The capacity of a multi-antenna (MIMO) wireless channel depends on the statistically independent degrees of freedom (DoF) in the MIMO channel matrix, which in turn depend on the physical scattering environment and the array resolution. We first review a virtual modeling framework for MIMO channels that clearly reveals the impact of scattering and array characteristics on channel statistics. The entries of the virtual channel matrix are approximately uncorrelated and the dominant non-vanishing entries represent the channel DoF. We show that the capacity of a MIMO channel is governed by two fundamental factors: 1) the number of DoF (a measure of channel power), and 2) the distribution of the DoF (distribution of scattering paths) in the spatial signal space dimensions. We introduce the notion of an ideal MIMO channel that represents an optimal distribution of the DoF from a capacity perspective. First, the ideal channel achieves the fastest asymptotic capacity scaling with the number of antennas, and reveals new sub-linear capacity scaling regimes. Second, for a given number of antennas, the ideal channel provides new insights for optimal signaling at any SNR, unlike existing results that emphasize either the low- or high-SNR regimes. Finally, we introduce the concept of adaptive-resolution spatial signaling and reception for creating the ideal channel from any given physical scattering environment. Our results indicate that existing MIMO capacity formulations are inaccurate in the low-SNR regime: adaptive-resolution signaling can result in significant (order-of-magnitude) capacity gains.

(Joint work with V. Raghavan and J. Kotecha)

Akbar M. Sayeed received the B.S. degree from the University of Wisconsin-Madison in 1991, and the M.S. and Ph.D. degrees in 1993 an 1996, respectively, from the University of Illinois at Urbana-Champaign, all in Electrical and Computer Engineering. During 1996-1997, he was a postdoctoral fellow at Rice University, Houston, TX. Since August 1997, he has been with the University of Wisconsin-Madison, where he is currently Associate Professor of Electrical and Computer Engineering. His research interests are in wireless communications, statistical signal processing, information theory, and networks.