For Rayleigh channel, we can model it as randn(1,L) + j* randn(1,L).
I am wondering how can we generate a real Nakagami-m channel using MATLAB? It seems that I cannot find a single bit of this on the Internet.
Could anyone help me this out? Thank you!
For real Nakagami-m channel in MATLAB, you can use the `nakagami` function. The `nakagami` function generates random samples from a Nakagami-m distribution with a given shape parameter `m` and scale parameter `omega`.
Example code snippet that generates a real-valued Nakagami-m channel:
```matlab
% Set the shape parameter
m = 1.5;
% Set the scale parameter
omega = 1;
% Set the number of samples to generate
num_samples = 1000;
% Generate random samples from the Nakagami-m distribution
x = nakagami(m, omega, num_samples);
% Plot the histogram of the generated samples
histogram(x, 'Normalization', 'pdf');
xlabel('x');
ylabel('Probability density');
title(['Nakagami-m distribution with m = ', num2str(m)]);
```
Set the shape parameter `m` to 1.5, and the scale parameter `omega` to 1. We then set the number of samples to generate to 1000. We generate random samples from the Nakagami-m distribution using the `nakagami` function with the specified `m`, `omega`, and number of samples. Finally, we plot the histogram of the generated samples using the `histogram` function, and label the plot with the distribution parameters.
`nakagami` function can also generate complex-valued samples by specifying a complex-valued `omega` parameter. To generate a real-valued channel, we use a real-valued `omega` parameter.
Hope it helps!!
Credit: mainly AI tools
clc;
clear all;
close all;
%link:https://www.researchgate.net/post/How_to_generate_a_real_Nakagami-m_channel_using_MATLAB
%start
% We are using QPSK modulation for test.
M = 4; % modulation index for psk
hpsk = comm.PSKModulator('ModulationOrder',M,...
'BitInput',false,...
'PhaseOffset',0); % M-psk modulator
nSample = 1500; % samples in signal
snr_db = -18;
snr = 10^(snr_db/10);
infoSignal = randi(M,nSample,1)-1; % random binary signal (bits = log2(M))
txSignal = step(hpsk,infoSignal); % M-psk signal
N=size(txSignal); %sample size
%txSignal = step(hpsk,infoSignal); % M-QAM signal
% Set the shape parameter
m = 1.5; %while it becomes a Rayleigh distribution for m=1. ref: "A New Statistical Model of the Complex Nakagami-m Fading Gain"
% A uniformly distributed phase for all m ≥ 1/2 does not satisfy all these requirements.
% Set the scale parameter
omega = 1;
[g , g1]= nakagami_fading(N, omega, m); % apply Nakagami-m fading
h = (randn(size(txSignal)) + 1j * randn(size(txSignal))) / sqrt(2); % generate Rayleigh fading channel
n = sqrt(1 / (2 * snr)) * (randn(size(txSignal)) + 1j * randn(size(txSignal))); % generate Gaussian noise
rxSignal = g.*h.*txSignal + n; % apply fading and noise
%% Nakagami-m fading function
function [g ,g1] = nakagami_fading(N, omega, m)
%h = (randn(size(tx_waveform)) + 1j * randn(size(tx_waveform))) / sqrt(2); % generate Rayleigh fading channel
g = sqrt(gamrnd(m, 1/m, N)); % generate Nakagami-m fading envelope
%g1=((2*m^m)/(gamma(m)*omega^m))*randn(N)^(2*m-1)*exp(-((m/omega)*randn(N)^2)); % Rule 2 generate Nakagami-m fading ::%https://en.wikipedia.org/wiki/Nakagami_distribution#cite_note-dl-1
g1=((2*m^m)/(gamma(m)*omega^m))*randn(N).^(2*m-1).*exp(-((m/omega)*randn(N).^2)); % Rule 2 generate Nakagami-m fading ::%https://en.wikipedia.org/wiki/Nakagami_distribution#cite_note-dl-1
%Generate a 2-by-3 array of random numbers from the gamma distribution with shape parameter 3 and scale parameter 7.
%sz = [2 3];
%r2 = gamrnd(3,7,sz)
%n = sqrt(1 / (2 * snr)) * (randn(size(tx_waveform)) + 1j * randn(size(tx_waveform))); % generate Gaussian noise
%rx_waveform = g .* h .* tx_waveform + n; % apply fading and noise
%rx_waveform = g .* h .* tx_waveform + n; % apply fading and noise
end
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