Message Transmission and Common Randomness Generation over MIMO Slow Fading Channels with Arbitrary Channel State Distribution

TL;DR

This paper analyzes message transmission and common randomness generation over MIMO slow fading channels with arbitrary state distribution, deriving bounds on outage capacities and establishing the capacity of a compound MIMO Gaussian channel.

Contribution

It provides the first bounds on outage transmission capacity for MIMO slow fading channels with arbitrary state distribution and characterizes the outage CR capacity in this setting.

Findings

Bounds on outage transmission capacity coincide except at countably many points.

Capacity of a specific compound MIMO Gaussian channel is established.

Lower and upper bounds on outage CR capacity are derived.

Abstract

We investigate the problem of message transmission and the problem of common randomness (CR) generation over single-user multiple-input multiple-output (MIMO) slow fading channels with average input power constraint, additive white Gaussian noise (AWGN), arbitrary state distribution and with complete channel state information available at the receiver side (CSIR). First, we derive a lower and an upper bound on the outage transmission capacity of MIMO slow fading channels for arbitrary state distribution and show that the bounds coincide except possibly at the points of discontinuity of the outage transmission capacity, of which there are, at most, countably many. To prove the lower bound on the outage transmission capacity, we also establish the capacity of a specific compound MIMO Gaussian channel. Second, we define the outage CR capacity for a two-source model with unidirectional communication over a MIMO slow fading channel with arbitrary state distribution and establish a lower and an upper bound on it using our bounds on the outage transmission capacity of the MIMO slow fading channel.