Capacity of sparse wideband channels with partial channel feedback

This paper studies the ergodic capacity of wideband multipath channels with partial/limited channel state feedback. Our work builds on recent results that show a significant capacity gain in the wideband/low‐SNR regime when there is perfect channel state information (CSI) at the transmitter and the receiver, relative to the case of perfect CSI at the receiver only. Furthermore, this benchmark capacity gain can be achieved with just one bit of feedback per channel coefficient. However, the input signals used in these works are peaky; that is, they have large peak‐to‐average power ratios. Signal peakiness requirement is related to channel coherence and many 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. In this work, we show that multipath sparsity significantly relaxes the requirement of peaky signalling in attaining the capacity gains with channel state feedback. First, we show that the benchmark capacity gain, with perfect CSI at the transmitter and the receiver, is achievable even under an instantaneous power constraint. In the more realistic non‐coherent setting, we study the performance of a training‐based signalling scheme with one bit of feedback per channel coefficient. We show that multipath sparsity can be leveraged to achieve the benchmark capacity gain under both average as well as instantaneous power constraints as long as the channel coherence scales at a sufficiently fast rate with the signal space dimension (time‐bandwidth product). We also present guidelines for choosing signalling parameters as a function of the channel sparsity parameters to maximally exploit channel state feedback for capacity gains. Copyright © 2008 John Wiley & Sons, Ltd.