Linear Transceiver Design for Interference Alignment: Complexity and Computation

TL;DR

This paper investigates the complexity of designing optimal linear transceivers for interference alignment in MIMO channels, proving NP-hardness in general and proposing a distributed algorithm that improves throughput.

Contribution

It establishes the NP-hardness of maximizing degrees of freedom in MIMO interference channels and introduces a distributed algorithm for transceiver design.

Findings

Maximizing degrees of freedom is NP-hard for general MIMO channels.

Checking the achievability of a degrees of freedom tuple is NP-hard with at least three antennas per receiver.

The proposed distributed algorithm outperforms existing interference alignment methods in simulations.

Abstract

Consider a MIMO interference channel whereby each transmitter and receiver are equipped with multiple antennas. The basic problem is to design optimal linear transceivers (or beamformers) that can maximize system throughput. The recent work [1] suggests that optimal beamformers should maximize the total degrees of freedom and achieve interference alignment in high SNR. In this paper we first consider the interference alignment problem in spatial domain and prove that the problem of maximizing the total degrees of freedom for a given MIMO interference channel is NP-hard. Furthermore, we show that even checking the achievability of a given tuple of degrees of freedom for all receivers is NP-hard when each receiver is equipped with at least three antennas. Interestingly, the same problem becomes polynomial time solvable when each transmit/receive node is equipped with no more than two antennas. Finally, we propose a distributed algorithm for transmit covariance matrix design, while assuming each receiver uses a linear MMSE beamformer. The simulation results show that the proposed algorithm outperforms the existing interference alignment algorithms in terms of system throughput.