Time-Varying Infostation Channel Characterization

Uche A.K. Chude-Okonkwo, Razali Ngah, Tharek Abd Rahman and Chollette Chude, Teguh Prokoso Wireless Communication Center Universiti Teknologi Malaysia

Skudai, Malaysia uche@utm.my

Abstract—Time-scale domain geometrical-based method for the characterization of the time varying infostation ultrawideband (UWB) channel is presented. This model arises primarily from the integration of geometrical, electromagnetic and statistical assumptions from a physical propagation point of view to account for frequency dependent path-loss, frequency/time dispersion in the UWB channel. Results show that the frequency dispersion of the channel depends on the frequency and not on the choice of bandwidth. And time dispersion depends on bandwidth and not on the frequency.

Keywords- Ultrawideband; geometrical model; time-varying; coherence time; delay spread

I. INTRODUCTION The concept of infostation first introduced in [1] provides a

new way to look at the problem of providing high data rate wireless access. It is an isolated pocket area with small coverage of high bandwidth connectivity that collects information requests from mobile users and delivers data while users are going through the coverage area. Infostations can be located in heavily populated areas such as the airport, shops, pubs, hotels, and along the highway.

Consider a scenario in which a user inside a vehicle moving along the highway desire to receive/transmit large chunk of data from/to an infostation network located along the highway [2] as shown in Fig. 1. This will require technologies that will be able to handle high data rate information transfer. The small coverage area of the infostation technology implies low transmitting power. The low power transmission requirement is

Figure 1. Illustration of infostation wave propagation channel

necessary in order to avoid interference with other existing systems. One of the transmission technologies that have the

potential to deliver the envisaged high-data rate infostation services is the ultrawideband (UWB) signalling [3]. The UWB has the basic attributes of extremely low transmission power (less than 1 mW), operating at unlicensed frequency, high data rate (up to 200 Mbits/s within 10 m) [4], multipath immunity and low cost.

Existing channel characterization of the UWB channel has been limited to the case where the channel is assumed to be fixed over the transmission duration [3]. However, for some infostation channels like highway, time variation is expected due to the mobility of one of the communication terminals/scatterers. From a propagation perspective, the use of UWB in infostation communication presents several challenges since many of the assumptions made for narrow- and wideband signals become invalid in the UWB case. One of such invalid assumption is the assumption of uniform Doppler shift across all composite frequencies in a signal. Hence, the existing channel models cannot be used to describe this new target scenario.

In this paper, the modified geometric based single bounce elliptical model (GBSBEM) appropriate for the time-varying UWB channel is presented. This model employed the time-scale domain channel representation [5] which offers compact eigenfunctions similar to the conventional UWB signaling waveform. The frequency dependency of the propagation phenomena is taken into account by means of the frequency dependent path-loss. The time and frequency variations of the channel are quantified using the coherence time and root-mean-square (rms) delay spread, respectively. These parameters are obtained from the delay-scale spectrum functions for different frequencies and bandwidths.

The rest of the paper is organized as follows. In Section II the time-scale characterization of wideband channel is presented. The GBSBEM model that emphasizes on frequency characteristic of UWB channel is presented in Section III. Section IV provides simulation results and discussions.

II. TIME-SCALE CHANNEL REPRESENTATION The linear continuous time-scale representation of the time-

varying (LTV) wideband channel Η, can be given by [5]:

( ) dssdstxtasty 2/)()(),()( −∫ ∫ −= τττΗW (1)

2011 IEEE International RF and Microwave Conference (RFM 2011), 12th - 14th December 2011, Seremban, Malaysia

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where )(tx and )(ty are the transmitted and received signals, respectively, and the term )(ta is the attenuation.

