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World Journal of Science and Technology 2011, 1(8): 125-131 ISSN: 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 1 Department of E & C, SDMCET Dharwad, India 2 Department of Telecommunication, R V College of Engineering, & Fellow IEEE Member, Bangalore-69, India 3 Department of applied Electronics, Bangalore University, Bangalore, India Correspon
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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 METHODWITH DIGITAL MODULATION TECHNIQUES Shreedhar A Joshi #1 , T S Rukmini #2 and Mahesh H M #3   1 Department of E & C, SDMCET Dharwad, India 2 Department of Telecommunication, R V College of Engineering, & Fellow IEEE Member,Bangalore-69, India 3 Department of applied Electronics, Bangalore University, Bangalore, IndiaCorresponding author e-mail: Shreedhar.j@rediffmail.com  Abstract Multiple Input Multiple Output (MIMO) systems with multiple antenna elements at both Transmitter and Receiverends are an efficient solution for future wireless communications systems. They provide high data rates byexploiting 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 proposedwork presents a comprehensive performance analysis of orthogonal space-time block codes (OSTBCs) withtransmit antenna selection under uncorrelated Rayleigh fading channel employing Alamouti’s code. The transmittedsymbols belong to BPSK, QPSK and Quadrature amplitude modulation (QAM) with partial CSI. The numericalevaluation 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 StateInformation (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 reliablecommunication 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 of this enormous capacity increase, such systemsgained a lot of interest in mobile communicationresearch [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 thereplicas will not undergo severe fading. A diversitytechnique makes use of an important property of wireless 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, for e.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  World Journal of Science and Technology | www.worldjournalofscience.com | 2011 | 1(8): 125-131   are equal to the number of transmit antennas. Thesecode symbols are generated by the STBCs can bedivided into two main classes, namely, OSTBCs andNon-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 n r  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 timeinstant the complex signals {s 1 , s 2 , · · · s n t } aretransmitted via n t transmit antennas, then n r  thereceived antenna j can be expressed as: Fig 1. MIMO model with n t transmitantennas and n r receive antennas. n t y i = ∑ h i,j S  j + n i ( 1)    j = 1Where n i is a noise term. Combining allreceive signals in a vector y, then (1) can be easilyexpressed in matrix formy = Hs + n. (2)Where y is the n r  × 1 receive symbol vector,H is the n r  × n t MIMO channel transfer matrix givenbyH = (3)s is the n t × 1 transmit symbol vector andn is the n r  × 1 additive noise vector. Note that thesystem model implicitly assumes a flat fading MIMOchannel, i.e., channel coefficients are constant duringthe transmission of several symbols. Flat fading, or frequency 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 meansE {s s H } = P S I S (4)Where Ps denotes the mean signal power of 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 for two transmit antennas [4]. The information bits arefirst modulated using a digital modulation scheme,then the encoder takes the block of two modulatedsymbols s 1 and s 2 in each encoding operation andhands it to the transmit antennas according to thecode matrixS = (5)The first row represents the firsttransmission period and the second row representsthe second transmission period. During the firsttransmission, the symbols s 1 and s 2 are transmittedsimultaneously from antenna one and antenna tworespectively. In the second transmission period, thesymbol -s *2 is transmitted from antenna one and thesymbols *1 from transmit antenna two. It is clear that 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:  World Journal of Science and Technology | www.worldjournalofscience.com | 2011 | 1(8): 125-131   ss H === (I 2 (6)Where I 2 is a (2 X 2) identity matrix. Thisproperty enables the receiver to detect s 1 and s 2 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 h 1 (t) for transmit antenna oneand h 2 (t) for transmit antenna