The Optimal DoF for the Noncoherent MIMO Channel with Generic Block Fading

TL;DR

This paper extends the understanding of the high-SNR capacity of noncoherent MIMO channels, showing that the optimal degrees of freedom are achievable under more general fading conditions beyond IID Rayleigh models.

Contribution

It proves that the optimal DoF for IID Rayleigh fading also applies to a broader class of generic block fading channels using a new duality-based converse proof.

Findings

Optimal DoF extends beyond IID Rayleigh fading

The capacity pre-log factor is preserved in general fading models

Novel duality approach for the converse proof

Abstract

The high-SNR capacity of the noncoherent MIMO channel has been derived for the case of independent and identically distributed (IID) Rayleigh block fading by exploiting the Gaussianity of the channel matrix. This implies the optimal degrees of freedom (DoF), i.e., the capacity pre-log factor. Nevertheless, as far as the optimal DoF is concerned, IID Rayleigh fading is apparently a sufficient but not necessary condition. In this paper, we show that the optimal DoF for the IID Rayleigh block fading channel is also the optimal DoF for a more general class of generic block fading channels, in which the random channel matrix has finite power and finite differential entropy. Our main contribution is a novel converse proof based on the duality approach.