Filter Design with Secrecy Constraints: The MIMO Gaussian Wiretap Channel

Abstract

This paper considers the problem of filter design with secrecy constraints, where two legitimate parties (Alice and Bob) communicate in the presence of an eavesdropper (Eve), over a Gaussian multiple-input-multiple-output (MIMO) wiretap channel. This problem involves designing, subject to a power constraint, the transmit and the receive filters which minimize the mean-squared error (MSE) between the legitimate parties whilst assuring that the eavesdropper MSE remains above a certain threshold. We consider a general MIMO Gaussian wiretap scenario, where the legitimate receiver uses a linear Zero-Forcing (ZF) filter and the eavesdropper receiver uses either a ZF or an optimal linear Wiener filter. We provide a characterization of the optimal filter designs by demonstrating the convexity of the optimization problems. We also provide generalizations of the filter designs from the scenario where the channel state is known to all the parties to the scenario where there is uncertainty in the channel state. A set of numerical results illustrates the performance of the novel filter designs, including the robustness to channel modeling errors. In particular, we assess the efficacy of the designs in guaranteeing not only a certain MSE level at the eavesdropper, but also in limiting the error probability at the eavesdropper. We also assess the impact of the filter designs on the achievable secrecy rates. The penalty induced by the fact that the eavesdropper may use the optimal non-linear receive filter rather than the optimal linear one is also explored in the paper.

arXiv comment38 pages, 11 figures. Accepted for publication in IEEE Transactions on Signal Processing

References in corpus (5)

• Secure Transmission with Multiple Antennas II: The MIMOME Wiretap Channel
• Robust Beamforming for Security in MIMO Wiretap Channels with Imperfect CSI
• Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes
• Towards the Secrecy Capacity of the Gaussian MIMO Wire-tap Channel: The 2-2-1 Channel
• Strong Secrecy for Erasure Wiretap Channels

Cited by in corpus (4)

• Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey
• Iterative distributed minimum total-MSE approach for secure communications in MIMO interference channels
• Remote State Estimation over Packet Dropping Links in the Presence of an Eavesdropper
• A Survey on MIMO Transmission with Discrete Input Signals: Technical Challenges, Advances, and Future Trends