Principal component filter bank for band partitioned sidelobe cancellation

Principal component filter banks (PCFBs) have been shown to be optimal, if they exist, for a variety of signal processing applications. Ideally, the filters in PCFBs are the eigenvectors of the spectral density matrix of the input random process and therefore depend on the statistics of the input random process. This paper investigates the application of PCFBs to the problem of band partitioned sidelobe cancellation for a two channel canceler. In this context, the filters are the eigenvectors of the cross-spectral density matrix. The ideal filters have an infinite impulse response and are not realizable. Therefore, they must be approximated. Several algorithms are available, but in this paper, the PCFB filters were approximated using a simple, although suboptimal, window method. The cancellation performance of the PCFB was compared to the performance of a time domain GramSchmidt canceler, and band partitioned cancelers utilizing a dyadic filter bank, a wavelet packet filter bank (WPFB), a cosine modulated filter bank (CMFB), and a maximally decimated discrete Fourier transform filter bank (DFTFB). The performance of the approximated PCFB was found to be better than the time domain and dyadic cancelers, but not as good as the DFT, wavelet packet, and cosine modulated cancelers. This shortfall is attributed to the approximation of the ideal PCFB filters.