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One of the most important processes in device-to-device communications of cellular devices is that of discovery, which determines the proximity of devices. When a discovery process is performed, there are several parameters to determine, including the discovery range, the discovery period, and the modulation and coding scheme of the discovery messages. In this paper, we address the relationships between these parameters and describe an optimization framework to determine them. In the proposed procedure, it is important to first optimize the discovery rate, which is defined as the number of discoverable devices per unit time. Once the discovery rate is maximized, the discovery period can be determined accordingly based on the device density and the target discovery range. Since the discovery rate is not affected by many of discovery parameters such as the discovery range, the device density, and the discovery period, it can be used as a performance metric for comparing discovery schemes with different discovery ranges or different discovery periods

Optimization Framework and Parameter Determination for Proximity-Based Device Discovery in D2D Communication Systems