On Integer-Forcing Forcing Precoding for the Gaussian MIMO Broadcast Channel
Abstract: forcing (IF) precoding precoding,, also known as downlink IF, is a promising new Integer-forcing approach to communication over multiple-input multiple input multiple-output multiple (MIMO) broadcast channels. Inspired by the integer integer-forcing forcing linear receiver for multiple multipleaccess channels, it generalizes linear precoding by inducing inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre pre-inversion inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, cheme, 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 NR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form 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. 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.