## 1 Introduction
To avoid this issue and improve the estimation resolution, an extensive sampling grid is required to minimize the gap between the correct AOAs and its nearest grid point since an estimated AOA is constrained to lie on the grid. However, an extensive sampling grid results in a highly correlated matrix that breaks the required conditions for the sparse signal recovery. To overcome such issues, an off-grid sparse Bayesian inference (OGSBI) estimation algorithm is invoked [35], combining the BCS approach and the quantization error problem for point sources--the quantization error is taken to be uniformly distributed and real valued. The OGSBI method offers good estimation performance at single or limited number of measured data; however, its performance is severely degraded with low signal to noise ratio as well as when source signals are highly correlated, and with a high burden of computation where a large number of iterations are required to find the solution in some scenarios [36]. In [37], the authors propose a BCS framework approach for DOA estimation problem. This approach directly utilizes the output voltages at the sensor array to determine DOAs without need to compute the observation/sampling matrix. Two methodologies addressed in their work are single task (ST) compressive sampling and multi-task (MT) compressive sampling. These methodologies have been investigated based on BCS by using single and multiple measurements. It was found that MT-BCS gives better performance than ST-BCS in both single and multiple snapshots cases. A root-SBL method for DOA estimation problem has been proposed recently to reduce the computation complexity of SBL in [38]. In the root-SBL algorithm, the authors adopt a coarse grid and consider the sampled positions in the coarse grid as adaptable parameters. An expectation-maximization (EM) method was utilized to smooth this coarse grid iteratively and clarify that every updated grid point is achieved by the root of a certain polynomial. Many applications call for a high resolution and low complexity AOA estimation method in these conditions. The contribution of this present paper is to propose a simple and low complexity method that can be used to estimate the DOAs of signals efficiently; the proposed method is called the propagator direct data acquisition (PDDA) method. The PDDA algorithm is based on computing the propagator vector which represents the cross correlation between the received data from the first sensor and the other sensors. This propagator vector retains all the information about how the phasors of signals arriving from various directions sum at each sensor, which has the effect of normalizing to the phase of the first sensor and eliminating the dependency on the signal time series, which in turn improves robustness to noise. Consequently, the DOA signals can be estimated efficiently with a single snapshot or a few snapshots even when the impinging sources are highly correlated. Furthermore, it does not require prior knowledge of the number of arriving signals, unlike MUSIC, ESPRIT and other techniques. The new method estimates the directions of the received signals directly from the measured data without the need to construct the covariance matrix, to invert the matrix or to use EVD/SVD approaches. This decreases the complexity considerably. Computational complexity is investigated in terms of the required number of computational operations and the execution time, the comparison results demonstrating that the PDDA method is efficient computationally. The proposed method is implemented by using linear and circular sensor arrays to perform 1D and 2D estimation; many numerical examples are presented to show its performance. It is compared with several popular and recent AOA methods in terms of numbers of snapshots collected, behaviour with SNR, correlation of signals sources and execution time. An intensive Monto Carlo simulation is achieved with random angles over different scenarios, with the identical conditions applied to all algorithms to ensure a fair comparison.