Signal Waveforms with Multiple Amplitude Levels
Matlab Coding,
1 % MATLAB script for the probability of a symbol error for M = 2, 4, 8, 16
2 echo on 3 SNRindB2=5:0.1:50; 4 j = 1; 5 for M = [2,4,8,16] 6 hold 7 for i=1:length(SNRindB2) 8 SNR_per_bit=exp(SNRindB2(i)*log(10)/10); 9 % theoretical error rate 10 theo_err_prb(i)=(2*(M-1)/M)*Qfunct(sqrt((6*log2(M)/(M^2-1))*SNR_per_bit)); 11 echo off; 12 end 13 D{j} = theo_err_prb; 14 j = j + 1; 15 end 16 echo on; 17 % Plotting commands follow. 18 hold 19 semilogy(SNRindB2,D{1}); 20 hold on 21 semilogy(SNRindB2,D{2}); 22 hold on 23 semilogy(SNRindB2,D{3}); 24 hold on 25 semilogy(SNRindB2,D{4}); 26 xlabel('SNR')
Simulation Result
1 % MATLAB script for a M = 16 PAM 2 echo on 3 SNRindB1=5:1:25; 4 SNRindB2=5:0.1:25; 5 M=16; 6 for i=1:length(SNRindB1), 7 % simulated error rate 8 smld_err_prb(i)=smldPe59(SNRindB1(i)); 9 echo off; 10 end; 11 echo on ; 12 for i=1:length(SNRindB2), 13 SNR_per_bit=exp(SNRindB2(i)*log(10)/10); 14 % theoretical error rate 15 theo_err_prb(i)=(2*(M-1)/M)*Qfunct(sqrt((6*log2(M)/(M^2-1))*SNR_per_bit)); 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 xlabel('SNR') 24 25 26 function [p]=smldPe59(snr_in_dB) 27 % [p]=smldPe59(snr_in_dB) 28 % SMLDPE59 simulates the error probability for the given 29 % snr_in_dB, signal-to-noise ratio in dB. 30 M=16; % 16-ary PAM 31 d=1; 32 SNR=exp(snr_in_dB*log(10)/10); % signal-to-noise ratio per bit 33 sgma=sqrt((85*d^2)/(8*SNR)); % sigma, standard deviation of noise 34 N=10000; % number of symbols being simulated
35 % generation of the data source 36 for i=1:N, 37 temp=rand; % a uniform random variable over (0,1) 38 index=floor(M*temp); % The index is an integer from 0 to M-1, where 39 % all the possible values are equally likely. 40 dsource(i)=index; 41 end;
42 % detection, and probability of error calculation 43 numoferr=0; 44 for i=1:N, 45 % matched filter outputs 46 % (2*dsource(i)-M+1)*d is the mapping to the 16-ary constellation. 47 r=(2*dsource(i)-M+1)*d+gngauss(sgma);
48 % the detector 49 if (r>(M-2)*d), 50 decis=15; 51 elseif (r>(M-4)*d), 52 decis=14; 53 elseif (r>(M-6)*d), 54 decis=13; 55 elseif (r>(M-8)*d), 56 decis=12; 57 elseif (r>(M-10)*d), 58 decis=11; 59 elseif (r>(M-12)*d), 60 decis=10; 61 elseif (r>(M-14)*d), 62 decis=9; 63 elseif (r>(M-16)*d), 64 decis=8; 65 elseif (r>(M-18)*d), 66 decis=7; 67 elseif (r>(M-20)*d), 68 decis=6; 69 elseif (r>(M-22)*d), 70 decis=5; 71 elseif (r>(M-24)*d), 72 decis=4; 73 elseif (r>(M-26)*d), 74 decis=3; 75 elseif (r>(M-28)*d), 76 decis=2; 77 elseif (r>(M-30)*d), 78 decis=1; 79 else 80 decis=0; 81 end;
82 if (decis~=dsource(i)), % If it is an error, increase the error counter. 83 numoferr=numoferr+1; 84 end; 85 end;
86 p=numoferr/N; % probability of error estimate
Simulation Result
Reference,
1. <<Contemporary Communication System using MATLAB>> - John G. Proakis