Parameter Estimation of LFM Signal Based on Bayesian Compressive Sensing via Fractional Fourier Transform

Compressive Sensing (CS) theory breaks through the limitations of traditional Nyquist sampling theorem, accomplishes the compressive sampling and reconstruction of signals based on sparsity or compressibility. In this paper CS is presented in a Bayesian framework for linear frequency modulated (LFM) cases whose likelihood or priors are usually Gaussian. In order to decrease the sampling pressure of hardware Bayesian CS (BCS) method is proposed which reconstructs the spectrum information of LFM signal via fractional Fourier transform (FRFT). On the different fractional orders of FRFT basis, the LFM signal has different forms of spectrum; from the spectrums we search the peak position to estimate the initial frequency and chirp rate of LFM signal. Simulation results show that by using the method this paper proposed it outperforms some existing algorithms demonstrating the superior performance of the proposed approach.