Lecture 5

More documents

Recommendations

Info

MIMO Channel Equalisation MATLAB Programming Conclusions MMSE Equaliser (cont’d) Similar to (4) the error covariance matrix using the MMSE filter in (7) is given as ( ) −1 Φ MMSE = σv 2 H H H+ σ2 v σs 2 I Nt (8) Obviously by comparing (8) and (4), the error rate of the MMSE solution Φ MMSE is less than its ZF counterpart Φ ZF specifically at low SNR defined as [ ] E ‖s‖ 2 2 SNR = [ ] = tr(Rss) E ‖v‖ 2 tr(R = σ2 sN t 2 vv) σvN 2 = P budget/N 0 (9) r where P budget is the total transmit power budget and N 0 is the total noise power at the receiver. At high SNR, the second term in (8) will vanish, which leads to asymptotic error performance similar to the ZF filter. Compared to the ZF filter in (2), the MMSE filter in (7) can be viewed as a“regularised”expression by a diagonal matrix of entries σ2 v σs 2 , which is equal to the reciprocal of the SNR in (9) for equal numbers of transmit and receive antennas. This regularisation introduces a bias that gives a much more reliable result than (2) when the matrix is ill-conditioned, A matrix is said to be ill-conditioned if its condition number (the absolute ratio between the maximum and minimum eigenvalues) is too large., and/or the estimation of the channel is noisy. Dr. Waleed Al-Hanafy Digital Signal Processing (ECE407) — <strong>Lecture</strong> no. 5 Linear Equalisation of MIMO Channels
MIMO Channel Equalisation MATLAB Programming Conclusions MATLAB Programing clc; clear all; nt = 4; nr = 4; d = 1000; MinErrs = 100; MaxData = 1e6; chs = 10; snr dB = 0:3:21; snr = 10.ˆ(snr dB/10); Lsnr = length(snr); berZF = zeros(1,Lsnr); berMMSE = zeros(1,Lsnr); for e = 1:chs disp([’ch ’ num2str(e) ’/’ num2str(chs)]); H = (randn(nr,nt)+sqrt(-1)*randn(nr,nt))/sqrt(2); G ZF = inv(H’*H)*H’; nErZF = zeros(1,Lsnr); nErMMSE = zeros(1,Lsnr); data = zeros(1,Lsnr); for z = 1:Lsnr disp([’ step ’ num2str(z) ’/’ num2str(Lsnr) ’: SNR(dB) = ’ num2str(snr dB(z))]); G MMSE = inv(H’*H + (1/snr(z))*eye(nt))*H’; while((nErZF(z)
Page 1 and 2: MIMO Channel Equalisation MATLAB Pr
Page 5: MIMO Channel Equalisation MATLAB Pr

Lecture 5

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?