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World Journal of Science and Technology | www.worldjournalofscience.com | 2011 | 1(8): 125-131

World Journal of Science and Technology 2011, 1(8): 125-131ISSN: 2231 2587

www.worldjournalofscience.com

SPACE TIME BLOCK CODING FOR MIMO SYSTEMS USING ALAMOUTI METHOD

WITH DIGITAL MODULATION TECHNIQUES

Shreedhar A Joshi#1

, T S Rukmini#2

and Mahesh H M#3

1Department of E & C, SDMCET Dharwad, India

2Department of Telecommunication, R V College of Engineering, & Fellow IEEE Member,

Bangalore-69, India3Department of applied Electronics, Bangalore University, Bangalore, India

Corresponding author e-mail: [email protected]

Abstract

Multiple Input Multiple Output (MIMO) systems with multiple antenna elements at both Transmitter and Receiver

ends are an efficient solution for future wireless communications systems. They provide high data rates by

exploiting the spatial domain under the constraints of limited bandwidth and transmit power. Space-Time Block

Coding (STBC) is a MIMO transmit strategy which exploits transmit diversity and high reliability. The proposed

work presents a comprehensive performance analysis of orthogonal space-time block codes (OSTBCs) with

transmit antenna selection under uncorrelated Rayleigh fading channel employing Alamoutis code. The transmitted

symbols belong to BPSK, QPSK and Quadrature amplitude modulation (QAM) with partial CSI. The numerical

evaluation of the BER for, BPSK, QPSK and exact average symbol error rate (SER) for QAM is done.

Keywords: Equivalent Virtual Channel Matrix (EVCM). Space-Time Block Coding (STBC), Orthogonal Space-

Time Block Codes (OSTBCs) and Non-Orthogonal Space-Time Block Codes (NOSTBCs), Channel State

Information (CSI), Maximal Ratio Combining (MRC),Maximum Likelihood (ML)Introduction

MIMO technology means multiple antennasat both ends of a communication system, i.e., at thetransmit and receive side. This idea in a wirelesscommunication link opens a new dimension in reliable

communication and also improves the systemperformance substantially. The idea behind MIMO isthat the transmit antennas at one end and the receiveantennas at the other end are connected andcombined in such a way that, the bit error rate (BER),or the data rate for each user is improved. The coreidea in MIMO transmission is space-time signalprocessing in which signal processing with time inspatial dimension by using multiple, spatiallydistributed antennas at both link ends. Because ofthis enormous capacity increase, such systemsgained a lot of interest in mobile communication

research [1],[2]. One essential problem of the wirelesschannel is fading, which occurs as the signal followsmultiple paths between the transmit and the receiveantennas. Fading can be mitigated by diversity, whichmeans that, the information is transmitted not onlyonce but several times, hoping that at least one of the

replicas will not undergo severe fading. A diversitytechnique makes use of an important property ofwireless MIMO channels. The different signal pathscan be often modeled as a number of separate,independent fading channels. These channels can bedistinct in frequency domain or in time domain.Several transmission schemes have been proposedthat utilize the MIMO channel in different ways, fore.g., spatial multiplexing, space-time coding or beamforming. Space-time coding (STC), introduced first byTarokh at el. [3], is a promising method where thenumber of the transmitted code symbols per time slot

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are equal to the number of transmit antennas. Thesecode symbols are generated by the STBCs can bedivided into two main classes, namely, OSTBCs and

Non-NOSTBCs. The OSTBCs achieve full diversitywith low decoding complexity, but at the price of someloss in data rate. Full data rate is achievable inconnection with full diversity only.

MIMO System (And Channel) Model

Let us consider point-to-point MIMO systemswith n t transmit and nr receive antennas as inFigure.1. Let h i,j be a complex number correspondingto the channel gain between transmit antenna i andreceive antenna j respectively. If at a certain time

instant the complex signals {s1, s2, s n t} aretransmitted via n t transmit antennas, then nr thereceived antenna j can be expressed as:

Fig 1. MIMO model with nt transmit

antennas and nr receive antennas.

n tyi = hi,j S j + n i ( 1)

j = 1

Where n i is a noise term. Combining allreceive signals in a vector y, then (1) can be easily

expressed in matrix form

y = Hs + n. (2)

Where y is the nr 1 receive symbol vector,H is the nr n t MIMO channel transfer matrix givenby

