Enhancing Direction-of-Arrival Estimation for Single-Channel Reconfigurable Intelligent Surface via Phase Coding Design
Abstract
1. Introduction
- We establish a single receiving channel RIS-aided DOA estimation system model. Unlike existing works, which directly modeled the complex-valued received signals, we construct a power-based signal model by averaging the received signals. Based on this model, the DOA estimation problem is transformed into a sparse signal recovery problem in the framework of compressed sensing, where the far-field power radiation pattern of the RIS behaves as the measurement matrix.
- We derive the decoupled expression of the measurement matrix, which consists of the phase coding matrix, propagation phase shifts, and array steering matrix. Building on this, we formulate the phase coding design problem as the minimization of the mutual coherence of the measurement matrix. To overcome the challenges posed by the resulting non-convex optimization, we further transform the problem into minimizing the Frobenius norm between the Gram matrix of the measurement matrix and the identity matrix.
- We propose a deterministic phase coding design, where the phase coding is constructed based on the product of a unitary matrix and a partial Hadamard matrix. The simulation results demonstrate that the proposed phase coding design significantly reduces the DOA estimation error and achieves a higher resolution probability compared with methods based on random phase coding.
2. Mathematical Model
2.1. Signal Model
2.2. Sparse Representation for DOA Estimation
Algorithm 1 OMP algorithm for DOA estimation. |
Require: , , K. |
|
3. Proposed Phase Coding Design Method
3.1. Mutual Coherence of the Measurement Matrix
3.2. Proposed Phase Coding Design Method
Algorithm 2 Proposed phase coding design algorithm. |
Require: Initial matrix , . |
|
Ensure: The optimized equivalent measurement matrix . |
4. Simulation Results
4.1. Details of Experiments
4.2. Validity Analysis
4.3. Performance Analysis Under Different SNRs
4.4. Performance Analysis Under Different L Values
4.5. Performance Analysis Under Different Angles
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. The Proof of Lemma 1
Appendix B. The Proof of Lemma 2
Appendix C. The Proof of Lemma 3
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Notation | Description |
---|---|
the complex conjugate of a matrix | |
the transpose of a matrix | |
the complex conjugate transpose of a matrix | |
tr() | the trace of a matrix |
diag() | the diagonal matrix with elements in vector as the diagonals |
the mathematical expectation of a function | |
the Kronecker product of two matrices and | |
the Khatri–Rao product of two matrices and | |
the Frobenius norm of a matrix | |
the -norm of a vector | |
the absolute value of a scalar a | |
the identity matrix of dimensions |
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Hu, C.; Zhang, R.; Wang, J.; Sima, B.; Ma, Y.; Miao, C.; Kang, W. Enhancing Direction-of-Arrival Estimation for Single-Channel Reconfigurable Intelligent Surface via Phase Coding Design. Remote Sens. 2025, 17, 2394. https://doi.org/10.3390/rs17142394
Hu C, Zhang R, Wang J, Sima B, Ma Y, Miao C, Kang W. Enhancing Direction-of-Arrival Estimation for Single-Channel Reconfigurable Intelligent Surface via Phase Coding Design. Remote Sensing. 2025; 17(14):2394. https://doi.org/10.3390/rs17142394
Chicago/Turabian StyleHu, Changcheng, Ruoyu Zhang, Jingqi Wang, Boyu Sima, Yue Ma, Chen Miao, and Wei Kang. 2025. "Enhancing Direction-of-Arrival Estimation for Single-Channel Reconfigurable Intelligent Surface via Phase Coding Design" Remote Sensing 17, no. 14: 2394. https://doi.org/10.3390/rs17142394
APA StyleHu, C., Zhang, R., Wang, J., Sima, B., Ma, Y., Miao, C., & Kang, W. (2025). Enhancing Direction-of-Arrival Estimation for Single-Channel Reconfigurable Intelligent Surface via Phase Coding Design. Remote Sensing, 17(14), 2394. https://doi.org/10.3390/rs17142394