Superanalysis of Optimum Combining with Application to Femtocell Networks

A femtocell technology-towards the deployment of small-cell networks-is a key enabler for improving indoor coverage and throughput per network area at a low cost in future wireless networks. However, these small-cell networking inevitably increases cochannel interference due to aggressive (even uncontrolled) reuse of spectral resources. One of the attractive approaches to alleviating the cochannel interference is a multiple-antenna technique for which accurately characterizing the effects of interference is crucial but challenging. To elucidate this important problem, we analyze the performance of interference rejection diversity combining, often called the optimum combining, in an uplink two-tier femtocell network. Specifically, we consider that a single-antenna femtocell user (transmitter) communicates with a closed femtocell access point (receiver) with multiple antennas in the presence of single-antenna cochannel interferers from co-tier (femtocells) and cross-tier (macrocell) networks. We introduce a new mathematical methodology to analyze the average symbol error probability of optimum combining diversity systems in Rayleigh fading, accounting for multiple unequal-power interferers, each is spatially correlated across receiving antennas. The analysis resorts to the so-called Berezin´s supermathematics that treats both commuting and Grassmann anticommuting variables on an equal footing. This powerful supermathematical framework enables us to quantify the cross- and co-tier interference effects in terms of interference power heterogeneity and spatial correlation.