A lower bound on the optimum feedback rate for downlink multi-antenna cellular networks

We consider a multi-antenna downlink cellular network using either single-user maximal ratio transmission (MRT) or multi-user zero-forcing (ZF) transmission. The locations of the base stations are modeled by a Poisson point process to allow the inter-cell interference to be tractably analyzed. A tight lower bound on the optimum number of feedback bits maximizing the net spectral efficiency is derived, whereby the cost of feedback sent via uplink is subtracted from the corresponding gain in downlink spectral efficiency. When using MRT, the optimum number of feedback bits is shown to scale linearly with the number of antennas, and logarithmically with the channel coherence time. With ZF, the optimum amount of feedback scales the same as with MRT, but additionally also increases linearly with the pathloss exponent.