Performance analysis of equal gain combining in Nakagami-m fading channels using approximate moment generating function

A moment generating function (MGF) based performance analysis is presented for N-branch equal gain combining (EGC) in independent Nakagami-m fading channels as well as dual-branch EGC in correlated Nakagami-m fading channels. Since exact MGFs of received SNRs are in general difficult to acquire, Gauss quadrature rule is employed to efficiently and accurately approximate relevant MGFs. As such, symbol error rates (SERs) of various binary and M-ary modulation formats can be readily calculated. We further investigate the performance of EGC in terms of diversity order. Assuming average SNR tends to infinity, we derive exact MGFs for EGC in both independent and correlated Nakagami-m fading channels. Then we prove that the diversity order achieved by EGC is equal to the sum of Nakagami-m fading indexes of all diversity branches.