Performance Analysis of Separating Function Estimation Test for Impropriety of Complex Signals

In this work, a separating function estimation test (SFET) based detector is proposed for the problem of impropriety test of complex signals. With the establishment of closed-form expressions concerning the first two raw moments of the proposed test statistic, we can obtain the analytic form for the probability of false alarm (PFA) based on moment-matching method. Moreover, the threshold can be further obtained for a given user-specified PFA. Numerical examples are provided to verify our theoretical results and demonstrate the performance gain of our proposed detector.