QPSK simulation with AWGN and BER

Hey,

I have a matlab code of QPSK simulation over baseband with AWGN noise, I'm calculating BER over each SNR value and plotting it along with

Theoretical BER.

When I'm generating SNR values in dB from 1 to 20 the code only computes simulated BER values from 0 to 10, why is this happening?

% QPSK MODULATION AND BER ESTIMATION IN AWGN CHANNEL

clc; clear all; close all;

N=1e6; % Number of bits transmited
SNRdB= 0:1:20; % SNR for simulation
SNRlin=10.^(SNRdB/10);
BER = zeros(1,length(SNRlin));% simulated BER
SER = zeros(1,length(SNRlin));% simulated SER

b1 = rand(1,N) > 0.5;
b2 = rand(1,N) > 0.5;

% QPSK symbol mapping
I = (2*b1) - 1;
Q = (2*b2) - 1;
S = I + 1j*Q; 

N0 = 1./SNRlin; % Variance


for k = 1:length(SNRdB)
    
    noise = sqrt(N0(k)/2)*(randn(1,N) + 1j*randn(1,N)); % AWGN noise
    
    sig_Rx = S + noise; % Recived signal
    
    % For BER calculation
    sig_I = real(sig_Rx); % I component
    sig_Q = imag(sig_Rx); % Q component
    
    bld_I = sig_I > 0; % I decision 
    bld_Q = sig_Q > 0; % Q decision
    
    b1_error = (bld_I ~= b1); % Inphase bit error
    b2_error = (bld_Q ~= b2); % Quadrature bit error
    
    Error_bit = sum(b1_error) + sum(b2_error); % Total bit error
    BER(k) = sum(Error_bit)/(2*N); % Simulated BER
    
    % For SER calculation
    error_symbol = or(b1_error, b2_error); % if bit in I or bit in Q either wrong than error
    SER(k) = sum(error_symbol)/N;
    
end

BER_theo = 2*qfunc(sqrt(2*SNRlin)); % Theoretical BER 
SER_theo = 2*qfunc(sqrt(2*SNRlin)) - (qfunc(sqrt(2*SNRlin))).^2; % Theoretical SER

figure(1);
semilogy(SNRdB, BER_theo,'r-')  
hold on
semilogy(SNRdB, BER,'k*')                                 
xlabel('SNR[dB]')                                    
ylabel('Bit Error Rate');                                         
legend('Theoretical', 'Simulated');
title(['Probability of Bit Error for QPSK Modulation']);
grid on;
hold off;

figure(2);
semilogy(SNRdB, SER_theo,'r-')  
hold on
semilogy(SNRdB, SER,'k*')                                 
xlabel('SNR[dB]')                                    
ylabel('Symbol Error Rate');                                         
legend('Theoretical', 'Simulated');
title(['Probability of symbol Error for QPSK Modulation']);
grid on;
hold off;

Here is my output plot:

Answer 1

[Ashutosh Singh Baghel]

Hi Daniel,

I understand you wish to plot BER vs. SNR on a semilog scale. If you see the value of 'BER,' it has a '0' value for 'SNR'>10. And only data points with non-zero entries are plotted because a logarithmic scale has no suitable value for a zero. For example -

x = 1:24;
y = [2 0 0 0 2 6 11 0 22 25 27 0 25 20 14 9 4 1 0 0 0 0 0 0];
figure;
semilogy(x, y,'r*--');

figure;
semilogy(x, max(eps, y));

In the second figure, the EPS values appear as 2e-16 (of course). To get a real zero, the scale must be infinitely large.

For more information, visit the link in Matlab Documnetation on 'semilogy' function.