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Hybrid-Field Channel Tracking for Extremely Large-Scale MIMO Systems with Mobility

Yilong Liu, Xi Yang, Ting Liu, Yu Han, Shi Jin

arXiv:2609.19047v1eess.SPcs.IT

TL;DR

Mobile XL-MIMO requires frequent channel updates, which can make CSI acquisition computationally costly, while hybrid-field sparsity is difficult to exploit directly. The paper tracks channels using historical CSI and separate LoS and NLoS updates. It reports a favorable accuracy-complexity trade-off, while discrete-grid peak search has an off-grid accuracy limitation addressed by Newton refinement.

  • Problem

    In mobile XL-MIMO, frequent CSI acquisition is costly, and hybrid-field energy leakage and spread make channel sparsity difficult to exploit directly.

    Source: §I · p. 1, A. System Model · p. 2

  • Method

    The tracker uses historical CSI for narrow-window LoS peak search, survival-based NLoS gain updates, and Newton refinement before searching for new paths.

    Source: §I · p. 1, §V · p. 6

  • Results

    The proposed algorithm achieves superior estimation accuracy with significantly lower computational complexity in the reported performance-complexity trade-off.

    Source: §IV · p. 6

  • Takeaways & Limitations

    The reported results support historical-CSI channel tracking as a lower-complexity approach that maintains strong estimation performance in the considered mobile hybrid-field setting.

    Source: §IV · p. 6, §V · p. 6

    DFrFT peak search uses discrete grids for continuously distributed path parameters, limiting estimation accuracy through off-grid effects; Newton refinement is used to improve it.

    Source: 1) Coarse Estimation for the LoS Path · p. 4

Abstract

from arXiv · show

In this paper, we propose a hybrid-field channel tracking algorithm for extremely large-scale multiple-input multiple-output (XL-MIMO) systems with mobility, leveraging the historical channel state information. The multiple path scenario is considered, and the line-of-sight path is coarsely estimated through the sparse peak search within a narrow window in the fractional Fourier domain based on the temporal continuity of the user's motion. Moreover, coarse estimations of the non-line-of-sight (NLoS) paths are determined by ensuring the scatterer survival probability, eliminating the necessity of detecting existing NLoS paths. Then, a Newton-based refinement is applied to the estimated paths before seeking possible new paths. Numerical results validate that the proposed algorithm achieves superior performance with low computational complexity.

I. INTRODUCTION

XL-MIMO mobility makes accurate, low-overhead channel tracking difficult: frequent CSI acquisition is costly, while hybrid-field sparsity is hard to exploit directly. The paper uses historical CSI to track the moving user's channel, with differentiated LoS and NLoS updates.

I. INTRODUCTION

  • Earlier hybrid-field sparse-estimation methods address static or quasi-static settings, motivating lower-complexity tracking for mobile users.Prior approaches include angle/polar-domain OMP, fractional-Fourier-domain gridless estimation, and adaptive on-grid estimation.Source: §I · p. 1
  • The proposed tracker searches for the LoS path within a narrow fractional-Fourier-domain window and updates NLoS path gains when scatterer survival is sufficient.A Newton-based refinement is applied before searching for possible new paths.Source: §I · p. 1
  • Mobility makes frequent CSI acquisition computationally costly, and hybrid-field energy leakage and spread make channel sparsity difficult to exploit directly.Source: §I · p. 1, A. System Model · p. 2
  • Historical CSI supports channel tracking by using prior user location, velocity, and channel estimates to estimate the current channel from the received signal.The paper focuses on tracking after an initial estimate at time slot 0.Source: A. System Model · p. 3

III. HYBRID-FIELD CHANNEL TRACKING

The tracking algorithm combines DFrFT-based sparsity extraction with coarse path estimation, Newton refinement, and detection of new paths.

