Theoretical Ber vs Snr for Alamouti Scheme

 

MATLAB Script

clc;

clear;
close all;

% SNR range in dB
SNRdB = 0:2:20;

% Convert SNR from dB to linear scale
EbN0Lin = 10.^(SNRdB / 10);

% Theoretical BER for 2x2 Alamouti with BPSK modulation

pAlamouti = 1/2 - 1/2*(1+2./EbN0Lin).^(-1/2);
theoryBerAlamouti_nTx2_nRx1 = pAlamouti.^2.*(1+2*(1-pAlamouti));

% Plot the theoretical BER vs SNR
figure;
semilogy(SNRdB, theoryBerAlamouti_nTx2_nRx1, '*-r', 'LineWidth', 2);
grid on;
xlabel('SNR (dB)');
ylabel('Bit Error Rate (BER)');
title('Theoretical BER vs SNR for 2x2 Alamouti Scheme with BPSK');
legend('Theoretical BER');

Output 

Copy the MATLAB Code from Here

% The code is written by SalimWireless.Com clc; clear; close all; % Parameters bit_stream = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0]; % Original bit stream N = length(bit_stream); % Number of samples filter_order = 10; % Order of the adaptive filter lambda = 0.99; % Forgetting factor for RLS algorithm delta = 1; % Initial value for the inverse correlation matrix SNR = 15; % SNR value in dB % Convert bit stream to bipolar format (-1, 1) original_signal = bit_stream * 2 - 1; % Channel impulse response h = [0.75, 0.05, 0.02]; % Pass the signal through the channel received_signal = filter(h, 1, original_signal); % Add some noise received_signal_noisy = awgn(received_signal, SNR, 'measured'); % Initialize the adaptive filter coefficients w = zeros(filter_order, 1); % Initialize buffer for the input to the adaptive filter x_buf = zeros(filter_order, 1); % Initialize output equalized_signal = zeros(N, 1); % Initialize the inverse correlation matrix P = delta * eye(filter_order); % Adaptive equalization using RLS for n = 1:N % Update the input buffer x_buf = [received_signal_noisy(n); x_buf(1:end-1)]; % Calculate the gain vector k = (P * x_buf) / (lambda + x_buf' * P * x_buf); % Calculate the error signal e = original_signal(n) - w' * x_buf; % Update the filter coefficients w = w + k * e; % Update the inverse correlation matrix P = (P - k * x_buf' * P) / lambda; % Store the equalized output equalized_signal(n) = w' * x_buf; end % Plot original and equalized signals figure; subplot(2, 1, 1); stem(original_signal, 'filled'); title('Original Signal'); xlabel('Sample Index'); ylabel('Amplitude'); grid on; subplot(2, 1, 2); stem(equalized_signal, 'filled'); title('Equalized Signal'); xlabel('Sample Index'); ylabel('Amplitude'); grid on;  

Further Reading

1.  Alamouti Scheme
2. Alamouti's Scheme for 2X2 MIMO in MATLAB
   
3. Theoretical BER vs SNR for m-ary PSK and QAM