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Alamouti Scheme for 2x2 MIMO in MATLAB


 

 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

 

 

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 S1,S2,S3,S4,,Sn1,SnS_1, S_2, S_3, S_4, \ldots, S_{n-1}, S_n, we first transmit S1S_1 and S2S_2 from antenna 1 and antenna 2, respectively. In the next time slot, we transmit S2-S_2^* and S1S_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, S3S_3 and S4S_4 are transmitted from antenna 1 and antenna 2. In the fourth time slot, S4-S_4^* and S3S_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)
  5. Alamouti Scheme Simulator

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