and for moderate aperturesizes. For lower aperture sizes the radiation pattern is strongly influenced by the homaperture flange structure. When we approach the 8=7(/2 zone the error in the predictionsincreases and obviously the method is no longer valid beyond 8=7(/2. To obtain theradiated field in those regions for which the aperture integration method produces weakresults one can use GTD techniques [14],[15] and [16]. However, the main goal of thissection is to investigate antenna effects on an indoor radio channel and we expect the zonebeyond 8=7(/2 to have little influence. Therefore, we will not apply complex GTDtechniques but a very simple approximation of the diffracted field in the zone 8> .,./2; wewill assume the diffracted E-field in this zone to be constant. The diffracted E-field canthen be calculated using the next relation:

4...

!G(O)dO = f P nd(O) dO + f p/diff dO = 4.,.P/4.,. P

t4.,.

0<0<'; ';<0< ...

(4.7)

Here, G(O) denotes the antenna gain function which is assumed to be equal to the antennadirectivity for 8=0 and Pt denotes the total power radiated by the hom. Prad denotes thefar field radiation pattern calculated with aperture integration. Pdiff denotes the diffractedpower which is assumed to be constant for Ih.,. < 8<.,. and zero for 0 <8< lh 7(. If wenormalize Pnd(O) and Pdiff to P/4.,., the previous expression can be rewritten to

...2... "!!!(E;,o + E;.•)sin8d8d4> + 2.,.Pn,diff = 4.,.

(4.8)

where Bu,o and Bu,. are the far-zone electric fields, (4.3) and (4.4), normalized to P/4.,..

-39-

Pa,diff denotes the diffracted power, defined for 1f2 T <9< T, which is also normalized toP/4T.

Figure 4.2 shows the E-plane and H-plane radiation pattern of a smooth walled pyramidalhorn design with a directivity D = 17.4 dBi (see table 4.1). Also included is the constantlevel of diffracted power for IhT < 8< T.

ro ro

Radiation Patternpyromidol horn, (E-plone). 0=17.4 dBi

20,---------,----------,

iii0

~

c -10"0Q.00 -20

-30

-40 '--------'---------'-_--'------'----1.--'------'-----'~___'_______'

-180 -140 -100 -60 -20 20 60 100 140 180

thota (dog)

(a)

Radiation Patternpyramidol horn, (H-plone). 0=17.4 dBi

20,---------,----------,

Of----------.I----t-------\-------l

c -10"0Q.oo -20

-30

-40 '--------'-----------'---'----'------'----1.--'--------'-------'--'_ ___'__---'

-180 -140 -100 -60 -20 20 60 100 140 180

theta (dog)

(b)

Figure 4.2: E-plane and H-plane radiation pattern ofa 17.4 dBi pyramidal hom

The intersection of the dotted lines with the E-plane and H-plane radiation pattern indicatethe 3-dB beamwidth in the E-plane and H-plane, respectively. The 17.4 dBi pyramidalhorn has 3-dB bearnwidths of 10 and 60 degrees in the E-plane and H-plane, respectively.

4.1.2 The Biconical Hom Antenna

The geometry of the biconica1 horn antennas applied in the simulations is depicted infigure 4.3. The analysis of the biconica1 horns has extensively been described in [3], [6]and [9], so a brief description of the analysis and design is presented in this section.

teflon matchingscrew ____

cylindricallJ,Jide

taper

...........:. ':r~ ....

L

Figure 4.3: Geometry ofa biconical hom antenna

-40-

Biconical hom antennas consist of a radial line with spacing b and a biconica1 hom withlength L and aperture width B. If the radial line is excited with the circularly polarisedTEll mode in the circular waveguide, then the biconica1 hom antenna exhibits anomnidirectional radiation characteristic in the azimuth plane. The polarisation is vertical[6] for b < IhX, with X = 2T/~ the wavelength in free-space. The radiation pattern inthe elevation plane is determined by the hom dimensions B and L (or cvJJ and can becalculated the same way as the E-plane radiation pattern of a smooth walled pyramidalhom (excited with the TEo. mode) described in the previous section.

Five different biconical horns have been designed for use in the simulations, all withdifferent directivity and radiation pattern in the elevation plane. 3-dB beamwidth in theelevation plane, geometrical dimensions and antenna directivity of the designed antennasare listed in table 4.2. Note that the 9.0 dBi antenna is also used in the measurementsperformed at the EUT.

Table 4.2: Design ofbiconical hom antennas

3-dBBW B ClB DE-pIane

(degrees) (mm) (degrees) (dBi)

5 54.3 4.36 12.7

9 28.8 11.50 9.0

20 13.5 17.41 6.9

30 9.0 26.04 5.3

40 6.5 18.15 4.5

-41-

4.2 The Software used for Simulation

4.2.1 Description of the Software

The software [2] which will be used for simulations is based on the theory of GeometricalOptics (G.O.), i.e. it assumes that EM waves in the frequency band under consideration(mm-waves) behave in the same way as light does after reflection against a surface. Thesoftware consists of three programmes.

The ftrst programme, STRAAL3D, constructs all possible rays up to four reflectionsleaving the transmit antenna, which is mounted at the remote station, and arriving at thereceive antenna, which is mounted at the base station. (The number of reflections islimited to 4 due to complexity of the programme and computing time). All reflectingsurfaces are modelled to be electromagnetically smooth, which means that rays only leavein the direction indicated by Snell's laws of reflection, and scattering due to irregularitiesis not incorporated in the model. EM ftelds of reflected waves are calculated by using thepolarization dependent Fresnel reflection coefftcients for infinite surfaces [17]. Each wavearriving at the receiver can thus be described by two perpendicular field components anda phase difference (between the two perpendicular field components). In STRAAL3D,both field components are weighted with the radiation pattern of the transmit antenna. Ofeach ray, the polarization components, the phase difference, the angle of arrival and thelength of the ray are written in an output file. The format of this output file is explainedin [2]. Only rectangular rooms and objects can be considered. The transmittivity ofsurfaces is not considered, so the programme can only be used if the transitting andreceiving antenna are positioned in the same room. The room configuration (dimensions,reflectivity of walls and objects, position and pointing angle of antenna) is stored in aninput file.

The second programme, POLPOWER, represents the receiving stage of calculating thepower delay proftle. This programme uses the input and the output file of STRAAL3D asinput. First of all, both perpendicular fteld components arriving at the receiver areweighted with the radiation pattern of the receive antenna. Next, the normalized powerdelay profile is calculated. Finally, the rms delay spread and the normalized total receivedpower are calculated according to (2.7) and (2.9).

The last programme is named CUMPOWER. It is used to calculate a cumulative powerdelay profile of several individual profiles. Also, the average rms delay spread iscalculated.

The existing software (STRAAL3D and POLPOWER) can handle various types ofantennas. However, directive antennas like pyramidal hom antennas were not yetimplemented and a special procedure is written to make simulations with pyramidal homantennas possible. The procedure is called HORNIMPL and is described in appendix E.

-42-

4.2.2 Validation of the Software

In [3] a comparison is made between measured and simulated average power delayprofiles of five different rooms. The rooms are modelled as empty rectangular structures.The applied antennas during the measurements are two identical 58 GHz biconical horns.To desribe the radio channel as accurately as possible a look-up table of a measuredelevation radiation pattern is used for the simulations. The 'simulated' antenna is assumedto be perfectly omnidirectional in the azimuth plane. Reflection coefficients needed for thesimulations. are obtained from some time domain reflection coefficient measurementsperformed at the EUT (see also table 3.1). Figure 4.4 shows the measured and thesimulated average delay profile of the reception room.

Average pdp reception roommeasurement at 58 GHz

Average pdp reception roomsimulation at 58 GHz

10 .-----------------, 10.-----------------,

o o

400300200

time (M)

100

-so L..-__~____'____..LIILL1UL.....U.............._----'

o

-40

go -20E

J

~ -10!

400300200

time (M)

100

go -20E

.r -30

~ -10!

(a) (b)

Figure 4.4: (a) Measured and (b) simulated average pdp in the reception room

Comparison of the measured and the simulated average power delay profiles in [3] clearlydemonstrates that the limiting number of reflections (four) causes the proflles to terminatequickly. Simulated average rms delay spread values are therefore unrealistic in smallrooms with highly reflective walls and simulations are inadequate for these rooms. Thesimulations are, however, adequate for small rooms with low reflective walls because theaverage power delay profiles decay rapidly in these rooms. For larger rooms like thereception room, the average power delay proflle is predicted correctly by simulations.The limited number of reflections considered in the simulations causes gaps in the averagepower delay profiles. However, the simulated rms delay spread values for these roomsare still a good representation of the measured results.

Comparison of the individual measured and simulated power delay profiles also gives agood impression of the correctness of the G.o. model. The graphs in figure 4.5 showtypical examples of measured and simulated profiles for two different positions of theremote in the reception room.

-43-

10.-----------------.50

10

30 120 f10 ~

40]

30 120 f

~

50

o400

..........1J 0300 400200

11.... ( ...)

~~-----------------. 40_t'--" !

100 200 300t_ (n_)

100

Power Delay Profilew.a..............1 Po.. 20

~------------------____.J

I I

o

o

10

-40

-soo

-40

i -10

r -20

~ -30

! -10

r -20

~ -30

Power Delay Profileu.a.........t P~. t

10 50

0 40]

ii"30 J~

It

20 f10

~

100 200 300

1_ (na)

Power Delay ProfileBiconical. P... t

10 50

0 40

#~-----~-----------_. ]ii" -10 .,

1I~

_...--- 30

r -:ao

I' 20 f-30

~-40 I

10

-50 00 100 200 300 400

11_ Cna)

Figure 4.5: Typical measured and simulated pdp in the reception room

Notice the dominant rays in both simulated and measured power delay profiles. In fact,the moment of occurence of these dominant rays in the simulated profiles agree very wellwith the ones in the measured profiles. The graphs also show the increase of rms delayspread if the maximum time considered in calculating u is increased. It can be observedthat the dominant rays in the measured and also in the simulated power delay profileaffect the rms delay spread greatly, at least for small t.

