  Direction of arrival (DOA) estimation is an important research in the area of
array signal processing, and has been studied for decades. High resolution DOA
estimation requires large array aperture, which leads to the increase of
hardware cost. Besides, high accuracy DOA estimation methods usually have high
computational complexity. In this paper, the problem of decreasing the hardware
cost and algorithm complexity is addressed. First, considering the ability of
flexible controlling the electromagnetic waves and low-cost, an intelligent
reconfigurable surface (IRS)-aided low-cost passive direction finding (LPDF)
system is developed, where only one fully functional receiving channel is
adopted. Then, the sparsity of targets direction in the spatial domain is
exploited by formulating an atomic norm minimization (ANM) problem to estimate
the DOA. Traditionally, solving ANM problem is complex and cannot be realized
efficiently. Hence, a novel nonconvex-based ANM (NC-ANM) method is proposed by
gradient threshold iteration, where a perturbation is introduced to avoid
falling into saddle points. The theoretical analysis for the convergence of the
NC-ANM method is also given. Moreover, the corresponding Cram\'er-Rao lower
bound (CRLB) in the LPDF system is derived, and taken as the referred bound of
the DOA estimation. Simulation results show that the proposed method
outperforms the compared methods in the DOA estimation with lower computational
complexity in the LPDF system.
