On Non-coherent MIMO Capacity in the Wideband Regime: Interplay of SNR, Antennas and Coherence

We 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 it’s 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. For the case when the channel state is perfectly known at the receiver, we analyze the effect of multiple antennas on the decoding error probability in the wideband limit. We show that though multiple transmit antennas do not improve the wideband capacity limit, they do reduce the error probability. The material in this paper was presented in part at the International Symposium on Information Theory and Applications (ISITA 2004), Parma, Italy, Oct 2004, Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov 2004 and Conference on Information Sciences and Systems (CISS) 2005, Baltimore, MD, Mar 2005. S. Ray ([email protected]), M. Médard ([email protected]) and L. Zheng ([email protected]) are with the Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139. Work is supported by NSF Ultra Wideband Wireless Award ANI0335256, NSF Career Award CCR 0093349 and Hewlett-Packard Award 008542-008.