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) + 1 i*randn(Nr,Nt))/sqrt(2);    % Channel coefficients
s = 2*randi([O 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:
wl = (H*H• + No*eye(2))A(-l) * H(:,1);            % Optimum weight vector 1
w2 = (H*H• + No*eye(2))A(-l) * H(:,2);           % Optimum weight vector 2
W = [wl w2];
s_h = W' *Yi
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 = H\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 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