A novel weak signal detection method for Linear Frequency Modulation signal based on bistable system and Fractional Fourier Transform

Fractional Fourier Transform (FRFT) is regarded as an effective method for detection of Linear Frequency Modulation (LFM) signals in recent years. However, the performance of FRFT detection will deteriorate sharply in the weak noise scene. An alternative solution is the use of bistable system, which can generate stochastic resonance (SR), and is relatively easy to achieve. This paper proposes a novel LFM weak signal detection algorithm based on bistable system and FRFT, named BSFRFT. We use the SR effect of bistable system to amplify LFM signal, and then apply FRFT to the previous output. We also present an evaluation criteria to measure the ability of detection methods and to compare performance of FRFT and BSFRFT. Numerical simulations show that the algorithm is effective for two cases – the LFM signal covered by white noise or colored noise (including pink noise).