SNR threshold region prediction via singular value decomposition of the Barankin bound kernel

Engineers are often interested in characterizing estimator performance for all possible SNR operating points. The Crámer-Rao lower bound (CRLB) is known to provide a tight lower bound on estimator mean-squared error (MSE) under asymptotic conditions associated with high SNR and/or large data lengths. The maximum likelihood estimator (MLE), a compact function, is known to exhibit the so-called threshold phenomenon in non-linear estimation problems. This threshold region is associated with the MLE selecting side-lobes over the main-lobe with high probability. Therefore, it is important to be able to determine the threshold SNR value past which the performance of the MLE rapidly deviates from the CRLB where small changes in SNR can produce large changes in MSE. One approach for predicting the SNR threshold is based on the computation of the Barankin bound (BB) that can provide a tighter bound than the CRLB on estimator performance. In this paper, we propose a threshold prediction algorithm based on the effective rank of the BB kernel matrix computed via singular value decomposition (SVD). We demonstrate the proposed prediction technique for the time-delay, frequency, and angle of arrival sensing problems and compare to other known prediction techniques from the literature.