For uniform linear arrays (ULAs), the z-polynomial of the clairvoyant minimum variance distortionless response (MVDR) beamformer theoretically has roots located on the unit circle (UC). Existing unit-circle root-constrained MVDR (UCRC-MVDR) methods require sample covariance matrix (SCM) inversion and polynomial rooting for initialization, which are computationally demanding and prone to instability, particularly for large arrays. This study proposes an alternative approach where the initial roots are already on the UC. Individual roots are sequentially optimized, rather than optimizing the full set of polynomial coefficients as in existing methods, thereby avoiding polynomial rooting. In addition, the algorithm leverages algebraic inversion of 2 x 2 matrices, eliminating the need for full SCM inversion and polynomial rooting, thereby improving both numerical stability and computational efficiency. The proposed method incorporates regularized covariance matrix estimates and rootwise variance sorting to achieve robust beamforming performance. By selectively optimizing a subset of UC roots, computational efficiency is further improved, making the method particularly suitable for large arrays. Simulation results demonstrate that the inverse-free UCRC-MVDR approach achieves superior beamforming performance across various ULA sizes and remains effective in low-sample scenarios, including single-snapshot cases.

This article proves that the roots of the $z$-polynomial corresponding to the ideal adaptive matched filter (AMF) lie on the unit circle (UC). Motivated by this proof, we propose UC roots-constrained AMF (UCRC-AMF), which enforces this fundamental UC roots property while maximizing the SINR to determine the detector polynomials. The UCRC algorithm exploits polynomial conjugate symmetry and applies it to the problem of radar moving target detection (MTD) in homogeneous and heterogeneous clutter. The algorithm splits the multidimensional AMF optimization problem into multiple 1-D AMF problems. Simulation studies show that the UCRC-based AMF for Gaussian clutter, as well as UCRC versions of NAMF and $\alpha$-AMF for compound Gaussian clutter significantly outperform existing state-of-the-art detection algorithms in the presence of limited secondary data and the performance gain is persistent for larger secondary data as well. This work will show that the combined enforcement of UC roots property on detector polynomials and complex-persymmetry of covariance matrices is most effective for superior detection performance. It is also shown that the proposed UCRC-AMF outperforms the existing methods when there is a mismatch with respect to the true target velocity and ideal covariance matrix structure. In addition, it will be demonstrated via simulation that the proposed UCRC-based detectors have approximate constant false alarm rate (CFAR) with respect to the unknown covariance matrix.

Moving target detection in heterogeneous clutter is a classic problem in the radar literature. Compound-Gaussian clutter models theoretically represent empirical radar data, and the K-distribution closely fits observed sea clutter for high-resolution radar with low grazing angle. The normalized adaptive matched filter (NAMF) and its persymmetric counterpart the PS-NAMF have been shown to be effective for compound-Gaussian clutter. Unit circle (UC) roots-based algorithms have been shown to be very effective for beamforming [1] and adaptive matched filters for homogeneous and heterogeneous clutter [2]–[4]. This paper presents a novel Unit Circle (UC) roots-based approach for heterogeneous clutter by leveraging the UC roots produced by the UCRC-AMF to develop a new UC roots-constrained Toeplitz Rectification (UCRC-TR) approach that is also proposed in this work. Simulation examples will be used to investigate the properties of the proposed Toeplitz rectification approach and to demonstrate its superiority when used in conjunction with the NAMF detector.

In this paper, we propose the modified unit circle roots constrained adaptive matched filter (M-UCRC-AMF) for radar moving target detection. By judiciously incorporating the forward-backward averaged sample covariance matrix (FB-SCM) within the previously reported unit circle roots constrained adaptive matched filter (UCRC-AMF) algorithm, substantial increases in the probability of detection can be achieved with limited secondary data. The superiority of the proposed approach is demonstrated via simulation examples under the assumption of limited secondary data.

