Bit error rate VS Signal to noise ratio plot in MATLAB

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chaaru datta 2025-3-20

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https://ww2.mathworks.cn/matlabcentral/answers/2175450-bit-error-rate-vs-signal-to-noise-ratio-plot-in-matlab

评论： vidyesh 2025-7-30

Hello all, I am trying to plot BER Vs SNR plot in MATLAB for the following case: V2V Communications using Doppler: Rayleigh channel, Fourier Transform (FT) and Inverse Fourier Transform (IFT), Orthogonal Frequency Division Multiplexing (OFDM),Modulation Techniques: 16-QAM and 4-QPSK modulation schemes. Use of LDPC (Low-Density Parity Check) for error correction. Encapsulation of the signal for protection from noise, improving transmission and reducing errors.

This is what I had tried:

clc; clear all; close all;
% Parameters
nSym = 10^4;         % Number of OFDM symbols
EbN0dB = 0:2:20;     % SNR Range
M_vals = [4, 16];    % Modulation schemes: 4-QAM (QPSK) and 16-QAM
N = 64;              % OFDM Subcarriers
Ncp = 16;            % Cyclic Prefix Length
L = 10;              % Number of channel taps
fd = 100;            % Doppler Frequency (Hz)
Fs = 1e3;            % Sampling Frequency
Ts = 1/Fs;           % Sampling Interval
t = (0:nSym-1) * Ts; % Time vector
ber_simulated = zeros(length(M_vals), length(EbN0dB)); % BER for QPSK & 16-QAM
for m = 1:length(M_vals)
    m
    M = M_vals(m);  % Current Modulation Order
    bitsPerSymbol = log2(M);
    
    for i = 1:length(EbN0dB)
        i
        errors = 0;
        total_bits = 0;
        for j = 1:nSym
            % **Generate Transmitted Symbols**
            data_bits = randi([0 1], 1, bitsPerSymbol * N); % Random bits
            
            if M == 4
                % **QPSK Modulation**
                si = 2 * (data_bits(1:2:end) - 0.5);
                sq = 2 * (data_bits(2:2:end) - 0.5);
                s = si + 1j * sq; % QPSK Symbols
            else
                % **16-QAM Modulation (Gray Coded)**
                sI = 2 * (mod(data_bits(1:4:end) + 2 * data_bits(2:4:end), 4) - 1.5);
                sQ = 2 * (mod(data_bits(3:4:end) + 2 * data_bits(4:4:end), 4) - 1.5);
                s = (sI + 1j * sQ) / sqrt(10); % Normalize power
            end
            % **Generate Rayleigh Fading**
            h = (randn(1, N) + 1j * randn(1, N)) / sqrt(2); % Rayleigh fading
            % **Noise Scaling (AWGN)**
            N0 = (10^(EbN0dB(i)/10))^-1;
            n = sqrt(N0/2) * (randn(1, N) + 1j * randn(1, N)); % AWGN
            % **Received Signal**
            r = h .* s + n; % Apply Rayleigh fading
            % **Zero-Forcing Equalization**
            h(abs(h) < 1e-3) = 1; % Avoid division by small values
            r_eq = r ./ h; % Equalized signal
            % **Hard Decision Decoding**
            if M == 4
                % **QPSK Detection**
                si_hat = 2 * (real(r_eq) > 0) - 1;
                sq_hat = 2 * (imag(r_eq) > 0) - 1;
                received_bits = [si_hat > 0; sq_hat > 0];
            else
                % **16-QAM Detection**
                sI_hat = real(r_eq) * sqrt(10) / 2;  % Scale to match constellation levels
                sQ_hat = imag(r_eq) * sqrt(10) / 2;
                % **Hard Decision Levels for 16-QAM**
                sI_decoded = 3 * (sI_hat > 2) + 1 * (sI_hat > 0 & sI_hat <= 2) ...
                    -1 * (sI_hat <= 0 & sI_hat > -2) - 3 * (sI_hat <= -2);
                sQ_decoded = 3 * (sQ_hat > 2) + 1 * (sQ_hat > 0 & sQ_hat <= 2) ...
                    -1 * (sQ_hat <= 0 & sQ_hat > -2) - 3 * (sQ_hat <= -2);
                % **Convert Symbol Decisions to Bits (Gray Mapping)**
                received_bits = [mod(sI_decoded + 3, 4) > 1; mod(sI_decoded + 1, 4) > 1;
                    mod(sQ_decoded + 3, 4) > 1; mod(sQ_decoded + 1, 4) > 1];
            end
            % **BER Calculation**
            errors = errors + sum(data_bits ~= received_bits(:)');
            total_bits = total_bits + length(data_bits);
        end
        ber_simulated(m, i) = errors / total_bits; % Compute BER
    end
end
% **Plot BER vs. Eb/N0**
figure;
semilogy(EbN0dB, ber_simulated(1, :), '-o', 'LineWidth', 2);
hold on;
semilogy(EbN0dB, ber_simulated(2, :), '-s', 'LineWidth', 2);
xlabel('E_b/N_0 (dB)');
ylabel('Bit Error Rate (BER)');
title('BER vs. SNR for QPSK and 16-QAM over Rayleigh Fading');
grid on;
legend('QPSK', '16-QAM');

My query is I am not getting how to implement LDPC part in above code. Any help in this regard will be highly appreciated.

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vidyesh 2025-7-30

Hello Chaaru,

Since LDPC is an error correction algorithm, you will have to add the LDPC Encoder before the Modulator and LDPC Decoder after the Demodulator.

The code generates 10^4 data bits, taking this into account create an appropriate Generator Matrix and use that to obtain the codewords.

For decoder the first k bits will be your codeword (If systematic) or use the Generator Matrix to decode the codeword.

There are multiple ways to create the Generator and Parity-Check Matrices, you can implement any one of them.

Alternatively you can use the "ldpcEncode" and "ldpcDecode" MATLAB functions.

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Bit error rate VS Signal to noise ratio plot in MATLAB

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