Performance Analysis of Wireless MIMO System using Precoded OSTBC

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Performance Analysis of Wireless MIMO System using Precoded OSTBC

Rahul Somani

    1. ech. Student, ECE Department Shrinathji Institute of Technology & Engineering

      Nathdwara, India rahsom58@gmail.com

      Mahesh Kumar Porwal

      Associate Professor, ECE Department Shrinathji Institute of Technology & Engineering Nathdwara, India


      Abstract The demand for mobile communication systems with high data rates and improved link quality for a variety of applications has dramatically increased in current years. New concepts and techniques are necessary in order to cover this huge demand. MIMO is one of the prime technologies that can achieve the goal of high speed demand. As MIMO systems utilizes multiple no of antennas both at the transmitter and receiver Therefore the necessary requirement to reduce the fading resulting from signal fluctuations in the channel is Diversity. STBC is a MIMO transmit strategy which exploits transmit diversity and high reliability. Orthogonal space-time block codes (OSTBC) achieve full diversity when a linear receiver, such as, zero-forcing (ZF) or minimum mean square (MMSE), is used. This paper involves a transmitted signal consists of a precode followed by an orthogonal space-time block code (OSTBC). A new design criterion and a corresponding design method of precoders are proposed which shows comparison of bit error rate (BER) performance of OSTBC and Precoded OSTBC in Zero Forcing and MMSE equalization techniques.

      Keywords OSTBC, Precoding, BER, ZF, MMSE.


        Multiple-Input multiple-output (MIMO) wireless channels have considerably higher capacities than traditional channels. Fading makes it extremely difficult for the receiver to recover the transmitted signal unless the receiver is provided with some form of diversity, i.e. replicas of the same transmitted signal with uncorrelated attenuation. In fact, diversity combining technology has been one of the most important contributors to reliable wireless communications. Consider transmit diversity by deploying multiple antennas at the base station. Moreover, in economic terms, the cost of multiple transmit antennas at the base station can be amortized over numerous mobile users. Hence transmit diversity has been identified as one of the key contributing technologies to the downlinks of 3G wireless systems such as W-CDMA and CDMA2000.We have analyzed the full diversity condition in MIMO to achieve the better BER performance. We take OSTBC (with 2, 4, and 8) transmit antenna to show that BER performance will improve when antenna size improved. But the cost of device improve make it practically impossible and power consumption will more for mobile device, so alternate is using same MIMO with turbo code so same will give better result, with two antenna.

        1. Transmit Diversity

          We now investigate a different goal, using the multiple antennas to achieve reliability. Here we focus on transmit diversity. So far, we have developed the capacity of MIMO systems in the case of the channel being known at the transmitter and receiver and in the more practical case of the channel known at the receiver only. This answers the question, How fast can data be transmitted? i.e., what is the theoretical maximum data rate that can be achieved in a MIMO system. When there is more transmitter than receiver antennas, this is called TX diversity. The simplest scenario uses two TX and one RX antenna. In figure 1, the same data is transmitted redundantly over two antennas. This technique has the advantage that the multiple antennas and redundancy coding is moved from the mobile unit to the base station, where these technologies are easier and cheaper to implement [1].



          Figure 1: Transmit diversity

        2. Receive Diversity

        Receiver diversity uses more antennas on the receiver side than on the transmitter side. The easiest scenario consists of two RX and one TX antenna. Figure 2 shows the antenna configurations of two RX and one TX antenna. Receive diversity are widely used in wireless communication systems; it can be achieved by receiving redundant copies of the same signal. The idea behind receive diversity is that each antenna at the receive end can observe an independent copy of the same signal [1].



        Figure 2: Receive diversity


        1. Alamouti STBC

          It is simple method for achieving spatial diversity with two

        2. Orthogonal Space-Time Block Codes (OSTBC)

          The transmit diversity scheme designed by Alamouti can be used only in a system with two transmit antennas. It turns out that this technique belongs to a general class of codes named SpaceTime Block Codes or, more precisely, Orthogonal STBCs, since they are based on the theory of orthogonal designs. The authors of [2] introduced the theory of generalized orthogonal designs in order to create codes for an arbitrary number of transmit antennas. The general idea behind STBCs construction is based on finding coding matrices X that can satisfy the following condition:

          . = . 2 .

          transmit antennas. The scheme is as follows: Consider that we have a transmission sequence, for example



          {1 , 2 , 3 ,……., }

          In this equation, is the Hermitian of X, p is a constant, is the identitymatrix of size × , represents the

          In normal transmission, we will be sending x1 in the first time slot, x2 in the second time slot, x3 and so on.








          number of transmit antennas, and is the number of symbols

          transmitted per transmission block in X. The generalized theory of orthogonal design is exploited to provide codes that satisfy the above equation.

