Training in multiple-antenna Rician fading wireless channels with deterministic specular component

We determine the optimum training strategy for a multiple-antenna wireless link in a Rician fading channel using a training based lower bound on capacity. We consider the standard Rician block fading channel where the channel coefficients are modeled as independent circular Gaussian random variables with non-zero means (the specular component). The specular component is known to both the transmitter and receiver. The channel coefficients of this model are constant over a block of T symbol periods but, independent over different blocks. For such a model, it is shown that the training based capacity, the optimum training signals, the training period, transmit and training energy are dependent on the Rician factor r along with SNR rho, the number of transmit antennas M, the number of receive antennas N and the coherence interval T. Also, unlike in the case of Rayleigh fading channels, it can be shown using the lower bound for Rician fading channels that for low SNR Rician fading channels behave like a purely AWGN channel and the optimum strategy is to spend no effort in learning the channel. When SNR is not low and training is required then the optimum training period is as many symbol intervals as there are transmit antennas.