Analysis of V-BLAST Techniques for MIMO Wireless Channels with different modulation techniques using Linear and Non Linear Detection

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1 74 Analysis of V-BLAST Techniques for MIMO Wireless Channels with different modulation techniques using Linear and Non Linear Detection Shreedhar A Joshi 1, Dr. Rukmini T S 2 and Dr. Mahesh H M 3 1 Senior faculty Member, SDM College of Engineering Dharwad-582, Karnataka, India 2 Professor, Dept of Telecommunication R V College of Engineering, Bangalore Associate Professor and Chairman, Department of applied Electronics Jnana Bharati, Bangalore 5656 Abstract The rich-scattering wireless channel is capable of huge theoretical capacities. The multiple input multiple output (MIMO) antenna system provides very promising gain in capacity without increasing the use of spectrum, throughput, and power consumption. This is also less sensitivity to fading, hence leading to a breakthrough in the data rate of wireless communication systems. There are many schemes that can be applied to MIMO systems such as space time block codes, space time trellis codes, and the Vertical Bell Labs Space-Time Architecture (V-BLAST). The V-BLAST is an ordered successive cancellation method applied to receiver and at every stage the stream with the highest SNR is decoded. This paper proposes the analysis and performance of general MIMO system V-BLAST architecture with Maximum Likelihood (), Zero-Forcing (), decomposition and Minimum Mean- Square Error (), Ordered Successive Interference Cancellation (OSIC), Interference Suppression (IS) techniques used for linear detectors in fading channels with different antenna selections and digital modulation methods. Keywords: MIMO, OSIC, IS,,, and. 1. Introduction Multi-antenna (MIMO) systems attract significant attention during the last few years due to an extraordinary high spectral efficiency they promise. A key part of the system is the receiver (Rx) signal processing algorithm. The first proposed algorithms were the Diagonal Bell laboratories layered space-time (D-BLAST) and V- BLAST [5-7]. While the D-BLAST achieves the full MIMO capacity, it is more complex as compared to the VBLAST, which, despite its simplicity, achieves a significant portion of the full MIMO capacity. V-BLAST (Vertical-Bell Laboratories Layered Space- Time) is a detection algorithm to the receipt of multiantenna MIMO systems. Its principle is quite simple, first it detects the most powerful signal (Highest SNR), and then it regenerates the received signal from this user from available decision. Then, the signal regenerated is subtracted from the received signal and with this new sign; it proceeds to the detection of the second user's most powerful signal, since it has already cleared the first signal and so forth. This gives less interference to a vector received [1]. In V-BLAST, however, the vector encoding process is simply a demultiplex operation followed by independent bit-to-symbol mapping of each sub stream. No inter-sub stream coding, or coding of any kind, is required, though conventional coding of the individual sub streams may certainly be applied. V-BLAST utilizes a combination of old and new detection techniques to separate the signals in an efficient manner, permitting operation at significant fractions of the Shannon capacity and achieving large spectral efficiencies in the process. [2]. To detect symbols in multiple antenna systems, we previously estimate channel coefficients from the received signal. In procedure of detection, it is generally assumed that the channel matrix estimate has no estimation error. However, in the real system, there exist the channel estimation errors, and they cause the degradation of system performance. As in other detection algorithms, channel estimation errors could bring the significant performance degradation.

