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Antenna design and angle-of-arrival (AoA) estimation are critical to the efficiency of wireless information and power transfer. The AoA estimation is challenging for energy-efficient lens antenna arrays (LAAs), due to discrete sets of fixed discrete Fourier transform (DFT) beams. This paper presents a novel fast and accurate approach for the AoA estimation of LAAs. The key idea is that we prove the two differential outputs of three adjacent lens beams, referred to as “DFT beam differences (DBDs),” that are the strongest at the two sides of an AoA. They are easy to identify and robust to noises, and their powers are proved to provide an accurate estimate of the AoA. Another important aspect is a new beam synthesis technique which produces different beam widths based on DFT beams and practical 1-bit phase shifts in real time. As a result, the angular region containing the AoA can exponentially narrow down, and the …