noise and fading channel formula for QPSK

Hi,

in QPSK system:
what are the matlab equations for noise and fading channel?

also;
what is the theoritical equation for calculating BER?

this is because I see several different formula, for example:


1-

N0 = 1/10^(SNR(i)/10);
n = sqrt(N0/2)*(randn(1,length(sig))+1i*randn(1,length(sig)));

h = sqrt(0.5*((randn(1,length(sig))).^2+(randn(1,length(sig))).^2));

EbN0 = 10.^(Eb_No/10);
theoryBer = 0.5.*(1-sqrt(EbN0Lin./(EbN0+1)));




2-

N_0=(1/sqrt(2))*(randn(1)+1j*randn(1))

ber_theory=0.5*erfc(sqrt(E_n_ln)/sqrt(2));




3-

sig = sqrt(1/10^(Eb_No_dB(i)/10)); % noise variance
n = sig*(randn(2,N) + 1i*randn(2,N)); % Additive white gaussian noise prototype

h = randn(2,N) + 1i*randn(2,N); % Rayleigh channel


EbNo_lin = 10.^(Eb_No_dB/10);
theoryBer_AWGN = 0.5*erfc(sqrt(EbNo_lin/2)); % theoretical BER of QPSK over AWGN channel
theoryBer_Rayl = 0.5.*(1-sqrt(EbNo_lin./(EbNo_lin+1))); % theoretical BER of QPSK over Rayleigh channel




Thanks

Rayleigh fading is important, but RICIAN fading is more dominant today, unless you can guarantee line of sight direct path and all reflections blocked as with high tower antenna to another high tower antenna.

its assumed there is no los path.
for the flat fading over rayleigh channel.