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Efficient Joint DOA and TOA Estimation for Indoor Positioning with 5G Picocell Base Stations

Mengguan Pan, Peng Liu, Shengheng Liu, Wangdong Qi, Yongming Huang, Xiaohu You, Xinghua Jia, Xiaodong Li

arXiv:2206.09748v1eess.SP

TL;DR

Indoor GNSS blockage and the limited spatial resolution and modeling accuracy of small picocell arrays complicate 5G indoor positioning. The paper calibrates direction-dependent array errors and decouples TOA and DOA estimation for efficient JADE. It reports 0.44 m triangulation positioning accuracy in 90% of indoor field-test cases using DOAs from two TRPs.

  • Problem

    Small picocell arrays have limited spatial resolution and substantial array-modeling errors, while two-dimensional JADE processing is computationally demanding for real-time use.

    Source: §I · p. 1

  • Method

    The scheme pre-calibrates steering vectors for array errors, then estimates TOA with IAA and DOA with CBF, with preprocessing and FFT acceleration.

    Source: §VIII · p. 17

  • Results

    0.44 m triangulation positioning accuracy was achieved in 90% of indoor field-test cases using DOAs estimated from two TRPs.

    Source: §VIII · p. 17

  • Takeaways & Limitations

    The indoor field test demonstrates 5G picocell positioning with a two-TRP configuration using the proposed DOA estimates.

    Source: §VIII · p. 17

Abstract

from arXiv · show

The ubiquity, large bandwidth, and spatial diversity of the fifth generation (5G) cellular signal render it a promising candidate for accurate positioning in indoor environments where the global navigation satellite system (GNSS) signal is absent. In this paper, a joint angle and delay estimation (JADE) scheme is designed for 5G picocell base stations (gNBs) which addresses two crucial issues to make it both effective and efficient in realistic indoor environments. Firstly, the direction-dependence of the array modeling error for picocell gNB as well as its impact on JADE is revealed. This error is mitigated by fitting the array response measurements to a vector-valued function and pre-calibrating the ideal steering-vector with the fitted function. Secondly, based on the deployment reality that 5G picocell gNBs only have a small-scale antenna array but have a large signal bandwidth, the proposed scheme decouples the estimation of time-of-arrival (TOA) and direction-of-arrival (DOA) to reduce the huge complexity induced by two-dimensional joint processing. It employs the iterative-adaptive-approach (IAA) to resolve multipath signals in the TOA domain, followed by a conventional beamformer (CBF) to retrieve the desired line-of-sight DOA. By further exploiting a dimension-reducing pre-processing module and accelerating spectrum computing by fast Fourier transforms, an efficient implementation is achieved for real-time JADE. Numerical simulations demonstrate the superiority of the proposed method in terms of DOA estimation accuracy. Field tests show that a triangulation positioning error of 0.44 m is achieved for 90% cases using only DOAs estimated at two separated receiving points.

I. INTRODUCTION

Indoor GNSS blockage motivates cellular alternatives, and 5G picocell gNBs offer bandwidth and antenna arrays for positioning. The paper addresses JADE accuracy and real-time complexity challenges through array-error calibration and an efficient cascaded estimator.

I. INTRODUCTION

  • Indoor GNSS blockage motivates RF positioning, while 5G offers abundant indoor signals, large bandwidth, high received power, and positioning reference signals.The paper identifies uplink SRS and downlink PRS as reference signals for positioning and sensing.Source: §I · p. 1
  • Small picocell arrays have limited spatial resolution and substantial modeling errors, and real array manifolds can lose the Vandermonde structure assumed by several JADE methods.The paper states that these issues limit DOA accuracy and can make smoothing, ESPRIT, matrix-pencil, and IQML methods infeasible.Source: §I · p. 1, A. Related Works · p. 2

A. Related Works

  • Existing JADE approaches trade computational cost against performance: MUSIC and subspace methods require high-dimensional operations, while ML and compressed-sensing approaches can remain computationally burdensome.The cited literature also identifies long convergence times for some ML algorithms and large dictionaries or optimization problems for compressed sensing.Source: A. Related Works · p. 2