The terms ( )∫ −= dtstxtatys /)()()(),( ττΗW denote

the delay-scale (wideband) spreading function [5, 6] which can be interpreted as the reflectivity of the scatterers associated to propagation delay τ and scale shift (or time scaling) s .The relationship between scale shift and Doppler shift is given by:

( ) Ppvcvcffs pp ....,3,2,1,)/()( =±= (2)

where c and v are the speeds of the electromagnetic wave and the mobile antenna unit, respectively, and pf is the frequency vector comprising stepwise of all the frequency components of the transmit signal )(tx . pf can be assumed to be the carrier frequency cf in narrowband applications. However, for UWB applications, the substitution of

pc ff ≅ into (2) does not suffice.

The delay-scale spectrum (D-SS) which indicates the relative contribution of the energy of the received signal at a specific delay and scale is given by: .|),(|),( 2ss ττ WH = The surface of ),( sτH emphasizes the delay and scale of dominant energetic features within the received signal and encompassed within the region ][][ maxminmaxmin ss×ττ . The power delay profile (PDP) and the scale spectrum are given by

0),()(=

= ssττ HH and 0),()(=

= ττ ss HH , respectively. The root mean squared (rms) delay spread rmsτ represents the standard deviation of the PDP and is given by:

( )( ) 2/112 )()()(

−=

−

∫∫ τττττττ ddmrms HH (3)

where ( )( ) 1)()(

−

∫∫= ττττττ ddm HH is the mean delay.

The rmsτ and coherence time α5/2=cT where 1α max pfs−= , are the values that indicate channel

dispersion in time and frequency, respectively. Thus, these parameters are very important in infostation system design. An important point to note is that the realization of

),( sτΗW is independent of the carrier frequency or any reference frequency but depends basically on the velocity of the mobile terminal. Thus, different values of cT can be obtained from a single realization for different values of frequencies. To compute the D-SS and subsequently delay/scale profiles, the knowledge of the attenuation, delay and scale characteristics of the respective multipaths. We can obtain these characteristics using the geometric elliptical channel model modified to include frequency characteristics.

III. GEOMETRIC-BASED UWB CHANNEL MODEL The geometric based elliptical model presented here

considers the geometric description of the spatial relationship among the infostation access point (IAP), scatterers and the mobile user equipment (MUE) within defined elliptical loops as shown in Fig. 2. It is assumed that wave propagation takes in the horizontal plane containing the tips of the transmitting and receiving antennas. The separation distance between the antennas is D.

Figure 2. Elliptical model for the UWB Infostation channel

Each scatterer is defined as a vector ns in a hypothetical space-complex dielectric coordinate ),,,( keyx i , where ie is the specific elliptical area within which the scatterers at global coordinate ),( yxsn with complex dielectric characteristics k lie. Let the xy coordinate system be such that the IAP is at the origin and the MUE lies on the −x axis. We assume that the communicating antennas are omnidirectional and of equal low heights.

We also make the following additional assumptions to those in [7]: the scatterers may not have identical scattering coefficients; the scatterers distributions (around the IAP and MUE) are assumed to follow known statistical distributions that are defined based on physical insight and mathematical tractability; signals received at the base station are plane waves propagating only along the azimuthal coordinate; and each scatters is an omni-directional re-radiating element whereby the plane wave, on arrival, is reflected directly to the receiving antenna without the influence of other scatterers.

For N number of scatterers at coordinates Nnyx ..,2,1),( = , and system bandwidth BW, the metric separation ∆τ between two bi-centric ellipses ie and je , 1..,2,1,0, −=∈ Llji is given by: τξτ ∆=∆ c ,where )2/(1 BW=∆τξ is the time delay resolution. The term 0≠ξ is the scaling factor which depends on the time scaling/ Doppler shift value of the MPCs associated with a particular delay. For most terrestrial communication channels, 1≈ξ . All MPCs received from scatterers within the

same elliptical separation )( ie∆τ have the same delay. However

their path gain may vary due to the intrinsic electromagnetic properties of the associated scatterers which define the scattering coefficients.

