Approximate MLE of High-Dimensional STAP Covariance Matrices with Banded & Spiked Structure -- A Convex Relaxation Approach

Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample Covariance Matrix (SCM) becomes ill-conditioned. To capture the ICM and high noise floor, we model the covariance matrix using a ``Banded+Spiked'' structure. Since the Maximum Likelihood Estimation (MLE) for this model is non-convex, we propose a convex relaxation which is formulated as a Frobenius norm minimization with non-smooth convex constraints enforcing banded sparsity. This relaxation serves as a provable upper bound for the non-convex likelihood maximization and extends to cases where the covariance matrix dimension exceeds the number of samples. We derive a variational inequality-based bound to assess its quality. We introduce a novel algorithm to jointly estimate the banded clutter covariance and noise power. Additionally, we establish conditions ensuring the estimated covariance matrix remains positive definite and the bandsize is accurately recovered. Numerical results using the high-fidelity RFView radar simulation environment demonstrate that our algorithm achieves a higher Signal-to-Clutter-plus-Noise Ratio (SCNR) than state-of-the-art methods, including TABASCO, Spiked Covariance Stein Shrinkage, and Diagonal Loading, particularly when the covariance matrix dimension exceeds the number of samples.

Radar Clutter Covariance Estimation: A Nonlinear Spectral Shrinkage Approach

In this paper, we exploit the spiked covariance structure of the clutter plus noise covariance matrix for radar signal processing. Using state-of-the-art techniques high dimensional statistics, we propose a nonlinear shrinkage-based rotation invariant spiked covariance matrix estimator. We state the convergence of the estimated spiked eigenvalues. We use a dataset generated from the high-fidelity, site-specific physics-based radar simulation software RFView to compare the proposed algorithm against the existing Rank Constrained Maximum Likelihood (RCML)-Expected Likelihood (EL) covariance estimation algorithm. We demonstrate that the computation time for the estimation by the proposed algorithm is less than the RCML-EL algorithm with identical Signal to Clutter plus Noise (SCNR) performance. We show that the proposed algorithm and the RCML-EL-based algorithm share the same optimization problem in high dimensions. We use Low-Rank Adaptive Normalized Matched Filter (LR-ANMF) detector to compute the detection probabilities for different false alarm probabilities over a range of target SNR. We present preliminary results which demonstrate the robustness of the detector against contaminating clutter discretes using the Challenge Dataset from RFView. Finally, we empirically show that the minimum variance distortionless beamformer (MVDR) error variance for the proposed algorithm is identical to the error variance resulting from the true covariance matrix.

Adaptive ECCM for Mitigating Smart Jammers

This paper considers adaptive radar electronic counter-counter measures (ECCM) to mitigate ECM by an adversarial jammer. Our ECCM approach models the jammer-radar interaction as a Principal Agent Problem (PAP), a popular economics framework for interaction between two entities with an information imbalance. In our setup, the radar does not know the jammer's utility. Instead, the radar learns the jammer's utility adaptively over time using inverse reinforcement learning. The radar's adaptive ECCM objective is two-fold (1) maximize its utility by solving the PAP, and (2) estimate the jammer's utility by observing its response. Our adaptive ECCM scheme uses deep ideas from revealed preference in micro-economics and principal agent problem in contract theory. Our numerical results show that, over time, our adaptive ECCM both identifies and mitigates the jammer's utility.