## 2 Related Works  
In this section, previous works on DOA estimation and source enumeration are surveyed. Machine learning techniques are also introduced briefly and previous works applying machine learning to DOA estimation and source enumeration are presented. Not only MUSIC and ESPRIT but also many DOA estimation studies are assuming that they know the number of signals a priori. [PERSON] et al. (2017) proposed a subspace-based localization of far-field and near-field signals without eigendecomposition; they assume that the number of far-field and near-field signals are known when they state the problem formulation. [PERSON] and [PERSON] (2018) and [PERSON] et al. (2019) proposed a low-complexity and fast two-dimensional DOA estimation, where they are assuming the a priori knowledge of the number of signals. [PERSON] et al. (2020) proposed a reduced-complexity algorithm for DOA estimation exploiting only the real part of the covariance matrix of the array and showed that it can lead to a real-valued version of the MUSIC algorithm with no dependence on array configurations, while their basic assumptions include that the number of sources is known. [PERSON] et al. (2018) address the problem of DOA estimation with coprime arrays with the emphasis on reduced computational complexity while preserving estimation accuracy; the number of sources is also assumed to be known. As described above, the source enumeration is critical to many applications of DOA estimation. There are a large number of studies on source enumeration approaches, and they can be classified into information theoretic based and threshold based approaches, etc. (2018). AIC and MDL, which are the information theoretic based approaches, are the most popular approaches for source enumeration. [PERSON] and [PERSON] (2012) are the first who applied AIC and MDL to detect the number of signals. These approaches use the eigenvalues of the covariance matrix and have advantages in which no subjective judgment (e.g., deciding on the threshold levels) is required in the decision process. However, AIC yields an inconsistent estimate that tends to overestimate the number of signals; hence, AIC does not reach 100% accuracy even at high SNR levels. Meanwhile, MDL has 100% accuracy at high SNR levels but has poor performance at low SNR levels ([PERSON] et al., 2019). Another eigenvalue-based approach named SORTE was proposed by [PERSON] et al. (2015) to detect the number of clusters; it also can be used to detect the number of signals and showed comparatively good estimation performances ([PERSON] et al., 2019). While AIC and MDL use the eigenvalues directly, SORTE uses _the gaps_ of the eigenvalues; hence, SORTE cannot detect as many signals as AIC and MDL can--two less signals than AIC and MDL. Meanwhile, a threshold based approach named the eigenthreshold (ET) approach was proposed by [PERSON] et al. (2014). ET detects the number of signals by setting the upper thresholds for the observed eigenvalues and then implementing a hypothesis testing procedure. Another threshold based approach, the eigen-increment threshold, was proposed by [PERSON] et al. (2015). This approach is based on the assumption that, without the existence of the signals, the noise eigenvalues distribute approximately along a straight line; if the signals exist, it causes the increase of the eigenincrement on the boundary between two subspaces. Based on this observation, they proposed a single threshold concerning about the information of signal and noise strength, data length, and array size. The studies on machine learning have attracted a great amount of attention over the past few years. Machine learning techniques can be divided into four categories: supervised, unsupervised, semi-supervised, and reinforcement learning (2018). Supervised learning uses a labeled training dataset to teach a model; after training, a new piece of unlabeled data can decide to be one of the trained labels according to the model.