Ill-Posed Theory and Applications for Guaranteeing the Security of Wireless Physical Layer

The Ill-posed security theoretical framework for guaranteeing wireless physical-layer security is proposed in the paper, by introducing the concept of ill-posed. Firstly, the ill-posed security transforms non-unique and instability of solutions into information redundancy, which transforms the original problem into two randomized problems with redundancy combining the theory of perturbation. The framework includes the first kind ill-posed secure theory based on non-unique solutions and the second kind ill-posed secure theory based on instable solutions of an ill-posed problem. The first one utilizes the non-uniqueness of ill-posed problem to introduce redundancy for the transmitted precoding parameters, which is used to randomize transmitted signals for guaranteeing physical-layer security. The second one utilizes the instability of ill-posed problem to introduce redundancy for the transmitted precoding parameters, which can be used to guarantee physical-layer security at a little cost of legitimate users’ performance. Secondly, the security of the proposed framework is measured by using secrecy capacity with imperfect channel statement information. At last, some typical examples are researched under the theoretical framework of ill-posed security. The results reveal that the existing signal processing based physical-layer security methods are all the special cases of the framework.