Final Report4.pdf

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ERROR REDUCTION CODING TECHNIQUESUSED IN WIRELESS COMMUNICATION

A Project Report Submitted

in Partial Fulfillment of the Requirements

for the Degree of

BACHELOR OF TECHNOLOGY

in

ELECTRONICS AND COMMUNICATION

By

Siddharth Sahu( 0914331049) Aman Wadhwa( 0914331005)

Siddharth Verma( 0914331050) Tushar Garg( 0914331053)

Under the Supervision of

Asst prof. Sandeep kumar Singh

IMS ENGINEERING COLLEGE

to the

Faculty of Electronics And Communication

GAUTAM BUDDH TECHNICAL UNIVERSITY

(Formerly Uttar Pradesh Technical University)

LUCKNOW

May, 2013


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CERTIFICATE

Certified that Siddharth Sahu, Siddharth Verma, Tushar Garg,

Aman Wadhwa (enrollment no 0914331049, 0914331050,0914331053, 0914331005) has carried out the research work presented in this thesis entitled Error Reduction Coding SchemeUsed In for the award of Bachelor of Technology from GautamBuddh Technical University, Lucknow under my supervision. Thethesis embodies results of original work, and studies are carried out

by the student himself and the contents of the thesis do not form the basis for the award of any other degree to the candidate or to

anybody else from this or any other Institution.

Signature

Signature

(Name of Supervisor)

(Name of Supervisor)

(Designation) (Designation) (Address) (Address) Date: ___


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TABLE OF CONTENTS

Certificate

Abstract

Acknowledgement

List Of Tables

List Of Figures


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CHAPTER 1

INTRODUCTION

In the last decade, there has been a dramatic increase in the demand for higher data rates in cellular networks, wireless local area networks and high-definition audio andvideo broadcasting services. Providing wireless access to the Internet and multimediaservices requires an increase in data rates. One of the most significant and promisingadvances in wireless communications that can meet the demand for higher data rates is theuse of multiple antennas at the transmitter and receiver. Deploying multiple antennas at thetransmitter and receiver creates a multiple-input multiple-output (MIMO) channel that notonly offers higher transmission rates, but it can also improve the system's reliability androbustness to noise compared to single antenna systems.

Signal transmission over the wireless channel suffers not only from additive noise, butalso from multipath fading. Specifically, a transmitted radio signal propagates throughmultiple paths, due to scattering and reflections from different objects in the environment,

before it reaches the receiver antenna. At the receiver due to multipath fading, the receivedsignal can be significantly attenuated and the receiver cannot correctly detect thetransmitted signal.

In order to guarantee a certain quality of service, not only high bit rates are required, butalso a good error performance. However, the disruptive characteristics of wirelesschannels, mainly caused by multipath signal propagation (due to reflections anddiffraction) and fading effects, make it challenging to accomplish both of these goals at thesame time.

One way to overcome the problem of multipath fading is diversity. The basic concept of diversity is to transmit the same information symbols over multiple channels that are

fading independently. This way, if one of the channels is in a deep fade, the receiver can


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still recover the transmitted signal if one of the other channels is in a good enough state toallow for reliable detection.

There are three types of MIMO systems. They are-1. Spatial Multiplexing2. Spatial Diversity3. Beamforming

Fig 1.Types of MIMO Systems


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1.1 Spatial Multiplexing

Spatial multiplexing techniques simultaneously transmit independent informationsequences, often called layers, over multiple antennas Using M transmit antennas, theoverall bit rate compared to a single-antenna system is thus enhanced by a factor of Mwithout requiring extra bandwidth or extra transmission power. Channel coding is oftenemployed, in order to guarantee a certain error performance. Since the individual layers are

superimposed during transmission, they have to be separated at the receiver using aninterference cancellation type of algorithm (typically in conjunction with multiple receiveantennas). A well-known spatial multiplexing scheme is the Bell-Labs Layered Space-Time Architecture (BLAST). The achieved gain in terms of bit rate (with respect to asingle-antenna system) is called multiplexing gain in the literature.

Fig 2. Basic Principle of Spatial Multiplexing

1.2 Spatial Diversity

In contrast to spatial multiplexing techniques, where the main objective is to provide

higher bit rates compared to a single-antenna system, spatial diversity techniques predominantly aim at an improved error performance. This is accomplished on the basis of


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a diversity gain and a coding gain. Indirectly, spatial diversity techniques can also be usedto enhance bit rates, when employed in conjunction with an adaptive modulation/channelcoding scheme.

There are two types of spatial diversity, referred to as macroscopic and microscopicdiversity. Macroscopic (large scale) diversity is associated with shadowing effects inwireless communication scenarios, due to major obstacles between transmitter and receiver (such as walls or large buildings).

Macroscopic diversity can be gained if there are multiple transmit or receive antennas, thatare spatially separated on a large scale. In this case, the probability that all links aresimultaneously obstructed is smaller than that for a single link.

Microscopic (small-scale) diversity is available in rich scattering environments withmultipath fading. Microscopic diversity can be gained by employing multiple co-locatedantennas. Typically, antenna spacing of less than a wavelength are sufficient, in order toobtain links that fade more or less independently. Similar to macroscopic diversity, thediversity gains are due to the fact that the probability of all links being simultaneously in adeep fade decreases with the number of antennas used.

The idea to utilize macroscopic diversity in wireless communication systems is not new. Itdates back to the 1970s. Even more so, the use of multiple receive antennas for gaining

microscopic diversity (diversity reception) has been well established since the 1950s.However, it took until the 1990s before transmit diversity techniques weredeveloped.

Fig.3 Basic Principle of Space-time Coding


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1.3 Beamforming

Beamforming can be interpreted as linear filtering in the spatial domain. Consider anantenna array with N antenna elements, which receives a signal from a certain direction.Due to the geometry of the antenna array, the impinging radiofrequency (RF) signalreaches the individual antenna elements at different time instants, which causes phaseshifts between the different received signals. However, if the underlying complex basebandsignal is assumed to be a narrowband signal, it will not change during these small timedifferences. As a result, the overall antenna pattern of the phased array will exhibit amaximum in the direction of the impinging signal. This principle is called conventional

beamforming in the literature.

If only the phases of the received signals are manipulated, the shape of the overall antenna pattern remains unchanged, and solely an angular shift results. Correspondingly,conventional beamforming is equivalent to a mechanical rotation of the antenna array(mechanical beam steering). In particular, an antenna array with N antenna elements

provides ( N 1) degrees of freedom, i.e., altogether ( N 1) angles can be specified for which the overall antenna pattern is supposed to exhibit either a maximum or a minimum(a null).

If the above narrowband assumption for the complex baseband signal is not met, the baseband signal can change during time intervals that are as small as the relative delays between the received RF signals. Thus, the individual antenna elements will observedifferent versions of the complex baseband signal. In this case, broadband beamformingtechniques are required that combine narrowband beamforming (i.e., spatial filtering) withtime-domain filtering, e.g., in the form of a two-dimensional linear finite-impulse-response(FIR) filter.

Fig.3 Basic Principle of Beamforming


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CHAPTER 2

SPATIAL DIVERSITY TECHNIQUES

In contrast to spatial multiplexing techniques, where the main objective is to provide higher bit rates compared to a single-antenna system, spatial diversity techniques predominantly aim at an improved error performance. This is accomplished on the basis of a diversity gain and a codinggain. Indirectly, spatial diversity techniques can also be usedto enhance bit rates, when employed in conjunction with anadaptive modulation/channelcoding scheme.

There are two types of spatial diversity:

1. Macroscopic Diversity2. Microscopic Diversity.

1.1 Macroscopic diversity

It is associated with shadowing effects in wirelesscommunication scenarios, due to major obstacles betweentransmitter and receiver (such as walls or large buildings).Macroscopicdiversity can be gained if there are multipletransmit or receive antennas, that are spatiallyseparated ona large scale. In this case, the probability that all links aresimultaneouslyobstructed is smaller than that for a single link.


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1.2 Microscopic diversity

It is available in richscatteringenvironments with multipath fading. Microscopicdiversitycan be gained by employing multiple co-locatedantennas. Typically, antenna spacings of less than a wavelengthare sufficient, in order to obtain links that fade more or lessindependently. Similar to macroscopic diversity, the diversitygains are due to the factthat the probability of all links beingsimultaneously in a deep fade decreases with thenumber ofantennas used.

The idea to utilize macroscopic diversity in wireless communication systems is not new. Itdates back to the 1970s Even more so, the use of multiple receive antennas forgainingmicroscopic diversity (diversity reception) has beenwell establishe d since the 1950s.

