Riciain Channel Capacity Comparison Between (8X8) And (4x4) MIMO

Transcription

1 International Journal of ngineering rends and echnology (IJ) Volume 4 Issue 6 - June 13 iciain Channel Capacity Comparison Between (8X8) And (4x4) MIMO Vivek Mankotia, Ankush ansal M student HAPA UNIVSIY PAIALA INDIA, Assistant Professor, CD HAPA UNIVSIY PAIALA INDIA ABSAC he 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. he need of wireless multimedia application require need of higher data rate. In this paper comparison of ician channel capacity has been used as measure for the efficiency of MIMO (8X8) and (4x4) system. We have calculated the ician channel capacity with CSI or without CSI at transmitter with simulating MALAB. eywords MIMO (Multi input Multi output), CSI(channel state Information),MISO, SIM 1. INODUCION MIMO system use array of multiple antennas at both transmitter and receiver end. In the case of MIMO system capacity increase and B reduces. Channel capacity is defined as the maximum rate at which data can be transmitted with small error probability. he capacity of MIMO channels is calculate for the ayleigh scenario. But in practice, MIMO channels do not always follow the ayleigh 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 ician fading model. Mathematically, the random channel matrix in a MIMO ician fading channel is a complex Gaussian matrix with a nonzero mean matrix, he ayleigh fading model is a special case of the ician fading model by setting the mean to zero. 11. SYSM MODL We have [1] consider a MIMO system with transmit array of N antenna and receive array of N antenna as shown in figure 1. he transmitted matrix is N 1 column matrix X where X is ith component which is transmitted from ith antenna. If channel is unknown at the transmitter side we assume [2] that equal power N. is given to each transmitter antenna. A N S M I X X X CHANNL FIGU 1 MIMO SYSM Where is the power across transmitter irrespective number of antennas where I is a N N identity matrix. he transmitted signal Y Y Y C I V ISSN: Page 89

2 International Journal of ngineering rends and echnology (IJ) Volume 4 Issue 6 - June 13 bandwidth is so small that channel is assumed to flat. DIFFACION he channel matrix H is a N N complex matrix. he 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. he channel matrix at receiver can be estimated by training sequence. Noise at the receiver is another column of size N 1, denoted by n. For a deterministic channel as ransmitter LOS receiver h, = N, i = 1, 2,3 N (1) 111. MIMO CHANNL CAPACY 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) = -[log (p(x y))] (3) For a linear complex model Fig. 2 WAV POPAGAION Y = Hx + n (4) he mutual information is given as I(y,x H) =log det I + HPH () he Shanon capacity is the maximum mutual information between received vector and transmitted vector C(H)=B det I + HPH (6) When full transmitter CSI and receiver CSI are available, the capacity of the MIMO system is maximum. SCAING LOS (line of sight) 1V. ICIAN CHANNL here is line-of-sight (LOS) path between the transmitter and the receiver, and in such conditions, the channel is represented by the ician fading model. We can express H in matrix notation as[9] H = ch +dh (7) Where the specular [3] and scattered components of H are denoted by superscripts, c>, d > and c + d = 1. H is a matrix of unit entries. If there is no correlation at the transmitter or at the receiver side then the entries of H are independent usually denoted by H. FLCION ISSN: Page 9

3 International Journal of ngineering rends and echnology (IJ) Volume 4 Issue 6 - June 13 If there is correlated fading then the H matrix can be modeled as [],[6] H = H (8) Where t and r are the correlation matrix at the transmitter and at the receiver side. he correlation matrix is defined[4] r = r a b r a > b (9) H(correlated)[7][8] = H1+ H () Nt=Nr=8;k= Nt=Nr=8;k=; Nt=Nr=8; k= Nt=Nr=8;k=very large; UNCOLAD CHANNL c a p a c it y ( b it s / s / H z ) 4 4 Nt=Nr=4;k=; Nt=Nr=4;k=; Nt=Nr=4; k=; Nt=Nr=4;k=VY LAG; v. SULS UNCOLAS CHANNL Fig. 3 ician chaneel capacity (4X4) when transmitter know the CSI Fig. 4 ician chaneel capacity (8X8) when transmitter know the CSI. ABL 1 FO MIMO(4X4) ( SN IN db) SN= 24 bps/hz 37 bps/hz 44 bps/h ABL 11 FO MIMO(8X8) ( SN IN db) SN= 3 bps/hz 8 bps/hz 92 bps/h In the case of mimo (8x8) capacity is more than as compare to (4X4) MIMO system. When k= 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. ISSN: Page 91

