Scale-invariant detection by a ratio of generalized variances

Motivated by the problem of designing a scale-invariant or self-normalizing test for detecting a multi-rank signal embedded in interference when no signal-free secondary data is available, a scale-invariant test based on a ratio of generalized variances is proposed in this paper. Computer simulations show that the prototype test works well. Remarkably, it is shown that the new ratio of generalized variances test can be interpreted as a ratio of the determinants of Wiener filter error covariance matrices, and in the case of a rank-1 signal, the new method is equivalent to a normalized version of Capon's method