Optimum Extrapolation Techniques for Two-Dimensional Antenna Array Tapered Beamforming

Abstract

Optimizing antenna arrays is essential for achieving efficient beamforming with very low sidelobe level (SLL) where adopting tapered window functions is one of the straightforward efficient techniques for achieving this goal. Recently, two-dimensional (2D) beamforming has been extensively required for many applications; therefore, this paper proposes two extrapolation techniques applied to one-dimensional (1D) tapered functions to efficiently feed 2D antenna arrays using cross-linear and adaptive radial tapering techniques. The first proposed 2D cross-linear tapering technique determines the 2D tapering coefficients by Hadamard multiplication of two right-angled grids of repeated 1D functions, while the second proposed adaptive radial tapering technique locates the antenna element in the 2D array in terms of its radial distance with respect to the array center, then converts this distance to an element index in a virtual 1D tapering window to determine the element weighting value. The adaptive radial tapering technique is optimized for achieving the minimum SLLs. The two proposed techniques are analyzed and discussed, where it is found that the adaptive radial tapering provides deeper SLLs compared to the cross-linear tapering technique. The two extrapolation techniques are examined for four window functions including triangular (Bartlett), Hamming, cosine-square, and Blackman windows, and the simulation results show that for extrapolating the Blackman window using adaptive radial tapering, a −50 dB SLL can be achieved which is independent on the array size, while cross-linear tapering provides −35 dB and −41 dB SLLs for 16×16 and 32×32 antenna arrays, respectively.