Minimum Mean Squared Error interference alignment

Abstract

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.

On the MIMO interference channel

“…For instance, the problem of joint transmitter and receiver design to minimize the sum-MSE of a multiuser MIMO uplink was considered in [12] where iterative algorithms that jointly optimize precoders and receivers were proposed. Subsequently [13] applied this algorithm to the MIMO IFC where each user transmits a single stream and a similar iterative algorithm to maximize the sum rate was proposed in [14].…”

Interference Alignment for UWB-MIMO Communication Systems

“…There is no known closed-form solution for K > 3 users, but iterative algorithms exist. In this section, we present implementation complexity estimates of the minimum mean square error (MMSE) IA algorithm presented in [27]. The MMSE-IA algorithm starts with arbitrary precoding matrices V k , then iteratively updates the decoding and precoding matrices U k and V k according to Eq.…”

“…where E single is the electric field of the sampling antenna used (a dipole in this case), N ant is the total number of transmitter or receiver antennas (since they both use the same sampling antenna configuration), β is the wave number, d is the distance from the origin of the sampling antenna to a far-field observation point, a i ∠ζ i is the weighting from the U and V beamforming matrices, d i − d = ∆ϕ in (27) and ∆x i , ∆y i , ∆z i are the position of the individual elements in the array according to the Cartesian coordinate system. …”

Cognitive Interference Alignment for Spectral Coexistence

“…The alternating minimization approach proposed in [49] uses similar distributed IA but does not explicitly assume channel reciprocity. An alternative approach based on weighted minimum mean square error (MMSE) beamforming proposed in [52] compares favorably to the max-Signal to Interference and Noise Ratio (SINR) algorithm and can also provide unequal priorities for the users' rates. Let us consider a cellular system with B BSs equipped with N antennas and each BS exclusively provides wireless service to K users each equipped with M antennas.…”