2 75 In this proposed work, the V-BLAST detection algorithm with various detection techniques is presented. We assume that the channel estimation errors are independent and identically distributed (i.i.d) Gaussian random variables, which is a reasonable assumption. Using this error model then, we are able to derive better nulling and ordering operations, which minimize the effect of channel estimation errors. Modulation Tx Data TX (a 1 a 2... a M ) ( r 1 r 2... r M ) RX V-BLAST Decoder Rx Data The remainder of this paper is organized as follows: Section 2 presents the proposed V-BLAST system model. Section 3 describes a V-BLAST detection Technique in brief.section 4 introduces our proposed methodology. Section 5 presents simulation results to show the performance of our proposed approaches. Section 6 concludes this paper. 2. System Model The system model considered for this proposed work is Shown in Figure.1. We consider Tx transmit antennas and Rx receive antennas. The channel is AWGN and its time variation is negligible over a frame. The overall channel can be represented as an M X N complex matrix H with the entries of [H] MN = h MN, where h MN is the fading coefficient of the channel from the N th transmit antenna to the M th receive antenna. The received signal at the M th receive antenna is where x N is the symbol transmitted from the N th transmit antenna, and V M is the zero-mean complex Gaussian noise with The overall received signals can be represented as[3] y1 = H x + v (1) Where y1 = [y 1 y 2 y Nr ] T, x = [x 1 x 2 xnt ] T, and v = [v 1, v 2 vnr ] T. Here, ( ) T means the matrix transpose. For the detection of transmitted symbols, the channel matrix H should be estimated at the receiver. The channel estimate can be represented as H = H + ΔH (2) Where Δ H means the channel estimation error. Each elementof Δ H is an i.i.d complex Gaussian random variable with zero-mean and variance σ 2 Δ h / 2 per dimension, which is generally assumed for the channel estimation Figure 1. Proposed VBLAST System model. 3. The V-Blast Technique V-BLAST detection uses of linear combinatorial nulling techniques (such as or ) or non-linear methods like symbol cancellation. Turn by turn each sub stream is considered to be the desired signal and all the others are interferers. Nulling is obtained by linearly weighting (W) the received signals. The MIMO system requires multiple antennas at both ends of radio link. It increases data rate by transmitting independent information streams on different antennas. For V-BLAST, No channel knowledge required at transmitter Main Steps for V-BLAST detection 1. Ordering: choosing the best channel. 2. Nulling: using,,. 3. Slicing: making a symbol decision 4. Canceling: subtracting the detected symbol 5. Iteration: going to the first step to detect the next symbol [4]. The detection process consists of two main operations: 1. Interference suppression (nulling): The suppression operation nulls out interference by projecting the received vector onto the null subspace (perpendicular subspace) of the subspace spanned by the interfering signals. After that, normal detection of the first symbol is performed. 2. Interference cancellation (subtraction): The contribution of the detected symbol is subtracted from the received vector V- BLAST Optimal Ordering Problem in SIC is error propagation is mainly described with the first decode channel is in low SNR, may decode in error and propagate to subsequent decoding process. So OSIC gives better performance. Ordered Successive Interference Cancellation (OSIC)

3 76 Here the main Idea is to detect the symbols in the order of decreasing SNR. It provides a reasonable trade off between complexity and performance (between and Rx). It also achieves a diversity order which lies between N M+ 1 and N for each data stream. 4. Analysis of V-Blast Algorithm The proposed work considers V-BLAST performance analysis with,, -SIC,, -SIC, decomposition detection techniques. The algorithms mentioned in this section consider BPSK and QPSK modulation. The algorithms presented in this proposed work, are divided into 5 different functions. Algorithm 4.1 depicts the modulation selection, signaling and output formats. Algorithm 4.2 depicts demodulation flow for I and Q signals. Similarly the mapping of BPSK and QPSK signals is given in 4.5. The algorithms 4.3 and 4.4 shows the BPSK and QPSK flow for,, (with OSIC) and detection Modulation function. 2. Choose input frame, Index value for Different modulation (ie.1- BPSK, 2-QPSK) and Frame length. 3. Define I as in phase component and Q is quadrature Component. 