two. Assuming that thefading is constant across two consecutive transmitperiods of duration T, expresses ash 1 (t) = h 1 (t + T) = h 1 = |h 1 |e jθ1 h 2 (t) = h 2 (t + T) = h 1 = |h 2 | e jθ2 , (7)Where |h i | and θi , 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 asr  1 = s 1 h 1 + s 2 h 2 + n 2 r  2 = -s *   2 h 1 + s *   1 h 2 + n 2 (8)Where r  1 and r  2 are the received signals attime t and t + T respectively. n 1 and n 2 are complexrandom variables representing receiver noise andinterference. This can be written in matrix form as:r = Sh + n (9)Where h = [h 1 , h 2 ] T is the complex channelvector and n is the noise vector at the receiver.Conjugating the signal r  2 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 = [r  1 ,r  2 ] T has been introduced. Hv will be termed theequivalent virtual MIMO channel matrix (EVCM) of theAlamouti STBC scheme. It is given byH V = (12)For MIMO channel matrix, the rows andcolumns of the virtual channel matrix are orthogonal:H vH H v = H v H vH  =   (h 12  +h 22 ) I 2 = h 2 I 2 (13)Where I 2 is the (2 X 2) identity matrix. Linear Signal Combining and MaximumLikelihood (ML) Decoding of the Alamouti Code If the channel coefficients h 1 and h 2 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 (ˆs 1 , ˆs 2 ) from the signal modulationconstellation that minimizes the decision metric asd 2 (r  1 , h 1 s 1 + h 2 s 2 ) + d 2 (r  2 − h 1 s   * 2 + h 2 s   * 1 )= |r  1 − h 1 s 1 − h 2 s 2 | 2 + |r  2 + h 1 s   * 2 − h 2 s   * 1 | 2 (14)Using a linear receiver, the signal combiner at the receiver combines the received signals r  1 and r  2  as follows= h 1  * r  1 + h 2 r    * 2 = ( |h 1 | 2 + |h 2 | 2 ) s 1 + h 1* n 1 + h 2 n *2 = h 2  * r  1 – h 1 r    * 2 = ( |h 1 | 2 + |h 2 | 2 ) s 1 + h 2* n 1 + h 2  n *2. (15)Hence ˜s 1 and ˜s 2 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 s 1 and s 2 namely [5]for detecting s 1 , and(16)for detecting s 2 .  World Journal of Science and Technology | www.worldjournalofscience.com | 2011 | 1(8): 125-131   The Alamouti transmission scheme is asimple transmit diversity scheme which improves thesignal quality at the receiver using a simple signalprocessing algorithm at the transmitter. The diversityorder can be obtained by applying maximal ratiocombining (MRC) with one antenna at the transmitter and two antennas at the receiver where the resultingsignals at the receiver are:r  1 = h 1 s 1 + n 1  (17)r  2 = h 2 s 2 + n 2 (18)and the combined signal is= h 1 * r  1 + h 2 * r  2 = (|h 1 | 2 + | h 2 | 2 ) s 1 + h 1 *n 1 + h 2 * n 2 . (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 for the BPSK modulation technique is shown in Figure.2.Here symbols are mapped into BPSK and transmittedwith alamouti technique. Figure.3. depicts theprocedure for alamouti and No alamouti techniquewith the BPSK modulation. StartDetermine No of symbols and SNRGenerate random binary sequence of +1’s and -1’s(BPSK)Group them into pair of two symbolsCode the mapped BPSK symbols to Alamouti Space Time code ,and sendwith antenna selection and Multiply the symbols with the channeland then add white Gaussian noise.Equalize the received symbolsPerform hard decision decoding and count the bit errorsStopRepeat for multiple values of and plot the simulation and theoretical resultsThis is done for transmitting and Receiving antennas   Fig 2. Flow chart for STBC techniquewith BPSK modulation StartDetermine No of bits to be transmitted ,SNR in dB.Mapping these symbols to BPSK modulation.For generating the data , splitting the data intotwo vectors (first transmition, secondtransmition in time) for Alamouti method STBCTransmit data through channel with SVD method by addingNoise receive the data, Plot SER Vs SNR for Alamouti methodRepeat some steps above but transmit Symbols withoutAlamouti method and Plot SER Vs SNRStop   Fig 3. Flow chart for alamouti/ Noalamouti STBC technique with BPSKmodulation 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. StartDetermine number of transmit and receive antennas, SNRGenerate 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 symbolsMapping transmitted bits into QPSK symbols with 4 constellation pointsForm the channel matrix, with MRC generateEstimates and received symbols add Noise factorGenerate plots with antennaSelections and BER Vs SNRStop   Fig 4. Flow chart for QPSK STBC withalamouti 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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