# Performance Study of MIMO-OFDM System in Rayleigh Fading Channel with QO-STB Coding Technique

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3 The idea behind the MIMO is that the signals on the transmit antennas at one end and the receiver antennas at the other end are combined in such a way that the quality BER or the data rate (bits/sec) of the communication for each MIMO user will be improved. This can be used to increase the network s quality of service [2]. The heart of MIMO systems is space time signal processing in which time (the natural dimension of digital communication data) is complemented with spatial dimension which is inbuilt in the use of multiple spatially distributed antennas. Thus it can be said that MIMO system is an extension of popular smart antennas. The key future of MIMO is ability to exploit multipath propagation for the benefit of user. The major advantages of MIMO system are high data rate transmission, robust communication, making use of variety of signal paths, higher spectral efficiency, reduction in bit error rate thereby increase in SNR. However, there are several limitations to MIMO system. Such as how to obtain perfect channel state information (CSI) accurately and promptly, system complexity increases with the increase in order of MIMO system, multipath character of the environment causes the MIMO channel to be frequency-selective. 2.3 Rayleigh Fading Channel Constructive and destructive nature of multipath components in flat fading channels can be approximated by Rayleigh distribution if there is no line of sight (NLOS) which means when there is no direct path between transmitter and receiver. The received signal can be simplified to: (3) r (t ) [s(t ) h(t )] n(t ) where h(t) is the random channel matrix having Rayleigh distribution and n(t) is the additive white Gaussian noise. The Rayleigh distribution is basically the magnitude of the sum of two equal independent orthogonal Gaussian random variables and the probability density function (pdf) given by: r2 r 2 p ( r ) e 2 2 (4) 0 r where 2 is the time-average power of the received signal [7]. III. QUASI ORTHOGONAL SPACE TIME BLOCK CODE It is proved in [6] that a complex orthogonal design and the corresponding space time block code which provides full diversity and full transmission rate is impossible for more than two antennas. So authors of [6] proposed space time block codes which achieve half of the full transmission rate for any number of transmission antennas. Therefore a code with 3/4 of the full transmission rate for the specific cases of three and four transmit antennas was proposed. So in [7], author proposed a different strategy for designing of space time block codes. So author designed rate 1 codes that provide half of the maximum possible diversity. The decoder of the new codes processes pairs of transmitted symbols instead of single symbols. Author proposed structures that are not orthogonal designs and, therefore, cannot separate all transmitted symbols from each other at decoder. Instead, in proposed coding technique, the transmission matrix columns are divided into groups. While the columns within each group are not orthogonal to each other, different groups are orthogonal to each other. Such a structure is called as quasi-orthogonal design. An example of a full-rate full-diversity complex space time block code is Alamouti scheme [5], which is defined by the following transmission matrix: x1 A12 x 2 x2 x1 (5) Here the subscript 12 is used to represent the indeterminate x1 and x2 in transmission matrix. Now, let us consider the following space time block code for N=M=4: [7] 192

4 A12 A 34 A x1 x2 x3 A34 x2 x1 x4 A12 x3 x4 x1 x4 x3 x2 x4 x3 x2 (6) x1 Here a diversity of 2M is achieved while the rate of the code is one. The proposed matrix for N=M=8 antenna s is given as: s2 s s 1 2 s s 4 3 s s3 4 s5 s6 s6 s5 s8 s7 s8 s7 s3 s4 s4 s3 s2 s5 s6 s7 s6 s5 s8 s7 s8 s5 s2 s7 s8 s8 s7 s2 s6 s3 s8 s7 s2 s4 s5 s6 s6 s5 s3 s4 s4 s3 s2 s8 s7 s6 s5 s4 s3 s2 (7) IV. SIMULATION RESULTS The system discussed above has been designed, simulated using MATLAB and results are shown in the form of SNR vs. BER, MSE and Throughput. For simulation of the system along with OFDM different antenna s such as 2x2, 4x4, 6x6 and 8x8 are considered for different digital modulation techniques like BPSK, QPSK, QAM-8, QAM-16, QAM-32 andqam-64. A quasi-orthogonal space time block coding technique is used for MIMO. For the simulation of system the medium considered is Rayleigh channel. 4.1 BER vs SNR: Fig. 3. BER vs. SNR performance of system with BPSK for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 4. BER vs. SNR performance of system with QPSK for 2x2, 4x4, 6x6 and 8x8 antenna 193

