# Simultaneous Correlative Interferometer Technique for Direction Finding of Signal Sources
## 1 Introduction
Moreover, there are several related studies adopting machine-learning-based DOA estimation [15; 16; 17; 18], but these techniques may induce significant implementation and operation complexity due to (neural network) training in advance, and thus they may not be feasible to be applied for real-time dynamic DOA estimation systems. DOA estimation extracting spatial characteristics through the phase of the received signal directly, called Correlative Interferometer (CI), is also being actively investigated in the literature thanks to its good performance, computational efficiency, high flexibility, and low-complexity implementation [19; 20; 21; 22; 23; 24; 25]. In [19], an antenna-array cascade system was proposed to improve DOA estimation performance by resolving DOA ambiguity due to the small number of antenna elements. In [20], a low-complexity CI algorithm using a modified cost function for real-time two-dimensional DOA estimation with uniform circular array (UCA) was proposed. In [21], a time-modulated array-based DOA estimation technique was proposed for improving the accuracy of direction finding. Specifically, the CI algorithm is a greedy DOA estimation technique that selects the most likely phase candidate using the difference between the phase of the received signal and all candidate phases, extracting the directional information of the selected phase. Herein, various cost functions can be used as the criteria for selecting the most plausible phase candidate. In [22], three cost functions for the CI algorithm were presented and verified by comparing the performance difference between each cost function and the Cramer-Rao bound. The CI algorithm was already used for direction finding with ULA [23] and UCA [24]. A modified CI using element-radiated power pattern to estimate the DOA of multiple signals with UCA was presented in [25]. However, most existing studies mainly require a single source environment or a high Signal-to-Noise Ratio (SNR) assumption. Furthermore, the CI algorithm has rarely been presented on how it works when receiving multiple time-domain received signal samples. If the receiver collects a few samples and jointly exploits the spatial features of the received signal within each sample, it might achieve improved DOA estimation performance while having higher resolution. To the best of our knowledge, the extended CI algorithms that can properly utilize the spatial characteristics of signal sources in multiple samples have not been reported in the literature. In this paper, we propose a novel simultaneous CI technique that extends the conventional CI algorithm for the direction finding of multiple signal sources by using multiple time-domain received signal samples. First, we investigate the conventional CI algorithm to address the direction-finding mechanism using phase difference. Then, we identify that the DOA estimation can be inaccurate due to the effect of the noise component on the signal phase when applying the CI algorithm to a single sample, especially in the low-SNR region. Finally, we present a novel simultaneous CI that can jointly explore the spatial characteristics of the received signal in each time-domain sample to guarantee robust DOA estimation performance even at low-SNR regions. In addition, it is worth noting that we propose the simultaneous CI technique from a signal processing perspective. In general, the experiments with hardware implementation of direction-finding techniques require significant time and cost. Hence, most studies utilize computer simulations to validate their proposed techniques [26; 27; 28; 29]. Hence, we also validate our proposed simultaneous CI technique through extensive computer simulations in this paper. We show that the simultaneous CI technique elaborately estimates the DOA of multiple signal sources at the low-SNR region and significantly outperforms the conventional MUSIC and CI algorithm for all SNR regions through extensive computer simulations.