Asymptotic generalized eigenvalue distribution of block Toeplitz matrices and application to space-time beamforming

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. In this paper, we extend the Szegö's theorem for the generalized eigenvalues of Hermitian block Toeplitz matrices derived under the assumption of absolutely summable sequences. Then, we apply this result to wideband spacetime beamforming performance analysis where the optimal SINR can be interpreted as the largest generalized eigenvalue of a block Toeplitz matrices' pair. We show that the optimal space-time SINR converges to an upper bound that can be interpreted as an optimal zero-bandwidth spatial SINR and interpret this result for several jamming scenarios.