How to code the following in MATLAB ?

Hello all, I am trying to code the following expression in MATLAB but not getting it clearly:

Scenario: The system consists of single antenna Transmitter and multiple antenna receiver. The signal received at the receiver is given by the following expression.

----(1)

where , is transmitted signal and is zero mean circularly symmetric complex Gaussian with variance P i.e., , is a received vector and is given as and and it is a Rayleigh channel between transmitter and each antenna of receiver.

My query is that I am getting confused due to presence of multiple (M) antennas at receiver.

Any help in this regard will be highly appreciated.

Answer 1

[Hassaan]

With multiple antennas at the receiver, you can think of ℎ as a vector (or matrix with a single column) where each element ℎ_n corresponds to the channel between the transmitter and the n-th receiving antenna. The received signal r(n) is then a vector of the signals received at each antenna. Each of these received signals is the transmitted signal s(n) affected by the corresponding channel ℎ and added noise η(n), which is complex Gaussian noise.

You can simulate this in MATLAB by creating a vector h to represent the channel effects for each antenna. Then, you generate a signal s to be transmitted, which could be a sequence of symbols in a communication system. You also generate the noise vector eta with the appropriate Gaussian distribution and variance P. Finally, you simulate the received signal r by multiplying the transmitted signal s by the channel h and adding the noise eta.

% Parameters
N = 4;  % Number of antennas
P = 1;  % Noise variance, assuming a noise power of 1 for simplicity

% Generate a transmitted signal s(n)
s = randn(N, 1) + 1i*randn(N, 1);  % A random complex signal

% Simulate the channel effects for each antenna
h = (randn(N, 1) + 1i*randn(N, 1))/sqrt(2);  % Rayleigh fading channel

% Generate the noise for each antenna
eta = sqrt(P/2)*(randn(N, 1) + 1i*randn(N, 1));

% Calculate the received signal r(n)
r = h.*s + eta;

% Plotting
figure;

% Plot transmitted signal
subplot(3, 1, 1);
stem(abs(s), 'filled');
title('Transmitted Signal |s(n)|');
xlabel('Antenna Index');
ylabel('Magnitude');

% Plot channel effects
subplot(3, 1, 2);
stem(abs(h), 'filled');
title('Channel Effects |h(n)|');
xlabel('Antenna Index');
ylabel('Magnitude');

% Plot received signal
subplot(3, 1, 3);
stem(abs(r), 'filled');
title('Received Signal |r(n)|');
xlabel('Antenna Index');
ylabel('Magnitude');

Make sure to adjust the variables N and P to match your scenario, and remember I am assuming that s is already defined as your transmitted signal[your s]. Also, this code assumes that s is a column vector; if it's a row vector, you'll need to adjust the dimensions accordingly.

-----------------------------------------------------------------------------------------------------------------------------------------------------

If you find the solution helpful and it resolves your issue, it would be greatly appreciated if you could accept the answer. Also, leaving an upvote and a comment are also wonderful ways to provide feedback.

It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.

Professional Interests

• Technical Services and Consulting
• Embedded Systems | Firmware Developement | Simulations
• Electrical and Electronics Engineering

Feel free to contact me.

[chaaru datta]

Thank u so much sir for ur response... But you have not considered the effect of n and M....

[Hassaan]

% Parameters
N = 4;  % Number of transmit antennas
M = 4;  % Number of receive antennas
P = 1;  % Noise variance

% Generate a transmitted signal s(n)
s = randn(N, 1) + 1i*randn(N, 1);  % A random complex signal

% Simulate the channel effects for each link
H = (randn(M, N) + 1i*randn(M, N))/sqrt(2);  % Rayleigh fading channel matrix

% Generate the noise for each receive antenna
eta = sqrt(P/2)*(randn(M, 1) + 1i*randn(M, 1));

% Calculate the received signal r(n) at each receive antenna
r = H*s + eta;

% Plotting
figure;
% Plot transmitted signal
subplot(4, 1, 1);
stem(abs(s), 'filled');
title('Transmitted Signal |s(n)|');
xlabel('Antenna Index');
ylabel('Magnitude');

% Plot channel effects (magnitude of the first row for simplicity or as an example)
subplot(4, 1, 2);
stem(abs(H(1,:)), 'filled');  % Example: showing the channel to the first receive antenna
title('Channel Effects to 1st Rx Antenna |h_1(n)|');
xlabel('Transmit Antenna Index');
ylabel('Magnitude');

% Plot overall channel effects using a heatmap
subplot(4, 1, 3);
imagesc(abs(H));  % Heatmap of channel magnitudes
colorbar;
title('Overall Channel Effects |H|');
xlabel('Transmit Antenna Index');
ylabel('Receive Antenna Index');

% Plot received signal
subplot(4, 1, 4);
stem(abs(r), 'filled');
title('Received Signal at Rx Antennas |r(n)|');
xlabel('Receive Antenna Index');
ylabel('Magnitude');

-----------------------------------------------------------------------------------------------------------------------------------------------------

If you find the solution helpful and it resolves your issue, it would be greatly appreciated if you could accept the answer. Also, leaving an upvote and a comment are also wonderful ways to provide feedback.

It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.

Professional Interests

• Technical Services and Consulting
• Embedded Systems | Firmware Developement | Simulations
• Electrical and Electronics Engineering

Feel free to contact me.