# Theoretical BER for M-ary PSK in Rayleigh Channel

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#### dminhle

##### Newbie level 1
m-ary psk

Hi,

I'm trying to calculate the theoretical BER for M-ary PSK in the presence of a Rayleigh Channel.

I've been using
https://www.dsplog.com/2008/08/10/ber-bpsk-rayleigh-channel/
as a reference on how to do it but I haven't made much progress.

In this example he says the BER for BPSK is the integral of 0.5erfc(sqrt)p from 0 to infinity where p is the pdf of y and y is the effective bit energy to noise ratio in the presence of a rayleigh channel.

He says the integral simplifies down to 0.5*(1-sqrt((eb/N0)/(eb/N0+1)) but he doesn't know how or why. Any ideas here?

I've read that the BER for M-ary PSK is 1/log2(M)*erfc(sqrt(Eb/N0)*sqrt(log2(M))*sin(pi/M)). I've been trying to get the constant term sqrt(log2(M))*sin(pi/M) out of erfc in the hope that I can treat it as a constant when integrating later but I haven't had any luck.

Any help would be appreciated.

Cheers,
Minh

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