Detection of number of sources via exploitation of centro-symmetry property

Forward/backward (FB) averaging is a technique which can be employed in sensor array signal processing for exploiting a so-called centro-symmetry property of the signal subspace to improve parameter estimation accuracy. Although FB averaging effectively doubles the number of data samples, it also introduces correlation among these data vectors. This correlation complicates not only the performance analysis, but also the detection of the number of sources. When FB averaging is employed, existing detection procedures such as sequential hypothesis (SH) likelihood ratio tests, minimum description length (MDL), and an information criterion (AIC) must be modified to correctly account for this preprocessing of the data. Herein, proper exploitation of the centro-symmetry property of the FB averaged covariance is described and a rigorous analysis is conducted. It is shown that the general scheme of existing methods is still applicable to the FB averaging case, but that the parameters (e.g., degrees of freedom) need to be adjusted