Optimizing Legal Detection Probability in Sensor Networks with Limited Power

In this article, we address the problem of maximizing detection probability while satisfying minimum signal-to-noise ratio (SINR) constraints for secure sensor networks. The goal is to protect confidential information from illegal eavesdroppers while ensuring successful transmission of information at legitimate receivers. We propose a three-step approach to solve this complex problem, which involves simplifying the detection probability, formulating the problem using the semi-definite random (SDR) method, and rigorously verifying the tightness of the solution.
The problem is highly challenging due to the intricate relationships between transmit beamforming vectors and legal sensing receivers/illegal sensing eavesdroppers, as well as non-convex communication SINR constraints. Our approach enables us to obtain a globally optimal solution by breaking down the problem into manageable parts. First, we reformulate the detection probabilities for legal sensing receivers and the eavesdropping probability. Next, we formulate the problem using the SDR method, which allows for an efficient solution via off-the-shelf toolboxes. Finally, we verify the tightness of the obtained solution to ensure global optimality.
To simplify the detection probability, we represent it as a composite matrix containing identity matrices and zeros. This allows us to separate the problem into manageable segments, each with its unique properties. We then reformulate the problem by adopting the SDR method, which enables us to tackle the non-convex constraints of communication SINR.
The proposed approach offers several advantages over existing methods. Firstly, it provides a globally optimal solution that takes into account both the minimum SINR constraints and the maximum tolerable SNR constraints at information eavesdroppers and sensing eavesdroppers. Secondly, it ensures the security of confidential information by safeguarding against illegal eavesdropping. Finally, it offers a simple and efficient solution via off-the-shelf toolboxes, making it easy to implement in real-world scenarios.
In conclusion, this article presents an optimal solution for maximizing detection probability while satisfying minimum SINR constraints for secure sensor networks. By breaking down the problem into manageable parts and using a three-step approach, we are able to obtain a globally optimal solution that ensures the security of confidential information and successful transmission of information at legitimate receivers.