Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM
Abstract
:1. Introduction
- (i)
- We present a joint estimation algorithm for TD and DOA. The algorithmic model integrates the RIS array response and the OFDM subcarrier response to build a coded channel frequency response (Coded-Response). The algorithm achieves excellent estimation performance under low signal-to-noise ratio (SNR) conditions.
- (ii)
- Due to the reasonable combination of the RIS time-domain coding function and the OFDM multi-subcarrier features, we construct frequency asymmetry of the space–time phase. This method reduces the singularity of the signal correlation matrix and thus effectively suppresses the coherence signal.
- (iii)
- The covariance matrix of Coded-Response is reconstructed by using the structural advantages of tensor. Further use of CANDECOMP/PARAFAC to decompose the covariance matrix results in corresponding TD and DOA signal subspaces, avoiding multi-dimensional spectral peak search and greatly reducing complexity.
- (iv)
- Compared with the existing RIS- and OFDM-based localization algorithms [23,24], the proposed algorithm can obtain the required parameters for localization based on a single station node in a coherent environment. Simulation results show that the proposed algorithm avoids the aperture loss of current smoothing algorithms [22,25] when processing coherent signals and thus has more advantages in terms of estimation accuracy.
2. Signal Model
2.1. Time-Domain Model
2.2. Frequency-Domain Model
3. The Joint TD and DOA Estimation
3.1. Tensor Approach
3.2. TD Estimation
3.3. DOA Estimation
3.4. Algorithm Steps
Algorithm 1 Algorithm steps. | |
step1: | The Coded-Response in tensor form is constructed according to (23). |
step2: | The tensor covariance matrix is constructed according to (25). |
step3: | Perform a CPD of , which solves the signal subspaces and , and then the corresponding noise subspaces and are obtained by (35) and (39), respectively. and . |
step4: | Proceed to conduct a 1D spectral peak search for to solve the by (36), and a 2D spectral peak search for to solve the by (40). |
4. Algorithms Complexity
5. Simulation Results
5.1. Performance at Low SNR
5.2. Performance versus SNR
5.3. Performance versus Time Intervals
5.4. Performance versus RIS Elements
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Proof of Proposition
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Transpose | |
Conjugate | |
Hermitian transpose | |
Khatri-Rao product | ⊙ |
Kronecker product | ⊗ |
Hadamard product | ⊕ |
Tensor outer product | ∘ |
Convolution | ∗ |
Identity matrix | I |
Statistical expectation | |
Orthogonalization | |
Tensor contraction along the dimension |
Algorithm | Complexity |
---|---|
Proposed | |
3D-Music | |
Joint-Smooth |
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Du, J.; Cui, W.; Ba, B.; Jian, C.; Zhang, L. Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM. Sensors 2022, 22, 7083. https://doi.org/10.3390/s22187083
Du J, Cui W, Ba B, Jian C, Zhang L. Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM. Sensors. 2022; 22(18):7083. https://doi.org/10.3390/s22187083
Chicago/Turabian StyleDu, Jinzhi, Weijia Cui, Bin Ba, Chunxiao Jian, and Liye Zhang. 2022. "Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM" Sensors 22, no. 18: 7083. https://doi.org/10.3390/s22187083