Uplink-downlink duality for integer-forcing: Effective SINRs and iterative optimization

Integer-forcing is a recently proposed framework for single-user encoding and decoding for MIMO channels. The key idea is that, by using appropriate nested lattice codebooks, we can ensure that every integer linear combination of codewords is itself a codeword. This permits the decoder is to first eliminate noise from the interfering data streams at the decoder, and only afterwards solve for the data streams. Here, we examine the integer-forcing framework from a signal-to-interference-and-noise ratio perspective and focus on the challenging problem of simultaneously optimizing the beamforming and projection matrices as well as the targeted integer matrix. Using recent results on uplink-downlink duality for integer-forcing, we propose an iterative algorithm for selecting these matrices and investigate its performance via simulations.