Summarizing, the comparisons show that simulations based on a Geometrical Opticsmodel are in close agreement with the measurements, except for small rooms with highlyreflective walls. To ensure that the model predicts the channel behaviour correctly inthese room, the software may be altered in such a way that the maximum number ofreflections considered is increased. Furthermore, to predict channel behaviour correctly,extensive measurements of reflection coefficients at 58 GHz are required.

-44-

4.3 Simulation Configurations

To test the antenna influence on an indoor radio channel, a low reflective room (room A)similar to the reception room at the EDT is chosen because in this room the simulationsclosely agree the measurements. A second room (room B) is chosen with the samedimension but higher reflectivity of walls. Both rooms are modelled as empty rooms.The base station (receive antenna) is positioned at the centre of the room, near theceiling. The remote station (transmit antenna) is placed at different positions, more or lessuniformly distributed over the room. Both the base station antenna and the remote antennause vertical polarisation. Relevant data about the room configurations and positioning ofthe antennas are also given in the table 4.3.

Table 4.3: Room configuration and positioning ofantennas

Room dimensions 11.15 x 24.30 x 4.50 m3

Average Reflection Coefficient" Room A I Room B 0.1 I 0.7

Location Base Station Centrally placed

Height Base Station 3.0 meters

Location Remote Station 24 Positions, uniformlydistributed

Height Remote Station 1.38 meters

"Average reflection coefficient of a room (not to be confused with the average refl. coef. of a single wall).Defined by the average of six reflection coefficients for zero incident angle (4 walls, floor and ceiling).

For every position of the remote a power delay profile is calculated. The parameters ofinterest, the rms delay spread and the normalized total received power G, are derivedfrom these power delay profiles.Simulations are performed for different antennas (with different directivity) and threedifferent antenna setups as depicted in figure 4.6. Figure 4.6a represents the antennasetup with a pyramidal horn at the remote and base station (the so called 'the hom-hom'setup). Figure 4.6b represents the antenna setup with a pyramidal hom at the remote anda biconical antenna at the base station (the 'omni-hom' setup). Figure 4.6c represents theantenna setup with a biconical hom at the remote and base station (the 'omni-omni'setup).

Ca) (b) (e)

Figure 4.6: The a) hom-hom b) omni-hom c) omni-omni setup

The pyramidal horns in figure 4.6a are steered so that they are pointing towards each

-45-

other. In order to assess the effects of antenna mispointing, pointing errors are introducedby turning both antennas away from the proper direction. The orientation of the errorangles at the remote and base station are mutually independent and randomly chosen. Theamount of pointing error is denoted by y, and listed in table 4.4. In the antenna setup offigure 4.6b the pyramidal hom at the remote is steered and pointed towards the biconicalhom antenna. Here, pointing errors are introduced by turning only the pyramidal hom onthe remote away from the proper direction. For the antenna setup of figure 4.6c nopointing errors are introduced.

Next to the effects of pointing errors, also the effects of obstructing the direct LOS-pathare investigated. The results for OBS situations are derived from the results for LOSsituations by mathematical removal of the direct ray. The simulation configurations aretabulated in detail in table 4.4.

Table 4.4: Simulation c01ifigurations in the low (A) and highly reflective (B) room

Antenna Directivity (dBi) Room A Room B

Base Remote Pointing Pointing Pointing Pointing

error '" error '" error '" error '"omni hom omni hom (degrees) (degrees) (degrees) (degrees)

LOS OBS LOS OBS

0 - 0 - 0 0 0 0

4.5 - 4.5 - 0 0 0 0

5.3 - 5.3 - 0 0 0 0

6.9 - 6.9 - 0 0 0 0

9.0 - 9.0 . 0 0 0 0

12.7 - 12.7 - 0 0 0 0

9.0 - - 9.1 0,5,10,15 0 0 0

9.0 - - 12.5 0,5,10,15 0 - -9.0 - - 14.1 0,5,10,15 0 - -9.0 - - 16.2 0,5,10,15 0 0 0

9.0 - - 17.4 0,5,10,15 0 - -

9.0 - - 25.1 0,5,10,15 0 0 0

- 9.1 - 9.1 0,5,10,15 0,5,15 0,5,10,15 0

- 12.5 - 12.5 0,5,10,15 - - -- 14.1 - 14.1 0,5,10,15 - - -- 16.2 - 16.2 0,5,10,15 0 0,5,10,15 0

- 17.4 - 17.4 0,5,10,15 0 - -

- 25.1 - 25.1 0,5,10,15 0,5,15 0,5,10,15 0,5,10,15

-46-

4.4 Simulation Results

In this section the simulation results will be discussed, starting with the results in the lowreflective room (room A). The results in the highly reflective room (room B) will bediscussed next. For each room, the results for the hom-horn, the omni-hom and finallythe omni-omni setup will be presented.

4.4.1 Simulation Results in the Low Reflective Room

-The hom-hom setup-In the hom-hom setup, six different pyramidal horns are tested, all with a differentdirectivity. The simulation configurations are tabulated in section 4.3, table 4.4. Inappendix F, figure F1 and F2, the simulation results for the LOS case with a zero degreepointing error are presented in scatter plots. The plots show the normalized total receivedpower versus rms delay spread (both derived from the power delay profIle) for everyposition of the remote.

Figure 4.7 shows the average performance in a scatter plot for the LOS and OBS casewith the antennas pointed exactly towards each other. In these scatter plots the averagenormalized total received power is given as function of average rms delay spread. Theplots are directly derived from figures Fl, F2, F3 and F4. Averaging is performed over24 different remote positions. Note that the average normalized total received power iscalculated with actual power values, not dB values. The average rms delay spread isdetermined by averaging over the 24 different values of 0'; it is not derived from theaverage power delay profIle as is usually the case. However, these values are in closeagreement with each other.

scatterplothorn-horn, LOS, Room A

scatterplothorn-horn, OBS, Room A

lD -20,--------------,

~

• 9.1 dBI

+ 25.1 dBI

o 16.2 dBi

t> 17.4 dBi

• + 9.

10 20 30 40 50-100 L.-~_~_~_~-----'

o

..,">',;~ -60

1: -80.~ti~oz

lD -20,--------------,

~~

"•ll. -40

• 12.5 dBi

t> 17.4 dB;

• 14.1 dBI

o 16.2 dB;

+ 25.1 dB;

• 9.1 dBI

10 20 30 40 50

-40

'0•

-60 ••

-60

"•ol:l...,">',;u~

ti

2...".~tiE~z -100 L.-~_~_~_~-----'

o

average rms delay spread (ns) average rms delay spread (ns)

(a) (b)

Figure 4.7: Average performance for aJ the LOS and bJ ORS case with zerodegree pointing error.

As can be observed in figure 4.7a, high gain antennas show a better performance than

-47-

low gain antennas in the LOS situation. The rms delay spread decreases and the receivedpower increases with increasing antenna directivity.

Average rms delay spread vs. directivityhorn-horn. LOS. Room A

5,-------------------,

I

"-------/')_c;;:s=_~~OO;E J

262320171~11

oL----~---'---------'------~----'---------'

B

"'"~ 1>

'"

Directivity (dBi)

(a) (b)

Figure 4.8: aJ Average rms delay spreadvs directivity

bJ Effect ofdirectivityfor the hom-hom setup

The effect of antenna directivity on rots delay spread is better visualized in figure 4.8.Decreasing rms delay spread values with increasing antenna directivity is obvious in thehom-hom setup if we look at figure 4.8b. In this case, far-away reflections are attenuatedand rms delay spread is decreased with increasing antenna directivity. This is consistentwith the observations made by Uhteenmaki [5].

If we look at figure 4.7a, we find that the average normalized total received power is alsodirectly related with the directivity of the antennas. For example, the average normalizedtotal received power amounts to -33 dB for the 25.1 dBi horns and -65 dB for the 9.1 dBihorns (a difference in received power of 32 dB). The gain of the LOS ray for the 25.1dBi horns relative to the gain of the LOS ray for the 9.1 dBi horns equals also 2*25.1 ­2*9.1 = 32 dB.

In practice, it is possible that the direct path between remote and base station is blocked(figure F3 and F4). The average performance in the OBS situation is shown in figure4.Th. Compared to the WS case, the plot shows a vast degradation of channel perfor­mance, i.e. (J increases and G decreases drastically. The direct relation between rms delayspread and directivity has disappeared for the OBS channel. As can be observed in figuresF3 and F4, the received power can be extremely low in the OBS case, especially forantennas with a high directivity.

Table 4.5 and 4.6 show the best and worst case performance (of 24 positions) for thehom-hom setup with 25.1 dBi pyramidal hom antennas and 9.1 dBi pyramidal homantennas. The values in the table are based on LOS and OBS situations with zero pointingerror. Note, that the values of q and G in the best and worst case do not have to belongto the same remote position.

-48-

Table 4.5: Performance for 25.1 dBi horns

(1 (us) G(dB)

Best case 1 -28

Worst case 80 -109

Table 4.6: Performance for 9.1 dBi horns

(1 (us) G(dB)

Best case 1 -60

Worst case 63 -109

The horns will often not be pointed exactly to each other. Therefore, a pointing error isintroduced in the simulations. Figures F5 to FlO show the simulation results that areobtained with a 5, 10 and 15 degrees pointing error in the LOS situation. It can beobserved in the plots that pointing errors of 5 degrees deteriorate the channel performan­ce. Increasing the pointing error makes the situation only worse, especially for high gainantennas. While for 25.1 dBi horns with a zero degrees pointing error a (worst case)received power of -40 dB is found, a (worst case) received power of -92 dB is found witha 15 degrees pointing error. The rms delay spread, for the same antennas, increases from2 ns to 33 ns (worst cases) with increasing pointing error.