B. Contributions

  • The proposed JADE scheme calibrates direction-dependent array errors and cascades IAA-based TOA estimation with CBF-based DOA estimation, using preprocessing and FFT acceleration.The paper also reports 10.1 ms average runtime for typical picocell configurations on a PC.Source: B. Contributions · pp. 2–3
  • The paper reports direction-dependent antenna-error characterization, offline steering-vector calibration, and experiments spanning simulations and field tests.The proposed calibration reduces average DOA error from 8.11° to 1.28° at +60° incidence; indoor tests report 0.44 m positioning accuracy in 90% of cases using two TRPs.Source: B. Contributions · p. 3

II. SYSTEM MODEL

The system model uses a UE's uplink SRS received at a 5G TRP to estimate path delays and directions from channel-frequency-response measurements. It formulates the task as estimating the line-of-sight TOA and DOA from a single space-frequency CFR matrix.

II. SYSTEM MODEL

  • The UE's SRS occupies M subcarriers; after FFT, the received frequency-domain signals from N antenna channels form the CFR matrix.The model considers K impinging paths and a single SRS symbol, corresponding to a single-measurement-vector scenario.Source: §II · p. 4
  • The signal model represents path delay with a known delay-signature function and direction with a known steering-vector function; noise is included in the CFR measurements.The delay signature describes the SRS frequency-domain structure, while the steering vector is determined by the array's spatial structure.Source: §II · p. 4
  • A single CFR matrix is used to estimate the line-of-sight DOA and TOA, with the model initially omitting array-modeling impairments.The positioning scenario receives uplink SRS at TRPs and uses joint estimates to determine UE position.Source: §II · pp. 3–4

III. ARRAY MODELING ERROR ANALYSIS BASED ON REAL-DATA

The real-data analysis examines a picocell gNB radio unit and antenna array to characterize their array-modeling errors.

III. ARRAY MODELING ERROR ANALYSIS BASED ON REAL-DATA

  • The experiments examine a six-element 5G FR1 ULA with 3 cm inter-element spacing; its two outer elements are dummy elements and its middle four are active.The array and radio unit are used to exemplify spatial-frequency characteristics of array-modeling errors.Source: §III · pp. 4–5, Figure 2 · p. 5

A. RF Channel Error Analysis

RF-channel errors vary with frequency and can bias DOA estimates and distort TOA spectra. Antenna phase errors are strongly direction-dependent, motivating spatial calibration.

A. RF Channel Error Analysis

  • RF-channel measurements show differing initial phase responses that can bias DOA, while nonlinear frequency components can distort TOA spectra.The measurements average 500 repeated amplitude and phase measurements; shaded areas mark their upper and lower bounds.Source: A. RF Channel Error Analysis · p. 5

B. Antenna Error Analysis

  • Antenna phase errors are dominated by nearly parallel linear frequency trends, unlike the nonlinear frequency components of RF-channel errors.The antenna phase-error measurements cover different incident directions.Source: A. RF Channel Error Analysis · p. 5, B. Antenna Error Analysis · p. 6
  • 2.0–2.2 m distance biases, with less than 0.2 m variance, imply a nearly identical TOA shift across channels and incident directions.The reported variance is much smaller than the 3 m distance resolution.Source: B. Antenna Error Analysis · p. 6
  • Antenna phase-error variance across frequencies is relatively small, but the errors are highly direction-dependent, so spatial calibration is sufficient across frequency.Because the unknown incident direction is the parameter being estimated, the gNB cannot determine antenna-error calibration coefficients directly.Source: B. Antenna Error Analysis · p. 6

C. Signal Model Refinement in the Presence of Array Modeling Errors

The signal model gathers frequency-selective RF-channel errors and direction-dependent antenna errors into separate models. The scheme calibrates channel responses in received data and pre-calibrates the steering vector for online DOA estimation.