4 International Journal of ngineering rends and echnology (IJ) Volume 4 Issue 6 - June 13 Nt=Nr=4;k=; Nt=Nr=4;k=; Nt=Nr=4; k=; Nt=Nr=4;k=VY LAG; FO MIMO(4X4) ( SN IN db) SN= 17 bps/hz 28 bps/hz bps/h c a p a c it y (b it s / s / H z ) Fig. Uncorrelated(4x4) rician chaneel capacity when transmitter has no idea of CSI In this case equal power is given to each transmitter When transmitter has no idea of csi ABL IV FO MIMO(8X8) ( SN IN db) SN= 32 bps/hz 7 bps/hz 7 bps/h In the case of mimo (8x8) capacity is more than as compare to (4X4) MIMO system. When k= 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. 7 6 Nt=Nr=8;k= Nt=Nr=8;k=; Nt=Nr=8; k= Nt=Nr=8;k=very large; UNCOLAD CHANNL Nt=Nr=4;rt=.3 rr=.;k= Nt=Nr=4;rt=.3 rr=.;k= Nt=Nr=4;rt=.3 rr=. k= Nt=Nr=4;rt=.3 rr=.;k= c ap ac ity (bit s / s /H z ) 4 c a p a c it y (b it s /s / H z ) Fig. 6 Uncorrelated(8x8) rician chaneel capacity when transmitter has no idea of CSI SN in db Fig. 7 Correlated ician chaneel capacity(4x4) when transmitter know the CSI ABL 111 ISSN: Page 92

5 International Journal of ngineering rends and echnology (IJ) Volume 4 Issue 6 - June Nt=Nr=8;rt=.3 rr=.;k= Nt=Nr=8;rt=.3 rr=.;k= Nt=Nr=8;rt=.3 rr=. k= Nt=Nr=8;rt=.3 rr=.;k= VI CONCLUSION he effect of CSI is negligible at high SN. For low and values of SN, CSI improves capacity for ician fading. For all values of SN, as the value of increases, the rgodic capacity decreases. ician channel capacity in case of (8X8) system is more than (4x4)MIMO system. V111 FNCS Fig. 8 Correlated ician chaneel capacity(4x4) when transmitter know the CSI ABL V FO MIMO(4X4) ( SN IN db) rt=.3 rr=o. SN= 19bps/Hz 29 bps/hz bps/h ABL VI SN in db FO MIMO(8X8) ( SN IN db) rt=.3 rr=o. SN= 38bps/Hz 9 bps/hz 7 bps/h Correlation decrease the MIMO capacity. [1] MohinderJankiraman,Space-ime Codes and MIMO Systems,British Library Cataloguing in Publication Data. 4J. [2] I.elar Capacity of multi antenna Gaussian Channels uro,rans,elecom,:6 (1999),8-9 [3] M.. Simon, and M. Alouini, Digital communication over fading channels: A unified approach to performance analysis, Wiley, New York, NY,. [4] S.L LOYA, Channel Capacity of MIMO ar chitecture matrix, I Commun. Lett., vol., no. 9, pp , Sept. 1. [] D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. ahn, Fading correlation and itseffects on the capacity of multi-element antenna systems, I rans. Communication.,vol. 48, no. 3, pp. 2 13, Mar. [6] D. Gesbert, H. Bolcskei,D.J. Gore,A.J Pau Lraj, Outdoor MIMO wireless. channels : Models and Performanceprediction, I rans. Commun., vol., no. 12, pp , Dec. [7]. U. Nabar, H. Bolcskei, and A. J. Paulraj, Diversity and Outage performance in ricean MIMO channels, Draft, Dec. 3. [8] S. M. Qaseem and Adel A. Ali, "Capacity of correlated MIMO icean channels" International Conference ofcommunicat ion Computer and Power - ICCCP,Fe b ,, Muscat, Oman. [9] F.. Farrokhi, G. J. Foschini, A. Lozano and.a. Valenzuela, Linkoptimal space-time processing with multiple transmit and receive antennas, ICommun. Lett., vol., no. 3, pp. 8-87, March Nt=Nr=8;rt=.3 rr=.3;k= Nt=Nr=8;rt=.7 rr=.7;k= Nt=Nr=8;rt=.3 rr=.3 k= Nt=Nr=8;rt=.7 rr=.7;k= 4 SN in db Fig. 9 ffect of correlation parameter on ician chaneel chaneel capacity ISSN: Page 93