The worst situation which can occur with a horn-horn setup is pointing errors andblockage of the direct path at the same time. Figures F11 and Fl2 show scatter plots forthe OBS case with 5 and 15 degrees pointing error, respectively. It can be observed fromthese plots that the received power ranges from about -70 to -110 dB while the rms delayspread ranges from 2 ns to 80 ns. In other words, a severe degradation in performancecan be expected if a pointing error is introduced and the direct path between remote andbase is blocked at the same time. This indicates that there is a strong dominance of theLOS ray for the hom-horn antenna setup.

-The omni-hom setup-In the omni-horn setup, six different pyramidal horns mounted on the remote are tested,all with a different directivity. The simulation configurations are tabulated in section 4.3,table 4.4. In appendix F, figure FI3 to F16, the simulation results for the LOS and OBScase with a zero degree pointing error are presented in scatter plots. Figure 4.9 shows theaverage performance in a scatter plot for the LOS and OBS case with zero degreepointing error.

-49-

scatterplotomni-horn, LOS, Room A

scatter plotomni-horn, 085, Room A

'iii' -20~~

"•ll. -40

+ 25.1 dBi

b. 17.4 dBi

'iii' -20r------------,

~~

"•ll. -40 + 25.1 dBi."

~'ij

~ -60 +

a 16.2 dBi

+ 1.... ' dBI

."

".~"u~ -60

b. 17.4 dBi

o 16.2 dBi

• 9.1 dBi

10 20 30 ...0 50-100l--~~~_~_~_----'

o

] -80<;E(;z

• 12.5 dBi

• 9.1 dB;•

10 20 30 ...0 50-100 l--~~~_~_~_-----'

o

] -80:aE5z

overage rms delay spread (ns) average rms delay spread (ns)

(a) (b)

Figure 4.9: Average performance for a) the LOS and b) OBS case with zerodegree pointing error.

Like in the hom-hom setup, the best performance in the LOS case can be achieved withantennas with a high directivity. For the omni-hom setup, the average nns delay spread isincreased by a factor 8 compared to the hom-hom setup.

The effect of hom directivity on the average rms delay spread in the LOS case is shownin figure 4.10. The average rms delay spread decreases and the average received powerincreases with increasing directivity of the pyramidal horns. The decrease in nns delayspread with increasing hom directivity is, again, obvious. Far-away reflections areattenuated and rms delay spread is decreased with increasing antenna directivity. Notethat the opposite effect will be true if the directivity of the omnidirectional antenna at thebase is increased. Far-away reflections are attenuated less if the directivity of theomnidirectional antenna is increased and the nns delay spread will increase.

Average rms delay spread vs. directivityomni-horn, LOS, Room A

50.------------------,

E c:~ I_-------=.JR~

26232017,...1101.....-----'-----------'------'----'-------'---------'

8

~ 20

"go

~ 10~<

Oirectivity (dBi)

(a) (b)

Figure 4.10: a) Average nns delay spreadvs directivity

b) Effect ofdirectivityfor the omni-hom setup

-50-

Until now, we have considered only the LOS situation. Figure 4.9b, and figure F15 andF16 in the appendices, show scatter plots for the OBS situation (with zero degree pointingerror). Compared to the LOS situation, the performance deteriorates drastically for highgain antennas, indicating a strong LOS ray dominance. Tables 4.7 and 4.8 show the bestand worst case performance based on the simulation results for LOS and OBS situationswith zero degree pointing error.

Table 4. 7: Peiformance for 25.1 dBi horns

(1 (ns) G(dB)

Best case 2 -60

Worst case 49 -103

Table 4.8: Peiformance for 9.1 dBi horns

II (1 (os) G(dB)

Best case 11 -75

Worst case 48 -95

In practice, the pyramidal hom at the remote will not be pointed exactly to the biconicalantenna at the base. Therefore, a pointing error will be introduced in the simulations. Thescatter plots in figure F17 to F22 show the results for 5, 10 and 15 degrees pointingerror, respectively (for LOS situations). For all antennas tested, a degradation in perfor­mance can be observed. The largest degradation can be observed for the high gainantennas with a 15 degrees pointing error; the rms delay spread ranges form 2 to 50 ns,the received power ranges from -70 to -90 dB. For low gain antennas with a 15 degreespointing error, the rms delay spread ranges from 10 to 50 ns while the received powerranges from -75 to -90 dB.

H pointing errors and blockage of the direct path occur at the same time, the performanceis expected to get worse (no simulations are performed for this situation). As in the hom­hom setup, this can mainly be explained to the strong LOS ray dominance.

-The omni-omni setup-Six different antennas (tabulated in table 4.4) are tested in the ornni-ornni setup, all withdifferent directivity. Note, that the 0 dBi antenna is an isotropic (imaginary) antenna. Inappendix F, figure F23 to 28, the simulation results are presented in scatter plots. Figure4.11 shows the average performance in a scatter plot for the LOS case and the OBS case,respectively.

-51-

scatterplotomni-omni. LOS, Room A

scatterplotomni-omni. OBS. Room A

ai' -20,------------,

3..s::. -40..,...~

::~ -60

+ 12.7 dBi

0. 9.0 dB;

o 6.9 dB;

+ 5.3 dBi

ai' -20,-----------------,

3~..s::. -40..,...~..u~ -60

+ 12.7 dBi

0. 9.0 dBi

o 6.9 dBi

+ 5.3 dBi

... 4.5 dB;

•20 30 40 5010

-100 '--~-~-~-~----'o

] -80

~oZ

... 4.5 dBi

• 0 dB;

50

"'. 0• 0.

10 20 30 40-100L--_~_~_~_~____J

o

~ -80~

Eoz

average rms delay spread (ns) average rms delay spread (ns)

(a) (b)

Figure 4.11: Average peiformancefor a) the LOS case and b) the OBS case.

The differences between the LOS case and the OBS case are minimal, especially for highgain omnidirectional antennas. High gain antennas show a uniform coverage in receivedpower for both the LOS case and the OBS case. In practice, this implies fair access toevery user. Low gain antennas provide a low rms delay spread compared to the high gainantennas resulting in a higher bit rate for low gain antennas. The received power for thelow gain antennas in the LOS situation is comparable to the received power for high gainantennas. In the OBS situation, however, the received power for low gain antennasdecreases noticably. The differences between the LOS situation and the OBS situation forlow gain antennas can be explained by the fact that the LOS ray is more dominant for lowgain antennas than for high gain antennas: the antennas at base and remote are positionedat different heights resulting in antenna gain compensation of free-space losses. Thiseffects is strongest for high gain antennas and makes the LOS ray less dominant.

The relationship between average rms delay spread and antenna directivity is presented infigure 4.12. It shows that an increase in antenna directivity results in an increase of theaverage rms delay spread (also reported by Uihteenmili, [5]). This is obvious, becausethe omnidirectional antennas do not attenuate reflected rays with high delay, so rms delayspread is increased with increasing directivity (see figure 4.12b). Note that the oppositeeffect occurs for the omni-horn or hom-horn setup; there, an increase in directivity ofpyramidal horns results in a decrease of the average rms delay spread.

-52-

Average rms delay spread vs. directivityomni-omni. LOS. Room A

50.---------------,..-----------,

~ASE I~<)

ROO_TE_iii _

18151296Jo'----'-----'------'--------'-------'--------'

o

.....s. 40

~g. 30>-.2

""~ 20

"'"~ 10><

Directivity (dBi)

(a) (b)

Figure 4.12: a) Average rms delay spreadvs directivity

b) Effect ofdirectivityfor the hom-horn setup

Figure 4.12a shows also that there is a strong dependence between the rms delay spreadand the directivity. This dependence is much stronger than in the hom-hom or omni-homantenna setup.

Table 4.9 and 4.10 show the best and worst case situations for the 12.7 dBi biconica1hom antennas and the 0 dBi isotropic antennas, respectively.

Table 4.9: Performance fOT 12.7 dBi antennas Table 4.10: Performance fOT 0 dBi antennas

I (J (ns) G(dB)

Best case 38 -81

Worst case 57 -86

I (J (ns) I G(dB) IBest case 10 -78

Worst case 37 -95

4.4.2 Simulation results in the highly reflective room

In this section the simulation results of the highly reflective room will be discussed,starting with the hom-horn setup. Next the omni-hom setup and finally the omni-omnisetup will be considered.

-The horn-hom setup-In appendix F, figures F29 to F34, the simulation results for the hom-hom setup arepresented in scatter plots. Figure F29 shows the results for three different antennas, allwith different gain, for the LOS case with a zero degrees pointing error. Figure F30shows the results for the same antennas for the OBS case. From the scatter plots in figure

-53-

F29 and F30 the average performance can be derived for the LOS and OBS case, res­pectively. The average performance is presented in the next scatter plot.

scatterplothorn-horn. Room B

'iii' -20

~

O!_ -40+ + 25.1 dBi.LOS

.. 16.2 dBi,LOS

o 9.1 dBi ,LOS

.. 16.2 dBi.OBS

• 9.1 dBi .OBS

+ 25.1 dBi.OBS..••o

10 20 30 40 50 60-100 L----~~_~~~_____'

o

] -80"6El;z

l:.~

~ -80

overage rms delay spread (ns)

Figure 4.13: Average peiformance in the LOS and OBS situation

The high gain (25.1 dBi) antennas show an excellent performance in the LOS situation.Low values for q are found, ranging from 1 ns to 14 ns, while high values for thenormalized total received power are found, ranging from -23 to -40 dB. Obstruction ofthe direct path between two high gain antennas leads, however, to a severe deteriorationwith extreme worst case situations (see figure F30).

