ROC Calculation for Burst Traffic Packet Detection—An Old Problem, Newly Revised

Burst traffic radio systems use short signal bursts, which are prepended with an a priori known preamble sequence. The burst receivers exploit these preamble sequences for burst start detection. The process of burst start detection is commonly known as Packet Detection (PD), which employs preamble sequence cross-correlation and threshold detection. One major figure of merit for PD performance is the so-called ROC—receiver operating characteristics. ROC describes the trade-off between the probability of missed detection vs. the probability of false alarm. This article describes how to calculate the ROC for specified preamble sequences by deriving the probability density function (PDF) of the cross-correlation metric. We address this long-standing problem in the context of LEO (low Earth orbit) satellite systems, where differentially modulated PN (pseudo-noise) sequences are used for packet detection. For this particular class of preamble signals, the standard Ricean PDF assumption no longer holds and needs to be revised accordingly within this article.