Secure Degrees of Freedom of the Multiple Access Wiretap Channel with Multiple Antennas

TL;DR

This paper characterizes the maximum secure data rates in a multi-antenna two-user communication system with an eavesdropper, revealing how eavesdropper antennas impact the system's security capacity.

Contribution

It derives the exact sum secure degrees of freedom for all antenna configurations, introducing new alignment schemes and matching converses to establish optimality.

Findings

Optimal sum s.d.o.f. depends on the number of eavesdropper antennas.

Achievable schemes are based on real and vector space alignment techniques.

Matching converses prove the optimality of the schemes.

Abstract

We consider a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel with $N$ antennas at each transmitter, $N$ antennas at the legitimate receiver, and $K$ antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of $N$ and $K$. We subdivide our problem into several regimes based on the values of $N$ and $K$, and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.