# Equal Gain Combining in Rayleigh Fading

When wireless signals travel from a single transmit antenna to multiple receive antennas they experience different fading conditions. While signal from one path may experience a deep fade the signal from another path may be stronger. Therefore selecting the stronger of the two signals (selection combining, threshold combining) or adding the signals (equal gain combining, maximal ratio combining) would always yield much better results (lower bit error rate). However, there must be sufficient spacing between the different receive antennas for the received signals to be dissimilar (uncorrelated). In the simulation below we consider a 1-Tx, 2-Rx scenario. The signals arriving at the two receive antennas are added together before detection.

```%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function[ber]=err_rate4(l,EbNo)
si=2*(round(rand(1,l))-0.5);
sq=2*(round(rand(1,l))-0.5);
s=si+j*sq;
n1=(1/sqrt(2*10^(EbNo/10)))*(randn(1,l)+j*randn(1,l));
h1=(1/sqrt(2))*((randn(1,l))+j*(randn(1,l)));
n2=(1/sqrt(2*10^(EbNo/10)))*(randn(1,l)+j*randn(1,l));
h2=(1/sqrt(2))*((randn(1,l))+j*(randn(1,l)));
r1=abs(h1).*s+n1;
r2=abs(h2).*s+n2;
r=r1+r2;
si_=sign(real(r));
sq_=sign(imag(r));
ber1=(l-sum(si==si_))/l;
ber2=(l-sum(sq==sq_))/l;
ber=mean([ber1 ber2]);
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%```
Equal Gain Combining

Note:

1. Not only the signals on the two paths experience uncorrelated fading but the the noise at the receiver front ends is also uncorrelated.

2. In reality the signals over both the paths would also experience random phase shifts but these can be removed before the combining process at the receiver.

#### Author: Yasir Ahmed (aka John)

More than 20 years of experience in various organizations in Pakistan, the USA, and Europe. Worked as a Research Assistant within the Mobile and Portable Radio Group (MPRG) of Virginia Tech and was one of the first researchers to propose Space Time Block Codes for eight transmit antennas. The collaboration with MPRG continued even after graduating with an MSEE degree and has resulted in 12 research publications and a book on Wireless Communications. Worked for Qualcomm USA as an Engineer with the key role of performance and conformance testing of UMTS modems. Qualcomm is the inventor of CDMA technology and owns patents critical to the 4G and 5G standards.

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## One thought on “Equal Gain Combining in Rayleigh Fading”

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