Sparse Multipath Wireless Channels: Modeling and Implications

Most existing works in wireless communications assume a rich multipath environment. In particular, the intense research on multi-antenna (MIMO) systems in the last decade was pioneered by results based on an i.i.d. channel model representing a rich multipath environment. However, there is growing experimental evidence that physical wireless channels exhibit a sparse multipath structure, even at relatively low antenna dimensions, and especially at large bandwidths. In this paper, we propose a model for sparse multipath channels and discuss its implications for channel learning and optimal communication. Our investigation is based on a virtual representation of physical wireless channels that corresponds to uniform sampling of the far-field scattering environment in angle-delay-Doppler at a resolution commensurate with the signal space dimensions (signaling duration, bandwidth, number of antennas). The virtual representation characterizes the statistically independent degrees of freedom (DoF) available for communication, and sparse channels correspond to a sparse set of dominant nonvanishing virtual coefficients. A key implication of sparse multipath is that the DoF scale sublinearly with the signal space dimensions in contrast to the linear scaling inherent in rich multipath. Sparsity of multipath in angle-delay-Doppler leads to channel coherence in time, frequency, and space that has significant implications for optimal communication in the low-SNR/wideband regime. In particular, we show that sparse multipath channels are asymptotically coherent and hence perfectly learnable in the limit of large dimensions. As a promising application of these results, we present a framework for maximizing MIMO capacity in sparse multipath by systematically adapting the array configurations (antenna spacings) at the transmitter and the receiver as a function of the level of sparsity and the operating SNR. Our results show that, surprisingly, three canonical array configurations are sufficient for near-optimum performance for all SNRs. The capacity gains due to reconfigurable arrays, relative to fixed configurations, are most pronounced in the low-SNR regime and are directly proportional to the number of antennas. Simulation results based on a realistic physical model are presented to illustrate the capacity gains. Implications of sparse multipath for channel sensing and adaptation in cognitive wireless systems are discussed.