Different fading (Rayleigh, Rician, Nakagami) for polar codes performance.

Question

Fahmid Mahmud 2023-6-23

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https://ww2.mathworks.cn/matlabcentral/answers/1987159-different-fading-rayleigh-rician-nakagami-for-polar-codes-performance

I am trying to compare Frame Error Rate (FER) vs SNR (Es/No) performance for polar codes. I have the performance for the "without fading" case. I have 3 functions for Rayleigh, Rician and Nakagami-m fadings using which I get the fading coefficient "h" to be considered for fading (given below):

clear all;
N=100;
%Rayleigh fading 
%Generate N independent complex fading coefficients, with real and imaginary parts
%being Gaussian. The variance is normilized to 1
%CSIR refers to the assumption that H_Rayleigh is perfectly known at the
%receiver. Under this case, we can ignore phase and focus on the effect of
%magnitute
%no CSI: non-coherent case where we assume H_Rayleigh is not known at the
%receiver
H_real=1./sqrt(2).*randn(1,N);
H_imag=1./sqrt(2).*randn(1,N);   
H_Rayleigh=H_real+j*H_imag;
H_Rayleigh_mag=abs(H_Rayleigh);%magnitude of H follows Rayleigh distribution!
%Rician fading with LoS component m; m is usually assumed to be constant; m can be complex 
%H_rician=m+H_Rayleigh
%Some good discussions regarding the knowledege of phase and magnitude: https://ma-mimo.ellintech.se/2020/03/02/rician-fading-a-channel-model-often-misunderstood/
%For non-coherent case, usually, m is still assumed to be known perfectly
%at the receiver; we just do not know H_Rayleigh
m=1;
H_real=1./sqrt(2).*randn(1,N);
H_imag=1./sqrt(2).*randn(1,N);   
H_Rayleigh=H_real+j*H_imag;
H_Rician=m+H_Rayleigh;
H_Rician_mag=abs(H_Rician);%magnitude of H follows Rician distribution! I think phase will follow a uniform distribution
%Nakagami-m fading: we generate magnitute using Nakagami m, and phase
%using uniform distribution. Note that Nakamagi m (amplitute) is a special case of
%squared root of gamma distribution with parameters [0,1/m,m]; I use
%randraw.m to generate this gamma distribution. BTW, randraw can be used to
%generate many other distributions.
m=1;
H_gamma_mag=randraw('gamma',[0 1/m,m],N)';
H_Nakagami_mag=sqrt(H_gamma_mag);      
H_Nakagami=H_Nakagami_mag.*exp(j*2*pi*rand(1,N));

Using these functions, when I try to plot the curve, it works for Rician and Rayleigh, but not for Nakagami-m. Nakagami one uses another function randraw which is of 4431 lines.

Can anyone please advise on the plot that I have obtained for Rayleigh and Rician? How can including Rician fading give us better performance than the "without fading" case?