On the Basis of transmission spatial diversity is divided into1. Recieve Diversity2. Transmit Diversity

1.3 Receive diversity

This Technique uses a single transmit antenna and multiple receive antennas. They perform a (linear) combining of the individual received signals, in order to provide amicroscopic diversity gain. In the case of frequency-flat fading, the optimum combiningstrategy in terms of maximizing the SNR at the combiner output is maximum ratiocombining (MRC), which requires perfect channel knowledge at the receiver. Severalsuboptimal combining strategies have been proposed in the literature, such as equal gaincombining (EGC), where the received signals are (co-phased and) added up, or selectiondiversity (SD), where the received signal with the maximum instantaneous SNR is selected

(antenna selection), whereas all other received signals are discarded. All three combiningtechniques achieve full diversity with regard to the number of receive antennas.


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Fig. Receive Diversity

1.4 Transmit Diversity

The main idea of transmit diversity is to provide a diversity and/or coding gain by sendingredundant signals over multiple transmit antennas (in contrast to spatial multiplexing,where independent bit sequences are transmitted). To allow for coherent detection at thereceiver, an adequate pre processing of the signals is performed prior to transmission,typically without channel knowledge at the transmitter. With transmit diversity, multipleantennas are only required at the transmitter side, whereas multiple receive antennas areoptional. However, they can be utilized to further improve performance. In cellular networks, for example, the predominant fraction of the overall data traffic typically occursin the downlink. In order to enhance the crucial downlink it is therefore very attractive toemploy transmit diversity techniques, because then multiple antennas are required only atthe base station. With regard to cost, size, and weight of mobile terminals this is a major advantage over diversity reception techniques.

Fig. Transmit Diversity


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An early beginning of transmit diversity schemes was made with two papersthat independently proposed a simple technique called delay diversity .The value of transmit diversity was only recognized in 1998, when Alamouti proposed a simpletechnique for two transmit antennas . In the same year, Tarokh, Seshadri, and Calderbank

presented their space-time trellis codes (STTCs)which are two-dimensional codingschemes for systems with multiple transmit antennas. While delay diversity andAlamoutis transmit diversity scheme provide solely a diversitygain (more precisely, fulldiversity with regard to the number of transmit and receive antennas), STTCs yield both adiversity gain and an additional coding gain.

1.5 Space-Time Codes

we will use the generic term space-time coding scheme for all transmitter-sided spatialdiversity techniques, irrespective of the presence of an additional coding gain. The basicstructure of a space-time coding scheme is illustrated in Fig. The pre processing of theredundant transmission signals is performed by the space-time encoder, which dependsvery much on the specific scheme under consideration. At the receiver, the correspondingdetection/decoding process is carried out by the space-time de-coder. In the delay diversity

scheme for example, identical signals are transmitted via the individual antennas, usingdifferent delays. This causes artificial ISI, which can be resolved at the receiver by meansof standard equalization techniques available for single-antenna systems. In contrast tothis, Alamoutis transmit diversity scheme performs an orthogonal space-timetransmission, which allows for ML detection at the receiver by means of simple linear

processing. STTCs may be interpreted as a generalization of trellis code demodulation tomultiple transmit antennas. Optimum decoding in the sense of MLSE can be performedusing the Viterbi algorithm. On the basis of simulation results, it was shown in figure thatSTTCs offer an excellent performance that is within 2-3 dB of the outage capacity limit.However, this performance comes at the expense of a comparatively high decodingcomplexity. Motivated by the simple receiver structure of orthogonal space-time block codes (OSTBCs) were introduced in which constitute a generalization of Alamoutisscheme to more than two transmit antennas. OSTBCs are designed to achieve full diversitywith regard to the number of transmit and receive antennas. In contrast to STTCs, OSTBCsdo not offer any additional coding gain. STTCs and OSTBCs can be combined withdifferent diversity reception techniques at the receiver side.


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Basic principle of space-time coding.

1.6 Conclusion:

Multi-antenna diversity provide greater reliability by smoothening channelvariations.

Multi-user diversity utilize the channel variability across users to increasethroughput

Choose diversity techniques according to channel conditions, mobility andapplication constraints

For example, low delay-applications with high reliability requirement may usemulti-antenna diversity with space time codes


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CHAPTER 3

DETECTION SCHEME

Communication over a wireless channel is challenging because of the deleterious effects of channel fading on the received signal strength . Diversity reception is a well knownfading-compensation technique . Diversity can be achieved by sending the same signal atdifferent time instances, which are separated by at least the channel coherence time, or

by sending the same signal over multiple frequencies, which are separated by at least thechannel-coherence bandwidth. Other forms of diversity can be realized by multipleantennas at the receiver that are adequately separated in space to realize independentfading. The multiple received signals can be combined in various ways. These are,traditionally, maximal-ratio combining (MRC), equal-gain combining (EGC), and

selection combining (SC) diversity schemes.

In practice, the channel gains have to be estimated at the receiver for diversity combining.Also, the channel-estimation errors affect the performance of the diversity-combiningschemes. Various diversity combining techniques can be distinguished:

Selection combining : Of the N received signals, the strongest signal is selected.When the N signals are independent and Rayleigh distributed, theexpected diversity gain has been

1

=1

shown to be , expressed as a power ratio. Therefore, any additional gain diminishesrapidly with the increasing number of channels.

Equal-gain combining : All the received signals are summed coherently.

Maximal-ratio combining : is often used in large phased-array systems: Thereceived signals are weighted with respect to their SNR and then summed. Theresulting SNR yields SNRk =1 where SNR k is SNR of the received signal .
http://en.wikipedia.org/wiki/Rayleigh_distributionhttp://en.wikipedia.org/wiki/Diversity_gainhttp://en.wikipedia.org/w/index.php?title=Equal-gain_combining&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Equal-gain_combining&action=edit&redlink=1http://en.wikipedia.org/wiki/Maximal-ratio_combininghttp://en.wikipedia.org/wiki/Maximal-ratio_combininghttp://en.wikipedia.org/wiki/Phased-arrayhttp://en.wikipedia.org/wiki/Signal-to-noise_ratiohttp://en.wikipedia.org/wiki/Signal-to-noise_ratiohttp://en.wikipedia.org/wiki/Phased-arrayhttp://en.wikipedia.org/wiki/Maximal-ratio_combininghttp://en.wikipedia.org/w/index.php?title=Equal-gain_combining&action=edit&redlink=1http://en.wikipedia.org/wiki/Diversity_gainhttp://en.wikipedia.org/wiki/Rayleigh_distribution


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Sometimes more than one combining technique is used for example, lucky imaging usesselection combining to choose (typically) the best 10% images, followed by equal-gaincombining of the selected images

.

Other signal combination techniques have been designed for noise reduction and havefound applications in single molecule biophysics, chemometrics among other disciplines.

3.1 Maximum Ratio Combining (MRC)

In telecommunications, maximal-ratio combining (MRC ) is a method of diversitycombining in which:

1. the signals from each channel are added together 2. the gain of each channel is made proportional to the rms signal level and inversely

proportional to the mean square noise level in that channel.3. different proportionality constants are used for each channel.

It is also known as ratio-squared combining and predetection combining . Maximal-ratiocombining is the optimum combiner for independent AWGN channels.

MRC can restore a signal to its original shape.

The received signal is

y = hx + nwhere

n = [n 1 .. n N]T represents AWGN and all nk are spatially and temporally i.i.d. as n k ~C N(0,N 0) for k = 1, ..,N.

Flat-fading channel vector h = [h 1 .. h N]

T

are also spatially and temporally i.i.d. ashk ~ C N(0, 1) for k = 1, ..,N.

Perfect CSI is assumed at the receiver for all the channels
http://en.wikipedia.org/wiki/Lucky_imaginghttp://en.wikipedia.org/wiki/Biophysicshttp://en.wikipedia.org/wiki/Chemometricshttp://en.wikipedia.org/wiki/Diversity_combininghttp://en.wikipedia.org/wiki/Diversity_combininghttp://en.wikipedia.org/wiki/Channel_(communications)http://en.wikipedia.org/wiki/Gainhttp://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Signal_levelhttp://en.wikipedia.org/wiki/Noise_levelhttp://en.wikipedia.org/wiki/Additive_white_Gaussian_noisehttp://en.wikipedia.org/wiki/Additive_white_Gaussian_noisehttp://en.wikipedia.org/wiki/Noise_levelhttp://en.wikipedia.org/wiki/Signal_levelhttp://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Gainhttp://en.wikipedia.org/wiki/Channel_(communications)http://en.wikipedia.org/wiki/Diversity_combininghttp://en.wikipedia.org/wiki/Diversity_combininghttp://en.wikipedia.org/wiki/Diversity_combininghttp://en.wikipedia.org/wiki/Chemometricshttp://en.wikipedia.org/wiki/Biophysicshttp://en.wikipedia.org/wiki/Lucky_imaging


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Fig.Recive diversity

3.2 Equal Gain Combining (EGC)

With EGC, each channel is provided with phase compensation to match the phase shift inthe channel (the phase is measured with respect to the reference antenna element). Allchannels have equal gain (without loss of generality, the gain is takenequal to unity). EGCis an attractive method due to its relative ease of implementation. The method wasinvestigated by several authors. Jakes provided an expression for the SNR in the case of Rayleigh fading . In , the cumulative density function of the SNR is evaluated by a seriesmethod for Rayleigh and Nakagami channels.

