Wideband non-coherent MIMO capacity

dWe consider a multiple-input, multiple-output (MIMO) wideband Rayleigh block fading channel, where the channel state is unknown to both the transmitter and the receiver. With only an average power constraint, we compute the capacity of this channel and consider its interaction with the coherence length, number of transmit and receive antennas and receive signal-to-noise ratio (SNR) per degree of freedom. We establish how large the coherence length has to be in order for the non-coherent channel to have a "near coherent" performance in the wideband regime. More specifically, we show that if the coherence length of the channel is above a certain SNR (bandwidth) dependent threshold, the non-coherent and coherent capacities are the same in the large bandwidth regime. We also propose a signaling scheme that is near-optimal in the wideband regime.