A Hilbert Transform for Antenna Array Beam Synthesizing

An analytical method is proposed to synthesize the flat-topped beam (FTB) with arbitrary beam directions for uniform linear arrays (ULAs). Following the analogy between the far-field pattern of ULAs and the spectrum function of finite impulse response (FIR) filters, the window method can be applied to synthesize both the broadside and end-fire FTBs, but failing in the synthesis of oblique FTB due to the undesired grating lobes. Thus, the Hilbert transform is introduced to suppress the grating lobe during the synthesis of oblique FTBs, and it can also further expand to a generalized method to design FTBs with arbitrary directions. The proposed approach is promising for offering efficient beamforming functionalities for wireless communications, imaging, and radar applications.