2011 IEEE International RF and Microwave Conference (RFM 2011), 12th - 14th December 2011, Seremban, Malaysia

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The ellipse has major axis half-length τ∆= lcal .5.0 and

minor axis half-length .).(5.0 22

−∆= Dlcbl τ The

maximum delay ττ ∆−= )1(max L occurs at the boundary of the biggest ellipse of consideration 1−Le for which maxaal = and maxbbl = . Thus all multipath components that arrive after

maxτ are considered insignificant.

For the scatterer density enn Ayx /1),( =Ψ , where eA is the area of the ellipse. The path length R from )0,0(MUE to

)0,(DIAP through ),,( kyxs nnn is given by: nne

n gfR +=)(

where 22nnn yxf += and .)( 22

nnn xDyg −+=

If we consider the case where the scatterers are distributed uniformly, then probability density function (p.d.f) of the time-of-arrival (TOA) and the angle-of-arrival (AOA) as seen from IAP given ),( nn yxΨ are given by [8]:

( )12221maxmax )cos)(()8()( −− −−=Ψ cDcDba ddD

τθτπθθ

and 222

222

maxmax

2.4

)(Dc

Dcba

c

−

−=Ψ

τ

τττ , respectively.

In narrowband and wideband geometrical channel models, the frequency characteristics of the scatterers are often neglected. However, in UWB, in order to obtain a more accurate channel description, the frequency characteristics of the scatterers should be taken into consideration.

Let us assume that a scatterer is impinged upon by a compactly supported signal like a Mexican hat wavelet:

2)1()( 2 t

oI etEtE −−= (4)

where IE has a unit power oP and ℜ∈t .

As shown in Fig. 3, the transmitted signal )()( tEtx I≡

Figure 3. Path-loss model for the UWB inforstation channel

with power TP experiences free-space path loss as it travels from the transmitter Tx to the scatterer position marked s(r,k).

At the scatterer surface, we assume that only the electromagnetic wave reflection and transmission phenomena are involved. Hence, part of the signal incident upon the scatterer surface is reflected towards the receiver Rx and part is transmitted through the scatterer. The transmission coefficient accounts for power loss if we assume single bounce. Then the reflected signal )()( tEtx R≡ experiences free-space path loss as it travels from the scatterer surface to the Rx. If we assume that the scatterer acts like a antenna (re-radiator), the power received at Rx is given by:

)5(4

.

),(4

),(

2

2

2

1

xp

RXTS

p

xp

RSTXTpR

dfcGG

fkdf

cGGPfdP

Λ

=

π

π

where d is the path distance from Tx to Rx , 1d path distance from Tx to scatterer surface, 2d path distance from scatterer surface to Rx , TXG transmitting antenna gain, RXG receiving antenna gain, TSG gain of the scatterer surface when assumed to act like a transmitting antenna, RSG gain of the scatterer surface when assumed to act like a receiving antenna, ),( fkΛ reflected power coefficient at the scatterer surface.

We do not consider path-loss due to shadowing since the locations of the infostation and the mobile transceiver are close to each other. Hence, for each elliptical area the power

leRP , associated with the propagation delay is given by the summation of the respective powers of each associated MPC:

( )∑−

=

=1

0,,,

U

uueReR ll

PP , 1,...2,1,0 −= Uu (6)

where NU ≤ is the number of scatterers inside a give elliptical area.

IV. SIMULATION RESULTS AND DISCUSSION Let us consider the transmission of the function given in

(4). We assume that the power TP and duration pulseT of this pulse is about 100 mW and 10 ns, respectively. The following parameters are defined for this simulation; 5000=N ,

ma 33max = mb 12max = , smv /10ˆ = , 30)( =Treerε , 1000)( =postlamprε , mTree Ω=100)(σ and

mpostlamp Ω×= 2107.3)(σ . All antenna gains in (5) are assumed to be unity. Delay and AOA obtained using expressions for )( dD

θθΨ and )(ττΨ are matched to the particular elliptical area for some bandwidth specification. For mobile velocity of v the scale is then computed using (2) where

)cos(ˆ AOAvv = .The cT and rmsτ are obtained from the D-SS which is computed using (1).

