Regarding the simulation of QAM on Rayleigh fading channel

Hi,

I am very new in wireless systems
I have tried to simulate QAM on Rayleigh fading channel
This is a mathematical model of Rayleigh fading channel
y = hx + n

where
y = complex receive vector
h = channel gain according to Rayleigh fading
x = complex transmit vector
n = complex AWGN noise

I'm so confused about h
Could anyone please suggest me about this ?


I generated h in two ways

-- First method --
G1 = 1/sqrt(2)*randn(1,1);
G2 = 1/sqrt(2)*randn(1,1);
h = ((G1.^2) + (G2.^2)).^(1/2);

which is the envelope of Rayleigh distribution
(obtained from 2 Gaussian random variable)

-- Second method --
h = 1/sqrt(2)*[ randn(1,1) + (i*randn(1,1)) ];

which is the complex Gaussian random variable


With both cases,
I obtained the same BER curves which are also agree with theoretical formula
But I'd like to ask "Are two methods identical to simulate Rayleigh fading channel ?"

Thanks in advance
:grin:


Sorry, I have mistyping in graph
black curve is theory
red curve is simulation
:lol:

Could any expert reply to OP question please. I would like to know too. Thank you.