By: Krishna Sankar

Krishna Sankar — Thu, 29 Dec 2011 00:29:18 +0000

@ash: The channel taps are not BPSK (i.e. modulation specific), rather to model the effect of reflections in wireless communication. Maybe the post on Rayleigh multipath channel model helps
http://www.dsplog.com/2008/07/14/rayleigh-multipath-channel/

By: ash

ash — Wed, 28 Dec 2011 09:46:06 +0000

why do we use channel taps in bpsk

By: Krishna Sankar

Krishna Sankar — Sun, 14 Nov 2010 21:06:41 +0000

@cherifi: Sorry, I could not look through the code. But, would not expect 4×4 to be better than 2×2.

By: cherifi

cherifi — Sat, 06 Nov 2010 08:56:06 +0000

Thanks for your great and helpful blog, I can’t have a good reuslts while Iam configure 4×4 mimo, I obtained that the 2×2 is better than 4×4
my program is:
clear
N = 10^4; % number of bits or symbols
Eb_N0_dB = [0:25]; % multiple Eb/N0 values
nTx = 2; nnTx=4;
nRx = 2; nnRx=4;
for ii = 1:length(Eb_N0_dB)

% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0

%2×2:
sMod = kron(s,ones(nRx,1));
sMod = reshape(sMod,[nRx,nTx,N/nTx]); % grouping in [nRx,nTx,N/NTx ] matrix
h = 1/sqrt(2)*[randn(nRx,nTx,N/nTx) + j*randn(nRx,nTx,N/nTx)]; % Rayleigh channel
n = 1/sqrt(2)*[randn(nRx,N/nTx) + j*randn(nRx,N/nTx)]; % white gaussian noise, 0dB variance
y = squeeze(sum(h.*sMod,2)) + 10^(-Eb_N0_dB(ii)/20)*n;

hCof = zeros(2,2,N/nTx);
hCof(1,1,:) = sum(h(:,2,:).*conj(h(:,2,:)),1); % d term
hCof(2,2,:) = sum(h(:,1,:).*conj(h(:,1,:)),1); % a term
hCof(2,1,:) = -sum(h(:,2,:).*conj(h(:,1,:)),1); % c term
hCof(1,2,:) = -sum(h(:,1,:).*conj(h(:,2,:)),1); % b term
hDen = ((hCof(1,1,:).*hCof(2,2,:)) – (hCof(1,2,:).*hCof(2,1,:))); % ad-bc term (det de matrix 2×2)
hDen = reshape(kron(reshape(hDen,1,N/nTx),ones(2,2)),2,2,N/nTx); % formatting for division
hInv = hCof./hDen; % inv(H^H*H)
hMod = reshape(conj(h),nRx,N); % H^H operation
yMod = kron(y,ones(1,2)); % formatting the received symbol for equalization
yMod = sum(hMod.*yMod,1); % H^H * y
yMod = kron(reshape(yMod,2,N/nTx),ones(1,2)); % formatting
yHat = sum(reshape(hInv,2,N).*yMod,1); % inv(H^H*H)*H^H*y
ipHat = real(yHat)>0;
nErr(ii) = size(find(ip- ipHat),2);