2011 IEEE International RF and Microwave Conference (RFM 2011), 12th - 14th December 2011, Seremban, Malaysia

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(a)

(b)

Figure 4. D-SS at (a) 3.6 GHz and (b) 5.5 GHz

The D-SS for 500 MHz bandwidth at the frequency range of 3.1-3.6 GHz and 5-5.5 GHz are shown in Fig. 4(a) and Fig. 4(b), respectively. The scale axis is )1ln()ln( pulseTms += , and the delay axis is obtained from a dimensionless value γ

where 1max)γ(τ −−= fz , z is half of the length of the signal

vector. It can be seen from Fig.4 that the dominant MPC is the LOS component. The magnitude of D-SS varies with frequency a phenomenon that is closely associated with the dependency of scattering coefficients on frequency. Thus, as frequency increases more energy is lost. In Fig. 5 and 6, the plots of different frequencies in the bands 3.1-3.6 GHz and 5-5.5 GHz for 500 MHz and 1 GHz bandwidth against cT and

rmsτ , respectively, are shown.

3.1 3.2 3.3 3.4 3.5 3.68.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

Frequency (GHz)

T c (ms)

Bandwidth=500 MHzBandwidth=1 GHz

Figure 5. Coherence time at different frequencies and bandwidths

3.1 3.2 3.3 3.4 3.5 3.615.5

16

16.5

17

17.5

Frequency (GHz)

τ rms (n

s)

Bandwidth=500 MHzBandwidth=1 GHz

Figure 6. Rms delay spread at different frequencies and bandwidths

Fig. 5 shows that within a given bandwidth , cT varies with frequency, but is independent of the change in bandwidth. This can be explained by the fact that cT depends on frequency and not bandwidth. However, rmsτ does not vary significantly with frequency, but with bandwidth as can be seen in Fig.6. This is so since the number of delay bin is proportional to the bandwidth of consideration.

V. CONCLUSION A 2D GBSBEM model for the characterization of time-

varying UWB in the time-scale domain was presented. Results show that the frequency dispersion of the channel depends on the frequency components in a given bandwidth, but does not depends on the choice of bandwidth. And time dispersion depends on bandwidth and not on the frequency. Future work will consider 3D model.

ACKNOWLEDGMENT The authors thank the Ministry of Higher Education

(MOHE), Malaysia for providing financial support for this study through the Grants (4D040 and Q.J130000.7123.02H31) managed by the Research Management Center (RMC), Universiti Teknologi Malaysia (UTM).

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[2] G. Rajappan, J. Achharya, H. Liu, N. Mandayam, I. Seskar, R.Yates, “Mobile infostation network technology,” Proc. SPIE on Wireless Sensing and Processing, Orlando, USA, 2006.

[3] H. Chowdhury, J.P. Mekela, and K. Pahlavan, “Statistical information transfer in random crossing of infostation coverage,” Proc. 2005 Finnish Signal Processinf Symposium, August 2005, Kuopio, Finland.

[4] P. Pagani et.al, Ultra-wideband radio propagation channels, Wiley: USA, 2008, pp.21–42.

[5] U. A. K. Okonkwo, R. Ngah, T.A. Rahman,”Wavelet-domain characterization for mobile broadband communication systems,” in: Proc. IEEE Intern. Conf. RFM 2008, 2-3 December 2008, 283-288.

[6] G. Matz, F. Hlawatsh, “Time-varying communication channels: fundamentals, resent developments, and open problems,” Invited paper in: Proc. of 14th EUSIPCO-06, Sept., 2006.

[7] J. C. Liberti, and T. S. Rappaport, “A geometrically based model for line of sight multipath radio channels," IEEE Vehicular Technology Conf., pp. 844-848, Apr. 1996.

[8] R. B. Ertel, and J. H. Reed, “Angle and time of arrival statistics for circular and elliptical scattering models,” IEEE J. Select. Area Commun. vol 17, no. 1. pp. 1829-1840, 1999.

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