Adaptive beamforming plays an increasingly vital role in various applications, including radar, sonar, telecommunications, and many other related fields. In this paper, we present an adaptive beamformer (called polarimetric Sparse-Reconstruction beamformer) based on cascaded sparse diversely polarized planar array. The cascaded sparse array consists of multiple parallel sparse linear subarrays, whose difference co-array has no holes. The beamformer is operated in the joint spatial and polarization domain; thus, can potentially suppress the interferences that are close to the desired signal with different polarization states. Two key building blocks of our proposed beamformer are polynomial rooting-based closed-form two-dimensional direction-of-arrival and polarization joint estimation procedures, where the involved polynomial coefficients are also derived. Then, the closed-form power distribution estimation is presented to reconstruct the interference-plus-noise covariance matrix by leveraging the sparsity of the desired signal and interferences in the joint spatial and polarization domain. Thus, the proposed adaptive beamformer is computationally efficient, since all the procedures involved are formatted by closed-form expressions. Finally, a set of simulation examples are given to evaluate the characteristics of the proposed cascaded sparse array as well as the performance and robustness of the proposed beamformer in different scenarios, and compared against several existing approaches.

Widely linear (WL) robust adaptive beamforming exhibits superior performance by effectively leveraging the additional noncircularity information. However, existing studies focus solely on the noncircular (NC) impinging interferences, often overlooking main-lobe interferences and suffering from high computational complexity. To tackle these challenges, this paper introduces a generalized WL sparse reconstruction (GWLSR) beamforming framework that addresses the general scenario where the impinging interferences consist of mixed circular and NC signals from a sparse reconstruction perspective. The framework considers two variants, GWLSR1 and GWLSR2, to accommodate circular and NC signal-of-interest, respectively. Within this framework, we can estimate the power of a larger number of interferences in the general scenario, supported by a root finding-based approach for direction-of-arrival (DOA) and NC phase (NCP) estimation. We then reconstruct the conjugate augmented interference-plus-noise covariance by leveraging the estimated DOAs, NCPs, and power associated with the interferences. The proposed beamformers are computational efficient as all the involved procedures can be formulated using close-form expressions. Additionally, they can effectively suppress main-lobe interferences. Simulation examples are provided to illustrate the advantages of the proposed beamformers.

The problem of closed-form parameter estimation using a diversely polarized antenna array of arbitrary configurations is herein considered, under the coexistence of circular and strictly noncircular signals that occurred in communication/radar systems. By incorporating noncircularity difference and polarization diversity of the incident sources with augmented polarimetric manifold decoupling, the conventional polynomial rooting based polarimetric element space (PES) subspace technique is enhanced for direction of arrival, polarization, and noncircularity phase (for strictly noncircular sources) estimation. A subspace constraint based method is also presented to improve parameter estimation of the strictly noncircular sources. Simulation results are included to illustrate the performance of the proposed methods.

Numerous studies on direction finding have focused on traditional passive sparse arrays with enhanced degrees-of-freedom (DoFs). However, many unexplored areas remain in the realm of active sparse multiple-input multiple-output (MIMO) radar, which holds the potential for further enhancing DoFs. In this study, we concentrate on direction, specifically two-dimensional (2D) direction-of-arrival and 2D direction-of-departure, finding for sparse bistatic MIMO radar. Unlike most existing studies that utilize only partial (cross-) covariance data associated with different subarrays, we propose a four-stage reconstruction-based approach that reconstructs the covariance data for the entire transceiver step by step while maintaining low computational complexity, as it requires only addition operations. This process includes a data rearrangement procedure utilizing our defined selection matrices. To evaluate the performance of our proposed approach, we also derive the Cramér-Rao bound for the multi-parameters involved in our sparse bistatic MIMO radar framework. Numerical simulations are conducted to validate the advantages of the proposed method, including increased identifiability and improved estimation performance, thanks to the enhanced DoFs.