For low gain antennas (9.1 dBi) in a LOS situation, higher values for q are found,ranging from 7 ns to 35 ns. For the normalized total received power, values are foundranging from -60 dB to -70 dB. Blockage of the direct path leads again to a deteriorationof channel performance. The deterioration, however, is less severe for low gain antennasthan for high gain antennas. This can be explained by the fact that high gain antennas,when pointed exactly towards each other, have a stronger LOS ray dominance than lowgain antennas.

The tables below show the best and worst case performance of 24 positions in the highlyreflective room based on the simulation results for the LOS and OBS case.

Table 4.11: Performance for 25.1 dB; horns Table 4.12: Peifonnance for 9.1 dB; horns

I (1 (ns) G(dB)

Best case 1 -23

Worst case 83 -88

II (1 (ns) G(dB)

Best case 7 -60

Worst case 70 -79

Pointing errors will result in a performance degradation, just like in the low reflective

-54-

room. In figures F31 to F33, the simulation results for the LOS case with 5,10 and 15degrees pointing error are presented. For high gain antennas, the channel performance isaffected most and it will deteriorate more with increasing pointing error. For the 25.1 dBiantennas with a 15 degrees pointing error, extreme values of q=73 ns and 0=-90 dB arefound. Compare this with the worst case situation for zero degrees pointing error in theLOS case: q=14 ns and G=-40 dB.

Low gain antennas show also a performance degradation but seem to be less dependent ofthe amount of pointing error. For the 9.1 dBi antennas, a worst case rms delay spread of72 ns is observed. This value is found for a pointing error of 5 degrees. A worst casereceived power of -78 dB is observed. This value is found for 10 and 15 degrees pointingerror.

Simulations are also performed for 25.1 dBi horns including pointing errors and blockageof the direct path at the same time. The results are presented in figure F34. The strongLOS ray dominance in the hom-hom setup leads again to severe performance degradationand makes this antenna setup not favourable.

-The omni-hom setup-Three different antennas are tested in the omni-hom setup in the highly reflective room.Figure F35 and F36 show the simulation results in scatter plots for both the LOS andOBS case. The average performance is derived from these plots and depicted in figure4.14.

scatterplotomni-horn. Room B

1D -20

~

l;+ 25.1 dBi.LOS

•0 -40 " 16.2 dBi.LOS.....,G.~ 0 9.1 dBi ,LOS~

~ -60 + + 25.1 dBi,OBS2 "2 + • • 16.2 dBi,OBS•! -80:g • 9.1 dB; ,OBS

E0z -100

10 20 30 40 50 60

average rms delay spread (n9)

Figure 4.14: Average performance in the LOS and ORS situation

It can be seen in the plot above, that the setup with the high gain pyramidal hom antenna(25.1 dBi) shows again the best performance in the LOS situation. Values for q are foundin figure F35, ranging from 4 ns to 48 ns, while values for the normalized total received

-55-

power are found, ranging from -60 dB to -65 dB. OBS channels result in a degradation ofchannel performance, at least for high gain antennas.

For the low gain antenna (9.1 dBi) in the LOS situation, values for (1 are found, rangingfrom 52 ns to 75 ns, while values for the normalized total received power are found,ranging from -72 dB to -77 dB. Blocking of the direct path causes the average normaliredtotal recieved power to decrease, as expected. However, the average rms delay spreaddecreases by about 9 nsf Evidently, the LOS ray is not dominant in a highly reflectiveroom for this low gain omni-hom antenna setup and the average power delay profile ismainly determined by the reflections in the room. This could also be observed in chapter3, figure 3.3; a weak LOS ray can produce values of (1 which are smaller in the OBS casethan in the LOS case. Uihteenm3.ki reported also in [5] that direct ray attenuation is notsupposed to increase rms delay spread. Similar results are found in measurement resultsperformed at the EUT and reported by Wagemans [3].

The tables below show the best and worst case performance of 24 positions in the highlyreflective room based on the simulation results for the LOS and OBS case.

Table 4.13: Petformancefor 25.1 dB; horns

I (f (ns) G (dB)

Best case 4 -60

Worst case 66 -87

Table 4.14: Performance for 9.1 dB; horns

II (f (ns) G(dB)

Best case 42 -72

Worst case 7S -80

Pointing errors in the low gain antenna setup do not necessarily imply a deterioration ofchannel performance, even if the path is blocked. This can again be explained by theweak LOS ray dominance. There are, however, no simulation results available to checkthis.

-The omni-omni setup-Until now, we have always assumed the simulation software to produce correct results inthe highly reflective room. However, in section 4.2.2 we mentioned that the simulationsare not adequate for small rooms with highly reflective walls because the number ofreflections considered by the software is limited to four. The hom-hom and omni-homantenna setup ensure a rapid decay of the average power delay profile because of the useof pyramidal horns in the setups. Simulations are therefore adequate for these setups. Theomni-omni antenna setup produces high values of (1, especially the high gain omni-omnisetup, indicating a slow decay of the average power delay profile. Simulations maytherefore not be adequate for an omni-omni antenna setup in a highly reflective room.

Figure 4.15a and 4.15b show the average power delay profile for the omni-omni setupwith 12.7 dBi and 4.5 dBi antennas, respectively. The graphs also show the increase ofaverage rms delay spread, (Jav, as function of the maximum time considered in calculating

-56-

(Jav. For the profile with the 12.7 dBi antennas, (Jav does not saturate for large t. Thisimplies that rays arriving for large t and reflecting more than 4 times have considerableinfluence on the average rms delay spread. The calculated values for the rms delay spreadand the normalized total received power which are obtained from the simulations willtherefore be smaller than the true values. The same can be observed for the 6.9 dBi andthe 9.0 dBi antenna setups (not presented here).

For the profile produced by the 4.5 dBi antenna setup, (fav seems to saturate for large t.The same can be observed for the 0 dBi antenna setup (not presented here). This impliesthat for these antenna setups, rays arriving for large t and reflecting more than 4 timeswill have practical no influence on the average rms delay spread.

It can be concluded that simulations for the low gain (0 dBi and 4.5 dBi) antennas areadequate and simulations for the high gain (6.9 dBi, 9.0 dBi and 12.7 dBi) antennas arequestionable. There is a simple explanation for this: low gain antennas attenuate far-awayreflections more than high gain antennas.

Average power delay profile12.7 d8; omni-omni, LOS, Room B

Average power delay profile4.5 d8i omni-omni, LOS, Room 8

0.-----------------, BO 0.--------------, BO

time (ns)

(a)

60 "iii'-=.m ..,~ -40 a

~

'" y- o.a 40 III

E /--- ...-60

a

'" U.Q I '"/ III

/ 20 ~-80

/

"-100 0

0 100 200 300 400

time (ns)

(b)

60 ]

11~0.

40 III

~

::i..20 ~

-20

_/,,'-80 /~-'-

-100 "--/__'--_--'IILLl--"----IJLJ.JII..LI:IlL..I-_-----' 0o 100 200 300 400

'" -60.Q

~

lD~ -40

'"~

Figure 4.15: Average power delay profile/or the 12.7 dBi and the 4.5 dBi antennas

The simulation results for the omni-omni setup in the highly reflective room are presentedin figure F37 to F41. The scatter plots in figure 4.16 shows the average performance forfive different antennas in the LOS and OBS situation. The plots are derived from thescatter plots in figure F37 to F41. Note, that both the values of (J and G for the 6.9 dBi,the 9.0 dBi and the 12.7 dBi antennas may be too small due to the limiting number ofreflections considered by the simulation software.

-57-

scatterplot scatterplotomni-omni. LOS. Room 8 omni-omni, 08S, Room 8

lil -20 lil -20

~ ~~ ~

" + 12.7 dBI " + 12.7 dB;• •0 -40 0 -400. 0.

" "- 9.0 dBI ... "- 9.0 dB;" ":> :>.j; .j;

" 0 6.9 dB; " -600 6.9 dB;

~ -60 ~

"0 06+ • 4.5 dBi "06 04 + • 4.5 dB;:e • :e... • • o dBi ...

-80 • • o dB;:: -80 ::a ~

~ E0 l;z

-100z

-10010 20 30 40 50 60 10 20 30 40 50 60

average rms delay spread (ns) average rms delay spread (ns)

(a) (b)

Figure 4.16: Average peifonnance for (a) the LOS case and (b) the OBS case

As can be observed in the plots, the differences between the LOS case and the OBS caseare minor, even for the low gain omnidirectional antennas. The 4.5 dBi antennas show anaverage rms delay spread value which is smaller in the OBS case than in the LOS case!This phenomena can also be observed in the low reflective room with the 12.7 dBi and9.0 dBi antennas and can be explained by the weak LOS ray dominance. In the highlyreflective room, a major part of the received power is obtained via reflections at walls,lessening the LOS ray dominance even more. Therefore, if low gain antennas show asmaller rms delay spread in the OBS case, this surely may be expected for high gainantennas. High gain antennas in the highly reflective room thus are expected to producesmaller rms delay spread values in the OBS case than in the LOS case. This, however,seems not to be the case for the 6.9 dBi, the 9.0 dBi and the 12.7 dBi antennas and canbe explained by the fact that for these antennas the simulations are not adequate anymore.

