Parameters estimation for mixed signals of low-level frequency-modulated signals with a combinational cubic phase function transformation

In this paper, a combinational cubic phase function(CCPF) transformation is introduced for the estimation and detection of low-level frequency-modulated signals. The CCPF transformation extends the standard cubic phase function (CPF) by studying random cubic phase function transform(RCT) and Integrated cubic phase function(ICPF) to handle cases involving low signal-to-noise ratio (SNR) and mixed signals interference of chirp signal (LFM) and quadratic frequency modulation signal(QFM) when parameters of each are approaching. The course of CCPF commonly includes two stages: firstly, realizing LFM reconstruction with ICPF; then estimating parameters of QFM when elimination LFM from mixed-signals is finished. The asymptotic mean squared error (MSE) of an CCPF-based estimator is verified by computer simulation. Comparison with traditional RCT is also included, which shows that the CCPF serves as a good candidate for mixed signal analysis.