C. Signal Model Refinement in the Presence of Array Modeling Errors

  • The refined signal model represents RF-channel errors with a frequency-selective matrix and antenna errors with a direction-dependent vector-valued function.The vector function returns an N-dimensional error vector for a given DOA, with each element defined by an antenna phase-error function.Source: C. Signal Model Refinement in the… · p. 6

IV. ARRAY MODELING ERROR CALIBRATION AND JADE

  • The JADE task uses one estimated space-frequency CFR matrix and pre-measured array-error data to estimate the desired LOS DOA and TOA.The overall scheme separates RF-channel and antenna calibration modules from an IAA-based TOA estimator and a CBF.Source: C. Signal Model Refinement in the… · p. 6, §IV · p. 7

A. Calibration Modules

  • The scheme calibrates RF-channel responses in the received CFR, while offline regression fits measured antenna phase errors and pre-calibrates the ideal steering vector.The fitted steering vector captures direction-dependent array errors and is used online to improve DOA estimation accuracy.Source: A. Calibration Modules · p. 7

B. Estimator Modules

The estimator first resolves multipath components by delay, then estimates the LOS direction from the isolated path. This cascading design avoids conventional two-dimensional DOA–TOA processing.

B. Estimator Modules

  • IAA-based TOA spectral estimation separates multipaths by delay before a conventional beamformer estimates their DOAs, avoiding two-dimensional joint processing.The design exploits the 5G signal's abundant subcarriers and IAA's super-resolution ability in the TOA domain.Source: B. Estimator Modules · p. 7
  • IAA estimates channel-specific attenuation coefficients over a uniform TOA grid using weighted least squares and iteratively estimates the spectrum.It can operate directly on a single-measurement-vector scenario, recover component amplitude and phase, and usually converges in 10–15 iterations.Source: B. Estimator Modules · pp. 7–8
  • After significant paths are detected and the LOS path identified, the scheme applies CBF to its multichannel component using the pre-calibrated steering vector.The LOS DOA is found by a one-dimensional search over a predefined uniform angular grid.Source: B. Estimator Modules · pp. 8–9
  • The estimated LOS DOA and TOA can feed a 2-D positioning and tracking framework such as an EKF, UKF, or particle filter.The paper does not detail signal detection or LOS-path identification because they are not its main concern.Source: B. Estimator Modules · pp. 8–9

C. Complexity Analysis

The proposed method has lower computational complexity and storage requirements than the compared 2-D subspace-based JADE methods. Its IAA-based TOA estimation dominates its computational burden.

C. Complexity Analysis

  • Overall computational complexity is O(NPM^2 + NM^3 + MN + NQ), reducible to O(NPM^2) when the TOA-grid count P is much larger than subcarrier count M.The IAA iteration count is described as small and independent of problem scale.Source: C. Complexity Analysis · p. 9
  • The proposed method's storage requirement is O(MP + M^2 + NP), storing the IAA delay signature matrix, covariance matrix, and channel TOA spectra.Only one channel's intermediate IAA results need to be stored at a time.Source: C. Complexity Analysis · p. 9
  • The compared 2-D MUSIC methods incur O(M^3N^3) covariance EVD complexity and O(PQM^2N^2) search complexity, while matrix-pencil methods require O(M^3N^3) complexity.The stated storage requirements are O(PQMN) and O(M^2N^2) for MUSIC and matrix-pencil methods, respectively.Source: C. Complexity Analysis · p. 9
  • The proposed method has much lower computational complexity and storage requirements than popular 2-D subspace-based JADE methods and the discussed CS-based methods.TABLE III summarizes computational complexity and storage requirements; the prose reports the comparisons without specific table values.Source: Table III · p. 9, C. Complexity Analysis · pp. 9–10

V. ENHANCEMENTS FOR EFFICIENT IMPLEMENTATION

The proposed JADE scheme still faces real-time implementation challenges despite reduced computation and storage relative to 2-D joint estimation methods. The paper adds CFR pre-processing and FFT acceleration to further reduce complexity.

