Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for Direction-of-Arrival Estimation

Source enumeration is an important procedure for radio direction-of-arrival finding in the multiple signal classification (MUSIC) algorithm. The most widely used source enumeration approaches are based on the eigenvalues themselves of the covariance matrix obtained from the received signal. However, they have shortcomings such as the imperfect accuracy even at a high signal-to-noise ratio (SNR), the poor performance at low SNR, and the limited detection number of sources. This paper proposestwo source enumeration approaches using the ratio of eigenvalue gaps and the threshold trained by a machine learning based clustering algorithm for gaps of normalized eigenvalues, respectively. In the first approach, a criterion formula derived with eigenvalue gaps is used to determine the number of sources, where the formula has maximum value. In the second approach, datasets of normalized eigenvalue gaps are generated for the machine learning based clustering algorithm and the optimal threshold for estimation of the number of sources are derived, which minimizes source enumeration error probability. Simulation results show that our proposed approaches are superior to the conventional approaches from both the estimation accuracy and numerical detectability extent points of view. The results demonstrate that the second proposed approach has the feasibility to improve source enumeration performance if appropriate learning datasets are sufficiently provided.