Utilizing Carathèodory's theorem on positive definite, Toeplitz matrices, this paper presents a new spatial-domain proof that all roots of the Minimum-Variance Distortionless Response (MVDR) polynomial for a uniform linear array (ULA) lie on the unit circle (UC). The new proof is derived in the spatial domain leveraging the Toeplitz structure of the theoretical covariance matrix. Next, new results on the recently developed UC roots constrained MVDR (UCRC-MVDR) beamformer are presented that demonstrate its effectiveness in a variety of interference scenarios including multiple discrete and distributed sources, as well as for fully coherent sources. It is also shown that the performance gain of unit-circle roots based approach is maintained for a wide range of sensor array sizes. The proposed approach will also be shown to achieve superior performance at smaller aperture sizes than the conventional approaches, justifying its suitability for applications with reduced SWAP requirements. The experimental results show that the unit-circle based approach in general exhibits significant performance improvement than their conventional counterparts that do not enforce the unit circle roots property.

Clutter often exhibits low-rank structure in many radar applications (e.g., airborne radar, STAP, etc.). It has been shown recently that significant performance improvement can be achieved by constraining the roots of the AMF polynomial onto the unit circle (UC) satisfying a theoretical property of the Adaptive Matched Filter (AMF). Principal component Inverse (PCI)-based filters are effective but lack UC roots and associated nulling property of UC roots. In this paper, the UC-roots approach is extended to develop a new technique for low-rank clutter for improved performance in low sample support. Based on low-rank assumption, we derive the generalized likelihood ratio test (GLRT) using both primary and secondary data. The low-rank clutter subspace is estimated using the dominant eigenvectors of the sample covariance matrix (SCM). The proposed unit circle GLRT (UC-GLRT) radially projects the roots of the PCI-based filter onto the unit circle using orthogonal projection matrices such that the test statistics can be expressed in closed-form.

This paper presents a new general proof that the roots of the polynomial corresponding to the minimum variance filter computed using the true Toeplitz covariance matrix must fall on the unit circle (UC). Unlike a previous proof applicable to the Minimum Variance Distortionless Response (MVDR) case only, the new proof does not rely on Wiener-Khinchin theorem to map the problem into frequency domain. Furthermore, the proof is applicable to a general class of sensor array signal processing problems beyond MVDR. Next, new closed-form solutions of UC roots constrained (UCRC) MVDR beamformer and Adaptive Matched Filter (AMF) will demonstrate significant performance improvement than the conventional, non-UC counterparts. The proposed approach will also be shown to achieve superior performance improvement at smaller aperture sizes than the conventional approaches, justifying its suitability for applications with reduced SWAP requirements.

A 2004 paper had offered a theoretical proof that ideally the roots of the minimum variance distortionless response (MVDR) beamformer array polynomial lie on the unit circle (UC). However, existing MVDR methods fail to exploit this fundamental property adequately. This paper proposes a new adaptive beamforming design via UC roots optimization for uniform linear arrays (ULA). The proposed method starts with the sample matrix inversion (SMI) roots and optimizes the MVDR criterion for each root separately by splitting the N-dimensional MVDR problem into multiple 1-D optimization problems. Conjugate symmetry is imposed on individual 1st-order factors of the MVDR polynomial during optimization that guarantees UC roots. The proposed UC Roots Constrained MVDR (UCRC-MVDR) method is non-iterative and has a closed-form solution. It also works well with limited number of snapshots. UCRC-MVDR is computationally efficient and parallelizable as all roots can be optimized concurrently. In extensive simulation studies, UCRC-MVDR exhibits consistently superior performance over existing MVDR approaches, and its performance is closer to the ideal clairvoyant case than existing MVDR methods.

In this paper, we derive a novel variation of the adaptive matched filter (AMF) which enforces the unit circle roots property by exploiting polynomial conjugate-symmetry. Motivated by the theoretical necessity of this property for the minimum-variance distortionless response (MVDR) beamformer and based on the proportionality of the AMF and MVDR solutions, we apply our approach to the problem of radar moving target detection from a stationary platform. The proposed unit-circle roots constrained AMF (UCRC-AMF) shows improved detection performance with limited secondary data compared to the conventional AMF. The improved performance of the UCRC-AMF is demonstrated using simulation examples and compared to the conventional AMF as well as the known-covariance case.

