A new probability density function enhancing packet detection analysis for low SNR links

Packet detection is the first task that a receiver has to perform in a random access communication scheme. The evaluation of different packet detection methods depends on the probability density functions of the decision variables and their construction process. This paper provides a new probability density function (PDF) that enhances evaluation and implementation of one method, due to Schimidl and Cox (SC method), in the low signal-to-noise ratio (SNR) region as required for ultra-wideband (UWB) systems. The new PDF is accurate from high SNR, where it is well-matched by a Gaussian approximation, to SNR = 0, where the Gaussian approximation breaks down. It is thus useful for analyzing packet detection, while the Gaussian approximation is not. We use the new PDF for this purpose, and we compare the packet detection performance of the SC method with that of other candidate methods. The SC method is shown to provide a good tradeoff between performance (including robustness to multipath) and complexity.