Theoretical and simulated BER vs. SNR for ASK, FSK, and PSK

📘 Overview
🧮 Simulator for calculating BER
🧮 MATLAB Codes for calculating theoretical BER
🧮 MATLAB Codes for calculating simulated BER
📚 Further Reading

BER vs. SNR denotes how many bits in error are received in a communication process for a particular Signal-to-noise (SNR) ratio. In most cases, SNR is measured in decibel (dB). For a typical communication system, a signal is often affected by two types of noises

1. Additive White Gaussian Noise (AWGN)

2. Rayleigh Fading

In the case of additive white Gaussian noise (AWGN), random magnitude is added to the transmitted signal. On the other hand, Rayleigh fading (due to multipath) attenuates the different frequency components of a signal differently. A good signal-to-noise ratio tries to mitigate the effect of noise.

Simulator for calculating BER vs SNR for binary ASK, FSK, and PSK

Calculate BER for Binary ASK Modulation

The theoretical BER for binary ASK (BASK) in an AWGN channel is given by:

BER = (1/2) * erfc(0.5 * sqrt(SNR_ask));

Enter SNR (dB):

BER vs. SNR curves for ASK, FSK, and PSK

Calculate BER for Binary FSK Modulation

The theoretical BER for binary FSK (BFSK) in an AWGN channel is given by:

BER = (1/2) * erfc(sqrt(SNR_bfsk / 2));

Enter SNR (dB):

Calculate BER for Binary PSK Modulation

The theoretical BER for binary PSK (BPSK) in an AWGN channel is given by:

BER = 0.5 * erfc(sqrt(SNR_bpsk))

Enter SNR (dB):

MATLAB Code for calculating theoretical BER vs SNR for ASK, FSK, and PSK

% The code is written by SalimWireless.Com clc; clear; close all; % SNR values in dB for ASK, BFSK, and BPSK SNRdB_ask = 0:1:20; SNRdB_bfsk = 0:1:20; SNRdB_bpsk = 0:1:20; % Convert SNR from dB to linear scale SNR_ask = 10.^(SNRdB_ask/10); SNR_bfsk = 10.^(SNRdB_bfsk/10); SNR_bpsk = 10.^(SNRdB_bpsk/10); % Theoretical BER for ASK BER_th_ask = (1/2) * erfc(0.5 * sqrt(SNR_ask)); % Theoretical BER for BFSK BER_th_bfsk = (1/2) * erfc(sqrt(SNR_bfsk / 2)); % Theoretical BER for BPSK BER_th_bpsk = 0.5 * erfc(sqrt(SNR_bpsk)); % Plotting all three BER curves in the same figure with y-axis on log scale figure; hold on; % ASK BER semilogy(SNRdB_ask, BER_th_ask, '-rh', 'LineWidth', 2.5); % BFSK BER semilogy(SNRdB_bfsk, BER_th_bfsk, '-kh', 'LineWidth', 2.5); % BPSK BER semilogy(SNRdB_bpsk, BER_th_bpsk, '-bh', 'LineWidth', 2.5); % Labels, title, grid, and legend xlabel('SNR (dB)'); ylabel('Bit Error Rate (BER)'); title('Theoretical BER vs. SNR for Binary ASK, FSK, and PSK Modulations'); grid on; legend('BASK Theoretical', 'BFSK Theoretical', 'BPSK Theoretical'); % Force the y-axis scale to specific ticks and limits set(gca, 'YScale', 'log'); yticks([1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1]); % Correct ascending order ylim([1e-6 1]); % Force y-axis limits from 1e-6 to 1 % Set the x-axis limits xlim([0 20]); hold off;

Output

MATLAB Code for calculating simulated BER vs SNR for ASK, FSK, and PSK

% The code is written by SalimWireless.Com
% Simulation Parameters
clc;
clear;
close all;

numBits = 1e6;    % Number of bits to simulate
SNRdB = 0:1:20;   % SNR range in dB
SNR = 10.^(SNRdB/10);  % Convert SNR from dB to linear scale

% Initialize BER results
BER_sim_ask = zeros(1, length(SNRdB));
BER_sim_fsk = zeros(1, length(SNRdB));
BER_sim_psk = zeros(1, length(SNRdB));

% Main simulation loop
for i = 1:length(SNRdB)
    %% ASK Modulation and BER Calculation
    % Generate random bits
    bits = randi([0 1], 1, numBits);
    
    % ASK Modulation: Map bits to symbols (0 -> 0, 1 -> 1)
    txASK = bits;
    
    % Add noise
    noise = sqrt(1/(2*SNR(i))) * randn(1, numBits);
    rxASK = txASK + noise;
    
    % Demodulation: Decide 0 or 1 based on threshold
    bits_rxASK = rxASK > 0.5;
    
    % Calculate BER
    BER_sim_ask(i) = sum(bits ~= bits_rxASK) / numBits;

%% FSK Modulation and BER Calculation (Corrected)
    % FSK Modulation: Map bits (0 -> 0+j1, 1 -> 1+j0)
    txFSK = (bits == 1) + 1j*(bits == 0);  % 1 -> 1+j0, 0 -> 0+j1
    
    % Add noise (complex Gaussian noise)
    noise = sqrt(1/(2*SNR(i))) * (randn(1, numBits) + 1j*randn(1, numBits));
    rxFSK = txFSK + noise;
    
    % Demodulation: Calculate Euclidean distance to decide 0 or 1
    % Distance to 1+j0 (for bit 1)
    dist1 = abs(rxFSK - (1 + 1j*0));
    % Distance to 0+j1 (for bit 0)
    dist0 = abs(rxFSK - (0 + 1j*1));
    
    % Demodulate: Assign 1 if closer to 1+j0, else assign 0
    bits_rxFSK = dist1 < dist0;
    
    % Calculate BER
    BER_sim_fsk(i) = sum(bits ~= bits_rxFSK) / numBits;

%% PSK Modulation and BER Calculation
    % PSK Modulation: Map bits (0 -> -1, 1 -> 1)
    txPSK = 2*bits - 1;  % BPSK symbol (0 -> -1, 1 -> 1)
    
    % Add noise
    noise = sqrt(1/(2*SNR(i))) * randn(1, numBits);
    rxPSK = txPSK + noise;
    
    % Demodulation: Decide 0 or 1 based on threshold
    bits_rxPSK = rxPSK > 0;
    
    % Calculate BER
    BER_sim_psk(i) = sum(bits ~= bits_rxPSK) / numBits;
end

% Plot simulated BER vs SNR
figure;
semilogy(SNRdB, BER_sim_ask, '-r', 'LineWidth', 2);
hold on;
semilogy(SNRdB, BER_sim_fsk, '-g', 'LineWidth', 2);
semilogy(SNRdB, BER_sim_psk, '-b', 'LineWidth', 2);
grid on;
xlabel('SNR (dB)');
ylabel('Bit Error Rate (BER)');
title('Simulated BER vs. SNR for Binary ASK, FSK, and PSK Modulations');
legend('BASK', 'BFSK', 'BPSK');
axis([0 20 1e-5 1]);

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