MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSK, BPSK (with Simulation)

🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together
🧮 MATLAB Code for M-ary QAM
🧮 MATLAB Code for M-ary PSK
📚 Further Reading

MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK

% Written by Salim Wireless
clc; clear; close all;
snr_db = -5:2:25;
psk_orders = [2, 4, 8, 16, 32];
qam_orders = [4, 16, 64, 256];
ber_psk_results = zeros(length(psk_orders), length(snr_db));
ber_qam_results = zeros(length(qam_orders), length(snr_db));
for i = 1:length(psk_orders)
    ber_psk_results(i, :) = berawgn(snr_db, 'psk', psk_orders(i), 'nondiff');
end
for i = 1:length(qam_orders)
    ber_qam_results(i, :) = berawgn(snr_db, 'qam', qam_orders(i));
end
figure;
semilogy(snr_db, ber_psk_results(1, :), 'o-', 'LineWidth', 1.5, 'DisplayName', 'BPSK'); hold on;
for i = 2:length(psk_orders)
    semilogy(snr_db, ber_psk_results(i, :), 'o-', 'DisplayName', sprintf('%d-PSK', psk_orders(i)));
end
for i = 1:length(qam_orders)
    semilogy(snr_db, ber_qam_results(i, :), 'x--', 'DisplayName', sprintf('%d-QAM', qam_orders(i)));
end
title('Theoretical BER vs SNR for Various PSK and QAM Schemes');
xlabel('SNR (dB)'); ylabel('Bit Error Rate (BER)');
legend('Location', 'best'); grid on; ylim([1e-6 1]); hold off;
web('https://www.salimwireless.com/search?q=m-ary%20PSK%20and%20QAM', '-browser');

Output

BER vs SNR for PSK & QAM

Fig: BER vs SNR graph for Various PSK and QAM

MATLAB Code for BER vs SNR for m-ary QAM

MATLAB Code for BER vs SNR for m-ary PSK

clc; clear all; close all; rng(0);
num_symbols = 1e5;
snr_db = 0:2:20;
psk_orders = [2, 4, 8, 16, 32];
ber_results = zeros(length(psk_orders), length(snr_db));
for i = 1:length(psk_orders)
    M = psk_orders(i); k = log2(M);
    for j = 1:length(snr_db)
        data_symbols = randi([0, M-1], 1, num_symbols);
        tx_bits = de2bi(data_symbols, k, 'left-msb');
        modulated_signal = pskmod(data_symbols, M, pi/M, 'gray');
        received_signal = awgn(modulated_signal, snr_db(j), 'measured');
        demod_symbols = pskdemod(received_signal, M, pi/M, 'gray');
        rx_bits = de2bi(demod_symbols, k, 'left-msb');
        [~, ber_results(i, j)] = biterr(tx_bits, rx_bits);
    end
end
figure; semilogy(snr_db, ber_results(1, :), 'o-', 'DisplayName', 'BPSK'); hold on;
for i = 2:length(psk_orders)
    semilogy(snr_db, ber_results(i, :), 'o-', 'DisplayName', sprintf('%d-PSK', psk_orders(i)));
end
title('Simulated Bit Error Rate vs. SNR for M-PSK');
xlabel('SNR (dB)'); ylabel('Bit Error Rate (BER)');
legend('Location', 'best'); grid on; hold off;
web('https://www.salimwireless.com/search?q=m-ary%20PSK%20and%20QAM', '-browser');

MATLAB Code for BER vs SNR for QPSK →

MATLAB Code for BPSK →

Error Probability Formulas

Digital Modulation Schemes (AWGN Channel)

Bit Error Rate (BER)

BPSK & QPSK (Gray Coded)

\[ P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right) \]

8-PSK (Approximation)

\[ P_b \approx \frac{2}{3} Q\left(\sqrt{\frac{2E_s}{N_0}} \sin\frac{\pi}{8}\right) \]

16-QAM (Gray Coded)

\[ P_b \approx \frac{3}{4} Q\left(\sqrt{\frac{4}{5}\frac{E_b}{N_0}}\right) \]

64-QAM (Gray Coded)

\[ P_b \approx \frac{7}{12} Q\left(\sqrt{\frac{2}{7}\frac{E_b}{N_0}}\right) \]

256-QAM (Gray Coded)

\[ P_b \approx \frac{15}{32} Q\left(\sqrt{\frac{8}{85}\frac{E_b}{N_0}}\right) \]

Symbol Error Rate (SER)

M-PSK (General Form)

\[ P_s \approx 2Q\left(\sqrt{\frac{2E_s}{N_0}} \sin\frac{\pi}{M}\right) \]

M-QAM (General Form)

\[ P_s \approx 4\left(1 - \frac{1}{\sqrt{M}}\right) Q\left(\sqrt{\frac{3}{M-1}\frac{E_s}{N_0}}\right) \]

Need help calculating the integral?

Understanding the Q-function and erfc

Implementation Notes

• BER formulas assume Gray coding mapping.
• Transmission is modeled over an AWGN channel.
• E_s = E_b \log_2 (M) (Energy per symbol vs. energy per bit).
• Q(x) is the area under the tail of a Gaussian PDF.
• QAM formulas are high-SNR approximations.
• For BPSK, P_b = P_s as k=1.

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