Adaptive detection using low rank approximation to a data matrix

Using an accurate formula for the error in approximating a low rank component, we calculate the performance of adaptive detection based on reduced-rank nulling. In this principal component inverse (PCI) method, one temporarily regards the interference as a strong signal to be enhanced. The resulting estimate of the interference waveform is subtracted from the observed data, and matched filtering is used to detect signal components in the residual waveform. We also present a generalized likelihood-ratio test (GLRT) for adaptively detecting a low rank signal in the presence of low rank interference. This approach leads to a test which is closely related to the PCI method and extends the PCI method to the case where strong signal components are present in the data. A major accomplishment of the work is our calculation of the statistics of the output of the matched filter for the case in which interference cancellation and signal detection are carried out on the same observed data matrix. That is, no separate data is used for adaptation. Examples are presented using both simulated data and real, active-sonar reverberation data from the ARSRP, the Acoustic Reverberation Special Research Program of the Office of Naval Research