Wideband Joint Elevation–Azimuth Angle Estimation Based on Multiple Frequency Model and Atomic Norm Minimization

Estimating the direction of arrival (DOA) has been a crucial problem in a wide range of applications. Current research predominantly focuses on narrow-band, 1-D signals, which are not directly applicable to practical scenarios involving wideband and multidimensional signals. To deal with this drawback, we propose a 2-D multiple frequency atomic norm minimization (2DMFANM) algorithm to estimate the elevation and azimuth angles of wideband signals in a grid-less manner. To be specific, we exploit the multiple frequency model to describe the wideband signals and derive the corresponding signal model. Based on the structure of the signal model, we formulated an atomic norm minimization (ANM) problem that allows for the gridless joint estimation of elevation and azimuth angles. The ANM problem is further converted into semidefinite programming (SDP) via analysis of the dual problem. To reduce the computational burden that hinders the deployment of 2DMFANM, we propose two fast algorithms called 2DMFDANM and 2DMFANM_SizeRedu. Specifically, 2DMFDANM reduces the size of the original algorithm by decoupling the information of spatial angular frequencies, while 2DMFANM_SizeRedu achieves fast speed by removing the redundancy in the original algorithm. Theoretical and numerical analyses indicate that these two algorithms significantly enhance the speed of computation with minor degradation in the estimation accuracy. Numerical simulations and experimental data analysis demonstrate the superior performance of the proposed methods compared to state-of-the-art algorithms.