Figure F41 shows a scatter plot for the 0 dBi antennas in the LOS and OBS situation. Inthe LOS situation, values of (J range from 33 ns to 44 ns, while values of G range from ­75 dB to -80 dB. In the OBS situation, (J ranges from 34 ns to 47 ns, while Grangesfrom -76 dB to -82 dB. Comparing these values with the values obtained in the lowreflective room (table 4.10) shows that deviation in rms delay spread and received powerbecomes smaller, indicating fair access to every user.

The tables below show the best and worst case performance of 24 positions in the highlyreflective room based on the simulation results for the LOS and OBS case.

Table 4.15: Performancefor 4.5 dBi antennas

II (1 (ns) I G(dB)

Best case I 40

I-71

IWorst case 55 -76

-58-

Table 4.16: Performance for 0 dBi antennas

II (1 (ns) G(dB)

Best case 33 -75

Worst case 47 -82

4.5 Concluding Remarks on the Simulations

In a LOS situation with zero degrees pointing error, the horn-hom setup is much to beprefered to the omni-horn and omni-omni setup. The performance gets better withincreasing antenna directivity, i.e. the rms delay spread decreases and the normalizedtotal received power increases. Also the deviation in rms delay spread decreases withincreasing antenna directivity.The deviation in received power as function of antenna directivity stays practically thesame. This deviation is mainly caused by the differences in free-space losses for thedifferent positions of the remote.The excellent performance of the hom-hom setup in a LOS situation with zero degreesmispointing can be explained by the dominance of the LOS ray. It is obvious that theadvantages of a strong LOS ray disappear if the direct path between remote and base isblocked or if the antennas are not pointed exactly towards each other.

The omni-omni setup shows some important advantages with respect to the hom-hornsetup: pointing errors need not to be considered and blockage of the direct path does notdeteriorate the received power significantly. Also the deviation in received power asfunction of the remote position is small compared to the horn-horn setup, especially foromnidirectional antennas with high (e.g. 25.1 dBi) directivity. This indicates a uniformcoverage of received power giving fair access to every user in the room.Antenna directivity in the omni-omni setup has major influence on the rms delay spreadand minor influence on the normalized total received power (indicating a weak LOS raydominance) compared to the horn-horn setup. The rms delay spread increases withincreasing antenna directivity. Antenna directivity in the omni-omni setup can thus beseen as a mechanism to control the rms delay spread while leaving the received powerunchanged!Blockage of the direct path has minor influence on the rms delay spread compared to theeffects we saw in the hom-hom setup. For omnidirectional antennas with high directivitythe rms delay spread decreases even slightly if the direct path is blocked. This impliesthat higher bit rates are possible in a OBS channel than in a LOS channel!

In the omni-horn setup we might expect to find results that combine the advantages of thehom-hom and omni-omni setup. However, the use of pyramidal horns on the remoteresults in extreme worst case situations if, for example, the direct path is blocked orpointing errors are present. Evidently, the LOS ray is still dominant in the omni-hornsetup.

In the highly reflective room, the rms delay spread is larger as expected because reflectedrays with long delay arrive stronger at the receiver. The horn-horn and omni-hom setupshow again severe worst case situations if the the direct path is blocked or pointing errorsare introduced. High values of rms delay spread and low values of normalized totalreceived power are found compared to the omni-omni setup.The omni-omni setup shows again a uniform coverage in received power (blockage of thedirect path does not deteriorate the channel performance), even for omnidirectionalantennas with low directivity. Furthermore, no extreme values for rms delay spread arefound like in the hom-hom setup. This makes the omni-ornni setup definitely favourite in

-59-

5 Conclusions and Recommendations

For antenna setups with biconical hom antennas, the average rms delay spread is animportant parameter characterizing the overall performance. A rule of thumb predictingthe value of the average rms delay spread could be a useful tool to get an impression ofthe maximum achievable data rate in an indoor radio channel. The rule of thumbpresented in this thesis is based on measured average power delay profiles at the EUT anddepends solely on the slope parameter 'Y and not on the direct LOS-ray, which is notdominant if biconical horns are used, or on the value of 1"1 (the duration of the constantlevel part at the beginning of the average power delay profile) which is more or lessconstant. For isotropic antennas the constant level part is likely to be missing and averagerms delay spread becomes equal to the slope parameter 'Y.

An engineering model for the slope parameter 'Y, based on Geometrical Optics, isproposed by formulating a power decay function for rays excited by a centrally placedantenna. In the model for the slope parameter 'Y, only rectangular shaped rooms can behandled. Furthermore, the model does regard only one antenna mounted on the centrallyplaced base station. It is an interesting task to find out whether a second antenna(mounted at the remote station) can be included in the model.To attain insight in the influence of the indoor environment on the slope parameter 'Y, theengineering model shows good use. Knowlegde of the reflection properties of walls isnecessary to complete the validation of the model. Actual measurements of reflectionproperties of walls are therefore recommended. However, even if the reflection propertiesof walls are known, the formula for the power decay function is still questionable becausethe simulation programme shows results that differ significantly from the results obtainedwith this power decay function.

The rms delay spread can be reduced drastically by using highly directive antennas suchas pyramidal horn antennas. This is demonstrated by using a simulation programme,based on Geometrical Optics, developed at the EUT. Antenna setups with pyramidalhorns, however, are extremely sensitive to blockage of the line-of-sight ray or pointingerrors between the antennas at base and remote station, and a severe performancedegradation can be observed for these situations. Antenna diversity techniques can be usedto avoid, or at least minimize, the severe performance degradation. An interestingexample of such a diversity antenna system is the Motorola ALTAIR™ antenna systempresented in [13]. This system exhibits a form of switched antenna diversity using acircular array of directional antennas. Further research on these antenna systems isrecommended.If no antenna diversity techniques are used, antenna setups with identical biconical hornsseem to be favourite in case a high degree of system flexibility is required.

The simulation programme predicts the channel characteristics correctly in the lowreflective room. In the highly reflective room the simulations may not be adequateanymore (e.g. if high gain omnidirectional antennas are used). This is caused by thelimited number of reflections considered by the simulation programme. To ensure that theprogramme predicts the channel behaviour correctly in all indoor environments thesoftware may be altered in such a way that a larger number of reflections is considered.

-61-

6 References

[1] Gradshteyn, I.S. and Ryzhik, I.M.TABLE OF INTEGRALS, SERIES, AND PRODUCTSNew York: Academic Press Inc., 3th edition, 1965Translation of: Tablitsy Integralov, Summ, Ryadov I Proievedeniy, Moscow,gosudarstvennoe Izdatel'stvo Fiziko-Matematicheskoy Literatury, 1963, p. 905

[2] Melters, M.A.A.SIMULATION OF AN INDOOR RADIO CHANNEL AT MM-WAVEFREQUENCIESEindhoven, Eindhoven University of Technology, Division EC, 1990,graduation thesis

[3] Wagemans, A.G.MEASUREMENT AND STATISTICAL MODELLING OF INDOOR RADIOCHANNELS IN THE MM-WAVE BANDEindhoven, Eindhoven University of Technology, Division EC, 1990,graduation thesis

[4] Stutzman, W.L. and G.A. ThieleANTENNA THEORY AND DESIGNNew York, John WIley and Sons, Inc., 1981, pp. 411-415

[5] Uhteenm3.ld., J.SIMULATION OF ANTENNA EFFECTS ON DELAY SPREADVienna, Euco-Cost, Cost 231 TD(92), 7-10 Jan. 1992

[6] Smulders, P.F.M. and A.G. WagemansMILLIMETER-WAVE BICONICAL HORN ANTENNA FOR NEAR UNIFORMCOVERAGE IN INDOOR PICOCELLSElectronic Letters, Vol. 28, 1992, pp. 679-681

[7] Smulders, P.F.M. and A.G. Wagemans·WIDEBAND MEASUREMENTS OF mm-WAVE INDOOR RADIO CHANNELSPmc. 3th Int. Symp. on Personal, Indoor and Mobile Radio Commun., Oct. 1992

[8] Smulders, P.F.M. and A.G. WagemansWIDEBAND MEASUREMENTS OF 58 GHz INDOOR RADIO CHANNELSURSI, Proc. Int. Symp. on Signals, Systems and Electronics, Sept. 1992, p.692

[9] Uenakada, K. and K. YasunagaHORIZONTAL POLARIZATION BICONICAL HORN ANTENNA EXCITEDBY TEll MODE IN CIRCULAR GUIDEInt. Symp. on Ant. and Prop., Sendai, 1971, summary of papers, pp.125-126

-62-

[10] Smulders, P.F.M. and A.G. WagemansWlDEBAND INDOOR RADIO PROPAGATION MEASUREMENTS AT 58 GHzElectronic Letters, Vol. 28, 1992, No.l3, pp. 1270-1271

[11] Sletten, C.J.REFLECTOR AND LENS ANTENNAS: ANALYSIS AND DESIGN USINGPERSONAL COMPUTERSBoston, Artech House, Inc. ,1988, pp. 92-100

[12] Lawton, M.C. et al.AN ANALYTICAL MODEL FOR INDOOR MULTIPATH PROPAGATION INTHE PICOCELLULAR ENVIRONMENTUniversity of Bristol'????