This work is extended to Ricean channels in. Here, we briefly study the EGC performancein the presence of CCI. The cases treated are of a desired signal subject to Rayleigh or


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Ricean fading and CCI subject to Rayleigh fading. These cases are referred to as Rayleigh Rayleigh and Rice Rayleigh, respectively. While with MRC and OC, performance isevaluated by regarding the SIR as a random variable and characterizing its densityfunction, with EGC our scope was limited to providing an expression for the ratio of meansignal power to mean interference power. This simplification is necessitated by the factthat the desired signal is expressed by a sum of Rayleigh or Rice distributions for whichclosed-form expressions are not available.

The received symbol

y = hx + nwhere

x is a BPSK symbol and x

{Es,Es}.

AWGN n = [n 1 n2...n N]T , where nk C N(0,N 0) for k = 1, 2, ...,N. Flat-fading channel vector h = [h 1 h2....h N]T are spatially and temporally i.i.d. as hk

~C N(0, 1) for k = 1, 2, ...,N.

Available CSI at the receiver is h r =[h 1/|h1|, ..., h N/|h N |]T

3.2.1 Detection rule at the receiver :

Detection variable (d)

d = h ry = h1 + . . hN x + w The received SNR( ) is = h1 + . . hN 2 c where = E s/N0. Taking N = 2 and z = 1 + 2 2 , the BER can be expressed as

= 0.5 1 ( + 2 0 )+ 0


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EGC with DPSK for 1 2 system

The received symbols at the kth time instant is

yk = h k xk + nk

where

yk = [y 1,k y2,k ] represents received symbols at both the antennas 1 and 2.

xk is a DPSK symbol with power E s.

n k = [n 1,k n2,k ]T represents AWGN at the two receive antennas, where n 1 and n 2 arespatially and temporally i.i.d. as n k ~ C N(0,N 0) for k = 1, 2.

We assume spatially independent quasi-static flat Rayleigh fading channel

h = [h 1,k h2,k ]T

.

3.2.2 Detection rule at the Receiver:

The decision variable d k = Re{ 1, 11, + 2, 12, }.BER (P e) performance:

Pe =14 2

3

+

3


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Where = EsEs + N 0 For L receive antennas

=12 1 + 1 +2 1=0

EGC with DPSK for 1 2 system .

3.3 Selection Combining

A selection combining scheme for a receiver operating over a multipath fading channel isintroduced, by which the m largest channel outputs are selected instead of only the largestone, as in the conventional selection combining receiver. Expressions for the error

probability of this scheme for an exponential multipath intensity profile (MIP) witharbitrary decay constant are found by first deriving the joint density function of the mordered channel outputs, then averaging the conditional error probability over the jointdensity function. The performance is compared with that of maximal ratio combining in

both an interference-limited and a noise-limited environment. The interference-limitedenvironment chosen is a multicell CDMA system. Numerical results show that the


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performance of the selection combining scheme is superior to that of conventionalselection combining, and can be very close to that of maximal ratio combining, dependingupon the value of m and the rate of decay of the MIP

Motivation for antenna selection

The received symbol can be represented as

y = h mx + n,

where

AWGN n

C N(0,N 0).

x is a BPSK symbol taken from x

{Es,Es}

The channel is flat fading and the coefficients hk, where k = 1, 2...,N are spatiallyi.i.d. as h k ~C N(0, 1).

The antenna selection criterion is maximization of received SNR. Therefore, m can be expressed by

m = arg max1k N hk 2

Considering coherent detection, the detection variable (d)

d = h m*y = |h m|2x + h m*n

The received SNR is = |h m|2c,where c = Es/N 0.

Taking z = |h m|2, the pdf of z can be determined using order statisticsas

p(z) = N[FX(z)]N1pX(z)

where x represents the channel gain for one path from the transmitter to the receiver.

For N = 2

p(z) = 2[F x(z)]p x(z)

p(z) = 2(1 e-z)e -z

= 2 2


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= 2 =

0

= 20 =

12

+ 1 + 12 + 2

Fig.Selection Combing Analytical And Simulation Comparision


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Fig. SISO, Selection Combining and MRC Comparision

3.4. 1 2 correlated MRC systems.

It is proved that a maximal ratio combiner operating on correlated branches and weightingthe branch signals as though they were independent is optimal. It is also proved that

performance measures of maximal ratio combining operating with correlated Rayleigh or Ricean fading input branches are identical to performance measures of an equivalentdiversity system operating with independent and, in general, unbalanced inputs.

The received symbol

y = hx + n

x is a BPSK symbol and x

{Es,Es}.

AWGN n = [n 1 n2]T at the two receive antennas, where n 1 and n 2 are spatially and temporally i.i.d. as n k ~ CN(0,N 0) for k = 1, 2.

Flat-fading channel vector h = [h 1 h2]T is temporally independent but spatially correlated and identically distributed as h k ~ C N(0, 1)for k = 1, 2.

The correlation

= [ 1

2 ]


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The correlation matrix R can be expressed as

=1

1

Detection rule at the Receiver: Taking coherent detection at the receiver,the decision variable d = Re { h*y}.

BER (P e) performance: The pdf of the received SNR( ) is

=2

2 1+

1

Now, the BER can be expressed as

= 0 = 20

1

2= 2 2 2

12

1+

1

=0

BER(P e) performance:

=1

41 + 1

1 +

1 + 1 +

1

1

11 + 1

For 0 i.e. uncorrelated fading. BER will be same as 12 MRC systems with spatiallyindependent fading.


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1 2 correlated MRC systems.

3.5 Conclusion

For the receiver diversity we have different diversity technique, out of which we used threetechniques-selection diversity, maximal ratio combining and equal gain combining for our work. BPSK modulation technique and Rayleigh fading is used for checking the

performance of these techniques. We observed that when we calculated the value of SNR with different no. of antenna for these three techniques, maximal ratio combining diversitytechnique gives the best result as compare to the equal gain combining and selectiondiversity. For the calculation the bit error rate with respect to the E b/N0 then again maximalratio combining have lesser value as compare to the equal gain combining and selectiondiversity. So, we can say that the performance of the maximal ratio combining is better ascompare to the equal gain combining and selection diversity E b/N0 are also proposed.


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CHAPTER 4

ALAMOUTIS SCHEME

Shivash M Alamouti published a paper on simple diversity technique. ThePaper Used transmit diversity technique. It Used Two Transmit Antenna and one Receiveantenna and may be defined by the following three functions.

The encoding and transmission sequence of information symbols at the receiver.

The combining scheme at the receiver. The decision rule for maximum likelihood receiver.

THE NEXT-generation wireless systems are required to have high voice quality ascompared to current cellular mobile radio standards and provide high bit rate data services(up to 2 Mbits/s). At the same time, the remote units are supposed to be small lightweight

pocket communicators.

Furthermore, they are to operate reliably in different types of environments: macro, micro,and picocellular; urban, suburban,and rural; indoor and outdoor. In other words, the next

generation systems are supposed to have better quality and coverage, be more power and bandwidth efficient, and be deployed in diverse environments. Yet the services mustremain affordable for widespread market acceptance. Inevitably, the new pocketcommunicators must remain relatively simple. Fortunately, however, the economy of scalemay allow more complex base stations. In fact, it appears that base station complexity may

be the only plausible trade space for achieving the requirements of next generation wirelesssystems.

The fundamental phenomenon which makes reliable wireless transmission difficult is time-

varying multipath fading,It is this phenomenon which makes tetherless transmission achallenge when compared to fiber, coaxial cable, line-of-sight microwave or even satellite


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transmissions. Increasing the quality or reducing the effective error rate in a multipathfading channel is extremely difficult. In additive white Gaussian noise (AWGN), usingtypical modulation and coding schemes, reducing the effective bit error rate (BER) from 10to 10 may require only 1- or 2-dB higher signal-to-noise ratio (SNR). Achieving the samein a multipath fading environment, however, may require up to 10 dB improvement inSNR.

