Sublinear Capacity Scaling Laws for Sparse MIMO Channels

Recent attention on performance analysis of single-user multiple-input-multiple-output (MIMO) systems has been on understanding the impact of the spatial correlation model on ergodic capacity. In most of these works, it is assumed that the statistical degrees of freedom (DoF) in the channel can be captured by decomposing it along a suitable eigenbasis and that the transmitter has perfect knowledge of the statistical DoF. With an increased interest in large-antenna systems in state-of-the-art technologies, these implicit channel modeling assumptions in the literature have to be revisited. In particular, multiantenna measurements have showed that large-antenna systems are sparse where only a few DoF are dominant enough to contribute towards capacity. Thus, in this work, it is assumed that the transmitter can only afford to learn the dominant statistical DoF in the channel. The focus is on understanding ergodic capacity scaling laws in sparse channels. Unlike classical results, where linear capacity scaling is implicit, sparsity of MIMO channels coupled with a knowledge of only the dominant DoF is shown to result in a new paradigm of sublinear capacity scaling that is consistent with experimental results and physical arguments. It is also shown that uniform-power signaling over all the antenna dimensions is wasteful and could result in a significant penalty over optimally adapting the antenna spacings in response to the sparsity level of the channel and transmit SNR.