Explicit lower bounds on the outage probability of integer forcing over N<inf>r</inf> × 2 channels

Abstract

The performance of integer-forcing equalization for communication over the compound multiple-input multipleoutput channel is investigated. An upper bound on the resulting outage probability as a function of the gap to capacity has been derived previously, assuming a random precoding matrix drawn from the circular unitary ensemble is applied prior to transmission. In the present work a simple and explicit lower bound on the worst-case outage probability is derived for the case of a system with two transmit antennas and two or more receive antennas, leveraging the properties of the Jacobi ensemble. The derived lower bound is also extended to random space-time precoding, and may serve as a useful benchmark for assessing the relative merits of various algebraic space-time precoding schemes. We further show that the lower bound may be adapted to the case of a 1 × Nt system. As an application of this, we derive closed-form bounds for the symmetric-rate capacity of the Rayleigh fading multiple-access channel where all terminals are equipped with a single antenna. Lastly, we demonstrate that the integer-forcing equalization coupled with distributed space-time coding is able to approach these bounds. 10 When using an ML receiver, this space-time code is known to achieve the DMT for multiplexing rates r ≤ 1 5 . As detailed in [16], whether this code achieves the optimal MAC-DMT also when r > 1 5 remains an open question.

Simple Bounds for the Symmetric Capacity of the Rayleigh Fading Multiple Access Channel

“…Specifically, in [10] a different upper bound for the outage probability was derived in the context of a randomly precoded compound single-user N r × 2 MIMO channel. It is easy to verify that the derived bound carries over to the setting considered in the present paper, when rewritten as follows: 3 Theorem 4 (Theorem 2 in [10]). For a two-user i.i.d.…”

“…The main step is to recall that the SVD decomposition of an i.i.d. circularly-symmetric complex Gaussian matrix yields left and right singular vector matrices that are uniformly (Haar) distributed, as is the precoding matrix considered in the analysis of[10].…”