Statistical analysis of the nonhomogeneity detector

We consider the statistical analysis of the recently proposed nonhomogeneity detector for Gaussian interference statistics. We show that a more stringent test can be constructed by accounting for the statistics of the generalized inner product (GIP) test under the condition of finite training data support. In particular, exact theoretical expressions for the GIP probability density function (PDF) and GIP mean are derived. Additionally, we show that for Gaussian interference statistics, the GIP admits a simple representation as the ratio of two statistically independent chi-square distributed random variables. Performance analysis of the more stringent GIP based test is presented.