Alamouti Scheme for 2x2 MIMO in MATLAB

• 📘 Overview & Theory
• 🧮 MATLAB Code for Alamouti Scheme
• 🧮 MATLAB Code for BER vs. SNR for Alamouti Scheme
• 🧮 Alamouti Scheme Transmission Table
• 📚 Further Reading

 

 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.

 

Copy the MATLAB Code from Here

% The code is written by SalimWireless.Com % 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 = 25; % 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)]);  

 

Alamouti Scheme Transmission Table

 

 

 

 

 

 

 

 

The above table illustrates how two orthogonal, time-diversity data streams are transmitted using two different time slots to improve the signal-to-noise ratio (SNR) at the receiver.

For a symbol stream $S_1, S_2, S_3, S_4, \ldots, S_{n-1}, S_n$, we first transmit $S_1$ and $S_2$ from antenna 1 and antenna 2, respectively. In the next time slot, we transmit $-S_2^*$ and $S_1^*$ from antenna 1 and antenna 2, respectively.

Note: To enable the Alamouti scheme, at least two transmit antennas and one receive antenna are required.

In the third time slot, $S_3$ and $S_4$ are transmitted from antenna 1 and antenna 2. In the fourth time slot, $-S_4^*$ and $S_3^*$ are transmitted from antenna 1 and antenna 2, respectively — and this pattern continues. [Read More ...]

 

Further Reading

1.  Modified Alamouti's Scheme (STBC) in MATLAB (using QPSK)
2. Alamouti's Scheme for MIMO Communication
3. Theoretical Ber vs Snr for Alamouti Scheme 
4. MATLAB Code for Multi-User STBC (using Alamouti's Scheme)