BER versus SNR for QPSK modulation. I have written following code. But BER not reducing with increasing SNR in case of simulation. Please check the above code and rectify it.

My MATLAB code is given as follows:

% Simulate the BER versus SNR curve for QPSK under AWGN communication channel.

% Assignment 3: Problem 1

% Empty workspace and close figures

clc; clearvars; close all;

% SNR in dB: snr_db = 10*log10(snr)

snr_db = -5 : 2 : 25;

% dB to linear scale conversion: snr = 10.^(snr_db/10)

snr = 10.^(snr_db/10);

% Define parameters and different numBits values for simulation

numBits = 1000 ;

numSimulations = 100;

%% Theoretical BER calculation for BPSK

qpsk_ber_theoretical = 2 * erfc(sqrt(snr/2)) - ( erfc(sqrt(snr/2))).^2;

qpsk_ber_simulations = zeros(size(snr_db));

%% Calculate BER for each SNR value

for j = 1:length(snr_db)

% Repeat simulations (as random quantities are involved) for numSimulations times

for sim = 1:numSimulations

% Generate Random Bits (0's and 1's) of size 1XnumBits, and it is a row vector

binaryBits_transmitted = randi([0, 1], 1, numBits);

% Make the binary sequence length a multiple of 2 (pad with zeros if needed)

numPaddingBits = mod(length(binaryBits_transmitted), 2);

if numPaddingBits > 0

binaryBits_transmitted = [binaryBits_transmitted, zeros(1, 2 - numPaddingBits)];

end

% Divide the binary sequence into groups of 2 bits each

qpsk_transmitted = reshape(binaryBits_transmitted,2,[])';

% Map each group of 2 bits to the corresponding QPSK symbol

% Initialize QPSK symbols (complex numbers)

qpsk_symbols = [exp(1i*0), exp(1i*pi/2), exp(1i*pi), exp(1i*3*pi/2)];

% Define the mapping from QPSK symbols to their corresponding 2-bit binary representation

qpsk_mapping = [0 0; 0 1; 1 0; 1 1];

% Map binary groups to the corresponding QPSK symbol

qpsk_modulated = qpsk_symbols (bin2dec(num2str(qpsk_transmitted)) + 1) ;

% Energy per bit = Symbol energy / 2

symbolEnergy = mean(abs(qpsk_modulated).^2);

Energy_bit = symbolEnergy / 2;

% Generate complex Gaussian noise samples

% Relate snr to the noise power (This is very important in this entire code)

Noise_Power = 1 / snr(j); % This holds true as Symbol energy is always 1

gaussian_noise = sqrt(Noise_Power) * (randn(1, numBits/2) + 1i * randn(1, numBits/2));

% Add noise to the QPSK modulated symbols to get noisy received signal

received_symbol = qpsk_modulated + gaussian_noise;

%% QPSK Demodulation with threshold as pi/4 in case of QPSK modulation scheme

% Initialize the decision regions (thresholds) for each quadrant

threshold = pi / 4; % ±45 degrees (±π/4 radians)

% Initialize a variable to store the demodulated symbols

qpsk_demodulated = zeros(1, length(received_symbol));

% Perform QPSK demodulation

for i = 1:length(received_symbol)

% Calculate the phase of the received signal

phase = angle(received_symbol(i));

% Perform threshold-based demodulation

if phase >= -3*threshold && phase < -threshold

qpsk_demodulated(i) = qpsk_symbols(1); % QPSK symbol at 0 degrees

elseif phase >= -threshold && phase < threshold

qpsk_demodulated(i) = qpsk_symbols(2); % QPSK symbol at 90 degrees

elseif phase >= threshold && phase < 3*threshold

qpsk_demodulated(i) = qpsk_symbols(3); % QPSK symbol at 180 degrees

else

qpsk_demodulated(i) = qpsk_symbols(4); % QPSK symbol at 270 degrees

end

end

%% QPSK received symbols using inverse process

qpsk_received = zeros(size(qpsk_demodulated));

% Find the closest QPSK symbol for each demodulated symbol

for i = 1: length(qpsk_demodulated)

% Calculate the distance b/w the demodulated symbol and each QPSK symbol

distances = abs(qpsk_demodulated(i) - qpsk_symbols) ;

% Find the index of the closest QPSK symbol

[~, index] = min(distances);

% Convert the index to its corresponding binary representation

binaryRepresentation = qpsk_mapping(index,:);

% Store the binary representation in the 'originalBinarySymbols' array

qpsk_received(2*i-1 : 2*i) = binaryRepresentation;

end

%% Number of bit errors

ErrorBits = xor( binaryBits_transmitted, qpsk_received);

Number_errorBits = sum(ErrorBits == 1); % bitErrors = sum(binaryBits ~= decodedBits)

Bit_Error_Rate = Number_errorBits / (numBits * 2) ;

% Store the calculated BER for this simulation

qpsk_ber_simulations(j) = qpsk_ber_simulations(j) + Bit_Error_Rate;

end

% Calculate Average Bit error rate for all the simulations for this SNR value and numBits

qpsk_simulation(j) = qpsk_ber_simulations (j) / numSimulations ;

end

%end

disp('binaryBits_transmitted');

disp(binaryBits_transmitted);

disp('qpsk_received');

disp(qpsk_received);

disp('qpsk_ber_simulations');

disp(qpsk_ber_simulations);

disp('qpsk_ber_theoretical');

disp(qpsk_ber_theoretical);

% Plot BER versus SNR curve for different numBits values

figure;

semilogy(snr_db, qpsk_simulation, '*-');

hold on;

semilogy(snr_db, qpsk_ber_theoretical, '*-');

hold on;

xlabel('Signal-to-Noise Ratio (SNR) [dB]');

ylabel('Bit Error Rate (BER)');

title('BER vs. SNR for QPSK Modulation');

legend('Simulation', 'Theoretical'); % Add more legends if needed

grid on;

hold off;

Graph is shown below:

Answer 1

[vidyesh]

Hi KAGANA SARATH,

I see that you are currently facing a challenge during the simulation of the Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) graph for QPSK modulation.

Please note that the ‘angle’ function, used to obtain the phase of the received symbol returns a value within the range of [- π, π].

To get the desired graph, you should modify the conditions within the if-else loop in the "Perform threshold-based demodulation" section as shown.

% Perform threshold-based demodulation
if phase >= -1*threshold && phase <threshold % phase between -45 and 45 degrees
    qpsk_demodulated(i) = qpsk_symbols(1); % QPSK symbol at 0 degrees
elseif phase >= threshold && phase <= 3* threshold % phase between 45 and 135 degrees
    qpsk_demodulated(i) = qpsk_symbols(2); % QPSK symbol at 90 degrees
elseif phase >=-3*threshold && phase < -1*threshold % phase between -135 and -45 degrees
    qpsk_demodulated(i) = qpsk_symbols(4); % QPSK symbol at 270 degrees 
else % phase greater thna 135 or lesster than -135 degrees
    qpsk_demodulated(i) = qpsk_symbols(3); % QPSK symbol at 180 degrees
end

You can refer to the below documentation for more information on the ‘angle’ function and QPSK.

https://mathworks.com/help/matlab/ref/angle.html

https://mathworks.com/matlabcentral/fileexchange/57625-ber-qpsk?s_tid=srchtitle_support_results_2_QPSK%2520BER