Abstract-The shadowing relationship between facet elements can be determined rapidly through analytical expressions. On the basis of modeling using curved surfaces, an effective shadowing processing algorithm is proposed which is in combination with that used in the shadowing judgement of facet elements. Firstly several sampling points are taken on the ergodic curved surface element to construct a group of facet elements, which can replace the curved surface element. Then the shadowing processing between the stationary phase point and the ergodic curved surface element is converted to that between the stationary phase point and several facet elements, thus avoiding utilizing optimization method and can increase the computation speed. Similarly, the shadowing processing between the stationary phase segment and the ergodic curved surface element is converted to that between the stationary phase segment and several facet elements. And the trimming algorithm is used to accurately find the visible part of the stationary phase segment, which gets rid of the rough shadowing processing technique that determines the visibility of the whole stationary phase segment through the visibility of the center of the stationary phase segment. Therefore, the computation precision is greatly improved. When there exists a huge number of curved surfaces, maximum-minimum preprocessing is utilized to increase the computation speed. Examples show that this novel algorithm is superior to the traditional one in both computation speed and precision.Corresponding author: Y. X. Xu (yxxu@mail.xidian.edu.cn). 326Xu et al.

Abstract-Traditionally, the direction of arrival (DOA) estimation usually employs homogeneous antenna arrays consisting of many identical antennas. This paper proposes a new technique of DOA estimation by using a heterogeneous array which has many elements with each element pointing to a different direction from others. A general expression of the manifold for planar heterogeneous array is derived. Then, a polarized MUSIC (Pol-MUSIC) method for unknown polarizations is proposed. One advantage of this Pol-MUSIC method is that it can obtain the DOA of signals with any unknown polarizations while no search of the polarizations is required. The proposed method is verified by simulation, and its performance is analyzed. The heterogeneous array is a polarization-sensitive array though it has one channel at each point of spatial sampling. This provides favorable conditions for simplifying the systems.