V. ENHANCEMENTS FOR EFFICIENT IMPLEMENTATION

  • Real-time implementation remains challenging despite the scheme's reduced computation and storage compared with 2-D joint estimation methods.The section identifies two enhancements aimed at reducing complexity further.Source: §V · p. 10
  • A CFR pre-processing module is prepended to facilitate the subsequent estimation procedures.Source: §V · p. 10
  • FFTs accelerate the IAA-based TOA spectrum estimator, which dominates computational complexity.Source: §V · p. 10

A. Pre-Processing: CFR Denoising

The enhancements reduce the CFR's dimension and noise before estimation, then use FFTs to lower the cost of IAA-based TOA spectrum computation. These changes target the substantial latency and resource demands of processing large-bandwidth SRS data.

A. Pre-Processing: CFR Denoising

  • The proposed pre-processing truncates CIR taps beyond the gNB's maximum delay, which add noise but no JADE information, then transforms the retained taps back into a reduced CFR.For 100 m coverage, the first 2% of delay taps preserve all LOS and multipath information.Source: A. Pre-Processing: CFR Denoising · p. 10
  • Random TOA offsets between consecutive SRS symbols shift informative CIR taps, so the scheme removes the CFR phase slope before denoising.After phase-slope removal, the main CIR peak is nearly centered at zero delay.Source: A. Pre-Processing: CFR Denoising · p. 10
  • In the illustrated example, the delay window retains 41 CIR points, allowing the subsequent FFT to use 64 points.The example uses a [−166.67 ns, +166.67 ns] window, corresponding to [−50 m, +50 m].Source: A. Pre-Processing: CFR Denoising · p. 10
  • Pre-processing smooths and reduces noise in the CFR, while the reduced subcarrier count lowers the JADE method's time and storage complexity.With ˜M ≪ M, pre-processing costs nearly O(M log2 M + ˜M log2 ˜M), and the reduced-CFR JADE complexity is O(NP˜M^2 + N˜M^3).Source: A. Pre-Processing: CFR Denoising · p. 10

B. TOA Spectrum Estimation: Accelerating Spectrum Computing by FFTs

  • FFT-IAA exploits the SRS comb pattern and Vandermonde delay signature structure to reduce computational complexity from O(NPM^2 + NM^3) to O(NP log2 P + NM^3).For 5G picocell gNBs, P ≫ M ≫ N; FFT-IAA also reduces storage from O(MP + M^2 + NP) to O(M^2 + NP).Source: B. TOA Spectrum Estimation:… · pp. 10–11

VI. PERFORMANCE EVALUATION

The evaluation compares the proposed method with established JADE approaches through chamber experiments, simulations, and indoor field tests. In the anechoic chamber, calibrated steering vectors substantially reduce DOA error, especially at large incident angles.

VI. PERFORMANCE EVALUATION

  • The evaluation compares the proposed method with periodogram-, smoothed-MUSIC-, and matrix-pencil-based JADE methods across chamber, simulation, indoor-channel, field-test, and runtime experiments.A CFR pre-processing scheme is applied before all compared methods.Source: §VI · p. 11
  • Experiments use a picocell gNB and a UE within a −60° to +60° sector and 50 m range; simulations assume perfect timing, while indoor field tests evaluate TDOAs.The timing assumption addresses the difficulty of separating synchronization error from absolute propagation delay.Source: §VI · pp. 11–12

A. Field Test in an Anechoic Chamber

  • The chamber experiment compares ideal and calibrated steering-vector functions to assess array-modeling errors and the calibration module.The receiving ULA was rotated from −60° to +60° in 5° steps, with 500 SRS symbols collected at each angle.Source: A. Field Test in an Anechoic Chamber · p. 12
  • At +60°, calibration reduces average DOA estimation error from 8.11° to 1.28°; improvements are especially marked beyond ±45°.Figure 11 summarizes RMSEs across 12 antennas, with average, minimum, and maximum values shown by dots and shaded bounds.Source: A. Field Test in an Anechoic Chamber · p. 12, Figure 11 · p. 12

B. Numerical Experiments Using Simulated Multipath Data

In simulated multipath data, the proposed method outperforms the compared JADE methods in DOA estimation, while its TOA performance is close to smoothed MUSIC in the specified five-path, low-SNR case. Its single-site positioning error remains below 1.3 m for 80% of cases under the stated simulation conditions.