4. For BPSK modulation chooses inputs as 1 and -1 by Referring to Table 82 of IEEE82.11a. 5. For QPSK modulation chooses inputs as -1 and 1 by Referring to Table 83 of IEEE82.11a. 6. For BPSK, input I =input I (input_frame+1) and output modulation = input I. 7. Define QPSK Output modulation as Ouput modulation = ( 1/ sqrt (2))*(input I + j * Input Q) 6. Stop Demodulation function. 2. Select Input modulation type according to index and Complex values representing constellation points 3. Increase the quantization levels into Input modulation =input modulation* index. 5. Output length=length (input modulation). 6. Divide Real and imaginary parts of in phase and quadrature Components as input_i = real (input_modu). input_q = imag (input_modu). 7. Define output frame, output bit stream (data unit is one bit) Output frame = zeros(1,length input_modu)*index). 8. Applying steps 1 to 8 and switching index 1 for BPSK BPSK_Demodu_I = [ 1]. Frame length f (m) = (m+1)/2 + 1, so I=-1 for 1, I=1 for 2 9. If (input_i > 1) then input_i (index) = 1. else if (input_i < -1) input_i (index) = Extract demodulated output (For BPSK) as Output frame = BPSK_Demodu_I (round ((input_i+1)/2) + 1). 11. For Demodulation of QPSK assume QPSK_Demodu_IQ = [ 1]. 12. With respect to index If (input_i > 1) then input_i (index) = 1. elsif (input_i < -1) then input_i (index) = Repeat Extract demodulated output (For QPSK) as Output frame (in phase) = (round ((input_i + 1) / 2) + 1). output frame (Quadrature) = (round((input_q + 1) /2) + 1) BPSK modulation with MIMO function 2. Assume transmitting and receiving antennas Tx_n = Rx_n =2,4 and so on. 3. Assume index = 4, frame length=12, SNR in db = : 2: Define a 1, a 2. as a1 = modulation (a, index). for reshaping a 2 = reshape (a1,tx_n,frame_length/index/tx_n). 5. Calculate standard deviation as sigma = 1/sqrt (2 * SNR (i) * Tx_n). 6. Add Noise factor (as fading parameter) AWGN_noise=sigma*(randn (Rx_n, frame length/index/tx_n)+ j * randn(rx_n, frame length /index/tx_n)). 7. Determine Channel matrix (With possible antenna selections) H= (randn (Rx_n, Tx_n) +j*randn (Rx_n, Tx_n))/sqrt (2), Equate h=h. 8. Determine Nulling rate (r) as r = H * a 2 (col_index) + AWGN_noise(col_index); 9. For choose best signal (Highest SNR)

4 77 G = pinv (H) ( Pseudo inverse of H) 1. For, the highest SNR signal is G1=inv (H' * H+ sigma.^2 * eye(tx_n))* H'. 11. For Ordered Successive Interference Cancellation, Perform min (sum(abs (G 1 )) for +IC with k 1 min (sum (abs(g)) for +OSIC with k 12. For decomposition, Perform [Q,R]= qr (H). Calculate output vector y= Q' * r. Choose Best signal G 2 = y (Tx_n) / R (Tx_n,Tx_n) - out_mapping 13. Perform = min (abs (G 2 )) for zero columns 14. For declare Count = :1:2 ^ Tx_n 1. Count 1 =zeros (Tx_n, 2 ^ Tx_n). Define a 4 = zeros (Rx_n, 2 ^Tx_n). 15. Determine the size of the determinanant det_zf = G * r. (Determine with Tx_n) and do reshaping. 16.Determine the size of the determinanant det_=g1*r. and do reshaping. 17.For +OSIC, perform H (k 1 (m)) = zeros (Rx_n,1). G = pinv (H). 18.For +OSIC y1=g1 (p1(n)) * r. r = r - b1*h( p1(n)). G1=inv (h' * h+sigma. ^2 * eye (Tx_n)) * h'. 19. Determine BER and SNR for different detection schemes. 2. Plot SNR Vs BER. 21. Stop QPSK modulation with MIMO function. 2. Repeat first 8 steps mentioned in Determine zeros in every frame length and index values for,,, with OSIC and declare as (dec () to dec (5)). 4. Repeat step No 1 to Step No 18 mentioned in Determine Number of errors by following functions dec (i) = reshape (dec (i),1,frame_length /index ). dec (i) = demodulation (dec (i),index). NumErr = sum (dec (i) ~=a). NumErr (i) = sum (abs (reshape(dec1. 1,frame_length)~=a)). Ber (i) = NumErr (i) / frame_length. 6. Determine BER and SNR for different detection schemes. 7. Plot SNR Vs BER. 8. Stop Output Mapping Function 2. Output_mapping= mapping (index) 3. For BPSK, output_mapping= [-1 1]. 4. For QPSK, output_mapping= (1/sqrt (2))*[-1+i -1-i 1+i 1-i]; 5. Stop. 5. Results and Discussions Computer simulations using MATLAB have been conducted to evaluate the performance of proposed algorithm. In simulations, all elements of channel matrix H are assumed to be i.e. zero mean complex Gaussian random variables with unit variance. The SNR is defined as the ratio of the expected received power at each antenna to the noise power. The channel estimation errors are randomly generated from a Gaussian distribution. Figure. 2 illustrates bit error rates (BERs) for various SNRs with Tx = 2, Rx = 2 using BPSK modulation. This figure shows the proposed algorithms have better performance but with OSIC V-BLAST detection algorithm gives far better results when channel estimation errors exist than. In Figure.2, we can see the performance improvement more clearly in high SNR. This is because the effect of channel estimation error becomes more dominant as the SNR increases. Figure.3 shows BER performance with Tx = 4, Rx = 4. In Figure. 