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The performance of integer-forcing equalization for communication over thecompound multiple-input multipleoutput channel is investigated. An upper boundon the resulting outage probability as a function of the gap to capacity hasbeen derived previously, assuming a random precoding matrix drawn from thecircular unitary ensemble is applied prior to transmission. In the present worka simple and explicit lower bound on the worst-case outage probability isderived for the case of a system with two transmit antennas and two or morereceive antennas, leveraging the properties of the Jacobi ensemble. The derivedlower bound is also extended to random space-time precoding, and may serve as auseful benchmark for assessing the relative merits of various algebraicspace-time precoding schemes. We further show that the lower bound may beadapted to the case of a $1 \times N_t$ system. As an application of this, wederive closed-form bounds for the symmetric-rate capacity of the Rayleighfading multiple-access channel where all terminals are equipped with a singleantenna. Lastly, we demonstrate that the integer-forcing equalization coupledwith distributed space-time coding is able to approach these bounds.

Explicit Lower Bounds on the Outage Probability of Integer Forcing over Nrx2 Channels