中文摘要：

本文将不适定的思想引入无线物理层安全领域,提出不适定安全理论框架。首先,把不适定问题解的不唯一性或者不稳定性转化为信息冗余,然后结合扰动理论,使原问题转化为两类冗余信息随机化问题,形成了保障无线物理层安全的第一、二类不适定理论框架;然后,在存在信道估计误差的情况下,利用安全容量概念对理论框架的安全性能进行度量;最后,应用不适定安全理论框架研究了几个典型实例,结果表明：现有基于信号处理的物理层安全传输方法均为该理论框架的特例。

英文摘要：

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.