5 Fig. 5 BER vs. SNR performance of system with 8QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 8. BER vs. SNR performance of system with 64QAM for 2x2, 4x4, 6x6 and 8x8 antenna 4.2 Mean Square Error (MSE): Fig. 6. BER vs. SNR performance of system with 16QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 7. BER vs. SNR performance of system with 32QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 9. MSE performance of system with BPSK for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 10. MSE performance of system with QPSK for 2x2, 4x4, 6x6 and 8x8 antenna 194

6 Fig.11. MSE performance of system with8-qam for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 14. MSE performance of system with 64-QAM for 2x2, 4x4, 6x6 and 8x8 antenna A. Throughput: Fig. 12. MSE performance of system with 16-QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 13. MSE performance of system with 32-QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 15. Throughput performance of system with BPSK for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 16. Throughput performance of system with QPSK for 2x2, 4x4, 6x6 and 8x8 antenna 195

7 Fig. 17. Throughput performance of system with 8QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 18. Throughput performance of system with 16QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 19. Throughput performance of system with 32QAM for 2x2, 4x4, 6x6 and 8x8 antenna Fig. 20. Throughput performance of system with 64QAM for 2x2, 4x4, 6x6 and 8x8 antenna V. CONCLUSIONS From the results obtained it can be concluded that combined MIMO-OFDM system provides much better results as compared with alone MIMO or OFDM system. Also it is observed that BER, MSE and throughput performance of system is improved for higher antenna s. It can be also noted that, as compared to lower order modulation schemes, higher order modulation schemes provides better results for all parameters considered for simulation. REFERENCES [1] D. Gesbert, M. Shafi, D. Shiu, P. J. Smith and A. Naguib From Theory to Practice: an Overview of MIMO Space Time Coded Wireless Systems, IEEE Journal on Selected Areas in Communications, Vol.21, No.3, April 03. [2] S. Catreux, P.F. Driessen, and L. J. Greenstein, Data Throughputs Using Multiple Input Multiple Output (MIMO) Techniques in a Noise Limited Cellular Environment, IEEE Transactions On Wireless Communications, Vol. 1, No. 2, April

8 [3] Luis Miguel Cortes-Pena, MIMO Space-Time Block Coding (STBC): Simulations and Results, Design Project: Personal And Mobile Communications, Georgia Tech (Ece6604), Pp. 1-8, April 2009 [4] L. Kansal, A. Kansal and K. Singh Performance Analysis of MIMO-OFDM System Using QOSTBC Code Structure for M-QAM, Canadian Journal on Signal Processing Vol. 2, No. 2, pp. 2-15, May [5] S. Alamouti, A simple transmit diversity technique for wireless communications, IEEE Journal on Selected Areas Comm., vol.16,no. 8, pp , October [6] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space-time block codes from orthogonal designs, IEEE Transactions on Information Theory, vol. 45, pp , July [7] H. Jafarkhani, A quasi-orthogonal space time block code, IEEE Transaction on Communication., vol. 49, no. 1,pp. 1 4, January 2001.V. Tarokh, N. Seshadri, and A.R. Calderbank, Space-Time Codes for High Data Rate Wireless Communications: Performance Criterion and Code Construction, IEEE Transactions on Information Theory, vol. 44, no. 2, pp , March [8] J. J. V. de Beek, O. Edfors, M. Sandell, S.K. Wilson and P. O. Borjesson, On channel estimation in OFDM systems, In proceedings of 45th IEEE Vehicular Technology Conference, Vol. 2, Issue 7, pp , (Chicago, IL)1995. [9] B. R. Saltzburg, Performance of an efficient parallel data transmission systems, IEEE Trans. on Comm. Tech., pp , Dec

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