[13] Mitzlaff, J.E.RADIO PROPAGATION AND ANTI-MULTIPATH TECHNIQUES IN THEWIN ENVIRONMENTIEEE Network Magazine, November 1991, pp. 21-26

[14] Andersen, J .B.LOW AND MEDIUM GAIN MICROWAVB ANTENNAS: in The Handbook ofAntenna DesignLondon, Peter Peregrinus, 1982, Vol. I, Chap. 7

[15] Russo, P.M. et al.A METHOD FOR COMPUTING E-PLANE PATTERNS OF HORNANTENNASIEEE Trans. on Ant. and Prop., Vol. AP-13, 1965, pp. 219-224

[16] Mentzer, C.A. et al.SLOPE DIFFRACTION AND ITS APPLICATION TO HORNSIEEE Trans. on Ant. and Prop., Vol. AP-23, 1975, pp. 153-159

[17] Maanders, E.J. and M.H.A.J. HerbenANTENNES EN PROPAGATIEEindhoven, Eindhoven University of Technology,Lecture Notes no.5P220, 1987, chap. 4

[18] Proakis, J.G.DIGITAL COMMUNICATIONSLondon: Mc Graw-Hill, 1983, chap. 7

[19] Saleh, A.A.M. and R.A. ValenzuelaA STATISTICAL MODEL FOR INDOOR MULTIPATH PROPAGATIONIEEE Journal on Selected Areas in Communication,Volume SAC-5, 1987, pp. 128-137

-63-

[20] Blakeborough, P.REFLECTION COEFFICIENTS IN THE RANGE 8 TO 50 GHz FOR TYPICALINDOOR BUILDING MATERIALSLeeds, Euro-Cost, Cost 231 TD(92) 50, April 1992

[21] Glance, B. and L.J. GreensteinFREQUENCY SELECTIVE FADING EFFECTS IN DIGITAL MOBILE RADIOWITH DIVERSITY COMBININGIEEE, Trans. on Commun., Vol. COM-31, no. 9, 1983, pp. 1085-1094

[22] Pahlavan, K. and S.J. HowardFREQUENCY DOMAIN MEASUREMENTS OF INDOOR RADIO CHANNELSElectronic Letters, Vol. 25, no. 24, 1989, pp. 1645-1647

[23] Abramowitz M. and I.A. StegunHANDBOOK OF MATHEMATICAL FUNCTIONSNew York, Dover Publications, Inc., 1972, pp. 255-256

-64-

Appendix A: Derivation of an Analytical Expressionfor the Average Rms Delay Spread

We will show that the average rms delay spread as defmed in section 3.1 with (3.4) canbe represented with an analytical expression. This expression is based on the continuousmodel of the average power delay prof11e obtained from the measurements performed atthe EUT.

In formula (3.5), the denominator contains the average normalized total received power.We can write the total received power with help of figure 3.1 and formula (3.2) as

ao 1", ClD -(t-1"J

Plot = !pav(t)dt = !Cdt + C I. e-"(-dt = C· (T1 + -y)

for the obstructed line-of-sight (OBS) situation.For the line-of-sight (LOS) situation, the total received power can be written like

ao 1", ao -(t-1",)

Plot = !Pav(t)dt = {c + D·{,(t)dt + C I. e-"(-dt = C'(T1 + -y) + D

Note that -y and Tl effect the total received power equal.

(A. 1)

(A.2)

The OBS situation can be seen as a special case of the LOS situation by substituting D =O. Therefore, only the LOS situation will be regarded. Evaluating formula 3.5 for q = 2yields

(A.3)

The integral in the last term of equation (A.3) is, in fact, a Gamma function [23]. Ingeneral, the Gamma function is expressed as

ao

(A.4)

The Gamma function can be solved analytically in two different ways. First of all, with

-AI-

help of the recurrence formula [23]:

r(z+ 1) = zr(z) = z!

The solution of the integral in the last term of (A.3) then yieldsOl> -(t-",j Ol> t'f t 2e-'Y-dt = f (t' +T

1)2e --:; dt' =

"', ~

Ol> t' ao t' Ol> t'!t'2e --:; dt' + 2T1!t' e --:; dt' + T~! e --:ydt' =

ao t' ao t' Ol> t'

! t' -- t' ! t' -- t' 2! -- t'y (_)2 e 'Y d- + 2Ttl (-)e 'Y d- + "YTI e 'Yd_ =I' I' -y I' I'

(A.5)

(A.6)

The Gamma function can also be solved by (partially) integrating the last term of (A.3).The solution yields

Ol> -(t-",j "', Ol> _ t "', Ol>

Jt2e-'Y-dt = e -:; Jt 2e ':Ydt = ye -:; f. t,2 e -t'dt' =

~ ~ ~ry

'7"1 CD "'I aa "'I CD

ye-:;[-t,2e -t'lh + ye-:; I 2t'e-t'dt' = "YT~ + ye-:; I 2t'e-t'dt' =

",,t'Y ",,t'Y

"'I T'a CID .,.

"YT~ + 'Ie -:;[-2t' e-t']"" + 'Ie -:; J2e-t'dt' = "YT~ + 2rTI + 'Ie ~[-2e-t']"" =~'Y ~ry

",,t'Y

(A.7)

Substituting (A.6) or (A.7) in equation (A.3) finally yields

(A.8)

This is the first term in the square root of formula (3.4). The second term will becalculated next.

-A2-

Evaluating formula 3.5 for q = 1 yields

1'1

C" 2 C-=;O> -f C" 2 C ( )__1 + _e_ Jt·e -::; dt = __1 + - 'Y"1 + r =2Pror Pror l' 2Pror Pror

1

,,2-+- + 'Y'T1 + r

D"1 + 'Y + C

Squaring this term leads to the second term in the square root of formula (3.4).Substitution of (A.9) and (A.6) or (A.7) in (3.4) leads after simplification to

The OBS situation can be found by substituting D=O:

'/12'Y4 + 24Y"1 + 12r"12 + 4'Y"13 + 'T14

(1 =(1('Y'''I) = -'-V _

2v'31'Y + 'TIl

-A3-

(A.9)

(A. 10)

(A. 11)

Appendix B: The number of reflections in a room as function oftime for a biconical horn antenna

Assume an omnidirectional antenna with a certain beamwidth in elevation. The normali­zed antenna radiation pattern equals I within 201llll and zero otherwise. Integration mustnow take place over the antenna solid angle which is given by

2,.. ;+6_

0lllll = ! ,..1 sinO dOd</> = 4 'I'" sinOQIII"'1-6_

Next, the average number of reflections at wall I and 2 can be calculated:

(B. I)

,..2,.. "'1

R. (r) = R. (r) = ~ 11 rsin</> sinO I dO = .r ! I ~in</>sin2~dOd</>bl,t bi,2 4'1'"s1OO 2b 4'1'"s1OO b

IIIIl _ IIIIl ,.. -6

'7 -

=

,..,.. '7

.r r I sin</> sin20dOdc/>2'1'" smOIIIIlb t ,..'7-6_

[ ] .r°tllllr '7

= - ~n20 I2 'I'"b sinOIIIIl 4'1'"b sin0lllll ;-6_

rOQIII r 0 Oat'I'" (B.2)= + --cosO < :S

2 'I'" bsinOGIll 2Tb tJIIl "2

Notice, inserting 0tJIIl = IhT leads to the expression for isotropic antennas. Inserting 0lllll =oleads to the two-dimensional expression as expected.The antenna is omnidirectional in the azimuth plane so Rbi,2(r) = Rbi,t(r).

~i,3(r) and ~i,4(r) can be calculated the same way:

-BI-

o < 0lllll < 'I'""2

(B.3)

~i.c(r) and ~i.r<r) are left to be calculated. If the transmit antenna placed in the middle ofthe room, then ~i.c(r) = ~i.r<r) and

11'

211' -,;

4T h:inB/IIII!) ~ sin2 BdB deb"'1-9_

rsin8/11114h

(B.4)

-B2-

Appendix C: Dimensions of the Measurement Environments

Table Cl: Dimensions of the different rooms

Room I a (m) I b (m) I h (m) ICorridor 2.43 44.68 3.12

Computer Room 8.65 9.86 3.12

Vax Room 32.20 33.50 3.12

Reception Room 11.15 24.30 4.50

Hall 41.00 43.00 8.50

Amphitheatre 21.00 30.00 7.20

Lecture Room 12.85 8.85 4.00

Room EH 11.21 11.30 7.30 3.07

-C1-

Appendix D: Error Consideration for formulas (3.16) and (3.17)

In section 3.2.2 we derived some expressions to determine the exact and approximatenumber of reflections in a 2-dimensional room. Expression (3.12) to (3.15) are disconti­nuous functions of propagation distance or time and produce the true number of reflecti­ons. Expression (3.16) and (3.17) are continuous functions of propagation distance andproduce the approximate number of reflections. Here, we will try to gain some insight inthe errors caused by the approximation.

Assume a 2-dimensional room with an omnidirectional transmit antenna placed centrally.A possible propagation path of a ray in the room is folded out as depicted in figure D1a.

a) b

2

4 3 4 3 4 3T

...-1

r

< >a

true number

approx. number

40

R~ (r,¢=O)

Rir,¢=O)

3020o

------------------

(J)

c J0- n0~ 2"-Q) 0

0:: ~

..:z

b)

Figure Dl: a) A possible propagation path b) Nr. of reflections vs. propagation distance

Figure Dlb shows both the true number of reflections, R/(r,cP=O), which is a discontinu­ous function of propagation distance and the approximate number of reflections,R3(r,cP=O), which is a continuous function of propagation distance. The (time-) averageslope of the true number equals the slope of the approximated number, Lo.w.

<dRf(r,cP) > = dR3 (r,cP) (D. 1)dr dr

-D1-

The difference between the approximate number and the true number of reflections islimited to + 1,4 for r < lha . For the interval Iha < r < 2a the difference is limited to ­*. Now, we will shift the level of the approximate number of reflections in figure Dlbwith 1,4, according to

(D.2)

The difference between the approximate number and the true number will not exceed +Ih as can be verified in figure Dlb. The level shift of 1,4 will thus bound the difference to±lh. The influence of a level shift on the slope will be made clear with help of (D.3).Expression (D.3) represents the decay of power in a room as defined in section 3.2.1.

