On Integer-Forcing Precoding for the Gaussian MIMO Broadcast Channel

TL;DR

This paper introduces a novel integer-forcing precoding scheme for MIMO broadcast channels, achieving near-capacity performance with low complexity and maximum spatial multiplexing gain, especially effective in high SNR regimes.

Contribution

It proposes the diagonally-scaled exact IF (DIF) scheme and its regularized version (RDIF), providing analytical insights and demonstrating near-capacity performance in simulations.

Findings

DIF achieves maximum spatial multiplexing gain.

Gap to sum capacity is bounded by 0.27 bits.

RDIF outperforms optimal linear precoding in simulations.

Abstract

Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach for communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally-scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.