Read about the Alamouti Scheme first
MATLAB Code for Alamouti's Precoding Matrix for 2 X 2 MIMO
% Clear any existing data and figures
clc;
clear;
close all;
% Define system parameters
transmitAntennas = 2; % Number of antennas at the transmitter
receiveAntennas = 2; % Number of antennas at the receiver
symbolCount = 1000000; % Number of symbols to transmit
SNR_dB = 15; % Signal-to-Noise Ratio in decibels
% Generate random binary data for transmission
rng(10); % Set seed for reproducibility
transmitData = randi([0, 1], transmitAntennas, symbolCount);
% Perform Binary Phase Shift Keying (BPSK) modulation
modulatedSymbols = 1 - 2 * transmitData;
% Define Alamouti's Precoding Matrix
precodingMatrix = [1 1; -1i 1i];
% Encode and transmit data using Alamouti scheme
transmittedSymbols = zeros(transmitAntennas, symbolCount);
for idx = 1:2:symbolCount
transmittedSymbols(:, idx:idx+1) = precodingMatrix * modulatedSymbols(:, idx:idx+1);
end
% Simulate Rayleigh fading channel
channelMatrix = (randn(receiveAntennas, transmitAntennas) + 1i * randn(receiveAntennas, transmitAntennas)) / sqrt(2);
% Receive signal and add AWGN
receivedSignal = awgn(channelMatrix * transmittedSymbols, SNR_dB, 'measured');
% Decode and demodulate received symbols
decodedSymbols = zeros(transmitAntennas, symbolCount);
for idx = 1:2:symbolCount
% Estimate received symbols using channel information
receivedEstimation = channelMatrix' * receivedSignal(:, idx:idx+1);
% Decode symbols using Alamouti decoding
decodedSymbols(:, idx:idx+1) = precodingMatrix' * receivedEstimation;
end
% Perform BPSK demodulation to retrieve received binary data
receivedBinaryData = decodedSymbols < 0;
% Calculate error rate
errorCount = sum(sum(transmitData ~= receivedBinaryData));
errorRate = errorCount / (transmitAntennas * symbolCount);
% Display the error rate
disp(['Error rate: ', num2str(errorRate)]);
Output
Error rate: 0
You can run a loop by varying the SNR values. You can plot the BER vs SNR graph easily.