3D-OMP and 3D-FOMP algorithms for DOA estimation

Abstract Adaptive antennas and antenna array processing have vital effects on enhancing the performance of wireless communication networks. One of the most significant applications of adaptive antenna systems is the Direction of Arrival (DOA) detection. Several schemes have been proposed in the literature for DOA estimation in two-dimensional space. Among them, Orthogonal Matching Pursuit (OMP) algorithm provides several advantages in comparison to other schemes. The OMP algorithm reduces complexity and improves resolution of detection. Furthermore, in this algorithm, the number of signal emitters is not required to be known. In this paper, we extend the OMP algorithm and propose Three Dimensional OMP (3D-OMP) scheme for DOA estimation in three dimensional space. We provide a redundant dictionary for 3D-OMP scheme by employing azimuth and elevation angles. Simulation results show the high performance of the 3D-OMP algorithm when the signal to noise ratio is higher than − 10 d B . Moreover, the 3D-OMP algorithm has a high efficiency in detecting multiple signal sources, simultaneously. Then, we evaluate the accuracy of the estimated directions by the 3D-OMP algorithm via comparing the variance of estimation error with the Cramer-Rao bound. Nevertheless, DOA estimation by the 3D-OMP algorithm has a substantial challenge where it cannot distinguish between two adjacent signal sources. To resolve this challenge, we propose Three Dimensional Focused Orthogonal Matching Pursuit (3D-FOMP) algorithm. The 3D-FOMP algorithm is an improved version of the 3D-OMP algorithm. It can detect two adjacent signal sources when the beam former has a single peak corresponding to a direction between right directions. In addition, we show the 3D-OMP and 3D-FOMP algorithms have lower complexities in comparison to the 3D-MUSIC and 3D-ESPRIT schemes when Root Mean Square Error (RMSE) > 0 . 3 o . This accuracy is persuasive for most applications. Moreover, simulation results show the capability of the 3D-FOMP algorithm to detect adjacent signal sources and it outperforms the 3D-OMP, 3D-MUSIC and 3D-ESPRIT algorithms for all values of signal to noise ratio.