Toeplitz Matrix Reconstruction Algorithm for Rectangular Hollow Array

Among the directional angle calculation models of Bluetooth 5.1, the rectangular hollow array offers the advantage of shorter sampling time due to its fewer elements compared to traditional planar arrays. However, the antimultipath algorithms suitable for traditional planar arrays cannot be applied to rectangular hollow arrays. Therefore, this study proposes a virtual array filling algorithm, wherein four virtual matrices are inserted into the hollow matrix to transform the array into a uniform rectangular array. This algorithm ensures translation invariance of the rectangular array, enabling the application of the antimultipath coherent source algorithm to a rectangular hollow array. An algorithm for reconstructing Toeplitz matrices in two-dimensional uniform planar arrays is also proposed. Through the analysis of the spatial spectrum and angle estimation results of various algorithms, the effectiveness of the signal angle of arrival estimation theory is verified.