Atomic Norm Minimization Based DoA Estimation with Lens Antenna Arrays

The conventional multiple-input multiple-output (MIMO) structure is impractical for large-scale arrays due to the huge hardware complexity and power consumption. This paper studies the direction-of-arrival (DoA) estimation with the promising lens antenna array (LAA). The main challenge is that not all incident signals can be received due to the limited number of RF chains. Therefore, the antenna selection procedure is proposed to select the subsets of array elements for receiving low dimensional signal data. Then, we formulate an atomic norm minimization and its dual problem to recover the original signal. However, roots finding based DoA estimation is no longer applicable in the LAA scheme. To circumvent this problem, we construct a trigonometric polynomial according to the relations between dual variables and the spatial frequencies, and maximum value search over a small interval is adopted to compensate for the power leakage errors. Numerical simulations show the superiority of the proposed algorithm by comparing it with state-of-the-art algorithms.