Optimal Combining for Optical Wireless Systems With Amplification: The $\chi ^{2}$ Noise Regime

We present novel analytical results on the optimal combiner (OC) for pre-amplified optical wireless receivers under chi-squared noise. The results show that the OC architecture that minimizes the average bit-error rate (BER) is determined by the level of the signal-spontaneous beating noise. Moreover, the OC provides increased gain to the diversity branches with the higher energies, up to the point where the beating noise becomes detrimental to the BER. The performance of the OC is simulated for practical receiver arrangements and it is shown that it performs better than the maximal-ratio and equal-gain combiners. The performance improvement amounts to an energy gain of less than 1 dB for implementations that utilize narrow optical filters and a modest number of diversity branches.