Hybrid alternate projection algorithm and its application for practical conformal array pattern synthesis

Based on the fabricated 12-element cavity-backed microstrip sector cylinder array,a novel hybrid alternate projection algorithm（HAPA）,which combines analytical method with numerical techniques effectively,is proposed for synthesizing the pattern of practical conformal array.The algorithm applies the variable direction aperture projection method with mutual coupling correction techniques to provide the good initial excitations of elements to the enhanced alternate projection algorithm（EAPA）.In order to do further optimization,which improves the convergent speed of the algorithm significantly.Finally,the HAPA has been applied to the fabricated sector cylinder array with mutual coupling considered.The results of synthesized patterns,such as low sidelobe with null points formed pattern,beam scanning with low sidelobe pattern and the shaped beam pattern are presented.It demonstrates the validity of HAPA in practical conformal array synthesis.

A NOVEL DIRECTION OF ARRIVAL ESTIMATOR

A Direction Of Arrival(DOA) estimator based on the signal separation principle is introduced, and one of representative multidimensional estimators is established by introducing Matrix Operator projection signal steering Vector Excision(MOVE) operation. Thanks to Alternating Separation (AS) technique, the multidimensional problem is transformed into a series of one-dimensional optimal ones. Furthermore, an equivalent simplified implementation of the AS is obtained. Finally the definiteness and uniqueness of the estimator are analyzed.

Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations

Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative matrix X0 = 0, the least Frobenius norm symmetric positive semidefinite solution of these matrix equations is obtained. A numerical example shows that the new algorithm is feasible and effective.

Some properties of the alternating separation (AS), alternating projection (AP) and ASAP algorithm

This paper analyzes some properties of the alternating separation (AS) and alternating projection (AP) algorithm. The analysis shows that AS converges to the optimal point steadily but slowly, while AP converges to the optimal point quickly but is prone to immersing into the local extreme of the maximum likelihood (ML) criterion. To avoid their disadvantages and make use of their advantages, ASAP, which is the combination of AS and AP, is proposed. Simulation results show that the ASAP algorithm has the ability of estimating the direction of arrival more accurately and converging to optimal point more quickly.

Exploiting AML algorithm for multiple acoustic source 2D and 3D DOA estimations

The approximate maximum likelihood (AML) algorithm shows promises for joint estimations of acoustic source spectrum and direction-of-arrival (DOA). For the multisource case, the AML algorithm remains feasible as one considers an alternating projection procedure based on sequential iterative search on single source parameters. In order to perform multisource beamforming operations, earlier, we used a two-dimensional (2D) sensor array with 2D AML to obtain the DOA estimations for sources in the far field of the array. Now, the 3D AML algorithm enables a 3D sensor array to collect acoustic data for estimation of DOA represented in azimuth and elevation angles. In this paper, we consider two acoustic sources being simultaneously active and derive Crame′r-Rao bound (CRB) on DOA estimation given by a 3D array. Also, we compare the two-source DOA estimation results of 2D AML and 3D AML, respectively. To construct reasonable constraints on sensor topology, we adopt the concept of isotropic array and decouple the interplay between azimuth and elevation angle variations. The 3D AML algorithm exhibits superior spatial separation over its 2D counterpart for multiple sources located at different azimuth and elevation angles. Although the 3D AML algorithm requires more demanding computational complexity, we have developed a number of efficiency enhancements to reduce the loading for the grid search.