## 1 Introduction  
In the battlefield of modern and future warfare, the importance of electronic warfare (EW) is increasing. EW consists of an electronic attack (EA), which controls the enemy's electromagnetic spectrum; electronic protection (EP), which is used for defense; and electronic warfare support (ES), which supports tasks such as surveillance and reconnaissance [1]. Direction-of-arrival (DOA) is a key process of ES for locating the signal sources of the enemies [2, 3]. DOA is used not only for EW applications but also in many applications such as radar, sonar, wireless communication, radio astronomy, and satellite communications [4]. Algorithms such as multiple signal classification (MUSIC) [5] and estimation of the signal parameters via rotational invariance techniques (ESPRIT) [6] are widely used for the DOA estimation, which are subspace-based techniques. They divide the covariance matrix of the received signals into two subspaces: signal-subspace and noise-subspace, and estimate the DOA of the received signals utilizing the orthogonal relation between the signal-subspace and noise-subspace [7; 8; 9]. Although the subspace-based techniques such as MUSIC and ESPRIT can estimate DOA with high-resolution, they need to know the exact number of sources to distinguish between the signal- and noise-subspace [10]. In practice, however, the number of sources is not known a priori; the source enumeration must be executed before the DOA techniques are performed. If we fail to estimate the exact number of sources, it will lead to a deterioration in the performance of the DOA estimation [11]. Therefore, the source enumeration is greatly important for DOA estimation. There are two famous source enumeration approaches by information theoretic criteria: Akaike information criterion (AIC) and minimum description length (MDL) [12]. AIC has fairly good estimation accuracy at low signal-to-noise ratio (SNR) but does not reach perfect (100%) accuracy even at high SNR [13], while MDL has 100% accuracy at high SNR, but the performance is sharply and extremely degraded at a low level of SNR [14]. Another algorithm called a second order statistic of the eigenvalues (SORTE) [15] outperforms other approaches in estimation accuracy but its numerical detectability extent--the maximum number of source signal detection with a given array--is less than that of AIC and MDL [16]. In this paper, two approaches that use gaps of the eigenvalues for the covariance matrix obtained from the received multiple signals are proposed to overcome the poweries of the accuracy of AIC at high SNR and MDL at low SNR, and the limited detectability extent of source enumeration for SORTE. In the first approach, the source signals are enumerated with the criterion formula selection that is comprised of the ratio of the eigenvalues gaps. In the second approach, the threshold-based estimation using the machine learning approaches is proposed; the optimal threshold that minimizes the estimation error is derived by the machine learning based clustering algorithm. In the performance evaluation, AIC, MDL, SORTE, and our two proposed approaches are compared in terms of source enumeration accuracy in a wide range of SNR. Conclusively, simulation results demonstrate that the first approach has better performance than SORTE for the overall range of SNR, and our proposed approach can detect one more source than SORTE can. In addition, results show that the second proposed approach has fairly good performance and its performance can be further enhanced if the appropriate learning data are provided. The main contributions of our study are summarized as follows:  
1. Our proposed approach based on the criterion formula selection shows the better performance of source enumeration accuracy than SORTE for the overall range of SNR, and it can detect one more signal than SORTE can. In addition, the source enumerating criterion formula of the proposed approach is much simpler than that of SORTE. 2.