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In randomly deployed networks, such as sensor networks, an important problem for each node is to discover its neighbor nodes so that the connectivity amongst nodes can be established. In this paper, we consider this problem by incorporating the physical layer parameters in contrast to the most of the previous work which assumed a collision channel. Specifically, the pilot signals that nodes transmit are successfully decoded if the strength of the received signal relative to the interference is sufficiently high. Thus, each node must extract signal parameter information from the superposition of an unknown number of received signals. This problem falls naturally in the purview of random set theory (RST) which generalizes standard probability theory by assigning sets, rather than values, to random outcomes. The contributions in the paper are twofold: First, we introduce the realistic effect of physical layer considerations in the evaluation of the performance of logical discovery algorithms; such an introduction is necessary for the accurate assessment of how an algorithm performs. Secondly, given the double uncertainty of the environment (that is, the lack of knowledge of the number of neighbors along with the lack of knowledge of the individual signal parameters), we adopt the viewpoint of RST and demonstrate its advantage relative to classical matched filter detection method.