Detection and Parameter Estimation of Quadratic Frequency Modulated Signal Based on Non-uniform Quadrilinear Autocorrelation Function

ObjectivePolynomial Phase Signal (PPS) analysis has attracted broad attention because many radar, sonar, and seismic signals are modeled as PPS of different orders. A first-order PPS can be focused into a frequency bin through the Fourier transform to estimate the center frequency. For higher order PPS, such as a Quadratic Frequency Modulated (QFM) signal, non-coherent characteristics limit the effectiveness of the Fourier transform for energy integration. Existing time–frequency distribution methods, such as the short-time Fourier transform and the Wigner-Ville distribution, do not resolve the conflicts between auto-terms and cross-terms or between time- and frequency-domain resolution. In addition, current algorithms face difficulties in balancing computational complexity and detection performance, which results in reduced parameter estimation accuracy. This study proposes a QFM detection method based on a non-uniform quadrilinear autocorrelation function to provide balanced performance for QFM parameter estimation with controlled computational cost.MethodsA time-frequency distribution method for QFM detection and parameter estimation is presented. The method applies non-uniform sampling and maps a one-dimensional signal into a two-dimensional time domain through a forth-order autocorrelation function. A non-uniform fast Fourier transform is used to resolve the time variable and concentrate the energy into a vertical line in the two-dimensional plane. Then, FFT is performed along this line to focuse the signal into a peak, from which the chirp rate and quadratic chirp rate are estimated. Finally, dechirp processing compensates high-order phase terms of the original signal, and FFT yields the center frequency estimation result can be obtaioned through FFT operation.Results and DiscussionsTheoretical analysis and simulation results show that the method balances computational complexity and detection performance. Under low signal-to-noise ratio conditions, it distinguishes targets effectively and produces accurate parameter estimates (Fig. 1). For multicomponent signals with large amplitude differences, it enables stepwise detection and estimation (Fig. 2). Comparative experiments with state-of-the-art algorithms show that the method is quasi-optimal in estimation accuracy and integration gain (Fig. 3–Fig. 6). Compared with the ML estimator, it offers markedly higher computational efficiency.ConclusionsA QFM detection and parameter estimation method based on non-uniform quadrilinear autocorrelation functions is proposed. The method maps the QFM signal into a two-dimensional time domain through a new autocorrelation kernel and achieves coherent integration through scaling and FFT. Mathematical analysis and simulation results show that, relative to the ML method, it sacrifices part of the detection performance but substantially reduces computational complexity. When computational efficiency is similar, it outperforms other classical methods in detection and parameter estimation accuracy. The method provides a balanced solution for QFM signal detection and parameter estimation.