The improvement in SNR may not be achieved by higher transmit power or additional bandwidth, as it is contrary to the requirements of next generation systems. It is thereforecrucial to effectively combat or reduce the effect of fading at both the remote units and the

base stations, without additional power or any sacrifice in bandwidth. Theoretically, themost effective technique to mitigate multipath fading in a wireless channel is transmitter

power control. If channel conditions as experienced by the receiver on one side of the link

are known at the transmitter on the other side, the transmitter can predistort the signal inorder to overcome the effect of the channel at the receiver. There are two fundamental

problems with this approach.

The major problem is the required transmitter dynamic range. For the transmitter toovercome a certain level of fading, it must increase its power by that same level, which inmost cases is not practical because of radiation power limitations and the size and cost of the amplifiers. The by the receiver except in systems where the uplink (remote to base) anddownlink (base to remote) transmissions are carried over the same frequency. Hence, the

channel information has to be fed back from the receiver to the transmitter, which results inthroughput degradation and considerable added complexity to both the transmitter and thereceiver. Moreover, in some applications there may not be a link to feed back the channelinformation.

Other effective techniques are time and frequency diversity. Time interleaving, together with error correction coding, can provide diversity improvement. The same holds for spread spectrum. However, time interleaving results in large delays when the channel isslowly varying. Equivalently, spread spectrum techniques are ineffective when thecoherence bandwidth of the channel is larger than the spreading bandwidth or,equivalently, where there is relatively small delay spread in the channel. In most scatteringenvironments, antenna diversity is a practical, effective and, hence, a widely appliedtechnique for reducing the effect of multipath fading .

The classical approach is to use multiple antennas at the receiver and perform combiningor selection and switching in order to improve the quality of the received signal. The major

problem with using the receive diversity approach is the cost, size, and power of theremote units. The use of multiple antennas and radio frequency (RF) chains (or selectionand switching circuits) makes the remote units larger and more expensive. As a result,

diversity techniques have almost exclusively beenapplied to base stations to improve their reception quality. A base station often serves hundreds to thousands of remote units. It is


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therefore more economical to add equipment to base stations rather than the remote units.For this reason, transmit diversity schemes are very attractive. For instance, one antennaand one transmit chain may be added to a base station to improve the reception quality of all the remote units in that base station s coverage area.1 The alternative is to add moreantennas and receivers to all the remote units. The first solution is definitely moreeconomical. Recently, some interesting approaches for transmit diversity have beensuggested.

A delay diversity scheme was proposed by Wittneben for base station simulcasting andlater, independently, a similar scheme was suggested by Seshadri and Winters for a single

base station in which copies of the same symbol are transmitted through multiple antennasat different times, hence creating an artificial multipath distortion. A maximum likelihoodsequence estimator (MLSE) or a minimum mean squared error (MMSE) equalizer is then

used to resolve multipath distortion and obtain diversity gain. Another interesting approachis space time trellis coding where symbols are encoded according to the antennas throughwhich they are simultaneously transmitted and are decoded using a maximum likelihooddecoder.

This scheme is very effective, as it combines the benefits of forward error correction(FEC) coding and diversity transmission to provide considerable performance gains. Thecost for this scheme is additional processing, which increases exponentially as a functionof bandwidth efficiency (bits/s/Hz) and the required diversity order. Therefore, for some

applications it may not be practical or cost-effective.

The technique proposed in this paper is a simple transmit diversity scheme which improvesthe signal quality at the receiver on one side of the link by simple processing across twotransmit antennas on the opposite side. The obtained diversity order is equal to applyingmaximal-ratio receiver combining (MRRC) with two antennas at the receiver. The schememay easily be generalized to two transmit antennas and receive antennas to provide adiversity order of . This is done without any feedback from the receiver to the transmitter and with small computation complexity. The scheme requires no bandwidth expansion, asredundancy is applied in space across multiple antennas, not in time or frequency.

The new transmit diversity scheme can improve the error performance, data rate, or capacity of wireless communications systems. The decreased sensitivity to fading mayallow the use of higher level modulation schemes to increase the effective data rate, or smaller reuse factors in a multi cell environment to increase system capacity. The schememay also be used to increase the range or the coverage area of wireless systems. In other words, the new scheme is effective in all of the applications where system capacity islimited by multipath fading and, hence, may be a simple and cost-effective way to addressthe market demands for quality and efficiency without a complete redesign of existing

systems.


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Furthermore, the scheme seems to be a superb candidate for next-generation wirelesssystems, as it effectively reduces the effect of fading at the remote units using multipletransmit antennas at the base stations.

4.1 Classical Maximal-Ratio Receive Combining (MRRC) Scheme

Fig. 1 shows the baseband representation of the classical two-branch MRRC.It a given time, a signal S 0 is sent from the transmitter. The channel including the effects

of the transmit chain, the airlink, and the receive chain may be modeled by a complexmultiplicative distortion composed of a magnitude response and a phase response. Thechannel between the transmit antenna and the receive antenna zero is denoted by h0 and

between the transmit antenna and the receive antenna one is denoted by h1 where

h0 = 0e j0 h1 = 1e j1

(1) Noise and interference are added at the two receivers. The resulting received basebandsignals are

r 0 = h 0 s0 + n0

r 1 = h 1s0 + n1

(2)where n 0 and n 1 represent complex noise and interference.Assuming n 0 and n 1 are Gaussian distributed, the maximum likelihood decision rule at thereceiver for these received signals is to choose signal if and only if (iff)

d(r0, h0si)+d(r1,h1si)d(r0,hosk)+d(r1,h1sk)

(3)where d(x,y) is the squared Euclidean distance between signals x and y calculated by thefollowing expression:

d(x,y) = (x-y) (x*-y*)

(4)The receiver combining scheme for two-branch MRRC is as follows:

0 = h 0*r 0 + h 1*r 1 = h 0*(h0s0 + n 0) + h 1*(h1s0 + n 1)


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= (0 + 1)s0 + h 0*n0 + h 1*n1

(5)

Expanding (3) and using (4) and (5) we getchoose iff

(0 + 1)|s i| - 0si* -0*si (0 + 1)|sk| - 0sk * -0*sk

(6)

TWO BRANCH MRC


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Or equivalentlyChoose Si iff

(0 +

1 - 1)|s

i| + d(

0,s

i) (

0 +

1 - 1)|s

k | + d(

0,s

k )

(7)For PSK signal

|si| = |s k | = E s

(8)Where E s is the energy of signal.Therfore for PSK signal,decision rule in (7) is simplifiedtoChoose S i iff

d(0,s i) d(0,sk )(9)

4.2. The New Transmit Diversity Scheme

A. Two-Branch Transmit Diversity with One Receiver Fig. 2 shows the basebandrepresentation of the new twobranch transmit diversity scheme. The scheme uses twotransmit antennas and one receive antenna and may be defined by the following threefunctions: the encoding and transmission sequence of information symbols at the transmitter; the combining scheme at the receiver; the decision rule for maximum likelihood detection


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New Two Branch Transmit Diversity Scheme with one receiver

Antenna 0 Antenna 1

Time t s0

s1

Time t + T -s1

s0


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4.3 The Encoding and Transmission Sequence:

At a given symbol period, two signals are simultaneously transmitted from the twoantennas. The signal transmitted from antenna zero is denoted by and from antenna one by.During the next symbol period signal ( ) is transmitted from antenna zero, and signal istransmitted from antenna one where is the complex conjugate operation. This sequence isshown in Table I.In Table I, the encoding is done in space and time (space time coding). The encoding,however, may also be done in space and frequency. Instead of two adjacent symbol

periods, two adjacent carriers may be used (space frequency coding).The channel at time may be modeled by a complex multiplicative distortion for transmitantenna zero and for transmit antenna one. Assuming that fading is constant across twoconsecutive symbols, we can write

h0(t) = h 0(t + T) = h 0 = 0 e j0 h1(t) = h 1(t + T) = h 1 = 1 e j1

(10)where is the symbol duration. The received signals can then be expressed as

r 0 = r(t) = h 0s0 + h 1s1 + n 0 r1 = r(t + T) = -h 0s1* + h 1s0* + n 1

(11)where r 0 and r 1 are the received signals at time t andand t+T and n 0 and n 1 are complex random variables representing

receiver noise and interference.

