Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for DirectionofArrival Estimation
Abstract
:1. Introduction
 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.
 To the best of our knowledge, this paper presents the first source enumeration approach based on the machine learning algorithm using gaps of eigenvalues. It is shown that our proposed machine learning based clustering approach has fairly good performances, and it also reveals the strong feasibility to improve its performance when the appropriate learning data are sufficiently supported for the designated SNR range.
 While in most existing literature, the performances of source enumeration approaches are evaluated with predefined fixed parameters (e.g., the number of sources and the arrival angles of the sources), which results in the eigenvalues of the covariance matrix being fixed. In this paper, the performances for the cases with a comprehensive number of sources and arrival angle of the sources are compared in this paper. It is shown that our proposed approaches have comparatively good performances in the various scenario conditions of signal sources.
2. Related Works
3. System Model
4. Proposed Approaches
4.1. Accumulated Ratio of Eigenvalues Gaps
4.2. Threshold for Gap of Normalized Eigenvalues
4.2.1. Datasets Generation
4.2.2. Learning and Computing Optimal Thresholds
Algorithm 1 Estimation of GMM parameters 
Input ${E}^{\mathrm{data}}$ Output$\varphi $ 1.5

4.2.3. Source Enumeration Using the Optimal Threshold
Algorithm 2 Source enumeration using the optimal threshold 
Input$\Delta {e}_{i}$ ($i=1,\cdots ,M1$), $\widehat{\gamma}$ Output$\widehat{D}$ 1.5

5. Simulation Analysis
5.1. Analysis of AREG
5.2. Analysis of TGANE
 Number of elements of ULA M is 7.
 Distance of the two adjacent elements $\xi $ is $\eta /2$.
 Number of signal sources D ranges from 1 to 6 (uniform random).
 Arrival angle of signals ${\theta}_{i}$ ($i=1,\cdots ,D$) ranges from ${\theta}_{\mathrm{min}}={60}^{\circ}$ to ${\theta}_{\mathrm{max}}={60}^{\circ}$ (uniform random, nondiscrete).
 Minimum angle difference between the two adjacent signals $\Delta {\theta}_{ab}\ge {15}^{\circ}$.
 Number of snapshots L is 1000.
 SNR ranges from $20$ dB to 10 dB (uniform random, nondiscrete).
 Number of situations for generating the datasets Q is 100,000.
5.3. Evaluation of Comprehensive Approaches
 Number of elements of ULA M is 7.
 Distance of the two adjacent elements $\xi $ is $\eta /2$.
 Number of signal sources D ranges from 1 to 4 (uniform random).
 Arrival angle of signals ${\theta}_{i}$ ($i=1,\cdots ,D$) ranges from ${\theta}_{\mathrm{min}}={60}^{\circ}$ to ${\theta}_{\mathrm{max}}={60}^{\circ}$ (uniform random, nondiscrete).
 Minimum angle difference between the two adjacent signals $\Delta {\theta}_{ab}\ge {15}^{\circ}$.
 Number of snapshots L is 1000.
 Number of trials for each SNR is 10,000 times.
 TGANE is trained the same as is mentioned in Section 5.2.
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Lee, Y.; Park, C.; Kim, T.; Choi, Y.; Kim, K.; Kim, D.; Lee, M.S.; Lee, D. Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for DirectionofArrival Estimation. Appl. Sci. 2021, 11, 1942. https://doi.org/10.3390/app11041942
Lee Y, Park C, Kim T, Choi Y, Kim K, Kim D, Lee MS, Lee D. Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for DirectionofArrival Estimation. Applied Sciences. 2021; 11(4):1942. https://doi.org/10.3390/app11041942
Chicago/Turabian StyleLee, Yunseong, Chanhong Park, Taeyoung Kim, Yeongyoon Choi, Kiseon Kim, Dongho Kim, MyungSik Lee, and Dongkeun Lee. 2021. "Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for DirectionofArrival Estimation" Applied Sciences 11, no. 4: 1942. https://doi.org/10.3390/app11041942