Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming

TL;DR

This paper develops convex semidefinite programming methods for optimal and robust transmit designs in MISO channels to maximize secrecy rates, addressing both perfect and imperfect channel state information scenarios.

Contribution

It reformulates the nonconvex secrecy-rate maximization problem as a tractable SDP, providing optimal solutions for both perfect and uncertain CSI cases.

Findings

SDP-based solutions outperform suboptimal designs in secrecy rate.

Transmit beamforming is optimal for secrecy-rate maximization.

Robust design effectively handles CSI uncertainties.

Abstract

In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.