Fractional Fourier transform based underwater multi-targets direction-of-arrival estimation using wideband linear chirps

Abstract

In underwater applications, linear chirp signal with linearly instantaneous frequency over the signal bandwidth also known as a linear frequency modulated (LFM) signal is often used in active sonar to realize direction of arrival (DOA) estimation of targets. For this kind of wideband signal, traditional array signal processing method firstly transforms the time domain signal into frequency domain using fast Fourier transform (FFT) and then does beamforming for each sub-band. Different from FFT based signal processing method, this paper uses fractional Fourier transform (FRFT) for preprocessing of wideband LFM signals. By FRFT preprocessing, the wideband LFM signals are transformed into narrowband signals in the fractional Fourier domain, avoiding the influence of cross-interference terms. This paper compares the performance of FRFT based DOA estimation using conventional beamforming (CBF), minimum variance distortionless response (MVDR) and robust Capon beamforming (RCB) respectively. Then the revised RCB (RRCB) algorithm is proposed to solve the DOA estimation problem with a small number of snapshots. Simulations are carried out for single target and multi-targets DOA estimation using FFT based and FRFT based array signal processing method respectively. Simulation results show that FRFT based array signal processing method can achieve much narrower main lobe and higher main-to-side lobe ratio in low signal-to–noise ratio conditions. Besides, it can realize accurate DOA estimation of two adjacent targets while FFT based array signal processing method fails.