Multiple-Antenna Capacity in a Deterministic Rician Fading Channel

We calculate the capacity of a multiple-antenna wireless link with M -transmit and N -receive antennas in a Rician fading channel. We consider the standard Rician fading channel where the channel coefficients are modeled as independent circular Gaussian random variables with non-zero means (non-zero specular component). The channel coefficients of this model are constant over a block of T symbol periods but, independent over different blocks. For such a model, the capacity and capacity achieving signals are dependent on the specular component. We obtain asymptotic expressions for capacity in the low and high SNR (ρ) scenarios. We establish that for low SNR the optimum signal is determined completely by the specular component of the channel and beamforming is the optimum signaling strategy. For high SNR, we show that Rayleigh optimal signaling (the signal that ignores the specular component) achieves the optimal rate of increase of capacity with respect to log ρ. Further, as ρ → ∞, the signals that are optimum for Rayleigh fading channel are also optimum for Rician channel in the case of coherent commumincations and in the case of non-coherent communications when T → ∞. Finally, we show that the the number of degrees of freedom of a Rician fading channel is atleast as much as that of a Rayleigh fading channel namely K(1− KT ) where K = min{M,N, T/2 }.