4.3.1 The Combining Scheme :

The combiner shown in Fig. 2builds the following two combined signals that are sent tothe maximum likelihood detector:

0 = h 0*r 0 + h 1r 1* 1 = h 1*r 0 h0r 1*

(12)


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It is important to note that this combining scheme is different from the MRRC in (5).Substituting (10) and (11) into (12)we get

0 = (

0 +

1)s

0+ h

0*n

0+ h

1n

1*

1 = (0 + 1)s1 - h0n1* + h 1*n0

(13)

4.3.2 The Maximum Likelihood Decision Rule :

These combined signals are then sent to the maximum likelihood detector which, for eachof the signals and , uses the decision rule expressed in (7) or (9) for PSK signals. Theresulting combined signals in (13) are equivalent to that obtained from two-branch MRRC

in (5). The only difference is phase rotations on the noise components which do notdegrade the effective SNR. Therefore, the resulting diversity order from the new two-

branch transmit diversity scheme with one receiver is equal to that of two-branch MRRC.

4.3.3 Two-Branch Transmit Diversity with M Receivers:

There may be applications where a higher order of diversity is needed and multiple receiveantennas at the remote units are feasible. In such cases, it is possible to provide a diversity

order of 2M with two transmit and M receive antennas. For illustration, we discuss thespecial case of two transmit and two receive antennas in detail. The generalization to Mreceive antenna is trivial.


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Antenna 0 Antenna 1

Time t r 0 r 2

Time t + T r 1 r 3

Fig.3 shows the baseband representation of the new scheme with two transmit and tworeceive antennas.

The encoding and transmission sequence of the information symbols for thisconfiguration is identical to the case of a single receiver, shown in Table I. Table II definesthe channels between the transmit and receive antennas, and Table III defines the notationfor the received signal at the two receive antennas.Where

r 0 = h 0s0 + h 1s1 +n0 r 1 = -h 0s1* + h 1s0* +n 1 r 2 = h 2s0 + h3s1 + n 2

r 3 = -h 2s1* + h 3s0* + n 3

(14), , , and are complex random variables representing receiver thermal noise and interference.The combiner in Fig. 3 builds the following two signals that are sent to the maximumlikelihood detector:

0 = h0*r 0 + h 1r 1* + h 2*r 2 + h 3r 3*1 = h1*r 0 h0r 1* + h 3*r 2 h2r 3*

(15)Substituting the appropriate equations we have

0 = (0 + 1 + 2 + 3)s0 + h 0*n0 + h 1n1* + h 2*n2 + h 3n3*1 = (0 + 1 + 2 + 3)s1 h0n1* + h 1*n0 h2n3* + h 3*n2

(16)


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These combined signals are then sent to the maximum likelihood decoder which for signaluses the decision criteria expressed in (17) or (18) for PSK signals.Choose iff

(0 + 1 + 2 + 3 - 1)|s i| + d(0,s i) (0 + 1 + 2 + 3 - 1|s k | + d(0,sk )

(17)Choose iff

d (0,si) d (0,sk )

(18)Similarly, for using the decision rule is to choose signalIff

(0 + 1 + 2 + 3 - 1)|s i|+ d (1,s i) (0 + 1 +2 + 3 - 1)|s k | + d(1,sk )

(19)or, for PSK signals,choose iff

d (1,s i) d (1,sk )(20)The combined signals in (16) are equivalent to that of fourbranch MRRC, not shown in the

paper. Therefore, the resulting diversity order from the new two-branch transmit diversity

scheme with two receivers is equal to that of the four-branch MRRC scheme. It isinteresting to note that the combined signals from the two receive antennas are the simpleaddition of the combined signals from each receive antenna, i.e., the combining scheme isidentical to the case with a single receive antenna. We may hence conclude that, using twotransmit and receiveantennas, we can use the combiner for each receive antenna and then simply add thecombined signals from all the receive antennas to obtain the same diversity order as

branch MRRC. In other words, using two antennas at the transmitter, the scheme doublesthe diversity order of systems with one transmit and multiple receive antennas. Aninteresting configuration may be to employ two antennas at each side of the link, with atransmitter and receiver chain connected to each antenna to obtain a diversity order of four at both sides of the link.

4.4. Error Performance Simulations

The diversity gain is a function of many parameters, including the modulation scheme andFEC coding. Fig. 4 shows the BER performance of uncoded coherent BPSK for MRRC


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and the new transmit diversity scheme in Rayleigh fading. It is assumed that the totaltransmit power from the two antennas for the new scheme is the same as the transmit

power from the single transmit antenna for MRRC. It is also assumed that the amplitudesof fading from each transmit antennato each receive antenna are mutually uncorrelated Rayleigh distributed and that the averagesignal powers at each receive antenna from each transmit antenna are the same. Further, weassume that the receiver has perfect knowledge of the channel. Although the assumptionsin the simulations may seem highly unrealistic, they provide reference performance curvesfor comparison with known techniques. An important issue is whether the new scheme isany more sensitive to real-world sources of degradation. This issue is addressed in SectionV. As shown in Fig. 4, the performance of the new scheme with two transmitters and asingle receiver is 3 dB worse than two-branch MRRC. As explained in more detail later inSection V-A, the 3-dB penalty is incurred because the simulations assume that each

transmit antenna radiates half the energy in order to ensure the same total radiated power as with one transmit antenna. If each transmit antenna in the new scheme was to radiate thesame energy as the single transmit antenna for MRRC, however, the performance would beidentical. In other words, if the BER was drawn against the average SNR per transmitantenna, then the performance curves for the new scheme would shift 3 dB to the left andoverlap with the MRRC curves. Nevertheless, even with the equal total radiated power assumption, the diversity gain for the new scheme with one receive antenna at a BER of 10is about 15 dB. Similarly, assuming equal total radiated power, the diversity gain of thenew scheme with two receive antennas at a BER of 10 is about 24 dB, which is 3 dB worse

than MRRC with one transmit antenna and four receive antennas. As stated before, these performance curves are simple reference illustrations. The important conclusion is that thenew scheme provides similar performance to MRRC, regardless of the employed codingand modulation schemes. Many publications have reported the performance of variouscodingand modulation schemes with MRRC. The results from these publications may be used to

predict the performance of the new scheme with these coding and modulation techniques.

4.5. Implementation Issues:

we have shown, mathematically, that the new transmit diversity scheme with two transmitandreceive antennas is equivalent to MRRC with one transmit antenna and receive antennas.From practical implementation aspects, however, the two systems may differ. This sectiondiscusses some of the observed difference between the two schemes.


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4.5.1. Power Requirements

The new scheme requires the simultaneous transmission of two different symbols out of two antennas. If the system is radiation power limited, in order to have the same totalradiated power from two transmit antennas the energy allocated to each symbol should behalved. This results in a 3-dB penalty in the error performance. However, the 3-dBreduction of power in each transmit chain translates to cheaper, smaller, or less linear

power amplifiers. A 3-dB reduction in amplifiers power handling is very significant andmay be desirable in some cases. It is often less expensive (or more desirable fromintermodulation distortion effects) to employ two half-power amplifiers rather than a singlefull power amplifier. Moreover, if the limitation is only due to RF power handling(amplifier sizing, linearity, etc.), then the total radiated power may be doubled and no

performance penalty is incurred.

4.5.2. Sensitivity to Channel Estimation Errors

It is assumed that the receiver has perfect knowledge of the channel. The channelinformation may be derived by pilot symbol insertion and extraction. Known symbols aretransmitted periodically from the transmitter to the receiver. The receiver extracts thesamples and interpolates them to construct an estimate of the channel for every datasymbol transmitted. There are many factors that may degrade the performance of pilot

insertion and extraction techniques, such as mismatched interpolation coefficients andquantization effects. The dominant source of estimation errors for narrowband systems,however, is time variance of the channel. The channel estimation error is minimized whenthe pilot insertion frequency is greater or equal to the channel Nyquist sampling rate,which is two times the maximum Doppler frequency. Therefore, as long as the channel issampled at a sufficient rate, there is little degradation due to channel estimation errors. For receive diversity combining schemes with antennas, at a given time, independent samplesof the channels are available. With transmitters and a single receiver, however, theestimates of the channels must be derived from a single received signal. The channelestimation task is therefore different. To estimate the channel from one transmit antenna tothe receive Antenna the pilot symbols must be transmitted only from the correspondingtransmit antenna. To estimate all the channels, the pilots must alternate between theantennas (or orthogonal pilot symbols have to be transmitted from the antennas). In either case, times as many pilots are needed. This means that for the two-branch transmitdiversity schemes discussed in this report, twice as many pilots as in the two-branchreceiver combining scheme are needed.


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4.5.3. The Delay Effects:

With branch transmit diversity, if the transformed copies of the signals are transmitted atdistinct intervals from all the antennas, the decoding delay is symbol periods. That is, for the two-branch diversity scheme, the delay is two symbol periods. For a multicarrier system, however, if the copies are sent at the same time and on different carrier frequencies, then the decoding delay is only one symbol period.

