On the Capacity of Gaussian MIMO Channels with Memory

TL;DR

This paper proves a conjecture that the capacity of Gaussian MIMO channels with memory is consistent across cases and provides explicit formulas for optimal input strategies, extending to various practical constraints.

Contribution

It confirms the conjecture that channel capacities are identical across cases and derives explicit optimal input spectral densities, including under joint practical constraints.

Findings

Proves the capacity conjecture for Gaussian MIMO channels with memory.

Provides explicit closed-form expressions for optimal input spectral densities.

Extends results to channels with practical constraints like per-antenna and energy harvesting.

Abstract

The operational capacity of Gaussian MIMO channels with memory was obtained by Brandenburg and Wyner in [9] under certain mild assumptions on the channel impulse response and its noise covariance matrix, which essentuially require channel memory to be not too strong. This channel was also considered by Tsybakov in [10] and its information capacity was obtained in some cases. It was further conjectured, based on numerical evidence, that these capacities are the same in all cases. This conjecture is proved here. An explicit closed-form expression for the optimal input power spectral density matrix is also given. The obtained result is further extended to the case of joint constraints, including per-antenna and interference power constraints as well as energy harvesting constraints. These results imply the information-theoretic optimality of OFDM-type transmission systems for such channels with memory.