A Toeplitz-induced mapping technique in sensor array processing

The paper has a two-fold purpose; it deals with the signal processing of nonuniform linear array, and it indicates a novel approach to achieving significant improvements in signal processing performance in sublattice array scenarios. All the efforts are based on a new concept called Toeplitz-induced mapping (TIM). A real-valued matrix associated with the Toeplitz-induced mapping is constructed in a specific manner: from a single vector that is able to be viewed as the coefficient vector of a polynomial. If the polynomial has any of roots on the unit circle, the real-valued matrix is singular, and the right singular vectors corresponding to the zero singular values are then associated with the roots on the unit circle, and consequently, the roots on the unit circle can be computed from these singular vectors. By virtue of the observations, we are able to implement array aperture interpolation (signal recovery) and signal enhancement. In particular, in the presence of highly correlated sources, application of a TIM-based signal enhancement algorithm to DOA estimation results in a considerable performance improvement. Computer simulation results are presented to show the effectiveness of the TIM technique