%4×4:
ssMod = kron(s,ones(nnRx,1));
ssMod = reshape(ssMod,[nnRx,nnTx,N/nnTx]);
hh= 1/sqrt(2)*[randn(nnRx,nnTx,N/nnTx) + j*randn(nnRx,nnTx,N/nnTx)]; %Rayleigh channel 4×4
nn = 1/sqrt(2)*[randn(nnRx,N/nnTx) + j*randn(nnRx,N/nnTx)]
yy = squeeze(sum(hh.*ssMod,2)) + 10^(-Eb_N0_dB(ii)/20)*nn;
hhCof = zeros(4,4,N/nnTx) ;
hhCof(1,1,:) = (sum(hh(:,2,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,2,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,2,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,2,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1));
hhCof(1,2,:) = (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1));
hhCof(1,3,:) = (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1));
hhCof(1,4,:) = (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,3,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,3,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,3,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,3,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,3,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,3,:).*conj(hh(:,3,:)),1));
hhCof(2,1,:) = (sum(hh(:,2,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,2,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,2,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,2,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1));
hhCof(2,2,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1));
hhCof(2,3,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1));
hhCof(2,4,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,3,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,3,:).*conj(hh(:,1,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,3,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,3,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,3,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,3,:).*conj(hh(:,1,:)),1));
hhCof(3,1,:) = (sum(hh(:,2,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,2,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,2,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,2,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1));
hhCof(3,2,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1));
hhCof(3,3,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1));
hhCof(3,4,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,3,:).*conj(hh(:,2,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,3,:).*conj(hh(:,4,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,3,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,3,:).*conj(hh(:,4,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,4,:)),1) .* sum(hh(:,3,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,4,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,3,:).*conj(hh(:,2,:)),1));
hhCof(4,1,:) = (sum(hh(:,2,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,2,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,2,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,2,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,2,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1));
hhCof(4,2,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,3,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,3,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,3,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1));
hhCof(4,3,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,4,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,4,:).*conj(hh(:,1,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,4,:).*conj(hh(:,2,:)),1));
hhCof(4,4,:) = (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,3,:).*conj(hh(:,3,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,3,:).*conj(hh(:,1,:)),1))+ (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,3,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,1,:)),1).* sum(hh(:,2,:).*conj(hh(:,3,:)),1) .* sum(hh(:,3,:).*conj(hh(:,2,:)),1))- (sum(hh(:,1,:).*conj(hh(:,2,:)),1).* sum(hh(:,2,:).*conj(hh(:,1,:)),1) .* sum(hh(:,3,:).*conj(hh(:,3,:)),1))- (sum(hh(:,1,:).*conj(hh(:,3,:)),1).* sum(hh(:,2,:).*conj(hh(:,2,:)),1) .* sum(hh(:,3,:).*conj(hh(:,1,:)),1));

hhDen = (hhCof(1,1,:).*hhCof(2,2,:).*hhCof(3,3,:).*hhCof(4,4,:))+(hhCof(1,1,:).*hhCof(2,3,:).*hhCof(3,4,:).*hhCof(4,2,:))+(hhCof(1,1,:).*hhCof(2,4,:).*hhCof(3,2,:).*hhCof(4,3,:))+(hhCof(1,2,:).*hhCof(2,1,:).*hhCof(3,4,:).*hhCof(4,3,:))+(hhCof(1,2,:).*hhCof(2,3,:).*hhCof(3,1,:).*hhCof(4,4,:))+(hhCof(1,2,:).*hhCof(2,4,:).*hhCof(3,3,:).*hhCof(4,1,:))+(hhCof(1,3,:).*hhCof(2,1,:).*hhCof(3,2,:).*hhCof(4,4,:))+(hhCof(1,3,:).*hhCof(2,2,:).*hhCof(3,4,:).*hhCof(4,1,:))+(hhCof(1,3,:).*hhCof(2,4,:).*hhCof(3,1,:).*hhCof(4,2,:))+(hhCof(1,4,:).*hhCof(2,1,:).*hhCof(3,3,:).*hhCof(4,2,:))+(hhCof(1,4,:).*hhCof(2,2,:).*hhCof(3,1,:).*hhCof(4,3,:))+(hhCof(1,4,:).*hhCof(2,3,:).*hhCof(3,2,:).*hhCof(4,1,:))-(hhCof(1,1,:).*hhCof(2,2,:).*hhCof(3,4,:).*hhCof(4,3,:))-(hhCof(1,1,:).*hhCof(2,3,:).*hhCof(3,2,:).*hhCof(4,4,:))-(hhCof(1,1,:).*hhCof(2,4,:).*hhCof(3,3,:).*hhCof(4,2,:))-(hhCof(1,2,:).*hhCof(2,1,:).*hhCof(3,3,:).*hhCof(4,4,:))-(hhCof(1,2,:).*hhCof(2,3,:).*hhCof(3,4,:).*hhCof(4,1,:))-(hhCof(1,2,:).*hhCof(2,4,:).*hhCof(3,1,:).*hhCof(4,3,:))-(hhCof(1,3,:).*hhCof(2,1,:).*hhCof(3,4,:).*hhCof(4,2,:))-(hhCof(1,3,:).*hhCof(2,2,:).*hhCof(3,1,:).*hhCof(4,4,:))-(hhCof(1,3,:).*hhCof(2,4,:).*hhCof(3,2,:).*hhCof(4,1,:))-(hhCof(1,4,:).*hhCof(2,1,:).*hhCof(3,2,:).*hhCof(4,3,:))-(hhCof(1,4,:).*hhCof(2,2,:).*hhCof(3,3,:).*hhCof(4,1,:))-(hhCof(1,4,:).*hhCof(2,3,:).*hhCof(3,1,:).*hhCof(4,2,:));
hhDen = reshape(kron(reshape(hhDen,1,N/nnTx),ones(4,4)),4,4,N/nnTx);
hhInv = hhCof./hhDen;
hhMod = reshape(conj(hh),nnRx,N);

