# Seminar: Interference Alignment in Single-Beam MIMO Networks: Algorithms and Large System Analysis

**Wolfgang Utschick
**

Mobile Communications

**Date:** April 21, 2010

**Location:** Eurecom - Salle des Conseils

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 sufciently 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 lters, and utility weights. In the second part we consider a network of K interfering transmitter receiver pairs, where each node has N antennas and at most one beam is transmitted per user. We investigate the asymptotic performance of different strategies, as characterized by the slope and y-axis intercept (or offset) of the high signal-to-noise ratio (SNR) sum rate asymptote. It is known that a slope (or multiplexing gain) of 2N − 1 is achievable with interference alignment. On the other hand, a strategy achieving a slope of only N might allow for a significantly higher offset. With the assumption that only a discrete number of strategies is able to achieve a slope of 2N − 1 for a given channel realization, we approximate the average offset when the best out of a large number L of these solutions is selected, by means of extreme statistics. Furthermore, we derive a simple large system approximation for a successive beam allocation scheme achieving a slope of N. We show that both approximations provide good matches to numerically simulated results for moderate system dimensions and discuss how the approximated asymptotes behave for larger systems depending on the relationship between L and N. (Joint work with David Schmidt from TUM and Michael L. Honig from Northwestern University, Illinois, USA)

**Permalink:** http://www.eurecom.fr/seminar/336

*Interference Alignment in Single-Beam MIMO Networks: Algorithms and Large System Analysis*