          The orthgonality property of STBCs is reflected in the fact that all rows of X are orthogonal to each other. In other words, the sequences transmitted from two different antenna elements are orthogonal to each other for each transmission block. For real signal, it is possible to reach full rate. However, it has been proven in [2] that this statement is false for two- dimensional constellations, i.e., complex signals. The encoding and decoding approaches follow the pattern described in Alamoutis scheme. For complex signals, the theory of orthogonal designs can be used to generate coding matrices that achieve a transmission rate of 1/2 for the cases of 3 and 4 transmission antennas:

          1 2 3 4 1 2 3 4


          = 2


          4 3


          1 x2

          2 2

          1 4 3


          3 4 1



          2 x

          3 4 1 2


          1 2 3 4 1 2 3 4


          = 2 1 4 3 2 1

          4 3


          2 3 4



          3 4 1 2

          4 3 2 1

          Figure 3: (a) Transmit, (b) Receive Alamouti STBC coding


          However, Alamouti suggested that we group the symbols into groups of two. In the first time slot, send x1 and x2 from the first and second antenna. In second time slot send x2 and x from the first and second antenna. In the third time slot send x3 and x4 from the first and second antenna. In fourth

          4 3 2 1

          Using the theory of orthogonal design to construct STBCs is not necessarily the optimal approach. There exist some sporadic STBCs that can provide a transmision rate of 3/4 for schemes of either 3 or 4 transmit antennas [4].


          time slot, send x and x3 from the first and second antenna and so on. Notice that though we are grouping two symbols,



          3 = 2




          0 ,

          4 3


          we still need two time slots to send two symbols. Hence, there 0 1 2

          is no change in the data rate. This forms the simple


          0 2 3

          explanation of the transmission scheme with Alamouti Space







          Time Block coding. Alamouti scheme is an example of a full-

          4 2 3


          rate full-diversity complex spacetime block code [3].




          2 0

          It is important to notice that the channel coefficients must remain constant during the transmission of a block of coded symbols X [5].

          , = with constant . When the constraint is not imposed, the above optimum solution is not unique,


          because || ||2 = || ||2 .Where Z is a unitary

        3. Precoded OSTBC

          Consider the MISO system with

          antennas, that

          matrix. The unconstrained optimum solution of equation (7) can be obtained by singular value decomposition (SVD) of

          is h C


          . Let C C


          denote a space-time codeword

          channel = , where the diagonal entry of S is in

          descending order. It is shown that the optimum solution of

          with a length of M, which is represented as

          C = [c1c2 cT ]

          above equation is given by the leftmost M columns of V, that is,


          = [ . . ]


          ck = [ck,1ck,2 ck,M ]T, k = 1,2, . . , T and M NT

          1 1



          In the precoded OSTBC systems, the space-time codeword C is multiplied by a precoding matrixW CNT ×M , which is chosen from the codebook.

          F = {W , W , W , W }

          Since is unitary, = 1, = 1,2, , where denotes the largest eigenvalue of the matrix . In case that a channel is not deterministic, the following criterion is used for the codebook design:

          || ||2 ||||2

          1 2 3 L



          The objective is to choose an appropriate codeword that improves the overall system performance such as channel capacity or error performance. Assuming that NT channels remain static over T, the received signal y C1×T can be

          Where the expectation is with regards to the random channel H. in equation (9) follows from equation (8) for the given channel H.

          The above expected value in equation (9) is upper-bounded as

          expressed as,




          y =


          hWC + z




          1 2


          In above equation the length of each vector is NT . The probability of codeword error can be derived as follows:



          Since 2 is given, the codebook must be designed so as

          For a given channel and precoding matrix W, we consider the pair wise codeword error probabilityPr (Ci Cj |H). The upper bound of the pair wise error probability is given as

          ||, ||2

          to minimize



          in equation (10).


