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Energy-efficient, highly integrated lens antenna arrays (LAAs) have found widespread applications in wideband millimeter wave or terahertz communications, localization and tracking, and wireless power transfer. Accurate estimation of angle-of-arrival (AoA) is key to those applications, but has been hindered by a spatial-wideband effect in wideband systems. This paper proposes to exploit (rather than circumventing) the spatial-wideband effect to develop a fast and accurate AoA estimation approach for LAAs. Specifically, we unveil new spatial-frequency patterns based on the spatial-wideband effect, and establish one-to-one mappings between the patterns and the strongest discrete Fourier transform (DFT) beam containing the AoA. With the strongest DFT beam identified, we propose a method to estimate the AoA uniquely and accurately, using only a few training symbols. This is achieved by deriving a new one-to-one mapping between the AoA and the set of DFT beams judiciously selected based on the strongest. In the case that an impinging path is uniformly distributed in
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