# QPSK simulation with AWGN and BER

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daniel cohen on 17 Dec 2021
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: Ashutosh Singh Baghel on 20 Dec 2021
Edited: Ashutosh Singh Baghel on 20 Dec 2021
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.

R2020a

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