Outage Behavior of Integer Forcing With Random Unitary Pre-Processing

TL;DR

This paper analyzes the outage behavior of integer forcing in MIMO channels with random unitary pre-processing, providing universal bounds on outage probability and gap-to-capacity for various channel conditions.

Contribution

It introduces a universal outage probability bound for integer forcing with random unitary pre-processing, applicable to a broad class of channels and aiding in understanding its reliability.

Findings

Derived explicit universal outage probability bounds for circular unitary ensemble.

Bound depends only on gap-to-capacity and number of transmit antennas.

Applied results to bounds on gap-to-capacity in multicast scenarios.

Abstract

Integer forcing is an equalization scheme for the multiple-input multiple-output communication channel that has been demonstrated to allow operating close to capacity for "most" channels. In this work, the measure of "bad" channels is quantified by considering a compound channel setting where the transmitter communicates over a fixed channel but knows only its mutual information. The transmitter encodes the data into independent streams, all taken from the same linear code. The coded streams are transmitted after applying a unitary transformation. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. Considering pre-processing matrices drawn from a random ensemble, outage corresponds to the event that the target rate exceeds the achievable rate of integer forcing for a given channel matrix. For the case of the circular unitary ensemble, an explicit universal bound on the outage probability for a given target rate is derived that holds for any channel in the compound class. The derived bound depends only on the gap-to-capacity and the number of transmit antennas. The results are also applied to obtain universal bounds on the gap-to-capacity of multiple-antenna closed-loop multicast, achievable via linear pre-processed integer forcing.