Figure 1.
Bartlett spectrum versus direction of arrival (DOA) for a uniform linear array of 15 elements in the presence of a single signal incident at 60°.
Figure 1.
Bartlett spectrum versus direction of arrival (DOA) for a uniform linear array of 15 elements in the presence of a single signal incident at 60°.
Figure 2.
Bartlett spectrum versus DOA for a uniform linear array of 15 elements in the presence of four signals incident at 65°, 70°, 115°, and 120°.
Figure 2.
Bartlett spectrum versus DOA for a uniform linear array of 15 elements in the presence of four signals incident at 65°, 70°, 115°, and 120°.
Figure 3.
Angular regions selected from the Bartlett spectra for a uniform linear array of 15 elements in the presence of four signals incident at 65°, 70°, 115°, and 120°.
Figure 3.
Angular regions selected from the Bartlett spectra for a uniform linear array of 15 elements in the presence of four signals incident at 65°, 70°, 115°, and 120°.
Figure 4.
Solution vector versus DOA for a uniform linear array of 15 elements in the presence of four signals at 65°, 70°, 115°, and 120°.
Figure 4.
Solution vector versus DOA for a uniform linear array of 15 elements in the presence of four signals at 65°, 70°, 115°, and 120°.
Figure 5.
versus for a uniform linear array of 15 elements in the presence of three signals at 55°, 75°, and 95°.
Figure 5.
versus for a uniform linear array of 15 elements in the presence of three signals at 55°, 75°, and 95°.
Figure 6.
Derivative of versus for a uniform linear array of 15 elements in the presence of three signals at 55°, 75°, and 95°.
Figure 6.
Derivative of versus for a uniform linear array of 15 elements in the presence of three signals at 55°, 75°, and 95°.
Figure 7.
Solution vector versus DOA for a uniform linear array of 15 elements in the presence of three signals at 55°, 75°, and 95°. For this scenario, . (top), (selected beta) (middle), (bottom).
Figure 7.
Solution vector versus DOA for a uniform linear array of 15 elements in the presence of three signals at 55°, 75°, and 95°. For this scenario, . (top), (selected beta) (middle), (bottom).
Figure 8.
Derivative of versus for a uniform linear array of 15 elements in the presence of three signals at 57°, 62°, and 67°.
Figure 8.
Derivative of versus for a uniform linear array of 15 elements in the presence of three signals at 57°, 62°, and 67°.
Figure 9.
Solution vector versus DOA for a uniform linear array of 15 elements in the presence of three signals at 57°, 62°, and 67°. For this scenario, . (top), (selected beta) (middle), (bottom).
Figure 9.
Solution vector versus DOA for a uniform linear array of 15 elements in the presence of three signals at 57°, 62°, and 67°. For this scenario, . (top), (selected beta) (middle), (bottom).
Figure 10.
Biases in the estimated direction of the two emitters versus angular separation: Proposed Method and the MUSIC Algorithm, SNR = 5 dB, 100 snapshots, 500 trials.
Figure 10.
Biases in the estimated direction of the two emitters versus angular separation: Proposed Method and the MUSIC Algorithm, SNR = 5 dB, 100 snapshots, 500 trials.
Figure 11.
Variance in the estimated direction of the first emitter versus angular separation: Proposed Method and the MUSIC Algorithm, SNR = 5 dB, 100 snapshots, 500 trials.
Figure 11.
Variance in the estimated direction of the first emitter versus angular separation: Proposed Method and the MUSIC Algorithm, SNR = 5 dB, 100 snapshots, 500 trials.
Figure 12.
Biases in the estimated direction of the two emitters versus SNR: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, 100 snapshots, 500 trials.
Figure 12.
Biases in the estimated direction of the two emitters versus SNR: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, 100 snapshots, 500 trials.
Figure 13.
Variance in the estimated direction of the first emitter versus SNR: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, 100 snapshots, 500 trials.
Figure 13.
Variance in the estimated direction of the first emitter versus SNR: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, 100 snapshots, 500 trials.
Figure 14.
Biases in the estimated direction of the two emitters versus snapshots: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, SNR = 5 dB, 500 trials.
Figure 14.
Biases in the estimated direction of the two emitters versus snapshots: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, SNR = 5 dB, 500 trials.
Figure 15.
Variance in the estimated direction of the first emitter versus snapshots: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, SNR = 5 dB, 500 trials.
Figure 15.
Variance in the estimated direction of the first emitter versus snapshots: Proposed Method, MUSIC Algorithm, and L1-SVD Algorithm, Emitters at 60 and 63 deg, SNR = 5 dB, 500 trials.
Table 1.
Number of Failures in 500 Trials with Respect to Emitter 2 Location. SNR = 5 dB, 100 snapshots.
Table 1.
