Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming (1012.3875v2)

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.

• The paper demonstrates that transmit beamforming optimized via semidefinite programming maximizes secrecy rates in MISO channels despite nonconvexity challenges.
• It develops robust designs by addressing both perfect and imperfect channel state information using a worst-case spherical uncertainty model.
• Simulation results validate the SDP method's superiority over traditional MRT techniques, especially with multiple eavesdroppers or strong interfering signals.

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

The paper presented in the paper addresses the increasingly significant concern of ensuring secure communication in wireless systems through physical-layer security techniques, specifically targeting the scenario where a multi-input single-output (MISO) channel is eavesdropped on by multiple multi-antenna adversaries. The scenario of interest is critical in environments such as downlink communications where eavesdroppers may have superior hardware capabilities compared to the intended single-antenna receiver.

Problem Formulation

The authors formulate the problem of maximizing the secrecy rate, defined as the rate at which information is communicated to the intended recipient while simultaneously ensuring that eavesdroppers obtain negligible information. This problem is inherently challenging due to its nonconvex nature stemming from the concave mutual information difference terms involved.

The paper distinguishes between cases of perfect and imperfect channel state information (CSI):

1. Perfect CSI: The authors propose converting the original secrecy rate maximization (SRM) problem into a semidefinite programming (SDP) problem, allowing for efficient solution via existing convex optimization techniques. They show that for both perfect and imperfect CSI scenarios, transmit beamforming emerges as the optimal strategy, which is consistent with intuitive expectations for known single-eavesdropper cases but generalized here to multiple eavesdroppers.
2. Imperfect CSI: The paper extends the SDP technique to handle channel uncertainties through a worst-case robust approach. The authors employ a spherical uncertainty model to represent the channel estimation errors, and they demonstrate that this more complex formulation can also be solved via SDP.

Numerical Results and Implications

The authors provide simulation results highlighting the advantages of the SDP approach over some suboptimal techniques like projected maximum-ratio transmission (projected-MRT) and plain maximum-ratio transmission (MRT). The SDP-based methods consistently outperform others, particularly as the number of eavesdroppers increases, or the eavesdroppers' signal strength becomes comparable to or stronger than the intended receiver's.

Theoretical Insights

A key theoretical finding is the confirmation that transmit beamforming is the optimal strategy under both perfect and imperfect CSI scenarios, aligning with previously known results for simpler setups and supporting their extension to more complex situations with multiple eavesdroppers.

The paper underscores the importance of developing transmit strategies that are robust against channel uncertainties, highlighting that simple non-robust designs can suffer significant secrecy rate losses when channel information is not perfectly known.

Future Research Directions

The paper opens avenues for further investigation, such as exploring the integration of artificial noise to enhance secrecy rates or extending the SDP approach to accommodate broader communication constraints, such as per-antenna power limits or multicast scenarios. Furthermore, the framework presented in this work can potentially be adapted to explore MIMO scenarios or other channel models in more dynamic and broader network environments. These extensions are critical as they provide practical relevance to emerging cognitive radio applications and other advanced wireless communication systems where security remains a pivotal concern.