# Simultaneous Correlative Interferometer Technique for Direction Finding of Signal Sources
## 1 Introduction  
Wireless positioning and sensing are expected to become emerging technologies as new service applications and scenarios for the next-generation mobile communication systems, such as autonomous driving, Industrial Internet of Things (IIoT), remote robots, etc. [1]. Therein, direction finding of (multiple) signal sources has been substantially developed and has become an important part of recent and ongoing standards, including the 3 rd Generation Partnership Project (3 GPP) [2] and Institute of Electrical and Electronics Engineers (IEEE) [3]. Recently, Direction of Arrival (DOA) estimation techniques using array antennas have attracted much attention for achieving high resolution and robust performance in directionfinding for various purposes [4; 5; 6]. In [4], DOA estimation was used for the Global Navigation Satellite System (GNSS) receiver to detect a spoofing signal, which is a counterfeit GNSS-like signal for deception. In [5], a DOA estimation method with improved accuracy was proposed with a reconfigurable intelligent surface in an environment considering the positional perturbation of an Unmanned Aerial Vehicle (UAV) swarm. In [6], considering Vehicle-to-Everything (V2X) communication, a DOA-based localization method with large-scale arrays was investigated to guarantee safety and security. In addition, many array-antenna-based DOA estimation algorithms for detecting directions of multiple signal sources have been investigated over the past few decades. Actually, when an array-antenna-based receiver estimates the DOA of multiple signal sources, the Maximum Likelihood Estimator (MLE) is known to be the optimal DOA estimation algorithm [7]. However, the MLE-based DOA estimation requires an extremely high computational complexity, and it may not be feasible to assume that the covariance of the noise component and the non-desired signal components must be known. On the other hand, Multiple Signal Classification (MUSIC) is one of the well-known practical DOA estimation techniques with an array antenna by exploiting the orthogonality between the subspaces of signal components and noise components in the covariance matrix of the received signal [8]. In [9], a two-dimensional DOA estimation technique with an imperfect aged antenna array was proposed, where two uniform linear arrays are not perpendicular to each other. In particular, two different DOA estimation techniques were considered, which are based on MUSIC and Iterative Maximum Likelihood Calibration (IMLC), respectively. However, in the practical MUSIC algorithm, calculating the covariance of the received signal should be performed by collecting a large number of (time-domain) received signal samples, and it also requires high-complexity computations such as eigenvalue decomposition. In addition, parameter-based DOA estimation algorithms such as root-MUSIC [10] and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) [11] have been frequently used to reduce the time and computational load of the existing MUSIC where the receiver estimates the DOAs by exhaustively exploring each candidate direction. However, since these algorithms use the phase difference between equally spaced array antennas, they can be applied to a certain array architecture. On the other hand, Compressed Sensing (CS)-based DOA algorithms using sparsity between incident directions are also being actively studied [12; 13; 14]. In [12], a robust phase-ambiguity-immune DOA estimation algorithm was proposed, which does not require the phase correction at the multi-channel receiver and enables the DOA estimation for multiple sources in a single-channel system. In [13], a novel CS-based DOA estimation technique was proposed for efficiently detecting GNSS spoofing attacks with a small number of time samples. In [14], another CS-based DOA estimation algorithm was proposed, which outperforms the conventional subspace-based DOA estimation method even in a lower number of array elements and in severely noisy environments.