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Low Time Complexity Near-Field Channel and Position Estimations

Xiyuan Liu, Qingqing Wu, Rui Wang, Jun Wu

TL;DR

The paper tackles near-field channel and position estimation in XL-MIMO where AoA and CoA are coupled. It introduces the JAC scheme to decouple these parameters by exploiting spatial autocorrelation to estimate CoA (via $p_1$) and then using cross-correlation (MUSIC) to estimate AoA (via $p_2$), followed by reconstructing the channel and deriving location estimates. It presents two concrete algorithms, JAC-ISF and JAC-GD, with CRLB analysis and a complexity assessment showing additive, rather than multiplicative, time complexity in angle and distance estimation. Simulations demonstrate that JAC-GD achieves near-CRLB performance across SNRs and distances with reduced time overhead, validating its practicality for fast near-field beam training and localization in XL-MIMO systems.

Abstract

With the application of high-frequency communication and extremely large MIMO (XL-MIMO), the near-field effect has become increasingly apparent. The near-field channel estimation and position estimation problems both rely on the Angle of Arrival (AoA) and the Curvature of Arrival (CoA) estimation. However, in the near-field channel model, the coupling of AoA and CoA information poses a challenge to the estimation of the near-field channel. This paper proposes a Joint Autocorrelation and Cross-correlation (JAC) scheme to decouple AoA and CoA estimation. Based on the JAC scheme, we propose two specific near-field estimation algorithms, namely Inverse Sinc Function (JAC-ISF) and Gradient Descent (JAC-GD) algorithms. Finally, we analyzed the time complexity of the JAC scheme and the cramer-rao lower bound (CRLB) for near-field position estimation. The simulation experiment results show that the algorithm designed based on JAC scheme can solve the problem of coupled CoA and AoA information in near-field estimation, thereby improving the algorithm performance. The JAC-GD algorithm shows significant performance in channel estimation and position estimation at different SNRs, snapshot points, and communication distances compared to other algorithms. This indicates that the JAC-GD algorithm can achieve more accurate channel and position estimation results while saving time overhead.

Low Time Complexity Near-Field Channel and Position Estimations

TL;DR

The paper tackles near-field channel and position estimation in XL-MIMO where AoA and CoA are coupled. It introduces the JAC scheme to decouple these parameters by exploiting spatial autocorrelation to estimate CoA (via ) and then using cross-correlation (MUSIC) to estimate AoA (via ), followed by reconstructing the channel and deriving location estimates. It presents two concrete algorithms, JAC-ISF and JAC-GD, with CRLB analysis and a complexity assessment showing additive, rather than multiplicative, time complexity in angle and distance estimation. Simulations demonstrate that JAC-GD achieves near-CRLB performance across SNRs and distances with reduced time overhead, validating its practicality for fast near-field beam training and localization in XL-MIMO systems.

Abstract

With the application of high-frequency communication and extremely large MIMO (XL-MIMO), the near-field effect has become increasingly apparent. The near-field channel estimation and position estimation problems both rely on the Angle of Arrival (AoA) and the Curvature of Arrival (CoA) estimation. However, in the near-field channel model, the coupling of AoA and CoA information poses a challenge to the estimation of the near-field channel. This paper proposes a Joint Autocorrelation and Cross-correlation (JAC) scheme to decouple AoA and CoA estimation. Based on the JAC scheme, we propose two specific near-field estimation algorithms, namely Inverse Sinc Function (JAC-ISF) and Gradient Descent (JAC-GD) algorithms. Finally, we analyzed the time complexity of the JAC scheme and the cramer-rao lower bound (CRLB) for near-field position estimation. The simulation experiment results show that the algorithm designed based on JAC scheme can solve the problem of coupled CoA and AoA information in near-field estimation, thereby improving the algorithm performance. The JAC-GD algorithm shows significant performance in channel estimation and position estimation at different SNRs, snapshot points, and communication distances compared to other algorithms. This indicates that the JAC-GD algorithm can achieve more accurate channel and position estimation results while saving time overhead.

Paper Structure

This paper contains 16 sections, 44 equations, 11 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System model
  3. JAC Scheme
  4. The Physical Meaning of Near-field Channel Parameters
  5. The Relationship Between Near-field Problems and Doppler Problems
  6. Estimation Model of Near-field Channel
  7. Near Field Localization Algorithms Based on JAC Scheme
  8. Inverse sinc function algorithm
  9. Gradient descent method for calculating CoA
  10. Cramer's lower bound and time complexity analysis
  11. Analysis of Cramer's Lower bound for Angle and Distance
  12. Time complexity analysis of JAC-ISF algorithm and JAC-GD algorithm
  13. Simulation Results
  14. The Results of Channel Estimation
  15. The Results of Position Estimation
  16. ...and 1 more sections

Figures (11)

  • Figure 1: Near-field channel model for ULA communication system.
  • Figure 2: Parameters for controlling the curvature and direction of spherical waves.
  • Figure 3: Spatial Doppler phenomenon.
  • Figure 4: The ${\rm arc}sinc$ function.
  • Figure 5: Comparison of achievable rates of algorithms under different SNR with $T=32$ and $|{\bm p}|\in (10, 50)$.
  • ...and 6 more figures