.4.5.4 Antenna Configurations:

For all practical purposes, the primary requirement for diversity improvement is that thesignals transmitted from the different antennas be sufficiently uncorrelated (less than 0.7

correlation) and that they have almost equal average power (less than 3-dB difference).Since the wireless medium is reciprocal, the guidelines for transmit antenna configurationsare the same as receive antenna configurations. For instance, there have been manymeasurements and experimental results indicating that if two receive antennas are used to

provide diversity at the base station receiver, they must be on the order of ten wavelengthsapart to provide sufficient decorrelation. Similarly, measurements show that to get thesame diversity improvement at the remote units it is sufficient to separate the antennas atthe remote station by about three wavelengths.This is due to the difference in the nature of the scattering environment in the proximity of the remote and base stations. The remote

stations are usually surrounded by nearby scatterers, while the base station is often placedat a higher altitude, with no nearby scatterers now assume that two transmit antennas areused at the base station to provide diversity at the remote station on the other side of thelink. The important question is how far apart should the transmit antennas be to providediversity at the remote receiver. The answer is that the separation requirements for receivediversity on one side of the link are identical to the requirements for transmit diversity onthe other side of link. This is because the propagation medium between the transmitter andreceiver in either direction are identical. In other words, to provide sufficient decorrelation

between the signals transmitted from the two transmit antennas at the base station, we musthave on the order of ten wavelengths of separation between the two transmit antennas.Equivalently, the transmit antennas at the remote units must be separated by about threewavelengths to provide diversity at the base station. It is worth noting that this propertyallows the use of existing receive diversity antennas at the base stations for transmitdiversity. Also, where possible, two antennas may be used for both transmit and receive atthe base and the remote units, to provide a diversity order of four at both sides of the link.


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4.5.5 Soft Failure:

One of the advantages of receive diversity combining schemes is the added reliability dueto multiple receive chains. Should one of the receive chains fail, and the other receivechain is operational, then the performance loss is on the order of the diversity gain. In other words, the signal may still be detected, but with inferior quality. This is commonly referredto as soft failure. Fortunately, the new transmit diversity scheme provides the same softfailure. To illustrate this, we can assume that the transmit chain for antenna one in Fig. 2 isdisabled, i.e., h1=0 . Therefore, the received signals may be described as

r 0 = h 0s0 + n 0 r 1 = -h 0s1* + n 1

(21)The combiner shown in Fig. 2 builds the following twocombined signals according to (12):

0 = h 0*r 0 = h 0*(h0s0 + n 0) = 0s0 + h 0*n0 1 = -h 0r 1* = -h 0(-h0*s1 + n 1*) = 0s1 h0n1*

(22)These combined signals are the same as if there was no diversity. Therefore, the diversity

gain is lost but the signal may still be detected. For the scheme with two transmit and tworeceive antennas, both the transmit and receive chains are protected by this redundancyscheme.

4.5.6. Impact on Interference:

The new scheme requires the simultaneous transmission of signals from two antennas.Although half the power is transmitted from each antenna, it appears that the number of

potential interferers is doubled, i.e., we have twice the number of interferers, each with half the interference power. It is often assumed that in the presence of many interferers, theoverall interference is Gaussian distributed. Depending on the application, if thisassumption holds, the new scheme results in the same distribution and power of interference within the system. If interference has properties where interferencecancellation schemes (array processing techniques) may be effectively used, however, thescheme may have impact on the system design. It is not clear whether the impact is

positive or negative. The use of transmit diversity schemes (for fade mitigation) inconjunction with array processing techniques for interference mitigation has been studied

for space-time trellis codes . Similar efforts are under way to extend these techniques to thenew transmit diversity scheme.


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Conclusion:

Using two transmit and one receive antenna Alamouti scheme provides the samediversity order as MRRC with one transmit and two receive antennas.

This scheme may easily be generalized to two transmit antenna and M receiveantennas to provide a diversity of order 2M.

This scheme can be used to provide diversity improvement at all remote unit atwireless system, using two transmitter at base station instead of using two receiver at mobile units.

The scheme does not require any feedback information from receiver to thetransmitter and its computational complexity is similar to MRRC.


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CHAPTER 5

SPACE TIME BLOCK CODE

A space time block code is dened by pn transmission matrix G. The entriesof the matrix G are linear combinations of the variables x1, x2, x3,. xk and their conjugates.The number of transmission antennas is n, and we usually use it to separate different codesfrom each other. For example,G 2 represents a code which utilizes two transmit antennasand is denedby-:

G2 =x1 221

We assume that transmission at the baseband employs a signal constellation A with 2 b elements. At time slot 1, kb bits arrive at the encoder and select constellation signals s1 ,

s2 ,.....,s k Setting xi = s i for i = 1,2,....,k in G we arrive at a matrix C with entries linear combinations of s1 , s 2 ,.....,s k and their conjugates. So, while G contains indeterminates x1, x2,

x3,., xk , C contains specic constellation symbols (or their linear combinations) whichare transmitted from antennas for each kb bits as follows. If ct i represents the element in thet th row and the ith column of C , the entries c ti,i = 1,2,3,....,n are transmittedsimultaneously from transmit antennas 1,2,3....,n at each time slot t = 1,2,3.....,p. So, the ithcolumn of C represents the transmitted symbols from the ith antenna and the t th row of C represents the transmitted symbols at time slot t . Note that C is ba sically dened usingG ,and the orthogonality of Gs columns allows a simple decoding scheme which will beexplained in the sequel. Since p time slots are used to transmit q symbols, we dene therate of the code to be p/q . For example, the rate of G2 is one.


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In Our Project we have studied different popular space time block code which are-;

1.Orthogonal Space Time Block Code (OSTBC)

2.Complex Orthogonal Space Time Block Code (COSTBC)3.Quasi Orthogonal Space Time Block Code (QOSTBC)

4.TBH Space Time Block Code

5.TBH Code With Correlated Jafarkhani

6.Jafarkhani With Correlated TBH

5.1 Orthogonal Space Time Block Code

In this section, we consider the applications of real orthogonal designs to coding for multiple-antenna wireless communication systems. Unfortunately, these designs only existin a small number of dimensions. Encoding using orthogonal designs is trivial . Maximum-likelihood decoding is shown to be achieved by decoupling of the signals transmitted fromdifferent antenna and is proved to be based only on linear processing at the receiver. The

possibility of linear processing at the transmitter, leads to the concept of linear processing orthogonal designs developed . To study the set of dimensions for which linear processingorthogonal designs exist, we need a brief review of the Hurwitz Radon theory. Using thistheory, we will know that allowing linear processing at the transmitter only increases thehardware complexity at the transmitter and does not expand the set of dimensions for which a real orthogonal design exists.

5.1.1. Real Orthogonal Design

A real orthogonal design of size is an orthogonal matrix with entries the indeterminates.The existence problem for orthogonal designs is known as the Hurwitz Radon problem inthe mathematics literature, and was completely settled by Radon in another context at the

beginning of this century. In fact, an orthogonal design exists if and only if n= 2,4,or 8.Given an orthogonal design O, one can negate certain columns of O to arrive at another orthogonal design where all the entries of the first row have positive signs. By permutingthe columns, we can make sure that the first row of O is x1, x2, x3,., xn.. Thus we mayassume without loss of generality that O has this property.


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The Examples of orthogonal designs are 22:

x1 x2x2 x1 The 44 design: 1 2 3 42 1 4 33 4 1 24 3 2 1 The 88 design:

1 2 3 4 5 6 7 8

2 1 4 3 6 5 8 73 4 1 2 7 8 5 64 3 2 1 8 7 6 55 6 7 8 1 2 3 46 5 8 7 2 1 4 37 8 5 6 3 4 1 28 7 6 5 4 3 2 1

5.1.2. Coding Scheme:

In this section, orthogonal designs are applied to construct space time block codes thatachieve diversity. It is assumed that transmission at the baseband employs a real signalconstellation with elements. The focus is on providing a diversity order of nm themaximum transmission rate is b bits per second per hertz (bits/s/Hz). This transmission rateis achieved using an nn orthogonal design. At time slot 1, bits arrive at the encoder andselect constellation signals s 1,s2,s3,....,s n. Setting x i = s i for i = 1,2,3....,n, we arrive at a

matrix C = O(s 1,s2,s3,....,s n) with entries s 1, s2, s 3,...., s n . At each time slot t = 1,2,....,n.the entries C ti, i = 1,2,....,n are transmitted simultaneously from transmit antennas 1,2......,n.