          Pr Ci

          Cj H = Q



        || ,




          1. Zero Forcing Equalizer

            Zero Forcing Equalizer is a linear equalization algorithm used in communication systems; it inverts the frequency

            response of the channel. The name Zero forcing corresponds

            Where is the signal-to-noise ratio (SNR), given as

            = /0 and, is the error matrix between the codewords and which is defined as , = for a given STBC scheme. From equation above we see that

            || , ||2 needs to be maximized in order to minimize the pairwise error probability. This leads us to the following codeword selection criterion:

            to bringing down the Inter Symbol Interference (ISI) to zero in a noise free case. This will be useful when ISI is more predominant when comparing to the noise.

            Consider a 2x 2 MIMO channel, the received signal on the first receive antenna is,

            = a r g ||, 2




            = 11


            + 12


            + 1

            = 11



            2 + 1



            = a r g ( , )


            = a r g ( )

            The received signal on the Second receive antenna is,

            = + + = 1

            2 21 1 22 2 2 21 22 2 + 2



            The equation can be represented in matrix notation as follows:

            = a r g ||||



            11 12



            = +

            In the course of deriving equation (7), we have used the fact that the error matrix of OSTBC has the property of

            2 21 22 2 2


            Equivalently, Y = HX + N

            Where, Y = Received Symbol Matrix. H = Channel matrix.

            X = Transmitted symbol Matrix. N = Noise Matrix.

            To solve for x, we need to find a matrix W which satisfies WH = I. The Zero Forcing (ZF) detector for meeting this constraint is given by,

            • Number of bits or samples in each data packet (Ns) =200

              = ( )1



              W – Equalization Matrix and H – Channel Matrix

              This matrix is known as the Pseudo inverse for a general m x n matrix where

              11 21

              11 21

              Figure 4: Comparison of BER performance of OSTBC without precoding


              and with precoding in ZF

              12 22 12 22

              11 2 + 21 2 11 12 + 21 22

              Figure 4 shows the performance of OSTBC and Precoded

              = 12


              + 22



              2 + 22



              OSTBC system with Zero Forcing equalization technique. At SNR=15dB, BER performance of Precoded OSTBC is 102.4 while without precoding it is 102.1. It is clear that precoded OSTBC performs better than normal OSTBC

              Zero forcing equalizer tries to null out the interfering terms when performing the equalization while doing so, there can be amplification of noise. Hence Zero forcing equalizer is not the best possible equalizer.

          2. MMSE Equalizer

        Minimum Mean Square Error (MMSE) approach alleviates the noise enhancement problem by taking into consideration the noise power when constructing the filtering matrix using the MMSE performance-based criterion.

        The MMSE approach tries to find a coefficient W which minimize the criterion,


        On solving

        = + 0 1



        Figure 5: Comparison of BER performance of OSTBC without precoding and with precoding in MMSE

        Figure 5 shows the performance of OSTBC and Precoded OSTBC system with MMSE equalization technique. At

        When comparing to the equalization, apart from the 0 team both the equations are comparable. When the noise term is zero, the MMSE equalization reduced to ZF equalizer.


        The proposed methodology is implemented in MATLAB software.

        Simulation Parameters:

          • Modulation scheme M = 2 (BPSK Modulation)

          • Simulation SNR ranges (SNR_db) = 0:3:21

          • Sampling rate of message sequence (Fd) =1

          • Sampling rate of the modulated signal (Fs) =1

          • Number of packets of data (N) =100

        SNR=15dB, BER performance of Precoded OSTBC is 102.6 whle without precoding it is102.2. It is clear that Precoded OSTBC performs better than normal OSTBC system.


The most prominent space-time block codes are OSTBCs. The approach in this paper has been to isolate the analysis of precoded MIMO systems. The proposed precoded OSTBC have a layered structure, which is implemented in the simplest Grassmannian precoding. Simulation results shows comparison of BER performance between OSTBC and Precoded OSTBC for Zero Forcing and MMSE equalization techniques. And finally it is found that the Precoded OSTBC shows better BER.


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