International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013 Riciain Channel Capacity Comparison Between (8X8) And (4x4) MIMO Vivek Mankotia, Ankush Kansal ME student THAPAR UNIVERSITY PATIALA INDIA , Assistant Professor, ECED THAPAR UNIVERSITY PATIALA INDIA ABSTRACT The growth demand of Multimedia application services and growth of contents of wireless application lead to increasing interest to high speed communication. Multiple input and multi output system are today considered as one of most important research area of wireless communication. The need of wireless multimedia application require need of higher data rate. In this paper comparison of Rician channel capacity has been used as measure for the efficiency of MIMO (8X8) and (4x4) system. We have calculated the Rician channel capacity with CSI or without CSI at transmitter with simulating MATLAB. Keywords MIMO (Multi input Multi output), CSI(channel state Information),MISO, SIM0 11. SYSTEM MODEL We have [1] consider a MIMO system with transmit array of antenna and receive array of antenna as shown in figure 1 . The transmitted matrix is × 1 column matrix X where is ith component which is transmitted from ith antenna. If channel is unknown at the transmitter side we ⁄ . is given to assume [2] that equal power each transmitter antenna. 1. INTRODUCTION MIMO system use array of multiple antennas at both transmitter and receiver end. In the case of MIMO system capacity increase and BER reduces. Channel capacity is defined as the maximum rate at which data can be transmitted with small error probability. The capacity of MIMO channels is calculate for the Rayleigh scenario. But in practice, MIMO channels do not always follow the Rayleigh fading condition. Actually, there is a line-of-sight (LOS) path between the transmitter and the receiver, and in such conditions, the channel is represented by the Rician fading model. Mathematically, the random channel matrix in a MIMO Rician fading channel is a complex Gaussian matrix with a nonzero mean matrix, The Rayleigh fading model is a special case of the Rician fading model by setting the mean to zero. ISSN: 2231-5381 T R A N S M I T T E R R E C E I V E R CHANNEL FIGURE 1 MIMO SYSTEM Where is the power across transmitter irrespective number of antennas where is a × identity matrix. The transmitted signal http://www.ijettjournal.org Page 2589 International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013 bandwidth is so small that channel is assumed to flat. The channel matrix H is a × complex matrix. The component ℎ , of the matrix is the fading coefficient from jth transmit antenna to ith receive. If we suppose that channel matrix is known at only receiver side not at transmitter side. The channel matrix at receiver can be estimated by training sequence. Noise at the receiver is another column of size × 1 , denoted by n. For a deterministic channel as ∑ |ℎ , | = , i = 1 , 2 ,3 … DIFFRACTION LOS Transmitter receiver (1) 111. MIMO CHANNEL CAPACTY For two random vector x and y the mutual information is defined as I(x,y) = H(y) – H(y|x) (2) Where H(y|x) the conditional entropy. ( ( | ))] H( x/y) = -E[ Fig. 2 WAVE PROPAGATION (3) For a linear complex model = + (4) The mutual information is given as I(y,x|H) =log det + (5) The Shanon capacity is the maximum mutual information between received vector and transmitted vector C(H)= det + (6) When full transmitter CSI and receiver CSI are available, the capacity of the MIMO system is maximum. SCATTERING LOS (line of sight) 1V. RICIAN CHANNEL There is line-of-sight (LOS) path between the transmitter and the receiver, and in such conditions, the channel is represented by the Rician fading model. We can express H in matrix notation as[9] H=c + (7) Where the specular [3] and scattered components of H are denoted by superscripts, c>0, d >0 and + = 1. is a matrix of unit entries. If there is no correlation at the transmitter or at the receiver side then the entries of are independent usually denoted by . REFLECTION ISSN: 2231-5381 http://www.ijettjournal.org Page 2590 International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013 • If there is correlated fading then the matrix can be modeled as [5],[6] UNCORRELATED CHANNEL 100 90 = ∗ ∗ (8) Where and are the correlation matrix at the transmitter and at the receiver side . The correlation matrix R is defined[4] ≤ = ∗ > (9) H(correlated)[7][8] • • • ∗H1+ = ∗ ∗ 80 70 capacity(bits /s /Hz) • • Nt=Nr=8;k=0 Nt=Nr=8;k=5; Nt=Nr=8; k=10 Nt=Nr=8;k=very large; 60 50 40 30 ∗ 20 (10) 10 0 v. RESULTS 0 5 10 15 SNR in dB 20 25 UNCORRELATES CHANNEL Fig. 4 Rician chaneel capacity (8X8) when transmitter know the CSI. 45 Nt=Nr=4;k=0; Nt=Nr=4;k=5; Nt=Nr=4; k=10; Nt=Nr=4;k=VERY LARGE; 40 TABLE 1 FOR MIMO(4X4) ( SNR IN db) K SNR=15 CAPACITY 0 24 bps/Hz 5 19 ‘’ 10 17 SNR=25 CAPACITY 37 bps/Hz 30 28 SNR=30 CAPACITY 44 bps/H 37 35 20 TABLE 11 15 FOR MIMO(8X8) ( SNR IN db) K SNR=15 SNR=25 CAPACITY CAPACITY SNR=30 CAPACITY 0 5 10 92 bps/H 78 72 35 c a p a c it y (b it s / s / H z ) 30 25 10 5 0 0 5 10 15 SNR in dB 20 25 30 Fig. 3 Rician chaneel capacity (4X4) when transmitter know the CSI ISSN: 2231-5381 53 bps/Hz 40 ‘’ 36 80 bps/Hz 65 60 In the case of mimo (8x8) capacity is more than as compare to (4X4) MIMO system. When k=0 it acts as rayleigh chaneel. When value of k is very very large it acts as gaussian chaneel. As value of k increases the capacity decreases. http://www.ijettjournal.org Page 2591 30 International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013 FOR MIMO(4X4) ( SNR IN db) K SNR=15 CAPACITY 0 17 bps/Hz 5 12 ‘’ 10 11 35 Nt=Nr=4;k=0; Nt=Nr=4;k=5; Nt=Nr=4; k=10; Nt=Nr=4;k=VERY LARGE; 30 SNR=25 CAPACITY 28 bps/Hz 23 21 SNR=30 CAPACITY 35 bps/H 29 27 c a p a c it y (b it s / s / H z ) 25 When transmitter has no idea of csi 20 TABLE IV FOR MIMO(8X8) ( SNR IN db) K SNR=15 CAPACITY 0 32 bps/Hz 5 22 ‘’ 10 19 15 10 SNR=25 CAPACITY 57 bps/Hz 42 28 SNR=30 CAPACITY 70 bps/H 54 49 5 0 0 5 10 15 SNR in dB 20 25 30 Fig. 5 Uncorrelated(4x4) rician chaneel capacity when transmitter has no idea of CSI In the case of mimo (8x8) capacity is more than as compare to (4X4) MIMO system. When k=0 it acts as rayleigh chaneel. When value of k is very very large it acts as gaussian chaneel. When transmitter has no idea of CSI equal power is given to each transmitter. As value of k increases the capacity decreases. In this case equal power is given to each transmitter 35 UNCORRELATED CHANNEL 70 Nt=Nr=8;k=0 Nt=Nr=8;k=5; Nt=Nr=8; k=10 Nt=Nr=8;k=very large; 60 Nt=Nr=4;rt=0.3 rr=0.5;k=0 Nt=Nr=4;rt=0.3 rr=0.5;k=5 Nt=Nr=4;rt=0.3 rr=0.5 k=10 Nt=Nr=4;rt=0.3 rr=0.5;k=1000 30 25 c a p a c it y (b it s /s / H z ) c ap ac ity (bit s / s /H z ) 50 40 30 20 15 20 10 10 5 0 0 5 10 15 SNR in dB 20 25 30 Fig. 6 Uncorrelated(8x8) rician chaneel capacity when transmitter has no idea of CSI 0 0 5 10 15 SNR in db 20 25 Fig. 7 Correlated Rician chaneel capacity(4x4) when transmitter know the CSI TABLE 111 ISSN: 2231-5381 30 http://www.ijettjournal.org Page 2592 International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013 VI CONCLUSION 80 Nt=Nr=8;rt=0.3 rr=0.5;k=0 Nt=Nr=8;rt=0.3 rr=0.5;k=5 70 The effect of CSI is negligible at high SNR . For low and values of SNR, CSI improves capacity for Rician fading. For all values of SNR, as the value of K increases, the Ergodic capacity decreases. Rician channel capacity in case of (8X8) system is more than (4x4)MIMO system. Nt=Nr=8;rt=0.3 rr=0.5 k=10 Nt=Nr=8;rt=0.3 rr=.5;k=1000 capacity(bits/s/Hz) 60 50 40 30 20 V111 REFERENCES 10 0 0 5 10 15 SNR in db 20 25 30 [1] Fig. 8 Correlated Rician chaneel capacity(4x4) when transmitter know the CSI [2] TABLE V FOR MIMO(4X4) ( SNR IN db) rt=0.3 rr=o.5 K SNR=15 SNR=25 CAPACITY CAPACITY 0 19bps/Hz 29 bps/Hz 5 13 ‘’ 21 10 12 19 [3] SNR=30 CAPACITY 35 bps/H 26 24 [4] [5] TABLE VI FOR MIMO(8X8) ( SNR IN db) rt=0.3 rr=o.5 K SNR=15 SNR=25 CAPACITY CAPACITY 0 38bps/Hz 59 bps/Hz 5 24 ‘’ 42 10 20 38 [6] SNR=30 CAPACITY 70 bps/H 54 48 . Correlation decrease the MIMO capacity. [7] [8] [9] MohinderJankiraman,Space-Time Codes and MIMO Systems,British Library Cataloguing in Publication Data. 2004J. I.ETelar “Capacity of multi antenna Gaussian Channels” Euro,Trans,Telecom,10:6 (1999),585-595 M. K. Simon, and M. 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Valenzuela,“Linkoptimal space-time processing with multiple transmit and receive antennas,” IEEECommun. Lett., vol. 5, no. 3, pp. 85-87, March 2001. 70 Nt=Nr=8;rt=0.3 Nt=Nr=8;rt=0.7 Nt=Nr=8;rt=0.3 Nt=Nr=8;rt=0.7 60 rr=0.3;k=0 rr=0.7;k=0 rr=0.3 k=5 rr=0.7;k=5 capacity(bits/s/Hz) 50 40 30 20 10 0 0 5 10 15 SNR in db 20 25 30 Fig. 9 Effect of correlation parameter on Rician chaneel chaneel capacity ISSN: 2231-5381 http://www.ijettjournal.org Page 2593

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