Generating Nakagami-m wireless channel in MATLAB

Hello all, I am working on wireless research wherein I want to generate Nakagami-m wireless channel and also want phase of the Nakagami-m channel. I tried to generate the Nakagami-m channel in the following way:

h_0 = random('Nakagami',m_0,Omega_0); % nakagami rv

where m_0 = Omega_0 = 1

My query is I am not getting how can I obtain phase of h_0 from above statement as h_0 is a real number.

Any help in this regard will be highly appreciated.

[chaaru datta]

Cant we get phase of Nakagami-m channel using MATLAB ?

Answer 1

[Aastha]

Hi @chaaru datta,

I understand that you would like to generate a Nakagami-m fading wireless channel. For a Nakagami-m fading channel, the envelope of the complex fading coefficient is Nakagami-m distributed, not the complex channel coefficient itself.

For example, in a Rayleigh fading scenario, the channel is commonly modelled as:

h = sqrt(1/2)*(randn(1,1) + 1i*randn(1,1));

Here, "h" is a complex Gaussian random variable, and the envelope which can be computed using the "abs" function in MATLAB follows a Rayleigh distribution.

For more information on the "randn" and "abs" function please refer to the MathWorks documentation links:

• randn: https://www.mathworks.com/help/matlab/ref/randn.html
• abs : https://in.mathworks.com/help/matlab/ref/double.abs.html

To simulate a Nakagami-m fading channel with envelope distributed as Nakagami in MATLAB with shape parameter “m” and spread parameter “ω”, you can construct the complex channel as using the below mentioned MATLAB code snippet:

pd_builtin = makedist('nakagami', 'mu', m, 'omega', 2*omega); 
r_builtin = random(pd_builtin, N, 1); %N is the number of samples

% Custom method using H = P + iQ, with P, Q ~ Nakagami(m/2, omega) 
pd_half = makedist('nakagami', 'mu', m/2, 'omega', omega); 
P = random(pd_half, N, 1); 
Q = random(pd_half, N, 1); 
r_custom = sqrt(P.^2 + Q.^2); 

where both "P" and "Q" are independently drawn from a Nakagami distribution with parameters "(m/2, ω)".

The phase of the channel can be extracted using MATLAB’s “angle” function.

Kindly refer to the MathWorks documentation for any further queries on "angle" function.

https://www.mathworks.com/help/matlab/ref/angle.html

I hope this is helpful!