CCS

Probability of Error for QAM in an AWGN Channel

 

Matlab Coding

 

 

 

% MATLAB script for Illustrative Problem 7.6.
echo on
SNRindB1=0:2:15;
SNRindB2=0:0.1:15;
M=16;
k=log2(M);
for i=1:length(SNRindB1),
    smld_err_prb(i)=cm_sm41(SNRindB1(i));    % simulated error rate
    echo off;
end;
echo on ;
for i=1:length(SNRindB2),
    SNR=exp(SNRindB2(i)*log(10)/10);        % signal-to-noise ratio
    % theoretical symbol error rate
    theo_err_prb(i)=4*Qfunct(sqrt(3*k*SNR/(M-1)));
    echo off ;
end;
echo on ;

% Plotting commands follow.
semilogy(SNRindB1,smld_err_prb,'*');
hold
semilogy(SNRindB2,theo_err_prb);


function [p]=cm_sm41(snr_in_dB)
% [p]=cm_sm41(snr_in_dB)
%        CM_SM41  finds the probability of error for the given
%           value of snr_in_dB, SNR in dB.
N=10000;
d=1;                      % min. distance between symbols
Eav=10*d^2;                   % energy per symbol
snr=10^(snr_in_dB/10);               % SNR per bit (given)
sgma=sqrt(Eav/(8*snr));                % noise variance
M=16;

% Generation of the data source follows.
for i=1:N,    
  temp=rand;                  % a uniform R.V. between 0 and 1
  dsource(i)=1+floor(M*temp);          % a number between 1 and 16, uniform 
end;

% Mapping to the signal constellation follows.
mapping=[-3*d 3*d;
       -d  3*d;
            d  3*d;
      3*d  3*d;
     -3*d  d;
       -d  d;
        d  d;
      3*d  d;
      -3*d  -d; 
       -d  -d; 
        d  -d;
          3*d  -d;
     -3*d  -3*d;
       -d  -3*d;
        d  -3*d;
      3*d  -3*d];

for i=1:N,
  qam_sig(i,:)=mapping(dsource(i),:);
end;

% received signal
for i=1:N,
  [n(1) n(2)]=gngauss(sgma);
  r(i,:)=qam_sig(i,:)+n;
end;

% detection and error probability calculation
numoferr=0;
for i=1:N,
  % Metric computation follows.
  for j=1:M,
    metrics(j)=(r(i,1)-mapping(j,1))^2+(r(i,2)-mapping(j,2))^2;
  end;
  [min_metric decis] = min(metrics);
  if (decis~=dsource(i)),
    numoferr=numoferr+1;
  end;
end;
p=numoferr/(N);     


Simulation Result

Reference,

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