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Neighbor discovery (ND) is a basic and crucial step for initializing wireless ad hoc networks. A fast, precise, and energy-efficient ND protocol has significant importance to subsequent operations in wireless networks. However, many existing protocols have a high probability of generating idle slots in their neighbor discovering processes, which prolongs the executing duration, thus compromising their performance. In this paper, we propose a novel randomized protocol FRIEND, which is a prehandshaking ND protocol, to initialize synchronous full-duplex wireless ad hoc networks. By introducing a prehandshaking strategy to help each node be aware of activities of its neighborhood, we significantly reduce the probabilities of generating idle slots and collisions. Moreover, with the development of single-channel full-duplex communication technology, we further decrease the processing time needed in FRIEND and construct the first fullduplex ND protocol. Our theoretical analysis proves that FRIEND can decrease the duration of ND by up to 48% in comparison with classical ALOHA-like protocols. In addition, we propose HD-FRIEND for half-duplex networks and variants of FRIEND for multihop and duty-cycled networks. Both theoretical analysis and simulation results show that FRIEND can adapt to various scenarios and significantly decrease the duration of ND.