H = (3)

s is the nt 1 transmit symbol vector andn is the nr 1 additive noise vector. Note that thesystem model implicitly assumes a flat fading MIMO

channel, i.e., channel coefficients are constant duringthe transmission of several symbols. Flat fading, orfrequency non-selective fading, applies by definitionto systems where the bandwidth of the transmittedsignal is much smaller than the coherence bandwidthof the channel. All the frequency components of thetransmitted signal undergo the same attenuation andphase shift propagation through the channel. Weassume that the transmit symbols are uncorrelated,that means

E {s sH} = PS IS (4)

Where Ps denotes the mean signal powerof the used in different modulation formats at eachtransmit antenna. This implies that only modulationformats with the same mean power on all transmitantennas are considered.

Theoratical Analysis of Alamouti Code.

Historically, the Alamouti code is the firstSTBC that provides full diversity at full data rate fortwo transmit antennas [4]. The information bits are

first modulated using a digital modulation scheme,then the encoder takes the block of two modulatedsymbols s1 and s2 in each encoding operation andhands it to the transmit antennas according to thecode matrix

S = (5)

The first row represents the firsttransmission period and the second row representsthe second transmission period. During the firsttransmission, the symbols s1 and s2 are transmittedsimultaneously from antenna one and antenna tworespectively. In the second transmission period, thesymbol -s*2 is transmitted from antenna one and thesymbol

s * 1 from transmit antenna two. It is clearthat the encoding is performed in both time (twotransmission intervals) and space domain (across twotransmit antennas). The two rows and columns of Sare orthogonal to each other and the code matrix (5)is orthogonal:

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ssH =

=

= ( I2 (6)

Where I2 is a (2 X 2) identity matrix. Thisproperty enables the receiver to detect s1 and s2 by asimple linear signal processing operation. Let thereceiver side has only one receive antenna. Thechannel at time t may be modeled by a complexmultiplicative distortion h1(t) for transmit antenna oneand h2(t) for transmit antenna two. Assuming that the

fading is constant across two consecutive transmitperiods of duration T, expresses as

h1 (t) = h1 (t + T) = h1 = |h1|e j1h2 (t) = h2 (t + T) = h1 = |h2| e j2, (7)

Where |hi| and i, where i = 1, 2,. are theamplitude gain and phase shift for the path from anytransmit antenna i to any receive antenna. Thereceived signals at the time t and t + T can then beexpressed as

r1 = s1 h1 + s2 h2 + n2r2 = -s*2 h1 + s*1 h2 + n2 (8)

Where r1 and r2 are the received signals attime t and t + T respectively. n1 and n2 are complexrandom variables representing receiver noise andinterference. This can be written in matrix form as:

r = Sh + n (9)

Where h = [h1, h2]T is the complex channelvector and n is the noise vector at the receiver.

Conjugating the signal r2 in (8) that is received in thesecond symbol period, the received signal may bewritten equivalently as

(10)

Thus the equation (10) can be written inmatrix form or in short notation:

(11)

Where the modified receive vector y = [r1,r2]T has been introduced. Hv will be termed the

equivalent virtual MIMO channel matrix (EVCM) of theAlamouti STBC scheme. It is given by

HV = (12)

For MIMO channel matrix, the rows andcolumns of the virtual channel matrix are orthogonal:

HvH Hv = Hv HvH=(h12+h2 2) I2 = h 2I 2 (13)

Where I2 is the (2 X 2) identity matrix.

Linear Signal Combining and MaximumLikelihood (ML) Decoding of the Alamouti Code

If the channel coefficients h1 and h2 can beperfectly estimated at the receiver, the decoder canuse them as CSI. Assuming that all the signals in themodulation constellation are equiprobable, amaximum likelihood (ML) detector decides for thatpair of signals (s1, s2) from the signal modulationconstellation that minimizes the decision metric as

d2 (r1, h1 s1 + h2 s 2 ) + d2 (r2 h1 s*2 + h2 s*1)

= |r1 h1 s1 h2 s2|2 + |r2 + h1 s*2 h2 s*1| 2 (14)

Using a linear receiver, the signal combinerat the receiver combines the received signals r1 and r2as follows

= h1* r1 + h2 r*2 = ( |h1|2 + |h2| 2) s1 + h1* n1 + h2 n*2

= h2* r1 h1 r*2 = ( |h1|2 + |h2| 2) s1 + h2* n1 + h2n*2.

