Abstract-In many detection and estimation problems associated with processing of second-order stationary random processes, the observation data are the sum of two zero-mean second-order stationary processes: the process of interest and the noise process. In particular, the main performance criterion is the signal-to-noise ratio (SNR). After linear filtering, the optimal SNR corresponds to the maximal value of a Rayleigh quotient which can be interpreted as the largest generalized eigenvalue of the covariance matrices associated with the signal and noise processes, which are block multilevel Toeplitz structured for -dimensional vector-valued second-order stationary -dimensional random processes x . In this paper, an extension of Szegö's theorem to the generalized eigenvalues of Hermitian block multilevel Toeplitz matrices is given, providing information about the asymptotic distribution of those generalized eigenvalues and in particular of the optimal SNR after linear filtering. A simple proof of this theorem, under the hypothesis of absolutely summable elements is given. The proof is based on the notion of multilevel asymptotic equivalence between block multilevel matrix sequences derived from the celebrated Gray approach. Finally, a short example in wideband space-time beamforming is given to illustrate this theorem.Index Terms-Asymptotic distribution, block multilevel Toeplitz matrix, generalized eigenvalues, multidimensional second-order vector valued stationary random process, Szegö's theorem.
In many detection and estimation problems associated with processing of second order stationary 2-D discrete random processes, the observation data are the sum of two zero-mean second order stationary processes: the process of interest and the noise process. In particular, the main performance criterion is the Signal to Noise Ratio (SNR). After linear filtering, the optimal SNR corresponds to the maximal value of a Rayleigh quotient which can be interpreted as the largest generalized eigenvalue of the covariance matrices associated with the signal and noise processes, which are Toeplitz block Toeplitz structured. In this paper, an extension of Szegö's theorem to the generalized eigenvalues of Hermitian Toeplitz block Toeplitz matrices is given, under the hypothesis of absolutely summable elements, providing information about the asymptotic distribution of those generalized eigenvalues and in particular of the optimal SNR after linear filtering.
This paper considers spatio-temporal filtering in ground-based rotating radar systems. After the drawbacks of the standard spatio-temporal processing in this context are underlined, an hybrid spatio-temporal scheme is proposed to overcome them. Finally, this introduced processing is compared to standard ones through Monte Carlo simulations.
In many detection applications, the main performance criterion is the Signal to Interference plus Noise Ratio (SINR). After linear filtering, the optimal SINR corresponds to the maximum value of a Rayleigh quotient, which can be interpreted as the largest generalized eigenvalue of two covariance matrices. Using an extension of Szegö's theorem for the generalized eigenvalues of Hermitian block Toeplitz matrices, an expression of the theoretical asymptotic optimal SINR w.r.t. the number of taps is derived for arbitrary arrays with a limited but arbitrary number of sensors and arbitrary spectra. This bound is interpreted as an optimal zero-bandwidth spatial SINR in some sense. Finally, the speed of convergence of the optimal wideband SINR for a limited number of taps is analyzed for several interference scenarios.
Abstract-This paper addresses the robustness of adaptive narrowband beamforming with respect to bandwidth based on the loss of performance in terms of signal-to-interference-plus-noise ratio (SINR). The criterion used by Zatman to define a narrowband environment, i.e., the ratio between the jammer plus noise covariance matrix and the noise eigenvalue, is studied from the point of view of a loss of SINR after narrowband beamforming under non narrowband conditions. Using theoretical results about the eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency by Lee, it is shown that Zatman's criterion can be interpreted as an upper bound on the SINR loss which is nearly reached under certain conditions that are specified.Index Terms-Adaptive beamforming, array signal processing, bandwidth, direction of arrival, narrowband, robustness, signal-tointerference-plus-noise ratio (SINR).
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