Scaling-law Optimal Training and Scheduling in the SIMO Uplink

In fading MIMO channels, there is a tradeoff between the time (or energy) spent gathering CSI and the remaining time in which to transmit data before the channel loses coherence. The tradeoff is more pronounced in multiuser systems as the number of usershence the number of channel vectors to be estimatedincreases, and is inherently coupled with multiuser scheduling. We consider a multiple access block fading channel with coherence time T , n independent users, each with one transmit antenna and the same average power constraint ρavg, and a base station with M receive antennas and no a priori channel state information. We construct a training-based communication scheme and jointly optimize the training and user selection: we find the optimal number of users to be trained, Lopt, and the optimal number to be scheduled for transmission out of those trained, in order to maximize sum rate. The optimal duration of training is shown to be equal to Lopt symbol times. We also show the necessary and sufficient condition for training sequences to satisfy. This optimized training-based scheme achieves the same scaling law with increasing SNR as the noncoherent capacity of a single user n×M MIMO channel: Lopt ( 1 − Lopt T ) log2(ρavg) + O(1) as ρavg → ∞, where Lopt = min(n, M, b2 c). We show this is also the scaling law of the sum capacity of the associated non-coherent SIMO uplink, hence our scheme is scaling-law optimal. Finally, the asymptotic behavior of sum rate and throughput per user under increasing n, M or T is explored.