(D.3)

We can see that the level shift in RJ(r,</>} of 1,4 will cause only a level shift of 1000g'7'" inthe power decay. It will not affect the slope B of the power decay or 'Y.

Until now, we only regarded the ray in the direction </>=0 radians. However, rays inother directions exist as well. With the right level shift we can bound the differencebetween the approximate and the true number of reflections for all directions to ±Ih. Thenumber of reflections can therefore be defined as

(D.4)

in which C(</» represents the level shift as function of </>.

It can be concluded that if the omnidirectional transmit antenna placed centrally, thedifference between the approximate number of reflections and the true number ofreflections will not exceed ± Ih. Furthermore, the average slope of the power decay whenusing the true number of reflections will equal the slope when using the approximatednumber of reflections. This is a consequence of the equality in (D. I).

-D2-

Appendix E Implementation of Pyramidal Horn Antennas

In section 4.1.1 we discussed the analysis and design of pyramidal hom antennas. Sixantennas are designed to test the influence of antennas on an indoor radio channel. Theantennas are directive which means that they have to be pointed in the desired direction.The software (STRAAL3D and POLPOWER), however, does not support directive anten­nas, so a procedure (HORNIMPL) which can handle directive antennas is written. Theprocedure can be added to the existing software. STRAAL3D or POLPOWER will thenmake a call to HORNIMPL.

The operation of HORNIMPL is explained with help of the block diagram on the nextpage. The input of HORNIMPL is first of all the direction (8mucP..J in which the antennais pointed and second, the direction (8ray,cPray) of an excited or received ray, calculated bySTRAAL3D. The direction of the antenna must be inserted before the fust row of thecommon input fIles of STRAAL3D in the order 8ant,fr - cPmt,tr - 8mt,rec - cPmt,rec. The newinput fIle is now used by STRAAL3D but also by POLPOWER.

HORNIMPL then proceeds as follows. The direction of the ray is calculated relative tothe direction in which the antenna is pointed. In calculating the relative direction of theray, the programme has to deal with different coordinate systems. Figure Ela shows thecommon carthesian and spherical coordinate system of a directive antenna. Figure Elbshows the carthesian and (uncommon) spherical coordinate system of the room configura­tion defined in STRAAL3D and POLPOWER.

x·

z·

(a)

x

z

........... ::::.

(b)

y

Figure El: coordinate systems ofa) directive antenna and b) room configuration

The main lob of the directive antenna is pointed in the direction z'. The polarisation ofthe electric field in the aperture plane Sap is assumed to be parallel to the y' direction. Thepolarisation of the radiated field in the room is assumed to be vertical. This implies thatthe x' axis is parallel to the xy-plane of the room configuration.

For the relative ray direction the perpendicular electric fields are determined from the

-El-

radiation pattern. The radiation pattern of the directive antenna is stored in a look-up tablewith a resolution of one degree; for every phi-cut (0 to 90 degrees) the two perpendicularelectric fields are stored in two columns for theta is 0 to 90.

Finally, the electric field components are transformed to the coordinate system which isused in STRAAL3D and POLPOWER. The transformed components are returned back toSTRAAL3D (in case of a transmitted ray) or POLPOWER (in case of a received ray).

read direction ray: 8ray ~ray

read direction antenna:

8.nt ~.nt

determine relative angles

erel = ellnt - erlly

4>rel = 4lllnt - 4lray

transformation

erel to e;el

'rei to , ;el

~

retrieve E8 .( e~el • 41 'rei)

E~ .( e ~el • 41 'rei)

from Iool::-tp table

ttransformat ion

Ea , to EeE., to E.

Figure E2: Block diagram ofprocedure HORNIMPL

-E2-

Appendix F: Simulation results presented in scatterplots

50403020

Room A. horn-horn, LOS, 'If-O'

10

-20

-40

OJ~

-60

~

-80

-10040 50 0302010

-80

Room A, horn-horn, LOS, 'If=0'-20.--------------'---------,

-100 '----.'----.'----.'----.'--------'o

rms delay spread (ns) rms delay spread (ns)+B85e:25.1 dBI '" Ba5e:16.2 dBI 0 B85e:9.1 dBI o Ba.e: 17.4 dBI + Bau:14.\ dBI V Base:12.5 dBI

Rem: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI Rem: 17.4 dB; Rem: 14.1 dBI Rem: 12.5 dBI

Figure Fl Figure F2

Room A, horn-horn. OB5. 1jf =0.