5.1.3. Decoding Algorithm:

Clearly, the rows of O are all permutations of the first row of O with possibly differentsigns. Let 1,....., n denote the permutations corresponding to these rows and let k (i) denotethe sign x i of in the k th row of O. Then k ( p) = q means that x p is upto a sign change the(k,q)th element of O. Since the columns of O are pairwise-orthogonal, it turns out thatminimizing the metric of (2) amounts to minimizing


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Si=1

Where

= , ( ) =1=1 2

+ 1 + , 2, 2 and where , denotes the complex conjugate of , .The value of S i only dependson the code symbol s i , the received symbols , the path coefficients , , and thestructure of the orthogonal design O . It follows that minimizing the sum given in (6)amounts to minimizing (7) for all 1

. Thus the maximum-likelihood detection rule

is to form the decision variables

= , ( ) =1=1

For all i = 1,2,3......,n and decide in favour of s i among all the constellation symbols if

= arg min

2 +

1 + ,

2

,

2

This is a very simple decoding strategy that provides diversity

5.1.4. Linear Processing Orthogonal Designs :

There are two attractions in providing transmit diversity via orthogonal designs.

There is no loss in bandwidth, in the sense that orthogonal designs provide themaximum possible transmission rate at full diversity.

There is an extremely simple maximum-likelihood decoding algorithm which onlyuses linear combining at the receiver. The simplicity of the algorithm comes fromthe orthogonality of the columns of the orthogonal design.

The above properties are preserved even if linear processing is allowed at the transmitter.Therefore, the definition of orthogonal designs is relaxed to allow linear processing at the

transmitter. Signals transmitted from different antennas willnow be linear combinations of constellation symbols.


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5.2 Quasi Orthogonal Space Time Block Code

An example of a full-rate full-diversity complex space time block code is Alamoutischeme , which is defined by the following transmission matrix

=x1 2

21(1) Here we use the subscript 12 to represent the indeterminates and in the transmissionmatrix. Now, let us consider the following space time block code for : N = T = K =4

=

12

34

34 12=

1 2 3 4

2

1

4

3

34 12 4 3 2 1 (2)

This matrix is partially orthogonal when a matrix of 22 is taken into considerationTherefore it is called quasi-orthogonal code .

It is easy to see that the minimum rank of matrix A(s1- 1 , s2- 2 , s3- 3 , s4- 4 ), thematrix constructed from A by replacing xi with s i - , is 2. Therefore, a diversity of 2 M isachieved while the rate of the code is one. Note that it has been proved in [3] that themaximum diversity of 4 M for a rate one code is impossible in this case. Now, if we definei, i = 1,2,3,4, as the ith column of A , it is easy to see that

1 ,2 = 1 ,3 = 2 ,4 = 3 ,4 = 0 where i ,j = 4=1 s the inner product of vectors i andj .. Therefore,the subspace created by

2 and

3 is orthogonal to the subspace created by and . Usingthis orthogonality, the maximum-likelihood decision metric (3) can be calculated as thesum of two terms 14 1 , 4 + 23 2 , 3 , where 14 is independent of 2 and 3 and


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23 is independent of 1 and 4 . Thus, the minimization of decision metric is equivalent tominimizing these two terms independently. In other words, firstthe decoder finds the pair 1 , 4 that minimizes

14 1 , 4 among all possible pairs

1,

4. Then, or in parallel, the decoder selects the pair

2,

3which minimizes

23 2 , 3 . This reduces the complexity of decoding without sacrificing the performance.Simple manipulation of decision matric provides the following formulas for 14 . and 23 . : 14 1 , 4 = ,

24

=1

12 + 4 2

=1

+ 2 1, 1,2,2, 3,3, 4, 4,1+ 4, 1,3,2, 2,3, 1, 4,4+ 1, 4,2,3, 2, 3,1,4, 1 4

23 2 , 3 =

,2

4

=12

2 + 3 2

=1

+ 2 2, 1,+ 1,2, 4,3, + 3, 4,2+ 3, 1,4,2, + 1,3, + 2, 4,3+ 2, 3,

1,4,

1, 4,+ 2,3, 2 3

where is Re{ } the real part of . Note that decoding pairs for the new code is morecomplex than decoding single symbols for Orthogonal space time block codes .There areother structures which provide behaviors similar to those of (2). A few examples are given

below-:

12

34

34

12

12

34

34

12

12

34

34

12


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The main idea in the structure of the transmission matrix in (2) is to build a 44 matrixfrom two 22 matrices to keep the transmission rate fixed. A similar idea can be used tocombine two rate 3/4 transmission matrices ( 44 ) to build a rate 3/4 transmission matrix(88 ) and so on. An example of an matrix which provides a rate 3/4 code is given below:-

1

2

3 0 4

5

6 0 2 10 3 540 6 30 1 2 60 4 5 0 3 21 0 65 4 4 5 6 0 1 2 3 0

5 40 6

2 10 6

6

0

4

5

3

0

1

2

0 654 0 321

5.3 Complex Space Time Block Code

Space-time block codes from orthogonal designs proposed by Alamouti, and Tarokh-Jafarkhani-Calderbank have attracted considerable attention due to the fast maximum-likelihood (ML) decoding and the full diversity. There are two classes of space-time block codes from orthogonal designs. One class consists of those from real orthogonal designsfor real signal constellations which have been well developed in the mathematics literature.The other class consists of those from complex orthogonal designs for complexconstellations for high data rates, which are not well developed as the real orthogonaldesigns.

5.3.1.Complex Orthogonal Design:

Complex orthogonal design (COD) in variables x1 , x2 , . . . , x n is an nn matrix O suchthat:(i) the entries of O are 0 , x1 , x2 , . . . , xn, or their conjugates x1* , x2*, . . . , xn* or

multiples of them by i where i =1; and(ii) O HO = 1 2 + 2 2 + + 2 In , where the superscript H stands for thecomplex conjugate and transpose of a matrix, and In is the nn identity matrix.


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Now it is Known that space-time block codes constructed in this way exist only for twotransmit antennas. Then the definition of complex orthogonal designs was relaxed to allowlinear processing at the transmitter, i.e., the entries of O may be complex linear combinations of x1 , x1*, x2 , x2* . . . ,x n, xn*.However this also provided very limited designcodes.

Tarokh, Jafarkhani and Calderbank [6] observed that it is not necessary for the complexorthogonal designs (with or without linear processing) to be square matrices in order toconstruct space-time block codes. Space-time block codes allow non-square designs.Subsequently, they introduced the definition of generalized complex orthogonal designs(GCODs). Furthermore, they proposed generalized complex orthogonal designs with linear

processing. With these new definitions, there are space-time block codes from GCODs thatcan be used for any number of transmit antennas. However, for more than six transmit

antennas, the known space-time block codes from GCODs with linear processing havesymbol transmission rate only 1 / 2, far from the maximum symbol transmission rate 1 of those codes from real orthogonal designs for real constellations.

The existing space-time block codes from (generalized) complex orthogonaldesigns with or without linear processing can be summarized as follows:

For 2 transmit antennas, space-time block code exists with the maximum symbol transmission

rate 1 from COD (Alamoutis scheme ) For 3 and 4 transmit antennas, space-time block codes exist with symbol transmission

rate 3 / 4 from GCODs with linear processing or from GCODs without linear processing ;

For 5 and 6 transmit antennas, space-time block codes exist with symbol transmission

rates 7 / 11 and 3 / 5, respectively, from GCODs with linear processing ; For any number of transmit antennas, space-time block codes exist with symbol transmission

rate 1 / 2 from GCODs with linear processing (Tarokh, Jafarkhani and Calderbank).

5.3.2. A generalized complex orthogonal design :

A generalized complex orthogonal design (GCOD for short) in variables x 1, x 2, . . . , x k isa p n matrix G such that:

(i) The entries of G are 0, x 1, x 2, . . . , x k , or their conjugates x 1* ,x 2*, . . . ,x k *, or multiples of them by i where i =1;

(ii) G HG = (|x 1|2+|x2|2+. . .+|x k |2)In, where G H is the complex conjugate and transpose of G.


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The rate of G is defined as R = k/p. If p = n = k, then G is a classical complex orthogonaldesign (COD for short).

The difference matrix G between two distinct codewords is also a GCOD of the samestructure, i.e., ( G)H(G)= (|x1|2 + + | xk |2)In, which implies that Ghas full rank unless x1 = = xk = 0. Thus, space-time block codes from GCOD achieve the fulldiversity.

5.3.3. Complex Matrices:

The first space-time block code from GCOD was proposed by Alamouti for two transmit antennas.

