Adaptive Threshold Detection and Estimation of Linear Frequency-Modulated Continuous-Wave Signals Based on Periodic Fractional Fourier Transform

摘要

The fractional Fourier transform (FRFT) has been used to detect and estimate the parameters of linear frequency-modulated continuous-wave (LFMCW) in low probability of intercept radar waveforms. The FRFT, which is optimal for single linear frequency-modulated (LFM) signals, becomes sub-optimal when applied to LFMCW signals because the observed waveform of this type of signal is composed of concatenated LFM pulses. A new signal processing method, called the periodic FRFT (PFRFT), is proposed for the detection of LFMCW signals. First, the discrete PFRFT is studied and the signal processing gain of this transform for LFMCW signals is analyzed. Second, an adaptive threshold detection and estimation algorithm for LFMCW signals is formulated after analysis of the test statistics of the squared modulus of LFMCW signals when using the probability density function in the presence of Gaussian white noise. It is then proved that PFRFT-based estimation is equivalent to maximum likelihood estimation in the detection and estimation of LFMCW signals. Finally, the results of both the theoretical analysis and verification simulations show that the PFRFT significantly outperforms the FRFT for LFMCW signals.