MIMO Multiple Access Channel with an Arbitrarily Varying Eavesdropper

TL;DR

This paper characterizes the secrecy degrees of freedom region for a MIMO multiple access channel with an arbitrarily varying eavesdropper, proposing a simple orthogonalization scheme that achieves optimal secrecy performance.

Contribution

It provides the first characterization of the s.d.o.f. region under strong secrecy for this channel model and introduces a straightforward transmission scheme to attain it.

Findings

Achieves the secrecy degrees of freedom region with a simple orthogonalization scheme.

Establishes an upper bound on the weighted-sum-rate using induction and channel grouping.

Demonstrates the effectiveness of single-user wiretap codes in a multi-user setting.

Abstract

A two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices at the legitimate terminals are fixed and revealed to all the terminals, whereas the channel matrix of the eavesdropper is arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver and uses a single-user wiretap code is shown to be sufficient to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using induction, where at each step one combines the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.