CCS

Three different detectors for recovering the transmitted data symbols and
evaluate their performance for Rayleigh fading and additive white Gaussian noise.

 

Matlab coding

Implement the three types of detectors.

Nt = 2;                                                                             % No. of transmit antennas
Nr = 2;                                                                             % No. of receive antennas
S = [1 1 -1 -1; 1 -1 1 -1];                                                  % Reference codebook
H = (randn(Nr,Nt) + 1i*randn(Nr,Nt))/sqrt(2); % Channel coefficients
s = 2*randi([0 1],Nt,1) - 1;                                               % Binary transmitted symbols
No = 0.1;                                                                         % Noise Noiance
noise = sqrt(No/2)*(randn(Nr,1) + 1i*randn(Nr,1));         % AWGN noise
y = H*s + noise;                                                              % Inputs to the detectors
disp(['The transmitted symbols are: ',num2str(s')])

% Maximum Likelihood Detector:
mu = zeros(1,4);
for i = 1:4
　　mu(i) = sum(abs(y - H*S(:,i)).^2);                           % Euclidean distance metric
end
[Min idx] = min(mu);
s_h = S(:,idx);
disp(['The detected symbols using the ML method are: ',num2str(s_h')])

% MMSE Detector:
w1 = (H*H' + No*eye(2))^(-1) * H(:,1); % Optimum weight vector 1
w2 = (H*H' + No*eye(2))^(-1) * H(:,2); % Optimum weight vector 2
W = [w1 w2];
s_h = W'*y;
for i = 1:Nt
　　if s_h(i) >= 0
　　　　s_h(i) = 1;
　　else
　　　　s_h(i) = -1;
　　end
end
disp(['The detected symbols using the MMSE method are: ',num2str(s_h')])

% Inverse Channel Detector:
s_h = Hy;
for i = 1:Nt
　　if s_h(i) >= 0
　　　　s_h(i) = 1;
　　else
　　　　s_h(i) = -1;
　　end
end
disp(['The detected symbols using the ICD method are: ',num2str(s_h')])

Output,

>> Round 1
The transmitted symbols are: 1 1
The detected symbols using the ML method are: 1 1
The detected symbols using the MMSE method are: 1 1
The detected symbols using the ICD method are: 1 1
>> Round 2
The transmitted symbols are: 1 -1
The detected symbols using the ML method are: 1 -1
The detected symbols using the MMSE method are: 1 -1
The detected symbols using the ICD method are: 1 -1
>> Round 3
The transmitted symbols are: -1 1
The detected symbols using the ML method are: -1 1
The detected symbols using the MMSE method are: -1 1
The detected symbols using the ICD method are: -1 1

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis