Throughput-Optimal Training for a Time-Varying Multi-Antenna Channel

A lower bound on the capacity of trained space-time modulation is presented for the case of a time-varying channel. We consider the case where the channel consists of two components of variable strength: a specular component from line-of-sight or strong coherent multipath, and a time-varying diffuse component due to a mobile receiver or scatterers. The training period and the data period are assumed quasi-static, with the time-autocorrelation function of the channel used to model the variation between each sub-block. The training signal, training signal length, power allocation and training frequency that optimize the capacity bound are derived. We compare the effective SNR of this bound to that of differential modulation at high SNR, and find it to be lower. We find the best number of antennas to use at high SNR with differential modulation, and compare it with the optimal value for trained modulation. For our time-varying channel model, trained modulation often has a higher achievable rate than differential modulation. Our results are supported by several numerical examples.