Near-Field Channel Parameter Estimation and Localization for mmWave Massive MIMO-OFDM ISAC Systems via Tensor Analysis
Abstract
1. Introduction
1.1. Background
1.2. Preliminaries
1.3. Organization
2. Related Works
3. Contributions and Notations
3.1. Contributions
- The proposed algorithm employs tensor decomposition technology for ISAC, i.e., channel parameter estimation and target localization. Firstly, considering the transceiver encoding architecture and the mmWave channel sparse characteristics, the received signal at the UT can be constructed as a third-order tensor model. Moreover, the decomposition of the constructed tensor model is proved to be unique, and an Alternating Least Squares (ALS) scheme can be applied to iteratively estimate the corresponding factor matrices.
- Based on estimated factor matrices, we design specific parameter estimation algorithms to achieve ISAC. Firstly, the ToA expression is derived by utilizing the maximum likelihood principle and the distribution law of the error vector, with the estimated value being obtained through a one-dimensional linear search approach. Then, we use the second-order Taylor expansion to decouple the angle and distance parameters in the near-field channel, approximating the model to a more general form. In addition, we develop a parameter estimation method based on the down sampling covariance matrix, which utilizes the rotational invariance to extract angle parameters.
- The positions of both the Scattering Points (SPs) and UT can be obtained in closed form based on their geometric relationships with the BS, enabling precise localization accuracy. Furthermore, the Cramér–Rao Bounds (CRBs) of channel parameters and positions are derived as theoretical lower bounds. Finally, numerical simulations validate that the proposed tensor-based algorithm achieves superior ISAC performance compared with the existing Phase Unwrapping for Distance Difference (PUDD) [39] and MUSIC-Like Spectrum Peak Searching (MUSIC-LSPS) [40] algorithms, and results are closer to the CRBs.
3.2. Notations
4. System Model
4.1. Tensor Representation of Received Signals
4.2. Second-Order Taylor Expansion
5. The Proposed Tensor-Based Algorithm
5.1. CP Decomposition
5.2. Parameter Estimation
5.3. UT and SPs Localization
Algorithm 1: The proposed tensor-based channel parameter estimation and localization algorithm |
Input: The combining matrix , precoding matrix , received tensor , error threshold , number of iterations M and sampling points 1: Take the first L left singular vectors of , and as the initial factor matrices , and 2. Set 3: While or (a) Update factor matrices , , by (29) (b) Reconstruct m = m + 1 End while 4: Get and by (31) 5: Compute by (32) 6: Get down sampling of covariance matrices corresponding to and 7: Obtain by (33)–(40) 8: Get and by (45) and (47) Output:, |
6. Uniqueness and Complexity
6.1. Uniqueness
6.2. Complexity
7. Simulation Results
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
Appendix B.1. CRBs of Channel Parameters
Appendix B.2. CRBs of UT and SPs Positions
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Symbol | Definition |
---|---|
Number of antennas at BS/UT | |
Number of horizontal antennas at BS/UT | |
Number of vertical antennas at BS/UT | |
Number of RF chains at BS/UT | |
Position coordinates of BS/UT/SP | |
Near-field range of BS/UT | |
OFDM subcarriers | |
K | Selected subcarriers for ISAC |
T | Number of time frames |
F | Number of sub-frames per time frame |
S | Number of pilot symbols |
RF precoding at time frame t | |
Digital precoding for subcarrier k at time frame t | |
Pilot symbol vector for subcarrier k at time frame t | |
The t-th column of hybrid precoder matrix | |
The f-th column of hybrid combiner matrix | |
Near-field channel for subcarrier k | |
Received signal for subcarrier k | |
L | Number of paths |
Time delay for path l | |
Complex gain for path l | |
Azimuth AoA/AoD at UT/BS | |
Elevation AoA/AoD at UT/BS | |
Distance from the SP l to the centers of UT/BS | |
Distance from the SP l to the -th/-th antenna of UT/BS | |
Response vector at UT/BS |
Targets | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|
UT | 0.0208 | 0.0663 | 0.0536 | 0.0670 |
SPs | 0.0873 | 0.1102 | 0.1344 | 0.2296 |
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Jiang, L.; Guan, J.; Du, J.; Jiang, W.; Cheng, Y. Near-Field Channel Parameter Estimation and Localization for mmWave Massive MIMO-OFDM ISAC Systems via Tensor Analysis. Sensors 2025, 25, 5050. https://doi.org/10.3390/s25165050
Jiang L, Guan J, Du J, Jiang W, Cheng Y. Near-Field Channel Parameter Estimation and Localization for mmWave Massive MIMO-OFDM ISAC Systems via Tensor Analysis. Sensors. 2025; 25(16):5050. https://doi.org/10.3390/s25165050
Chicago/Turabian StyleJiang, Lanxiang, Jingyi Guan, Jianhe Du, Wei Jiang, and Yuan Cheng. 2025. "Near-Field Channel Parameter Estimation and Localization for mmWave Massive MIMO-OFDM ISAC Systems via Tensor Analysis" Sensors 25, no. 16: 5050. https://doi.org/10.3390/s25165050
APA StyleJiang, L., Guan, J., Du, J., Jiang, W., & Cheng, Y. (2025). Near-Field Channel Parameter Estimation and Localization for mmWave Massive MIMO-OFDM ISAC Systems via Tensor Analysis. Sensors, 25(16), 5050. https://doi.org/10.3390/s25165050