Fundamental Capacity of MIMO Channels

We provide an overview of the extensive recent results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon-theoretic capacity definitions and, for each definition, different correlation models and channel side information assumptions that we consider. We first provide a comprehensive summary of ergodic and outage capacity results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends on the amount of channel knowledge at either the receiver or transmitter, the channel SNR, and the correlation between the channel gains on each antenna element. We then focus attention on the capacity regions for MIMO broadcast and multiple access channels. In contrast to single-user MIMO channels, capacity results for these multiuser MIMO channels are quite difficult to obtain, even for constant channels. We summarize capacity results for the MIMO broadcast and multiple access channel for channels that are either constant or fading with perfect instantaneous knowledge of the antenna gains at both transmitter(s) and receiver(s). We also show that the MIMO multiple access and broadcast capacity regions are intimately related via a duality transformation. This transformation is not only useful for proving capacity theorems; it also facilitates finding the optimal transmission strategy of the nonconvex MIMO broadcast channel using convex optimization techniques applied to the dual MIMO multiple access channel. Last we discuss capacity results for multicell MIMO channels with base station cooperation. The base stations then act as a spatially diverse antenna array, and transmission strategies that exploit this structure exhibit significant capacity gains. This section also provides a brief discussion of system level issues associated with MIMO cellular. Open problems in this field abound and are discussed throughout the paper.