yyMod = kron(yy,ones(1,4)); % formatting the received symbol for equalization
yyMod = sum(hhMod.*yyMod,1); % H^H * y
yyMod = kron(reshape(yyMod,4,N/nnTx),ones(1,4)); % formatting
yyHat = sum(reshape(hhInv,4,N).*yyMod,1); % inv(H^H*H)*H^H*y

ippHat = real(yyHat)>0;
% counting the errors

nnErr(ii) = size(find(ip- ippHat),2);
end

simBer = nErr/N; % simulated ber
simBerr = nnErr/N;
EbN0Lin = 10.^(Eb_N0_dB/10);
theoryBer_nRx1 = 0.5.*(1-1*(1+1./EbN0Lin).^(-0.5));
p = 1/2 – 1/2*(1+1./EbN0Lin).^(-1/2);
theoryBerMRC_nRx2 = p.^2.*(1+2*(1-p));

close all
figure
semilogy(Eb_N0_dB,theoryBer_nRx1,’bp-’);
hold on
semilogy(Eb_N0_dB,theoryBerMRC_nRx2,’kd-’);
semilogy(Eb_N0_dB,simBer,’mo-’);
semilogy(Eb_N0_dB,simBerr,’r-*’);
axis([0 25 10^-5 0.5])
grid on
legend(‘theory (nTx=1,nRx=1)’, ‘theory (nTx=1,nRx=2, MRC)’, ‘sim (nTx=2, nRx=2, ZF)’, ‘sim (nTx=4, nRx=4, ZF)’);
xlabel(‘Average Eb/No,dB’);
ylabel(‘Bit Error Rate’);
title(‘BER for BPSK modulation with 2×2 MIMO and ZF equalizer (Rayleigh channel)’);

By: Krishna Sankar

Krishna Sankar — Thu, 22 Jul 2010 00:56:06 +0000

@Divya: Thanks. Well, scaling to higher antenna configurations require you to do the channel inversion appropriately.

By: Divya

Divya — Wed, 21 Jul 2010 14:51:13 +0000

Sir, am a research scholar from south India. i found your blog about 2*2 MIMO & zero forcing equalizer and is very interesting. am quite thankful to u if u suggest me some ideas to modify the code for various ocnfigurations 4*4 ,1*4 .. etc.

By: Krishna Sankar

Krishna Sankar — Wed, 23 Jun 2010 23:04:10 +0000

@boukhari: hermitian operation is conjugate transpose

Comments on: MIMO with Zero Forcing equalizer

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