Threshold Setting of Generalized Likelihood Ratio Test for Impropriety of Complex Signals

Abstract

Testing the impropriety of complex signals is of great importance in complex signal processing. Such test is often accomplished by the generalized likelihood ratio test (GLRT) in the literature. However, when the sample size is small, the associated decision threshold obtained via the existing methods is not accurate enough, which might produce incorrect decisions in practice. Moreover, few methods are available to deal with scenarios where the system dimensionality may be either low or high. To overcome these drawbacks, this letter develops two new methods to compute the threshold for a given nominal false alarm probability (FAP), without any assumptions on the sample size and system dimensionality. Specifically, the exact result of FAP in terms of MeijerG function is established, which enables us to accurately determine the threshold through numerical solution. We also develop an approximate method with low computational load and high precision, by means of box approximation as well as the properties of chi-square distribution. The effectiveness of our proposed methods is demonstrated via simulation results.