3, the performance improvement is more apparent. This is because mutual interfering signals due to channel estimation errors are originally generated from the transmitted signal. As more symbols are transmitted simultaneously, there are more interfering signals. Therefore, if we do not consider the influence of channel estimation errors, the performance degradation becomes more significant in the system with more spatial streams. As the SNR increases, the interference caused by channel estimation errors becomes dominant and the interferenceplus noise level becomes nearly constant. The conventional with OSIC algorithm only considers

5 78 the noise power and ignores the interference when generating the nulling weight Tx = 2,Rx = 2,BPSK modulation +IS Tx = 2,Rx = 2,BPSK modulation +IS Figure 4. BER Performance of V-BLAST (Without ) Figure 2. BER Performance of V-BLAST with Tx=Rx=2. For our best analysis purpose, we deactivate related functions of the ruuning mat lab program and only considering estimation error performance of other detection algorithms. In Figure 4 and Figure 5, we can clearly demonstrate the Interference suppression from and in more clear way. From these figures the decomposition gives optimal results Tx = 4,Rx = 4,BPSK modulation +IS 1-4 Figure 3. BER Performance of V-BLAST with Tx=Rx=4. In a similar manner, we carry out the BER performance results for QPSK modulation. Figure. 6 illustrates bit error rates (BERs) for various SNRs with Tx = 2, Rx = 2. This figure shows the proposed algorithms have better performance but with OSIC V-BLAST detection algorithm gives far better results when channel estimation errors exist than Tx = 4,Rx = 4,BPSK modulation +IS Figure 5. BER Performance of V-BLAST (Without ) Tx = 2,Rx = 2,QPSK modulation +IS Figure 6. BER Performance with Tx=Rx=2 for QPSK. Figure.7 shows BER performance with Tx = 4, Rx = 4. In Figure. 7, the performance improvement with different V- BLAST detection algorithms is clearly depicted when

6 79 More antennas are added. Figure.7 gives good improvement results. Comparing to BPSK, QPSK gives still better results. Again for more clarity, we skip part and display the comparison of other detection algorithms through Figure 8 and Figure Tx = 4,Rx = 4,QPSK modulation +IS Tx = 4,Rx = 4,QPSK modulation +IS Figure 9. BER Performance with Tx=Rx=4 for QPSK. 1-4 Figure 7. BER Performance with Tx=Rx=4 for QPSK Tx = 2,Rx = 2,QPSK modulation +IS Figure 8. BER Performance with Tx=Rx=2 for QPSK. 6. Conclusion Based on bit error rate, we show the performance of these receiver schemes indicates that the ordered OSIC detector based receiver with or combined with symbol cancellation and optimal ordering to improve the performance with lower complexity and compare the computational complexity of these schemes. The different modulation schemes definitely help in analyzing these detection algorithms. The Maximum-Likelihood () detection most effectively balances the accuracy of symbol detection with any SNR values. Acknowledgments Authors want to express their sincere thanks to their family members, R V Centre for Cognitive Technology Bangalore, Department of Applied Electronics, Bangalore University, Bangalore and SDMCET Dharwad. References [1] V-BLAST architecture from Bell Labs, wikipedia. [2] P. W. Wolniansky, G. J. Foschini, G. D. Golden, R. A. Valenzuela. V-BLAST: An architecture for realizing very high data rates over the rich scattering. Bell Laboratories, Lucent Technologies, Holmdel, NJ [3] Kyungchun Lee and Joohwan Chun. Symbol Detection in V- BLAST Architectures under Channel Estimation Errors. IEEE Transactions on Wireless Communications, Vol. 6, No. 2, February 27. [4] Shreedhar. A. Joshi, Dr. Rukmini T S, Dr.Mahesh H M. Performance analysis of MIMO Technology using V-BLAST Technique for different linear Detectors in a slow fading channel. IEEE International Conference on Computational conference on Computational Intelligence and Computing Research (ICCIC 21) /1. p [5] G.J. Foschini et al, Analysis and Performance of Some Basic Space-Time Architectures, IEEE Journal Selected Areas Comm. 21, N. 3, pp , April 23. [6] G.J Foschini, Layered space-time architecture for wireless communication in a fading environment when using multiple antennas, Bell Lab. Tech. J., vol. 1, N. 2, pp , [7] G.J Foschini et al, Simplified Processing for High Spectral Efficiency Wireless Communication Employing Multielment Arrays, IEEE Journal on Selected Areas in Communications, v.17, N. 11, pp , Nov