A novel adaptive beamforming design is proposed that optimizes the minimum variance distortionless response (MVDR) beamformer array polynomial to guarantee unit circle (UC) roots for planewave beamforming with a uniform linear array (ULA), satisfying its theoretical property. The proposed method splits the multidimensional MVDR problem into multiple 1-D optimization problems. It uses the sample matrix inversion (SMI) roots and optimizes the MVDR criterion for each root while imposing conjugate symmetry constraints on individual 1st-order factors to ensure UC roots. The proposed method is non-iterative, has a closed-form solution and works well with limited number of snapshots using diagonal loading. UCRC-MVDR is computationally efficient and parallelizable as all roots can be optimized concurrently. In simulation studies, UCRC-MVDR exhibits consistently superior performance, and its performance is closer to the clairvoyant case than existing MVDR methods.

This paper concerns detection of a moving target in compound-Gaussian clutter with inverse-Gamma distributed power using a distributed active MIMO radar network. Adaptive detection requires an estimate of the clutter covariance matrix from a finite set of, possibly non-homogeneous, target-free training data. If the number of available training data are limited, conventional covariance matrix estimators will fail to provide adequate detection performance. This motivates the use of structured estimators which do not rely upon large amounts of training data. In this paper, a clutter covariance matrix estimator based non-negative linear least-squares is applied to the problem of adaptive moving target detection in the context of distributed MIMO radar. For each transmit-receive pair of the distributed radar network, an improved estimate of the clutter covariance matrix is computed using the non-negative least-squares estimator. Then, we apply the improved estimates in conjunction with a detector derived using inverse-Gamma distributed clutter power. Simulation examples are used to demonstrate the performance improvement of the constrained least-squares method as compared to a conventional technique. As a baseline, we a compare the performance of both the conventional and constrained least-squares methods against the clairvoyant detector.

Radar-based automatic target recognition (ATR) experiments rely on accurate and repeatable synthetic aperture radar (SAR) measurements performed in an anechoic chamber. Yet, the chamber poses challenges to joint electro-optic (EO) and SAR experiments. Here, we present an open-room approach that is suitable for simultaneous EO collection. The local measurement technique, data processing, and SAR ATR feature extraction are discussed with emphasis on EO fusion and the various tradeoffs at each stage. Examples of inverse SAR imagery at Ka -band demonstrate the relatively inexpensive, fast, and repeatable measurements. Finally, candidate EO fusion experiments are discussed.

A spatial filtering method is introduced for improving continuous-wave inverse synthetic aperture radar (ISAR) measurements in a partially controlled chamber. Twodimensional angle of arrival (AoA) estimation using a modified matrix pencil algorithm first identifies directions of interference sources outside the target zone. Then, each radar sweep is prefiltered to eliminate strong sources of chamber reflections without using radar absorbing materials. The system repeatabilty is also analyzed using a student T-test and results of before and after ISAR imagery are presented.

The primitive type attribute as recently reported in the spectrum parted linked image test algorithm is used for the first time in a 10-vehicle classification experiment. Attributed scattering centres (ASCs) from wideband polarimetric synthetic aperture radar imagery are surveyed and two highly complementary sets of attributes are compared in a nearest neighbour classifier. The classifier performance for each set of attributes is shown to be over 90% with 10 degrees sub-apertures and 10 dB additive white Gaussian noise which had not been considered in earlier works. Using a common image formation and ASC extraction method to ensure that only the pixel attributes differed, two different sets of complementary attributes are compared under precisely the same conditions. In addition, the query sets of attributed images are formed from azimuth and elevation angles that are not in the set of training angles. The results show that the classifier performance degrades gracefully as the signal-to-noise ratio (SNR) decreases below 10 dB and that the sensitivity to aspect angle is nearly the same for all vehicle classes as the SNR approaches 10 dB and above. The primary limitation of the approach is the use of wide-band, wide-aperture, and polarimetric radar data.