(15)

Hence s1 and s2 are two decisions statisticsconstructed by combining the received signals withcoefficients derived from the CSI. These noisy signalsare sent to ML detectors and thus the ML decodingrule can be separated into two independent decodingrules for s1 and s2 namely [5]

for detecting s1, and

(16)for detecting s2.

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The Alamouti transmission scheme is asimple transmit diversity scheme which improves thesignal quality at the receiver using a simple signal

processing algorithm at the transmitter. The diversityorder can be obtained by applying maximal ratiocombining (MRC) with one antenna at the transmitterand two antennas at the receiver where the resultingsignals at the receiver are:

r1 = h1 s1 + n1(17)r2 = h2 s2 + n2 (18)

and the combined signal is

= h1* r1 + h2* r2= (|h1|2 + | h2 |2) s1 + h1*n1 + h2* n2. (19)

Working Methodology

Literature survey is carried out for Alamoutiencoding and decoding methods and few digitalmodulation schemes like BPSK,QPSK and QAM areselected. Modeling and simulation for the proposeddesign is done with mat lab. Initially the procedure forthe BPSK modulation technique is shown in Figure.2.Here symbols are mapped into BPSK and transmitted

with alamouti technique. Figure.3. depicts theprocedure for alamouti and No alamouti techniquewith the BPSK modulation.

Start

Determine No of symbols and SNR

Generate random binary sequence of +1s and -1s(BPSK)

Group them into pair of two symbols

Code the mapped BPSK symbols to Alamouti Space Time code ,and send

with antenna selection and Multiply the symbols with the channel

and then add white Gaussian noise.

Equalize the received symbolsPerform hard decision decoding and count the bit errors

Stop

Repeat for multiple values of and plot the simulation and theoretical results

This is done for transmitting and Receiving antennas

Fig 2. Flow chart for STBC technique

with BPSK modulation

Start

Determine No of bits to be transmitted ,SNR in dB.

Mapping these symbols to BPSK modulation.

For generating the data , splitting the data into

two vectors (first transmition, second

transmition in time) for Alamouti method STBC

Transmit data through channel with SVD method by adding

Noise receive the data, Plot SER Vs SNR for Alamouti method

Repeat some steps above but transmit Symbols without

Alamouti method and Plot SER Vs SNR

Stop

Fig 3. Flow chart for alamouti/ No

alamouti STBC technique with BPSK

modulation

Figure.4. gives the procedure for the QPSKconstellation generation with gray codes mapped intofour symbols [00, 01, 10, and 11]. The MRCtechnique estimates the received symbols from thetransmitted antenna selection assumed earlier.

Start

Determine number of transmit and receive antennas, SNR

Generate QPSK symbols, Angle [pi/4, 3*pi/4, -3*pi/4 ,-pi/4]

corresponds to Gray code vector [00 10 11 01], respectively.

Generate Gray code mapping pattern for QPSK symbols

Mapping transmitted bits into QPSK symbols with 4 constellation points

Form the channel matrix, with MRC generate

Estimates and received symbols add Noise factor

Generate plots with antenna

Selections and BER Vs SNR

Stop

Fig 4. Flow chart for QPSK STBC with

alamouti technique

Similarly Figure.5. Depicts the workingmethodology for STBC technique with QAMemploying alamouti technique.

This procedure can be applied for any QAMorders such as 4, 16, and 64. In all the above cases,the channel is modeled with Raleigh flat fading

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conditions. Decoding is hard decision based MLmethod.

Start

Set the parameters like

Number of blocks of data to be transmitted

The QAM modulation order 4,16,64

Set SNR in dB

Generating the data and splitting the data into two vectors

(first transmition, second transmition in time)

Mapping QAM Modulation of transmit data selecting antennas

determining channel gain and the channel varinance is set to unity

and a Ray Leigh flat fading channel in each path is assumed

Transmit antenna set in Alamouti method and

half of the power will be sent

Adding noise factor in STC and No STC

Cases & Defining Channel and Decode

Stop

Plot SER Vs SNR

For QAM order 4,16,64

Fig 5. Flow chart for QAM mapping for

STBC with alamouti technique

Result Analysis and Discussions

The performance of the Alamouti schemeusing BPSK symbols with realizations obtained bysimulations of slow Rayleigh fading channels isshown in Figure 6. It is assumed that the totaltransmit power from the two antennas used with theAlamouti scheme is the same as the transmit powersent from a single transmit antenna to two receiveantennas and applying an MRC at the receiver. It isalso assumed that the amplitudes with fading fromeach transmit antenna to each receive antenna aremutually uncorrelated and Rayleigh distributed suchthat the average signal powers at each receive

antenna from each transmit antenna are the same.Further, it is assumed that the receiver has perfectknowledge of the channel. Figure.7. shows the SERperformance with alamouti and without alamoutitechnique for BPSK.

