On the Structured Design Methodology of Effective PRACH Detection: Multi-Stage Thresholding Perspective

In this paper, we provide a tutorial on the structured design of effective Physical Random Access CHannel (PRACH) preamble detection based on correlation power. Specifically, the main contribution of this paper is to provide the design methodology leveraging multi-stage thresholds by which Preamble ID and PRACH-related time information (Timing Advance) for identifying the transmitted PRACH preamble signal are obtained. For enhancing the effectiveness of the designed PRACH preamble detector, we also consider joint optimization of multi-stage thresholds beyond the individual optimization of each threshold based on the Power Delay Profile. Consequently, the designed PRACH preamble detector is shown to have a reasonable performance in the sense of detection and false alarm probabilities, which is validated through numerical simulations considering the 3rd Generation Partnership Project conformance test.