Performance Analysis of Matched Filter Bank for Detection of Linear Frequency Modulated Chirp Signals

Chirp signals arise in many applications of signal processing. In this paper, we address the problem of detection of chirp signals that are encountered in a bistatic radar which we are developing for remote sensing of cosmic ray induced air showers. The received echoes from the air showers are wideband and characterized by very short sweep periods. This makes our astrophysical problem a challenging one, since a very short sweep period is equivalent to a very low energy chirp signal. Furthermore, the related parameters of the received echoes are nondeterministic since they are tied to the physical parameters of the air showers. The primary focus of this research is to address these challenges and to find an optimized detection approach in the additive white Gaussian noise channel for low signal-to-noise ratio (SNR) levels. Matched filters are commonly used in the radar systems when the chirp signal is known. In this paper, we revisit this context and use a "matched filter" as a basis of building a rake-like receiver which consists of a set of filters matched to quantized chirp rates, logarithmically distributed within the chirp-rate interval of interest. We examine the detection capability of the proposed structure through extensive theoretical and numerical analysis. Theoretical analysis and simulation results prove that the proposed detector has high detection capability for a range of chirp slopes in a low-SNR environment.