Probability of Error for QAM in an AWGN Channel

Matlab Coding

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

19 % Plotting commands follow.
20 semilogy(SNRindB1,smld_err_prb,'
 
*');
21 hold
22 semilogy(SNRindB2,theo_err_prb);
23 
24 
25 function [p]=cm_sm41(snr_in_dB)
26 % [p]=cm_sm41(snr_in_dB)
27 %        CM_SM41  finds the probability of error for the given
28 %           value of snr_in_dB, SNR in dB.
29 N=10000;
30 d=1;                      % min. distance between symbols
 
31 Eav=10*d^2;                   % energy per symbol
32 snr=10^(snr_in_dB/10);               % SNR per bit (given)
33 sgma=sqrt(Eav/(8*snr));                % noise variance
34 M=16;

35 % Generation of the data source follows.
36 for i=1:N,    
37   temp=rand;                  % a uniform R.V. between 0 and 1
38   dsource(i)=1+floor(M*temp);          % a number between 1 and 16, uniform 
39 end;

40 % Mapping to the signal constellation follows.
41 mapping=[-3*d 3*d;
42        -d  3*d;
43             d  3*d;
44       3*d  3*d;
45      -3*d  d;
46        -d  d;
47         d  d;
48       3*d  d;
49       -3*d  -d; 
50        -d  -d; 
51         d  -d;
52           3*d  -d;
53      -3*d  -3*d;
54        -d  -3*d;
55         d  -3*d;
56       3*d  -3*d];

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

60 % received signal
61 for i=1:N,
62   [n(1) n(2)]=gngauss(sgma);
63   r(i,:)=qam_sig(i,:)+n;
64 end;

65 % detection and error probability calculation
66 numoferr=0;
67 for i=1:N,
68   % Metric computation follows.
69   for j=1:M,
70     metrics(j)=(r(i,1)-mapping(j,1))^2+(r(i,2)-mapping(j,2))^2;
71   end;
72   [min_metric decis] = min(metrics);
73   if (decis~=dsource(i)),
74     numoferr=numoferr+1;
75   end;
76 end;
77 p=numoferr/(N);     


Simulation Result

Reference,

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