# Regarding the simulation of QAM on Rayleigh fading channel

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#### puripong

##### Member level 2
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
h = channel gain according to Rayleigh fading
x = complex transmit vector
n = complex AWGN noise

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 ?"

:grin:

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

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• 256QAM_Rayleigh.png
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#### mazdaspring

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