We herein describe an autonomous peer discovery scheme for Device-to-Device (D2D) communications. With the increasing popularity of D2D communications, an efficient means of finding the neighboring node, i.e., peer discovery, is required. To this end, we propose a new autonomous peer discovery scheme that uses azimuth spread (AS), delay spread (DS), and shadow fading of the uplink pilot from each mobile station (MS). Given that AS, DS, and shadow fading are spatially correlated, nodes that have similar values must be neighbors. The proposed scheme filters out the MSs that are unlikely to be neighbors and uses the Kolmogorov-Smirnov (K-S) test to improve the accuracy of neighbor discovery. Unlike previous peer discovery schemes that incur additional signaling overheads, our proposal finds neighboring nodes by using the existing uplink pilot transmission from MSs such that neighboring peers can be found autonomously. Through analysis and simulation, we show that neighboring MSs can be found accurately with low latency.