It is, in fact, a 2 2 COD in two variables x 1, x2:

A =x1 x2x2x1

Clearly, the rate of A is 1. From later discussion, we know that for space-time block codes fromGCODs, the rate 1 is achievable only for two transmit antennas.

For three and four transmit antennas, space-time block codes from GCODs with rate R = 3 / 4 are

given by:-

3 =

1 2 32 1030 10 3 2 4 =

1 2 3 02 10 330 120 3 2 1

4.4 TBH Code

Tirkkonen-Boariu-Hottinen (TBH) proposed STBCs from quasi orthogonal designs, wherethe orthogonality is relaxed to provide higher symbol transmission rate.


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The ML decoding becomes the pairwise information symbol decoding instead of singleinformation symbol decoding.

They do not have the full diversity.

For 4 transmit antennas, a similar scheme is given as follows:

= A BB A

=

1 2 3 4 2 1 43 3 4 1 2

4 3

2 1

Where

A =x1 x2x2x1, B = x3 x4x4x3

Assume the whole system is

= + ,

Then the maximum-likelihood decoding at the receiver is

min( 1 , 2 , 3 , 4 )4 2

== min

1 , 22 1 1 , 3 , arg min2 , 42 1 2 , 4 - In the orthogonal space-time code case.

min( 1 , 2 , 3 )

3

2

= min1 1 1 , arg min2 2 3 , min3 3 3


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5.5 Jafarkhani Code

The Alamouti code is the first STBC that provides full diversity at full data rate for twotransmit antennas. However, if the transmitting antennas are more than two, usingorthogonal space time codes would not obtain the maximum transmission rate. SoJafarkhani proposed a space time code structure based on the full rate. In Jafarkhanismethod, the transmission matrix columns are divided into groups while the columns withineach group are not orthogonal to each other, different groups are orthogonal to each other.Thus this method is also called the quasi-orthogonal space time block codes, another codewas proposed in called TBH (ABBA) it give the same performance as Jafarkhani whenthere is no correlation in channel but for spatially correlated channel the performance of this codes degrade compared to Jafarkhani. The suggested codes are designed by replacingthe Alamouti based sub block matrix with different matrices as in Jafarkhani and TBH.

Let the number of transmitting antennas and receiving antennas is N and M respectively, acomplex space time block codes is given by TN transmission matrix G, T represents thenumber of time slots for transmitting one block of symbols, supposing quasi-static flatRayleigh fading channel the receiver vector will be

r (k ) = H (k ) s(k ) + n(k )


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where r(k) is the receiving vector , s(k) is the transmitting vector n(k) is additive white Gaussian noise

H is the channel matrix andij is the fading coefficients from the i transmitting antenna to jtransmitting antennas.

Based on Alamouti scheme, Jafarkhani construct his quasi orthogonal space time block codes for four antennas. Two (2 2) Alamouti codes S12 and S34 are defined equation (2),and they are used as sub-blocks to build Jafarkhani code for four transmit antennas.

Using these matrices as sub-block matrix, the coding matrix of Jafarkhani codes could beexpressed as follows.

The decoder is based on the multiplication of SEA with its Hermitian matrix leading to thenon-orthogonal Gramian matrix QEA.

A Gramian matrix A is a Hermitian symmetric matrix that fulfils A H = A, where H indicates conjugate transpose.


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is the channel dependent interference parameter, it is the interference parameter that define how close such a matrix to be orthogonal From equation (3), the symbols s1 , s 4 and the symbols s2 , s 3 appear in pairs, a fact that simplifies the analysis of the code.

5.6 Jafarkhani with Correlated TBH

Using a unitary pattern idea introduced in to investigate the distribution of conjugates inthe transmission matrices, we find that it is related to the positions of correlated values. Bychanging the distribution of conjugates, we can obtain matrices with different positions of correlated values.

We change the conjugates distribution of Jafarkhani matrix, and let

By exchanging the last row and the third row from earlier equation, we may get thecharacter matrix as

where the correlated value , but the positions of correlated values are thesame as the TBH case.

In addition, the measurement of error probability is from calculatingthe diversity product. We show it as


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where n is the number of transmit antennas, and is the error code words from C.

Based on the same diversity product, these two cases have similar performances by using

the same maximum ratio combing (MRC) decoding algorithm proposed earlier.


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5.7 TBH with Correlated Jafarkhani

In A Similar fashion we achieve A code TBH with correlated Jafakhani and let

thus we obtain the character matrix as

where and the positions of correlated values are the same as the Jafarkhani

case. Similar to the above analysis, we have , because

where . By using the MRC decoding

algorithm, these two cases present similar performances, and the simulations are shown in Fig. 1.Therefore, generalizing the above two modified cases, the different distribution of the conjugates intransmission matrix can lead to different positions of correlated values and the positions of correlated values in the character matrix are not directly corresponding to the performances of quasi-orthogonal STBC.

According to the above analysis, we know the positions of correlated values do not affect the BER.Therefore, now we derive some new matrices with different positions of correlated values from thedistribution of conjugates in the bottom of transmission matrices.


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Case 1: Let the sub-matrix be denoted as

Then we design a new form as

where are from (15). Thus we can write

where is a real number.

Based on the same MRC decoding algorithm, the performance of the new design case1( ND1 ) is very close to that of TBH case. The diversity product of ND1 also is similar toTBH case as

Conclusion:

In this chapter we give the modeling of space time block codes. ALAMOUTI space time block code is based upon this modeling. We explain different space time block codes withtheir code matrix. Finally we give comparisons of the different space time block codes andshow that Complex space time block code is showing better results comparing with

different cases.


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SIMULATION AND RESULTS-:

We Simulated following Results on Matlab-

1. We Compared EGC and MRC combining Scheme and we obtained the result as shown below


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2. Then we compared SISO, Selection Combining and MRC Scheme on Matlab result isgiven below


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3. We compared SISO, MRC And Alamouti(21) scheme:


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4. We compared Analytical SISO, MRC, Alamouti(21) and Simulation Alamouti(22)


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5. We also compared simulated Alamouti(21) and simulated Alamoti(22):


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6. We also simulated Alamouti Scheme With Zero forcing:


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7. We Compared OSTBC ,QSTBC ,COMPLEX STBC,TBH Code, TBH WithCorrelated Jafarkhani And Jafarkhani With Correlated TBH Codes in 32-PSK.


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8. We Compared OSTBC ,QSTBC ,COMPLEX STBC,TBH Code, TBH WithCorrelated Jafarkhani And Jafarkhani With Correlated TBH Codes in 64-PSK.


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8.We compared receive diversity performance with 1,2,3 and 4 receive antennas:


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REFERENCES

1. S. M. Alamouti, Oct. 1998, A simple transmit diversity technique for wirelesscommunications, IEEE J. Select. Areas Commun., vol. 16, no. 8, pp..

2. V. Tarokh, H. Jafarkhani, and A. R. Calderbank, July 1999 , Space-time block codes fromorthogonal designs, IEEE Trans. Inform. Theory, vol. 45, no. 5, pp. 1456 1467.

3. V.Tarokh, A. R. Calderbank, March 1999 , Space Time Block Coding for WirelessCommunications: Performance Results , IEEE J. Select. Areas Commun ., vol. 17, no. 3, pp.451-460.

4. H. Jafarkhani, Jan. 2001, A quasi-orthogonal space- time block code, IEEE Trans. Commun.,vol. 49, no. 1, pp. 1 4.

5. Jia Hou, Moon Ho LeE and Ju Yong Park, August 2003,Matrices Analysis of the Quasi-Orthogonal Space Time Block Codes, IEEE Communications Letters, vol. 7, no. 8.

6. H. Wang, D. Wang, and X.-G. Xia, March 2009, Optimal Quasi-Orthogonal Space-TimeBlock Codes with Minimum Decoding Complexity , IEEE Trans. on Information Theory .

7. Eman Hamdan, Onsy Abdel Alim, and Noha Korany , September 2012, Quasi OrthogonalSpace Time Block Codes Using Various Sub- Block Matrices, International Journal of Computer and Communication Engineering, Vol. 1, No. 3.

8. Y. Zhu, H. Jafarkhani, 2005, Differential Modulation Based on Quasi-Orthogonal Codes, IEEE Transactions on Wireless Communications ,vol.4,pp.3018-3030.

9. D. N. Dao, C. Yuen, C. Tellambura, Y. L. Guan, T. T. Tjhung, 2008, Four - Group DecodableSpace- Time Block Codes, IEEE Transactions on Signal Processing , vol. 56,pp. 424-430.

10. Z. Chen, J. Vucetic, Z. Zhou, Performance of Alamouti scheme withtransimit antennaselection, Electronic Letters ,vol.39,pp.1666-1668

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