III. HYBRID-FIELD CHANNEL TRACKING

  • The tracking pipeline comprises coarse estimation, Newton-based refinement, and new-path detection.Source: §III · p. 3
  • DFrFT is used to expose the channel's hybrid-field sparsity within the tracking pipeline.Source: §III · p. 3
  • The algorithm estimates paths coarsely before refining them and checking for possible new paths.Source: §III · p. 3

A. Discrete Fractional Fourier Transform

The DFrFT maps received signals into a domain where hybrid-field propagation paths appear as distinct peaks, enabling sparse path-parameter searches.

A. Discrete Fractional Fourier Transform

B. Coarse Estimation

Coarse tracking uses motion continuity to narrow LoS detection and scatterer survival to avoid re-estimating existing NLoS path geometry.

B. Coarse Estimation

  • Temporal motion continuity lets the tracker search for the LoS path only within a narrow two-dimensional window centered on the previous user location.Source: B. Coarse Estimation · p. 3
  • When scatterer survival exceeds the threshold, existing NLoS path angles and distances need not be re-detected; only their gains are updated.The passage attributes this to most scatterers remaining valid between adjacent time slots and their large-scale fading parameters remaining nearly stable.Source: B. Coarse Estimation · p. 3
  • The LoS window and NLoS gain-only update reduce tracking computation by limiting the search and avoiding repeated geometry estimation.Source: B. Coarse Estimation · p. 3

1) Coarse Estimation for the LoS Path:

Historical user location and motion yield a predicted LoS path distribution, which confines DFrFT peak detection to a narrow three-sigma window. The discrete-grid search leaves an off-the-grid estimation error.

1) Coarse Estimation for the LoS Path:

  • A three-sigma window derived from predicted LoS path distributions narrows DFrFT peak detection and reduces search complexity.The predicted user location uses the previous slot's location and velocity.Source: 1) Coarse Estimation for the LoS Path · p. 3
  • The maximum-amplitude peak in the residual vector's DFrFT spectra gives the coarse LoS path estimates.The peak is selected across the fractional-order spectra and frequency indices in the search window.Source: 1) Coarse Estimation for the LoS Path · p. 4
  • Because DFrFT peak search uses discrete grids for continuous path parameters, its estimates are subject to off-the-grid error.The paper identifies this as a limit on estimation accuracy, addressed by Newton-based refinement.Source: 1) Coarse Estimation for the LoS Path · p. 4

2) Coarse Estimation for NLoS Paths:

When scatterer survival probability meets a threshold, most NLoS scatterers persist between adjacent tracking slots, so prior path geometry supplies coarse estimates without redetecting path parameters. The tracking interval is bounded by the survival requirement.

2) Coarse Estimation for NLoS Paths:

  • PT(∆t) models the probability that an arbitrary NLoS scatterer survives after ∆t, with recombination rate, moving-scatterer percentage, relative velocity, and space correlation informing it.The space-correlation coefficient is scenario-dependent.Source: 2) Coarse Estimation for NLoS Paths · p. 4
  • When survival probability PT(∆t) meets threshold ξ, most scatterers survive adjacent tracking cycles and prior NLoS path parameters provide coarse estimates.Path geometry remains essentially unchanged, although complex path gains may vary significantly.Source: 2) Coarse Estimation for NLoS Paths · p. 4
  • With ξ = 0.8, low- and medium-mobility scenarios allow maximum tracking intervals exceeding 0.38 s.The paper states these intervals exceed multiple 10 ms 5G NR radio frames.Source: 2) Coarse Estimation for NLoS Paths · p. 4, Figure 3 · p. 4

C. Refinement Based on Newton Method

Newton-based refinement follows coarse path estimation to address LoS off-the-grid effects and improve NLoS estimation accuracy. It locally adjusts path parameters to reduce residual energy.

C. Refinement Based on Newton Method

1) Local Refinement:

Local refinement iteratively adjusts path parameters under descent and Hessian conditions, followed by gain updates using least squares. The global refinement includes a regularization term to ensure the system matrix is full rank.

