2D-DOA Estimation in Switching UCA Using Deep Learning-Based Covariance Matrix Completion
<p>System model.</p> "> Figure 2
<p>Switching scheme: (<b>a</b>) the first switching; (<b>b</b>) the second switching; (<b>c</b>) the third switching; (<b>d</b>) the fourth switching.</p> "> Figure 3
<p>Structure of <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="bold">R</mi> <mo>^</mo> </mover> </semantics></math>.</p> "> Figure 4
<p>Vectorization of the upper triangular part of <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="bold">R</mi> <mo>^</mo> </mover> </semantics></math>.</p> "> Figure 5
<p>Architecture of DFN.</p> "> Figure 6
<p>Block diagram of the DFN training system.</p> "> Figure 7
<p>Evolution of loss on the validation set in the training of different FC networks.</p> "> Figure 8
<p>RMSE versus SNR, <math display="inline"><semantics> <mi mathvariant="italic">K</mi> </semantics></math> = 1024: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="italic">D</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="italic">D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="italic">D</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p> "> Figure 9
<p>RMSE versus <math display="inline"><semantics> <mi mathvariant="italic">K</mi> </semantics></math>, SNR = 15 dB: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="italic">D</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="italic">D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="italic">D</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p> "> Figure 10
<p>RMSE, Success Probability versus SNR, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">K</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">D</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>: (<b>a</b>) RMSE versus SNR; (<b>b</b>) Success Probability versus SNR.</p> "> Figure 11
<p>RMSE, Success Probability versus <math display="inline"><semantics> <mi>ε</mi> </semantics></math>, <math display="inline"><semantics> <mi mathvariant="italic">K</mi> </semantics></math> = 1024, SNR = 10 dB: (<b>a</b>) RMSE versus <math display="inline"><semantics> <mi>ε</mi> </semantics></math>; (<b>b</b>) Success Probability versus <math display="inline"><semantics> <mi>ε</mi> </semantics></math>.</p> "> Figure 12
<p>RMSE versus SNR, <math display="inline"><semantics> <mi mathvariant="italic">K</mi> </semantics></math>: <math display="inline"><semantics> <mi mathvariant="italic">D</mi> </semantics></math> = 4. (<b>a</b>) RMSE versus SNR, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">K</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math>; (<b>b</b>) RMSE versus <math display="inline"><semantics> <mi mathvariant="italic">K</mi> </semantics></math>, SNR = 15 dB.</p> "> Figure 13
<p>RMSE versus SNR, <math display="inline"><semantics> <mi mathvariant="italic">K</mi> </semantics></math>. <math display="inline"><semantics> <mi mathvariant="italic">D</mi> </semantics></math> = 5: (<b>a</b>) RMSE versus SNR, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">K</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math>; (<b>b</b>) RMSE versus <math display="inline"><semantics> <mi mathvariant="italic">K</mi> </semantics></math>, SNR = 15 dB.</p> "> Figure 14
<p>Spatial spectrum using SUMC estimator for solving four sources, SNR = 15 dB, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">K</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math>: (<b>a</b>) front; (<b>b</b>) top.</p> "> Figure 15
<p>Spatial spectrum using SUMC estimator for solving five sources, SNR = 15 dB, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">K</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math>: (<b>a</b>) front; (<b>b</b>) top.</p> ">
Abstract
:1. Introduction
- A SUMC algorithm is proposed to estimate the complete covariance matrix from the sample covariance matrix of the SUCA, which means that fewer RF chains than antennas are needed. Therefore, the proposed algorithm can be applied to underdetermined 2D-DOA estimation.
- A 2D spatial spectrum search scheme based on the classical MUSIC algorithm is performed to estimate the coupled elevation and azimuth angles.
- Multiple 2D-DOA estimation simulations are carried out to demonstrate that the proposed SUMC-based 2D-DOA estimator (SUMC estimator) is able to preserve the advantage of a FUCA with fewer RF chains.
2. System Model
- antennas are locked, which means these antennas are always connected to RF chains;
- () antennas are selected and connected to RF chains in each switching;
- The remaining () antennas are dumped, which means these antennas are not connected to the RF chain in each switching.
3. Deep Feedforward Network for Covariance Matrix Completion
3.1. Data and DFN Architecture
3.2. Training Strategy
4. Simulation Results
4.1. Simulation Conditions
4.2. Network Architecture Analysis
4.3. Comparison to Fully Sampled UCA
4.4. Comparison to Partial Array
- The number of peaks searched by 2D spatial spectrum search scheme is equal to ;
- The divation of each DOA estimate satisfies
4.5. Resolution of 2D-DOA Estimation
- The total angular separation of two sources is defined as
- The is randomly selected from , is then calculated by
- The DOA of the first source is randomly selected from the two-dimensional angular space
- The DOA of the second source is then given by
4.6. Underdetermined 2D-DOA Estimation Problem
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
2D-DOA | Two-Dimensional Direction of Arrival |
UCA | Uniform Circular Array |
SUCA | Switching Uniform Circular Array |
FUCA | Fully Sampled UCA |
PA | Partial Array |
SLA | Sparse Linear Array |
RF | Radio Frequency |
DOFs | Degrees of Freedom |
MUSIC | Multiple Signal Classification |
ESPRIT | Estimation of Signal Parameters via Rotational Invariance |
GSDC | Generalized Sum and Difference Coarray |
SNACD | Sparse Nested Arrays with Coprime Displacement |
SIMC | Shift-Invariant Matrix Completion |
NSCA | Nested Sparse Circular Array |
DL | Deep Learning |
NN | Neural Network |
CNN | Convolutional Neural Network |
DFN | Deep Feedforward Network |
SUMC | Switching UCA Matrix Completion |
LeakyReLU | Leaky Rectified Linear Unit |
CS | Cosine Similarity |
GPU | Graphics Processing Unit |
SGD | Stochastic Gradient Descent |
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Setting | DFN |
---|---|
Maximum Epochs | 150 |
Initial learning rate | |
Learning rate decay | Exponential, rate 0.02, step one epoch |
Optimizer | Adam |
Mini-batch size |
Parameter | Value |
---|---|
Number of antennas | 10 |
Number of RF chains | 4 |
Radius of UCA | 0.7 |
Number of Monte Carlo trials W | 500 |
Number of snapshots | 128, 256, ⋯, 8192 |
Number of sources | 1, 2, 3, 4, 5 |
Elevation angle | |
Azimuth angle | |
SNR | 5:5:30 dB |
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Mei, R.; Tian, Y.; Huang, Y.; Wang, Z. 2D-DOA Estimation in Switching UCA Using Deep Learning-Based Covariance Matrix Completion. Sensors 2022, 22, 3754. https://doi.org/10.3390/s22103754
Mei R, Tian Y, Huang Y, Wang Z. 2D-DOA Estimation in Switching UCA Using Deep Learning-Based Covariance Matrix Completion. Sensors. 2022; 22(10):3754. https://doi.org/10.3390/s22103754
Chicago/Turabian StyleMei, Ruru, Ye Tian, Yonghui Huang, and Zhugang Wang. 2022. "2D-DOA Estimation in Switching UCA Using Deep Learning-Based Covariance Matrix Completion" Sensors 22, no. 10: 3754. https://doi.org/10.3390/s22103754