Interference Alignment Designs for Secure Multiuser MIMO Systems: Rank Constrained Rank Minimization Approach

TL;DR

This paper introduces a novel interference alignment approach for secure multiuser MIMO systems by formulating a rank minimization problem and proposing convex relaxations, leading to improved secrecy performance.

Contribution

It formulates the secure IA problem as a rank constrained rank minimization and develops convex relaxation methods for practical solutions.

Findings

Proposed IA schemes outperform conventional designs in secrecy sum rate.

Convex relaxations enable tractable solutions for the rank minimization problem.

The new designs match or surpass existing secure IA methods in performance.

Abstract

In this paper, we formulate the interference alignment (IA) problem for a multiuser multiple-input multiple-output (MIMO) system in the presence of an eavesdropper as a rank constrained rank minimization (RCRM) problem. The aim of the proposed rank minimization IA schemes is to find the precoding and receiver subspace matrices to align interference and wiretapped signals into the lowest dimension subspaces while keeping the desired signal subspace spanning full available spatial dimensions. To deal with the nonconvexity of the rank function, we present two convex relaxations of the RCRM problem, namely nuclear norm (NN) and reweighted nuclear norm (RNN), and transform the rank constraints to equivalent and tractable ones. We then derive a coordinate decent approach to obtain the solutions for IA schemes. The simulation results show that our proposed IA designs outperform the conventional IA design in terms of average secrecy sum rate. On the other hand, our proposed designs perform the same or better than other secure IA schemes which account for low interference and wiretapped signal power rather than for low dimensions of interference and wiretapped signal matrices in the systems which achieve the perfect IA.