1) Local Refinement:

  • Local Newton updates are accepted only when the Hessian is negative definite and residual energy decreases, so each iteration reduces that energy.After local refinements, path gains are updated by least squares to further reduce residual energy.Source: 1) Local Refinement · p. 4, 2) Global Refinement · p. 5

2) Global Refinement:

  • The global refinement's regularization term ensures full rank of A^HA + σ²I.The algorithm repeats local refinement within its global loop, then updates gains and the residual.Source: 2) Global Refinement · p. 5

D. Detect New Paths

The algorithm adds newly detected paths to the tracked path set, refines their parameters, and repeats detection and refinement until the residual-energy stopping condition is met. It then forms the channel estimate from the detected paths; the paper also states that the overall algorithm converges.

D. Detect New Paths

  • New paths are detected from residual peaks, added to the path and gain sets, and refined using Algorithm 1.The new-path search uses p ∈ [0.5, 1.5] and estimates path parameters and gain via (13) and (14).Source: D. Detect New Paths · p. 5

E. Overall Channel Tracking Algorithm

  • The final channel estimate is formed from the detected paths, whose total number is denoted by ˆK = dim(P).Source: E. Overall Channel Tracking Algorithm · p. 5
  • The overall procedure initializes the path estimates, refines them, then detects and refines additional paths while residual energy remains above the threshold.The algorithm updates the residual after path estimation and stops when the residual-energy condition is no longer met.Source: E. Overall Channel Tracking Algorithm · p. 5
  • The authors state that local refinement converges and least-squares refinement of path gains reduces residual energy, guaranteeing convergence of Algorithm 2.Source: E. Overall Channel Tracking Algorithm · p. 5

IV. NUMERICAL RESULTS

Simulations compare channel-tracking accuracy and computational complexity against hybrid-field and near-field algorithms. The proposed method has a favorable accuracy–complexity trade-off and achieves the best NMSE at medium SNR.

  • The evaluation tracks the current time slot using historical CSI from the previous slot and compares NMSE across SNRs.The stated setup uses 2000 channel realizations at each SNR unless otherwise specified.Source: §IV · p. 5
  • At medium SNR, the proposed algorithm achieves the best NMSE; it also outperforms hybrid-field OMP with true K from low to medium SNR without requiring prior K.The authors additionally report that exploiting historical CSI lets the proposed method outperform hybrid-field NOMP.Source: §IV · p. 6, Figure 4 · p. 6
  • Wrong-K hybrid-field and near-field OMP can show lower NMSE through spectral leakage, but this produces spurious paths that do not reflect the physical channel geometry.With true K, both OMP methods saturate at high SNR because off-grid quantization error becomes dominant over additive noise.Source: §IV · p. 6
  • The proposed algorithm has lower computational complexity than hybrid-field OMP, near-field OMP, and hybrid-field NOMP.The paper attributes the reductions to a narrow LoS search window and avoiding re-detection of existing NLoS path parameters.Source: §IV · p. 6, Figure 5 · p. 6
  • The proposed algorithm achieves the most favorable NMSE–complexity trade-off as oversampling varies.The comparison is shown in Fig. 5(b), where NMSE decreases as computational complexity increases across the considered algorithms.Source: §IV · p. 6, Figure 5 · p. 6

V. CONCLUSION

The conclusion presents historical-CSI-based hybrid-field channel tracking as a way to reduce computational complexity and enhance estimation accuracy.

  • The proposed tracker exploits historical CSI to reduce computational complexity and enhance estimation accuracy.Source: §V · p. 6
  • It coarsely estimates LoS paths with a narrow-window sparse peak search and NLoS paths using scatterer survival probability.Source: §V · p. 6
  • Newton-based refinement is applied to estimated paths before the algorithm seeks potential new paths.Source: §V · p. 6
  • Numerical results demonstrate the effectiveness and superiority of the proposed algorithm.Source: §V · p. 6
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