Figure.8. shows the performance of theAlamouti scheme using QPSK constellations. Herethe BER performance of the Alamouti scheme iscompared with a (1 1) system scheme (no diversityor STC) and with a (1 2) MRC scheme. Thesimulation results show that the Alamouti (21)scheme achieves the same diversity as the (12)

scheme using MRC. However, the performance ofAlamouti scheme is 3 dB worse due to the fact thatthe power radiated from each transmit antenna in the

Alamouti scheme is half of that radiated from thesingle antenna and sent to two receive antennas andusing MRC. In this way, the two schemes have thesame total transmit power. The other digitalmodulation technique employed in this proposed workis QAM which compares the Symbol error rate (SER)performance of Alamouti space-time coding with 2transmitting antennas and 1 receive antenna. TheSER performance is done for different orders of QAMis shown from figures 9, 10 and 11 respectively. [6],[7]

0 5 10 15 20 25

10-4

10-3

10-2

10-1

Eb/No, dB

BitErrorRate

Plot for Alamouti STBC (Rayleigh channel)

theory (nTx=1,nRx=1)theory (nTx=2, nRx=1, Alamouti)

sim (nTx=2, nRx=2, Alamouti)

Fig 6. The BER performance of the BPSKAlamouti Scheme, nt = 2, nr= 1,2

Fig 7. The SER performance of the BPSK

Alamouti Scheme, nt = 2, nr = 2 with or

without alamouti coding

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Fig 8. The BER performance of the QPSK

Alamouti Scheme, nt = 2, nr = 1,2

Fig 9. The SER performance of the 4

QAM Alamouti Scheme, nt = 2,nr = 1

Fig 10. The SER performance of the 16

QAM Alamouti Scheme, nt = 2,nr = 1

Fig 11. The SER performance of the

64QAM Alamouti Scheme, nt = 2, nr = 1

Conclusions

This work is devoted to space-time codingfor multiple- input/multiple-output (MIMO) systems.The concept of space-time coding is explained in asystematic way. The performance of space-timecodes for wireless multiple-antenna systems withchannel state information (CSI) at the transmitter hasbeen also studied. Alamouti code is the only OSTBCthat provides full diversity at full data rate (1symbol/time slot) for two transmit antennas.

Acknowledgement

This work is supported by R V Center forCognitive Technology Bangalore and Department ofResearch in Electronics, Kuvempu UniversityShimoga, and Karnataka. The authors would like tothank the Management, Principal and Director, Staffof S.D.M College of Engineering and Technology,Dharwad, Karnataka, India, for encouraging us forthis research work.

References

1. I.E.Telatar, Capacity of Multi-Antenna GaussianChannels, AT&T Bell Labs.

2. G. J. Foschini, M. J. Gans, (1998). On Limits ofWireless Communications in FadingEnvironments when Using Multiple Antennas,Wireless Personal Communications, vol. 6, pp.311-335.

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3. V. Tarokh, N. Seshadri, A. R. Calderbank,(1998). Space-Time Codes for High Data RateWireless Communication: Performance Criterion

and Code Construction, IEEE Trans. Inform.Theory, vol. 44, no. 2, pp. 744-765.

4. S. Alamouti, (1998). A Simple TransmitterDiversity Technique for WirelessCommunications, IEEE Journal on SelectedAreas of Communications, Special Issue onSignal Processing for Wireless Communications,vol.16, no.8, pp.1451-1458.

5. Lennert Jacobs and Marc Moeneclaey,.Exact BER Analysis for Alamoutis Code on

Arbitrary Fading Channels with ImperfectChannel Estimation ,Ghent University,

6. Liang Yang and Jiayin Qin, Performance ofAlamouti Scheme with Transmit AntennaSelection forM-ray Signals

7. Sebastian Caban, Christian Mehlf uhrer,Arpad L. choltz, and Markus Rupp IndoorMIMO Transmissions with Alamouti Space -TimeBlock Codes Vienna University of Technology,Institute of Communications ,Gusshausstrasse25/389, A-1040 Vienna, Austria.

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