Number of Failures in 500 Trials with Respect to Emitter 2 Location. SNR = 5 dB, 100 snapshots.
Location Emitter 2 [deg] | MUSIC | Proposed Method |
---|
61 | 500 | 13 |
62 | 497 | 0 |
63 | 30 | 0 |
64 | 2 | 0 |
65 | 0 | 0 |
Table 2.
Average and selected value over 500 Trials with Respect to Emitter 2 Location. SNR = 5 dB, 100 snapshots.
Table 2.
Average and selected value over 500 Trials with Respect to Emitter 2 Location. SNR = 5 dB, 100 snapshots.
Location Emitter 2 [deg] | | |
---|
61 | 0.0491 | 0.0638 |
62 | 0.0517 | 0.0670 |
63 | 0.0518 | 0.0674 |
64 | 0.0570 | 0.0743 |
65 | 0.0569 | 0.0740 |
66 | 0.0592 | 0.0769 |
67 | 0.0624 | 0.0808 |
68 | 0.0640 | 0.0830 |
69 | 0.0659 | 0.0852 |
70 | 0.0681 | 0.0878 |
Table 3.
Number of Failures in 500 Trials with Respect to SNR. Two emitters at 60° and 63°, 100 snapshots.
Table 3.
Number of Failures in 500 Trials with Respect to SNR. Two emitters at 60° and 63°, 100 snapshots.
SNR [dB] | MUSIC | L1-SVD | Proposed Method |
---|
0 | 473 | 0 | 0 |
1 | 396 | 0 | 0 |
2 | 338 | 0 | 0 |
3 | 221 | 0 | 0 |
4 | 118 | 0 | 0 |
5 | 44 | 0 | 0 |
6 | 6 | 0 | 0 |
7 | 3 | 0 | 0 |
8 | 3 | 0 | 0 |
9 | 2 | 0 | 0 |
10 | 2 | 0 | 0 |
Table 4.
Average and selected value over 500 Trials with Respect to SNR. Two emitters at 60° and 63°, 100 snapshots.
Table 4.
Average and selected value over 500 Trials with Respect to SNR. Two emitters at 60° and 63°, 100 snapshots.
SNR [dB] | | |
---|
0 | 0.1543 | 0.2006 |
1 | 0.1287 | 0.1672 |
2 | 0.1002 | 0.1304 |
3 | 0.0834 | 0.1084 |
4 | 0.0651 | 0.0847 |
5 | 0.0518 | 0.0674 |
6 | 0.0427 | 0.0558 |
7 | 0.0334 | 0.0434 |
8 | 0.0270 | 0.0352 |
9 | 0.0209 | 0.0272 |
10 | 0.0170 | 0.0225 |
Table 5.
Number of Failures in 500 Trials with Respect to Number of Snapshots. SNR = 5 dB, Two emitters at 60° and 63°.
Table 5.
Number of Failures in 500 Trials with Respect to Number of Snapshots. SNR = 5 dB, Two emitters at 60° and 63°.
Snapshots | MUSIC | L1-SVD | Proposed Method |
---|
40 | 362 | 17 | 0 |
50 | 288 | 6 | 0 |
60 | 219 | 0 | 0 |
70 | 152 | 0 | 0 |
80 | 105 | 0 | 0 |
90 | 57 | 0 | 0 |
100 | 41 | 0 | 0 |
110 | 23 | 0 | 0 |
120 | 12 | 0 | 0 |
130 | 8 | 0 | 0 |
140 | 5 | 0 | 0 |
150 | 3 | 0 | 0 |
160 | 3 | 0 | 0 |
170 | 2 | 0 | 0 |
180 | 0 | 0 | 0 |
190 | 0 | 0 | 0 |
200 | 0 | 0 | 0 |
Table 6.
Average and selected value over 500 Trials with Respect to Number of Snapshots. SNR = 5 dB, Two emitters at 60° and 63°.
Table 6.
Average and selected value over 500 Trials with Respect to Number of Snapshots. SNR = 5 dB, Two emitters at 60° and 63°.
Snapshots | | |
---|
40 | 0.0531 | 0.0690 |
50 | 0.0595 | 0.0772 |
60 | 0.0528 | 0.0688 |
70 | 0.0566 | 0.0740 |
80 | 0.0534 | 0.0692 |
90 | 0.0563 | 0.0729 |
100 | 0.0518 | 0.0674 |
110 | 0.0569 | 0.0745 |
120 | 0.0536 | 0.0694 |
130 | 0.0544 | 0.0704 |
140 | 0.0533 | 0.0690 |
150 | 0.0557 | 0.0725 |
160 | 0.0529 | 0.0686 |
170 | 0.0540 | 0.0702 |
180 | 0.0528 | 0.0685 |
190 | 0.0551 | 0.0717 |
200 | 0.0531 | 0.0689 |