How Much Training Is Required For Multiuser MIMO?

An M-element antenna array (the basestation) transmits, on the downlink, K=M sequences of QAM symbols selectively and simultaneously to K autonomous single-antenna terminals through a linear pre-coder that is the pseudo-inverse of an estimate of the forward channel matrix. We assume time-division duplex (TDD) operation, so the basestation derives its channel estimate from pilot symbols which the terminals transmit on the reverse link. A coherence interval of T symbols is expended on three distinct activities: reverse pilot symbols (the number greater than or equal to K), one symbol for computations, and the transmission of forward QAM symbols to each terminal. For a given coherence interval, number of basestation antennas, and forward- and reverse-SINR's we determine the optimum number of terminals to serve simultaneously and the optimum number of reverse pilot symbols to employ by choosing these parameters to maximize a lower bound on the net sum-throughput. The lower bound rigorously accounts for channel estimation error, and is valid for all SINR's. Surprisingly it is always advantageous to increase the number of basestation antennas, even when the reverse SINR is low and the channel estimate poor: greater numbers of antennas enable us to climb out of the noise and to serve more terminals. Even within short coherence intervals (T=10 symbols) and with low SINR's (-10.0 dB reverse, 0.0 dB forward) given large numbers of basestation antennas (M>=16) it is both feasible and advantageous to learn the channel and to serve a multiplicity of terminals simultaneously as well.