似然比检验在雷达、通信信号的检测中具有重要意义。在简单的二元假设检验问题中,最终需要由似然比和判决门限做比较。根据似然比的不变性,可以将不同假设下似然比的条件概率密度函数进行关联。因此,在其他概率密度函数难以得到的情况下,检测概率和虚警概率可以仅仅根据某一个似然比的概率密度函数计算得到,从而降低了计算复杂度。另外,似然比的不变性可以证明接收机工作特性曲线的斜率特性。文中给出了似然比不变性的严格证明,可为似然比检验的应用提供更坚实的理论依据。

Likelihood ratio (LR) plays a key role in the signal detection of radar and communication field. In a simple binary hypothesis test problem, the decision making criterion is based on the LR. Based on the invariance property of LR, the conditional probability density functions of the LR under different hypotheses are associated. Thus, the calculation of the probability of detection or a false alarm only involves one of the conditional probability density functions, which reduces computational complexity when the other density function is difficult to obtain. In addition, the invariance property of the LR can be used to prove the slope property of the receiver operating characteristic (ROC). In this paper, a strict proof of this property is proposed which supplements a solid theoretical support for the LR test application.

TN957.51