Direction of Arrival Estimation of Generalized Nested Array via Difference–Sum Co-Array
Abstract
:1. Introduction
2. Signal Model
3. Generalized Nested Array
- (a)
- Self-difference: , where .
- (b)
- Cross-difference: , where , while .
- (c)
- Self-sum: , where .
- (d)
- Cross-sum: , where , while .
- (a)
- Difference co-array: .
- (b)
- Sum co-array: .
- (c)
- Difference–sum co-array: .
3.1. Review of GNA-DCA
- (a)
- When, the range of positive and negative consecutive lags can be presented asand, respectively, whereand.
- (b)
- If, the number of unique lags reaches, where.
- (c)
3.2. Proposed GNA-DSCA
- (a)
- Provided that,possesses all the consecutive lags in the range, whereand. Provided that,enjoys all the consecutive lags in the range.
- (b)
- In the case, the total number of unique lags inreaches, where.
Maximum DOFs | |||
---|---|---|---|
Even | or | ||
Odd |
4. DOA Estimation
5. Simulation Results
5.1. Virtual Array Properties
5.2. MUSIC Spectra
5.3. Root-Mean-Square Error
5.4. Resolution Performance
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Proof of Lemma 2
- (a)
- For Lemma 2(a), since , we need to analyze the elements in and , respectively. The set can be expressed as [20]
- (b)
- For Lemma 2(b), we take the positive set as an example. We need proof that possesses unique lags for the case , where .
Appendix B. Solution of Equation (17)
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Maximum DOFs | |||
---|---|---|---|
Even | or | ||
Odd |
Sparse Array | Configuration | DOFs | Virtual Aperture | Coupling Leakage |
---|---|---|---|---|
NA-DCA | {0, 1, 2, 3, 4, 5, 11, 17, 23, 29} | 59 | 29 | 0.5022 |
CPA-DCA | {0, 5, 6, 10, 12, 15, 18, 20, 24, 25} | 39 | 25 | 0.2929 |
GNA-DCA () | {0, 5, 10, 15, 20, 25, 31, 37, 43, 49} | 59 | 49 | 0.1215 |
CPA-DSCA | {0, 5, 6, 10, 12, 15, 18, 20, 24, 25} | 95 | 50 | 0.2929 |
DsNA | {0, 3, 5, 7, 8, 17, 26, 35, 44, 53} | 125 | 106 | 0.3187 |
INAwSDCA−I | {0, 16, 17, 18, 19, 20, 26, 32, 38, 44} | 117 | 88 | 0.4806 |
INAwSDCA−II | {0, 9, 15, 21, 27, 28, 29, 30, 31, 32} | 119 | 64 | 0.5022 |
GNA-DSCA () | {0, 1, 2, 3, 4, 5, 16, 27, 38, 49} | 117 | 98 | 0.4991 |
GNA-DSCA () | {0, 5, 10, 15, 20, 25, 31, 37, 43, 49} | 117 | 98 | 0.1215 |
GNA-DSCA () | {0, 5, 10, 15, 20, 25, 36, 47, 58, 69} | 117 | 138 | 0.1126 |
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Zhang, Y.; Hu, G.; Zhou, H.; Bai, J.; Zhan, C.; Guo, S. Direction of Arrival Estimation of Generalized Nested Array via Difference–Sum Co-Array. Sensors 2023, 23, 906. https://doi.org/10.3390/s23020906
Zhang Y, Hu G, Zhou H, Bai J, Zhan C, Guo S. Direction of Arrival Estimation of Generalized Nested Array via Difference–Sum Co-Array. Sensors. 2023; 23(2):906. https://doi.org/10.3390/s23020906
Chicago/Turabian StyleZhang, Yule, Guoping Hu, Hao Zhou, Juan Bai, Chenghong Zhan, and Shuhan Guo. 2023. "Direction of Arrival Estimation of Generalized Nested Array via Difference–Sum Co-Array" Sensors 23, no. 2: 906. https://doi.org/10.3390/s23020906
APA StyleZhang, Y., Hu, G., Zhou, H., Bai, J., Zhan, C., & Guo, S. (2023). Direction of Arrival Estimation of Generalized Nested Array via Difference–Sum Co-Array. Sensors, 23(2), 906. https://doi.org/10.3390/s23020906