B. Numerical Experiments Using Simulated Multipath Data

C. Numerical Experiments Using Simulated 5G Wireless Channel Data

The proposed JADE method achieves accurate indoor positioning in simulated 5G channels and an underground-parking-lot field test, while reducing computation time and extending to arbitrary array structures.

C. Numerical Experiments Using Simulated 5G Wireless Channel Data

  • At least 72% lower DOA error (1.8° to 0.5°) and at least 67% lower positioning error (1.54 m to 0.51 m) were achieved for default InF-LOS channels.TOA error increased by at most 0.02 m, from 0.06 m to 0.08 m; Fig. 13 compares 80th-percentile errors across simulated InF-LOS and InO-LOS channels.Source: C. Numerical Experiments Using… · p. 14, Figure 13 · p. 15

D. Field Test in an Indoor Environment

  • Field-test DOA and TDOA errors varied substantially by location, which the authors attribute to differing multipath effects.The 80th-percentile DOA errors were 0.88° and 1.49° for the two RRUs, and the TDOA error was 0.31 m.Source: D. Field Test in an Indoor Environment · p. 14
  • 0.44 m is the total 90th-percentile positioning error across 9000 field-test samples, meeting the cited 1 m-for-90%-of-cases 3GPP R17 requirement.Positioning uses triangulation from DOA estimates at two TRPs.Source: D. Field Test in an Indoor Environment · p. 14

E. Running Time Evaluation

  • The proposed cascading JADE scheme reduced computation time by two orders of magnitude versus smoothed-MUSIC JADE, with FFTs cutting it by nearly another order.The comparison used identical input CFR dimensions after shared preprocessing.Source: E. Running Time Evaluation · pp. 14–15, Table IV · p. 15

VII. DISCUSSION

  • The framework is adaptable beyond the evaluated setup, with extensions discussed for other potential scenarios.The discussion introduces extensions to irregular array structures and nonuniform subcarrier distributions.Source: §VII · p. 15

A. Extension to Arbitrary Array Structures

  • Unlike several JADE methods requiring a Vandermonde array manifold, the proposed CBF-based DOA estimator applies to arbitrary array structures.It can handle space-domain nonuniformity.Source: A. Extension to Arbitrary Array… · p. 15

B. Extension to Nonuniformly Distributed Subcarriers

The method extends to nonuniform subcarriers and planar-array 3-D localization; the paper concludes that its calibrated, efficient JADE scheme achieves real-time estimates and strong indoor positioning results.

B. Extension to Nonuniformly Distributed Subcarriers

  • FFT-IAA extends to nonuniform subcarriers by discarding contaminated tones and using the remaining irregularly distributed subcarriers for TOA estimation.Selection and zero-padding operations have little impact on computational complexity.Source: B. Extension to Nonuniformly… · pp. 15–16

C. Extension to 3-D Localization Parameter Estimation

  • For 3-D positioning with an arbitrary planar array, temporal-delay processing is retained while the 1-D CBF search is replaced by a 2-D search over azimuth and elevation.The paper emphasizes delay and azimuth estimation for 2-D positioning based on a linear array.Source: C. Extension to 3-D Localization… · p. 16

VIII. CONCLUSION

  • The proposed scheme calibrates direction-dependent antenna errors and uses cascading IAA-based TOA analysis and CBF-based DOA estimation for real-time JADE.Dimension-reducing preprocessing and FFT-based IAA yield an average running time of 10.1 ms in a typical gNB configuration, nearly three orders lower than MUSIC-based JADE.Source: §VIII · p. 17
  • 0.44 m positioning error was achieved for 90% of field-test cases using two separate TRPs, while simulated channel tests showed improved DOA accuracy at slightly reduced TOA performance.The conclusion describes the method as a viable option for real-time JADE in 5G and beyond networks for indoor positioning.Source: §VIII · p. 17
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