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Neighbor discovery is an essential step for the self-organization of wireless sensor networks. Many algorithms have been proposed for efficient neighbor discovery. However, most of those algorithms need nodes to keep active during the process of neighbor discovery, which might be difficult for low-duty-cycle wireless sensor networks in many real deployments. In this paper, we investigate the problem of neighbor discovery in low-duty-cycle wireless sensor networks. We give an ALOHA-like algorithm and analyze the expected time to discover all n - 1 neighbors for each node. By reducing the analysis to the classical K Coupon Collector's Problem, we show that the upper bound is ne(log2 n + (3 log2 n - 1) log2 log2 n + c) with high probability, for some constant c, where e is the base of natural logarithm. Furthermore, not knowing number of neighbors leads to no more than a factor of two slowdown in the algorithm performance. Then, we validate our theoretical results by extensive simulations, and explore the performance of different algorithms in duty-cycle and non-duty-cycle networks. Finally, we apply our approach to analyze the scenario of unreliable links in low-duty-cycle wireless sensor networks.