Room A. horn-horn, OB5. 1jf=0-30 -30

-50 -50

CD m~ ~

-70 -70

~~~ + *+ 6/:;,AA

~ 66. A '" ~ 0+ + ++ o§:Jo illig 0+

" + " 0 0

" + o r;:P o 00 0

-90 11>" +'" + -90 '60 Iil OO0

0° 0 0 000

+~ '""+

0

0 00 0 0+

-110 -110a 10 20 30 40 50 0 10 20 30 40 50

rms delay spread (ns)+ BII5e:25.1 dBI '" BII5e:16.2 dBI

Rem: 25.1 dB; Rem: 16.2 dBI

rms delay spread (ns)o Ba.e:17.4 dBI 0 B8.,,:9.1 dBI

Rem: 17.4 dBI Rem: 9.1 dBI

Figure F3 Figure F4

Roam A, horn-horn, LOS. 'V -5'-20 r---------'----'------'.......:--'-.......:...L..----~ Room A, horn-horn. LOS. 'V ~5'-20 .- ~~~-.:.::.:..:.:..-.:.::.:.:.::....::..:..:::....1:........::~__~

5040302010

-100 L-__----' -L --'- .'-__--l

o

-40

m~

~0

5'*"':; 1:' +0 ~ v +

-80 000 + +

v 0" vv 0

'""00

0

"-1000 10 20 30 40 50

rms delay spread (ns)+B8.,,:25.1 dBI '" Ba5e:16.2 dBI 0 B8.e:9.1 dBI

Rem: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI

rms delay spread (ns)o B8.,,:17.4 dB; + B85e:14.1 dBI V B..e:12.5 dBI

Rem: 17.4 dB; Rem: 14.1 dB; Rem: 12.5 dBI

Figure F5 Figure F6

-Fl-

Appendix F (continued): Simulation results presented in scatterplots

Room A, horn-horn, LOS, ljf=lO"

vv•

504030

•2010

Room A. horn-horn. LOS. 1Jf=lO'-20 -20

-40 ... -40

m m~ ~

-60 -60...t3

'" ~

-80b. -80

b.

0

-100 -1000 10 20 30 40 50 0

rms del<JY spre<Jd (ns)+ 8as.:25.1 dBI {;. B85e:16.2 dBI 0 8a5e:9.1 dBI

Rem: 25.1 dBI Rem: 16.2 dB I Rem: 9.1 dBI

rm. delay .preod (ns)

o B8.e:17.4 dBI + Base:14.1 dBI V Base:12.5 dBIRem: 17.4 dB' Rem: 14.1 dB; Rem: 12.5 dBI

Figure F7 Figure F8

Room A. horn-horn. LOS. 'V-IS·-20,--------------'-----------,

Room A, horn-horn, LOS 'V= 15·-20,---------------'-----------,

-40

'" ... 0

o

+

-40

+v v

v

40 50

V Base: 12.5 dBIRem: 12.5 dB;

-100 L-__----'- -'- -'-__----''--__--'

o 10 20 30

rms delay .pread (n.)

o Bau:17.4 dBI + Base:14.1 dBIRem: 17.4 dBI Rem: 14.1 dBI

40 50

o Bo.e:9.1 dBIRem: 9. 1 d8 I

302010

rm. delay .pre<Jd (n.)+ Bo.e:25.1 dBI {;. B05.:16.2 dBI

Rem: 2 S. 1 dB I Rem: 16.2 dB I

-100 L- L-__--''--__--' ----L --'

o

Figure F9 Figure FlO

-30 .- R_o_o_m_A_,_h_o_rn_-_h_o_rn_,_O_B_S_._1Jf-'-=_S -, Room A. horn-horn, OB5, 1V =lS·-30,-----------------'-------,

-50 -50

100

rms delay spre<Jd (ns)o S05e:9.1 dBI + Bo.e:25.1 dBI

Rem: 9.1 dBI Rem: 25.1 dBI

rms delay spre<Jd (ns)o Base:9.1 dBI + Base:25.1 dBI

Rem: 9.1 dB I Rem: 25.1 dBI

Figure Fll Figure Fl2

-F2-

Appendix F (continued): Simulation results presented in scatterplots

Room AI omni-horn, lOS, 1V =0"-20...----------------------,

Room A, omni-horn. LOS, 'II' -0'-20,-------------------,

-40 -40

-60

-80

40 50

V Bat.:9.0 dBIRem: 12.5 dBI

20 30

rms delay spread (ns)+ Base: 9.0 dBI

Rem: 14.1 dBIo B... : 9.0 dBI

Rem: 17.4 dBI

-100 '-__--'- --'- .L-__--' ~

o 1040 50

o Base:9.0 dB;Rem: 9.1 dBI

20 30rms delay spread (ns)

l>. B.se: 9.0 dB;Rem: 16.2 dB;

Bas.: 9.0 dBIRem: 25.1 dBI

-100 '- L-. L-.__----' ----'- -'

o 10

Figure FI3 Figure FI4

Room A, omni-horn, OB5, lI'-O' Room A, amni-horn. OB5, "'=0'

-50

Iii'~

-70++ t:)

t~+A A A++

AA~ + AA ~ A +

A ..+++ ~-90

+ A 4-++ +

+

-30 r-------------------,

-110 '------"'-----'-----'----'--------'o ro w ~ ~ ~

lb iiio 0

D

5040302010

-30

-50

Iii'~

-70

l.:l

-90

-1100

rms delay spread (ns)+ Base: 9.0 dB; l>. Base: 9.0 dB;

Rem: 25.1 dBI Rem: 16.2 dBI

rms deloy spread (ns)o Base: 9.0 dBI 0 Base: 9.0 dBI

Rem: 17.4 dBI Rem: 9.1 dBI

Figure FI5 Figure FI6

-F3-

Appendix F (continued): Simulation results presented in scatterplots

Room At omni-horn. LOS. '=5'-20,-------------------,

Room A, omni -horn, lOS, ljf =5'-20,--------------------,

-40 -40

-60

-80

5040302010

-100 L- '-- '-- -'- -'-__---'

o5040302010

-100 L-__~'________' ____' ____L ...J

o

rms delay spread (ns)+ Bose: 9.0 dBI (; Bose: 9.0 dBI [J Bos.:9.0 d81

Rem: 25.1 dBI Rem: 16.2 d81 Rem: 9.1 d81

rms delay spread (ns)o Bose: 9.0 dBI + Base: 9.0 dBI V Base:9.0 dBI

R.... : 17.4 dBI Rem: 14.' dBI Rem: '2.5 dBI

Figure F17 Figure F18

Room A, amnl-horn, lOS, ljf-l0' Room A. omni-horn, LOS, 1jI' =10'-20,--------------------, -20,----------------------,

-40 -40

-60 -60

-80~~,~~.& ~+o 0 ~

~·~o t;"'~. .P v + +~ ~vo Ov csT 0 '"" ..

0 0 vO 0"'''0 v +061+

5040

V Bo,e:9.0 dBIRom: 12.5 dBI

3020

rms delay .pread (ns)+ B.se: 9.0 dBI

Rem: 14.1 dBI

Figure F20

10

o Bose: 9.0 dBIRem: 17.4 dBI

-100 L- '-- '__ '-- '--__--'

a20 30 40 50

rm. delay spread (ns)

(; Bose: 9.0 dBI 0 Base: 9.0 dBIRem: 16.2 dBI Rem: 9. , dBI

Figure F19

10

Base: 9.0 dBIRo.. : 25.' dBI

+

-100 '------'-------'------'------'------'o

50403020

rms delay spread (ns)+ Bose: 9.0 dBI V Bo.o:9.0 dBI

Rem: '4.1 dBI Rem: '2.5 dBI

10

o Bose: 9.0 dBIRem: 17.4 dBI

-100 l-__--'- -'--__---L -'--__---I

a

-20,---------------------,Room A. omni-horn, LOS, '1'=15'

-40

iii'3

-60

l:J

-80

50

Room A, amni-horn, LOS, 'V e 15'

.t-.h..~6 .. ltlo»~~~_(; /',

-80 ... t~~~~'JI"~~~"~~:~+ + + [J C +

,+ + + ++-100 '----~'_____--''''____........___'_----L ...J

o 10 20 30 40rms delay opreod (ns)

+ Bo... : 9.0 dBI '" 805e: 9.0 dBI 0 805e:9.0 dBIRem: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI

-20

-40

m~

-60

Figure F21 Figure F22

-F4-

Appendix F (continued): Simulation results presented in scatterplots

Room A. omni-omni. Oir=12.7 dBi Room A. omni-omni. Oir=9.0 dBi-20 -20

-40 -40

m m3. 3.

-SO -SO

l:l l:l

-80.~~~.AIi~+.t+

-80" +A·\~~6I-~ +

-100 -10010 20 30 40 50 SO 10 20 30 40 50 SO

rms deloy spreod (ns) rms delay spread (ns)

+ LOS '" OBS + LOS '" OBS

Figure F23 Figure F24

Room A. omni-omni. Oir=S.9 dBi Room A. omni-omn'. Oir=5.3 dBi-20 -20

-40 -40

m m3. 3.

-SO -SO

l:l l:l

-80 + ++ ~+1~...." + + -80 +........~ +..,... b.".6A,,-t. ......ot!' ....

-100 -10010 20 30 40 50 SO 10 20 30 40 50 SO

rms delay spread (ns) rms deloy spread (ns)

+ LOS '" OBS + LOS '" OBS

Figure F25 Figure F26

Room A. omni-omni. Oir=4.5 dBi Room A. omni-omni. Oir=O dBi (isotropic)-20 -20

-40 -40

m ~

m3. 3.

-SO -SO

l:l (,:J

-80 l-~"'+ + ....+ + -80.t~"",+"0."'-"0. £ " ~b.~,,6 .w " 'h'k

-100 -10010 20 30 40 50 SO 10 20 30 40 50 SO

rms delay spread (ns) rms deloy spread (ns)

+ LOS '" OBS + LOS '" DBS

Figure F27 Figure F28

-F5-

Appendix F (continued): Simulation results presented in scatterplots

Room B, horn-horn, LOS, 1jf=0' Room B. horn-horn, OBS, 'I' -0'-20 -20

".. +

-40 !j:t- + ++ -40

<Ii' I; " ... <Ii'~ "" ~~ll ~ +......

-60~s., D§&D

-60 + + +

t:l ° t:l + " + 0 ° ~ef ... +...... " +'"+ +"6 ° 0 ~D+ "'" "'''''t + "-BO -BO '" 1)0' ° ° 1:f.+~" ... °"'t-t to

-100 -1000 20 40 60 BO 100 0 20 40 60 80 100

rm. delay spread (n.) rms delay spread (ns)

+ Bo.e:25.1 dBI'"

ao.e:16.2 dBI o Bo.e:9.1 dB I + B.se:25.1 dBI l> aose: 16.2 dBI 0 Bo.e: 9.1 dBIRem: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI Rem: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI

Figure F29 Figure F30

Room B, horn-horn, LOS, 1jf=S' Room B. horn-horn, LOS, IV = 10'-20 -20

+-40 -40

m <Ii' Iii+ ++*:~ + ~

+ ++

-60 -60.~t¥i#" ..t:l " " a ... "6 JJ,.~ li..fl (,:> a " "0 + !:p@ IJI 0+ toa

-80 -80 a", a

"-100 -100

0 20 40 60 80 100 0 20 40 60 BO 100

rm. delay spread (ns) rms delay spread (ns)+ B..e:25.1 dBI

'"Bo•• :16.2 dBI o Base 9.1 dBI + Bo.e:25.1 dBI l> Bo.e:16.2 dBI OBo.e:9.1 dBI

Rem: 25.1 dBI Rem; 16.2 dB I Rem: 9.1 dBI Rem: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI

Figure F31 Figure F32

Room B, horn-horn, LOS, 1jf =15' Roam B. horn-horn, OBS, Oir=25.1 dBi

-20-20

-40 -40

<Ii' <Ii'~

~ CO

-60 tn" + -60 V ,~J V V:tl-+: +"-h Go. V vQ." 0 voo

t:l ... " ~ ~ ~. 0 .~•••~VO$. 0 ~'1iat!'t a"a " " +0 VJ ~ V •• ~~~<t1; ~v~;JSi~.~-80 ° -80

+ vI • • ~ ~ v. +to.. .+ ~ • • *

-100 -100

0 20 40 60 BO 100 0 20 40 60 BO 100

rms delay spread (ns) rms delay spread (n.)

+ Bo.. :25.1 dBI l> Bas.:16.2 dBI D B••e:9.1 dBI 0 ..,=5" V 1p'=10' • ",=15 •Rem: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI

Figure F33 Figure F34

-F6-

Appendix F (continued): Simulation results presented in scatterplots

Room B, omni-horn, lOS. 1jT =0' Room B. omni-horn. OBS. 1jT=0'-20 -20

-40 -40

'Iii' 'Iii'~ ~

-60 "" ~.... ....+ +.fI++-60

l:l +A AA"A AAII>A-. "& A A l:l ++

++A~~"l.~o 0 o~ Clo + +~... iA o?-80 -80+ + +

+ +

-100 -1000 20 40 60 80 100 0 20 40 60 80 100

rms delay spread (ns)... Base: 9.0 dBI 6. Base: 9.0 dBI 0 Base:9,D dBI

Rom: 25.1 dBI Rem: 16.2 dBI Rem: 9.1 dBI

Figure F35

Room B. omni-omni. Oir= 12.7 dBi-20 r----------------------,

rml delay spread (nl)+ Bose: 9.0 dBI 6. Base: 9,0 dBI 0 Base:9.0 dBI

Rem: 25. 1 dB I Rem: 16. 2 dB I Rem: 9. 1 dB I

Figure F36

Room B. omni-omni. Oir=9.0 dBi-20 r----------------------,

-40 -40

'Iii' ~m~ ~

-60 -60

l:l 4-~+ l:l

-80 -80

-100 -10010 20 30 40 50 60 10 20 30 40 50 60

rms delay spread (ns)

+ lOS 6. OBS

Figure F37

Room B. omni-omni. Oir=6.9 dBi-20 r----------------------,

rmo delay spread (ns)

... LOS l!. OBS

Figure F38

Room B. omni-omni. Oir=4.5 dBi-20 r------------------------.

-40

'Iii'~

-60

l:l

-80

-10010 20 30 40 50

-40

'Iii'~

-60

l:l

-80

-10060 10 20 30 40 50 60

rmo delay spread (ns)

+ lOS 6. aBS

Figure F39

-F7-

rmo deloy spread (no)

... LOS l!. OBS

Figure F40

Appendix F (continued): Simulation results presented in scatterplots

Room B, omni-omni, Dir=O dBi (isotropic)-20

-40

'iii'~

-60(:J

-80

-10010 20 30 40 50 60

rms deloy spreod (ns)

+ LOS t. OBS

Figure F41

-F8-