A pseudo-matched filter for chaos

TL;DR

This paper introduces a simple pseudo-matched filter for chaotic signals that, while slightly less effective than the optimal matched filter, is easier to implement at high speeds for radar systems.

Contribution

The authors propose a practical pseudo-matched filter consisting of a notch and low-pass filter, offering a high-speed alternative to the complex matched filter for chaos-based radar.

Findings

Pseudo-matched filter achieves 2.0 dB lower correlation SNR than the matched filter.

The pseudo-matched filter is easily realizable at >1 GHz speeds.

Performance comparison shows the pseudo-matched filter is a viable, simpler alternative.

Abstract

A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms produced by a piecewise-linear system. Motivated by these results, we describe a pseudo-matched filter, which removes noise from the same chaotic signal. It consists of a notch filter followed by a first-order, low-pass filter. We compare quantitatively the matched filter's performance to that of our pseudo-matched filter using correlation functions in a simulated radar application. On average, the pseudo-matched filter performs with a correlation signal-to-noise ratio that is 2.0 dB below that of the matched filter. Our pseudo-matched filter, though somewhat inferior in comparison to the matched filter, is easily realizable at high speed (> 1 GHz) for potential radar applications.