Linear time-varying matched filter for known and unknown SOI generalized cyclostationary signal with multiple cyclic frequencies

Chirp cyclic matched filter has been designed for chirp cyclostationary (CCS) signals, a kind of generalized cyclostationary signals, recently. However, it is designed based on statistical prior information and waveform of the signal-of-interest (SOI) CCS signal, which works only for CCS signal with a single chirp cyclic frequency. As known, the prior information of SOI signal may not be exactly known or the measured waveform of SOI signal is noised in practical applications, which decreases performance of the algorithm. In this study, by decomposing the imprecisely known SOI signal as the summation of SOI signal and an unknown additive disturbance, three kinds of chirp cyclic matched filters are designed according to the value of signal-to-noise ratio (SNR). Furthermore, noticing the CCS signal usually contains multiple chirp cyclic frequencies, three kinds of combined chirp cyclic matched filter are designed for known/unknown SOI CCS signals by linearly combining the chirp cyclic matched filter at every chirp cyclic frequency. Moreover, ramifications of the truncation process and complexity of the proposed algorithms are analyzed. Finally, simulation results validate the improvement of the chirp cyclic matched filter based on multiple chirp cyclic frequencies than on a single chirp cyclic frequency in different SNR situations.