Theoretical vs. 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 for a given signal-to-noise ratio, typically measured in dB. Common noise types in wireless systems:

• 1. Additive White Gaussian Noise (AWGN)
• 2. Rayleigh Fading

AWGN adds random noise; Rayleigh fading attenuates the signal variably. A good SNR helps reduce these effects.

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

Calculate BER for Binary ASK Modulation

Enter SNR (dB):

Calculate BER for Binary FSK Modulation

Enter SNR (dB):

Calculate BER for Binary PSK Modulation

Enter SNR (dB):

BER vs. SNR Curves

MATLAB Code for Theoretical BER

% 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; web('https://www.salimwireless.com/search?q=ask%20fsk%20psk', '-browser');

MATLAB Code for Simulated BER

% 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]); web('https://www.salimwireless.com/search?q=ask%20fsk%20psk', '-browser');

Further Reading

1. Theoretical BER for ASK and FSK
2. Theoretical BER for BPSK
3. BER for m-ary PSK
4. BER for m-ary QAM