Barankin-Type Bound for Constrained Parameter Estimation

In constrained parameter estimation, the classical constrained Cramer-Rao bound (CCRB) and the recent Lehmann-unbiased CCRB (LU-CCRB) are lower bounds on the performance of mean-unbiased and Lehmann-unbiased estimators, respectively. Both the CCRB and the LU-CCRB require differentiability of the likelihood function, which can be a restrictive assumption. Additionally, these bounds are local bounds that are inappropriate for predicting the threshold phenomena of the constrained maximum likelihood (CML) estimator. The constrained Barankin-type bound (CBTB) is a nonlocal mean-squared-error (MSE) lower bound for constrained parameter estimation that does not require differentiability of the likelihood function. However, this bound requires a restrictive mean-unbiasedness condition in the constrained set. In this work, we propose the Lehmann-unbiased CBTB (LU-CBTB) on the weighted MSE (WMSE). This bound does not require differentiability of the likelihood function and assumes uniform Lehmann-unbiasedness, which is less restrictive than the CBTB uniform mean-unbiasedness. We show that the LU-CBTB is tighter than or equal to the LU-CCRB and coincides with the CBTB for linear constraints. For nonlinear constraints the LU-CBTB and the CBTB are different and the LU-CBTB can be a lower bound on the WMSE of constrained estimators in cases, where the CBTB is not. In the simulations, we consider direction-of-arrival estimation of an unknown constant modulus discrete signal. In this case, the likelihood function is not differentiable and constrained Cramer-Rao-type bounds do not exist, while CBTBs exist. It is shown that the LU-CBTB better predicts the CML estimator performance than the CBTB, since the CML estimator is Lehmann-unbiased but not mean-unbiased.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A general class of lower bounds on the probability of error in multiple hypothesis testing

In this paper, a new class of lower bounds on the probability of error for m-ary hypothesis tests is proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP) criterion, is usually not tractable. The new class is derived using Hölder's inequality. The bounds in this class are continuous and differentiable function of the conditional probability of error and they provide good prediction of the minimum probability of error in multiple hypothesis testing. It is shown that for binary hypothesis testing problem this bound asymptotically coincides with the optimum probability of error provided by the MAP criterion. This bound is compared with other existing lower bounds in several typical detection and classification problems in terms of tightness and computational complexity

Neural Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with a-priori unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.Comment: Submitted to IEEE Transactions on Aerospace and Electronic System

Neural Network-Based Multi-Target Detection within Correlated Heavy-Tailed Clutter

This work addresses the problem of range-Doppler multiple target detection in a radar system in the presence of slow-time correlated and heavy-tailed distributed clutter. Conventional target detection algorithms assume Gaussian-distributed clutter, but their performance is significantly degraded in the presence of correlated heavy-tailed distributed clutter. Derivation of optimal detection algorithms with heavy-tailed distributed clutter is analytically intractable. Furthermore, the clutter distribution is frequently unknown. This work proposes a deep learning-based approach for multiple target detection in the range-Doppler domain. The proposed approach is based on a unified NN model to process the time-domain radar signal for a variety of signal-to-clutter-plus-noise ratios (SCNRs) and clutter distributions, simplifying the detector architecture and the neural network training procedure. The performance of the proposed approach is evaluated in various experiments using recorded radar echoes, and via simulations, it is shown that the proposed method outperforms the conventional cell-averaging constant false-alarm rate (CA-CFAR), the ordered-statistic CFAR (OS-CFAR), and the adaptive normalized matched-filter (ANMF) detectors in terms of probability of detection in the majority of tested SCNRs and clutter scenarios.Comment: Accepted to IEEE Transactions on Aerospace and Electronic System