Optimal bit error analysis of Nr-branch EGC under Rayleigh fading channels

To date, several analyses of diversity systems involve very complex mathematical derivations. These complex methods achieve precise analytical results, but some lack insightful engineering representations which can be used to implement the systems directly. Concerned for equal-gain combiner (EGC), a simple closed-form error analysis of N_r-branch EGC system in the presence of Rayleigh fading is presented. The average output signal-to-noise ratio (SNR) of the EGC combiner is split into equal N_r power splitter output SNRs. Since the average output SNR of the splitter equals the sum of the outputs, EGC system reduces to maximal ratio combiner (MRC) whose properties are well known. By devising SNR coefficient for EGC, optimal bit error rate (BER) is derived using the properties of the MRC. Besides an approach of splitter design is illuminated.