How Much Training is Required for Multiuser Mimo?

An M-element antenna array (the base station) transmits, on the downlink, K les 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 base station derives its channel estimate from tau_rp pilot symbols which the terminals transmit on the reverse link. A coherence interval of T symbols is expended as follows: tau_rp reverse pilot symbols, one symbol for computations, and (T-l-tau_rp) forward QAM symbols for each terminal For a given coherence interval, number of base station 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 base station 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 base station antennas (M ges 16 ) it is both feasible and advantageous to learn the channel and to serve a multiplicity of terminals simultaneously as well.