Direction-of-Arrival Estimation for Wideband Chirps via Multi-Line Fitting in the Fractional Fourier Domain

Estimating the direction-of-arrival (DoA) of a wideband chirp signal is an important topic in several modern systems. The referred estimation can be carried out using array signal processing in the fractional Fourier transform (FrFT) domain, which involves searching for peak amplitude in order to select the optimal (fractional) order. This paper addresses the arithmetic complexity associated with the aforementioned task. More specifically, we propose replacing the conventional FrFT with a simplified FrFT (SmFrFT) that is obtained as a special case of linear canonical transforms. In this context, we also introduce the so-called local discrete SmFrFT, an algorithm for computing partial points of the (discrete) SmFrFT with a further reduction in the number of involved arithmetic operations. We demonstrate that SmFrFT is not just an FrFT with simplifications in the amplitude spectrum, but it satisfies properties that bring benefits to chirp signal processing. The reduction in the number of complex multiplications is about 77%. The effectiveness of the proposed method is verified by considering single- and multi-target DoA estimation using a uniform linear array. In subspace-based algorithms, peak alignment is proposed as a pre-processing step. For the multi-target scenario, this operation can be generalized as a multi-line fitting problem. In this context, two approaches are considered: piecewise slope fitting and line detection in the Hough space. Numerical simulations demonstrate that these methods can offer low computational complexity. However, in applications where high estimation accuracy is critical, the use of the ESPRIT algorithm with spatial smoothing and incorporating the discrete SmFrFT is recommended.