Minimum Mean Squared Error interference alignment

TLDR

In MIMO interference networks, achieving full multiplexing gain at high SNRs requires aligning interference into lower‑dimensional subspaces, and a distributed max‑SINR precoder algorithm has recently been proposed to accomplish this. The study specifies a class of utility functions that guarantee convergence of the sum utility to a local optimum under asynchronous updates of beams, receiver filters, and utility weights. The authors use a weighted sum MSE objective to compute beams, updating the weights based on the sum utility, and define a class of utility functions that ensures convergence under asynchronous updates. The algorithm, interpretable as a sum‑MSE minimization, achieves interference alignment at high SNRs and can trace different points on the rate‑region boundary by adjusting MSE weights, as demonstrated by numerical results.

Abstract

To achieve the full multiplexing gain of MIMO interference networks at high SNRs, the interference from different transmitters must be aligned in lower-dimensional subspaces at the receivers. Recently a distributed ¿max-SINR¿ algorithm for precoder optimization has been proposed that achieves interference alignment for sufficiently high SNRs. We show that this algorithm can be interpreted as a variation of an algorithm that minimizes the sum Mean Squared Error (MSE). To maximize sum utility, where the utility depends on rate or SINR, a weighted sum MSE objective is used to compute the beams, where the weights are updated according to the sum utility objective. We specify a class of utility functions for which convergence of the sum utility to a local optimum is guaranteed with asynchronous updates of beams, receiver filters, and utility weights. Numerical results are presented, which show that this method achieves interference alignment at high SNRs, and can achieve different points on the boundary of the achievable rate region by adjusting the MSE weights.