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Multi-Antenna Capacity of Sparse Multipath Channels

Existing results on multi-input multi-output (MIMO) channel capacity implicitly assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. While this assumption may be justified in systems with few antennas, it leads to violation of fundamental power conservation principles in the limit of large number of antennas. Furthermore, recent measurement results have shown that physical MIMO channels exhibit a sparse multipath structure, even for relatively few antenna dimensions. Motivated by these observations, we propose a framework for modeling sparse channels and study the coherent capacity of sparse MIMO channels from two perspectives: 1) capacity scaling with the number of antennas, and 2) capacity as a function of transmit SNR for a fixed number of antennas. The statistically independent degrees of freedom (DoF) in sparse channels are less than the number of signal-space dimensions and, as a result, sparse channels afford a fundamental new degree of freedom over which channel capacity can be optimized: the distribution of the DoF’s in the available signal-space dimensions. Our investigation is based on a family of sparse channel configurations whose capacity admits a simple and intuitive closed-form approximation and reveals a new tradeoff between the multiplexing gain and the received SNR. We identify an ideal channel configuration that yields the fastest capacity scaling at any SNR. For fixed number of antennas, we show that the capacity maximizing configuration depends on the operating SNR and optimizes the multiplexing gain-received SNR tradeoff. Surprisingly, only three such configurations suffice for near-optimal performance over the entire SNR range. Different channel configurations can be realized in practice by appropriately adjusting the antennas’ spacings at the transmitter and the receiver.