Capacity of Sparse Wideband Channels with Limited Feedback

Recent results in the wideband/low-SNR regime show that even one bit of perfect feedback is sufficient to achieve the same rate of capacity scaling as in the benchmark case of perfect CSI at the transmitter. However, the capacity achieving signals are peaky in the non-coherent scenario when CSI is estimated at the receiver. Signal peakiness is related to channel coherence and recent measurement campaigns show that, in contrast to previous assumptions, wideband channels exhibit a sparse multipath structure that naturally leads to coherence in time and frequency. With perfect receiver CSI, we show that limited feedback, even with an instantaneous power constraint, is sufficient to achieve the benchmark capacity in sparse multipath channels. Our analysis reveals the benefits of channel sparsity in the non-coherent scenario, where we employ a training-based signaling scheme. With an average power constraint, it is shown that the benchmark is achievable, provided the channel coherence scales at a sufficiently fast rate with signal space dimension. Furthermore, in contrast to peaky signaling schemes that violate instantaneous power constraints, we show that the benchmark is attainable in sparse channels even with finite instantaneous transmit power. We present rules of thumb on choosing the signaling parameters as a function of the channel parameters so that the full benefits of sparsity can be realized.