Sum Secrecy Spectral Efficiency Maximization in Downlink MU-MIMO: Colluding Eavesdroppers

In this paper, we consider a single-cell downlink multi-user multi-input multi-output (MU-MIMO) system in which multiple eavesdroppers coexist. The eavesdroppers overhear confidential information sent from a base station (BS). In particular, we assume a scenario of colluding eavesdroppers in which they cooperate with each other to decode the information. We develop a secure linear precoding method that maximizes the sum secrecy spectral efficiency. To this end, we formulate an optimization problem and propose a computationally-efficient algorithm that achieves a sub-optimal stationary point of the problem. Simulation results validate the proposed algorithm. The proposed method possesses several benefits:
$i)$
it is applicable in general systems, for example, an arbitrary number of eavesdroppers and confidential information set,
$ii)$
the associated complexity is relatively low, and
$iii)$
it is also applicable when only channel covariance of the eavesdroppers is available.