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Large Intelligent Surface for Positioning in Millimeter Wave MIMO Systems

Jiguang He, Henk Wymeersch, Long Kong, Olli Silvén, Markku Juntti

arXiv:1910.00060v1eess.SPcs.IT

TL;DR

The paper addresses how LIS-assisted mmWave MIMO can improve single-anchor positioning. It models direct and LIS-reflected links, derives Cramér-Rao bounds, and evaluates LIS phase and element-count effects. The analyses and simulations show better positioning performance with LIS assistance, including gains from incremental phase design and larger LISs.

  • Problem

    The paper investigates whether a LIS can improve mmWave MIMO positioning beyond a conventional direct-link and NLoS-path scheme.

  • Method

    The paper derives Cramér-Rao lower bounds using an equivalent Fisher information matrix and studies LIS phase control and element count.

  • Results

    LIS assistance yields better positioning performance, while incremental phase design outperforms random phase and larger LISs improve estimation performance.

  • Takeaways & Limitations

    LIS phase shifters and element counts are important design factors for mmWave MIMO positioning and orientation accuracy.

Abstract

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Millimeter-wave (mmWave) multiple-input multiple-output (MIMO) system for the fifth generation (5G) cellular communications can also enable single-anchor positioning and object tracking due to its large bandwidth and inherently high angular resolution. In this paper, we introduce the newly invented concept, large intelligent surface (LIS), to mmWave positioning systems, study the theoretical performance bounds (i.e., Cramér-Rao lower bounds) for positioning, and evaluate the impact of the number of LIS elements and the value of phase shifters on the position estimation accuracy compared to the conventional scheme with one direct link and one non-line-of-sight path. It is verified that better performance can be achieved with a LIS from the theoretical analyses and numerical study.

I. INTRODUCTION

The paper introduces LIS-assisted mmWave MIMO positioning as an extension of single-anchor positioning, leveraging controllable propagation and multiple subcarriers. It evaluates theoretical bounds and shows superior performance over a conventional direct-link plus NLoS scheme.

  • I. INTRODUCTION: Single-anchor mmWave MIMO positioning exploits geometric relationships between the base station and mobile station.Prior work showed that even one base station can achieve promising positioning accuracy.
  • I. INTRODUCTION: LIS elements can control propagation phase and amplitude without baseband processing units.They have been proposed for positioning beamforming and relay-type communication reflection.
  • I. INTRODUCTION: The paper studies LIS-assisted positioning with multiple mmWave subcarriers using equivalent-FIM-based Cramér-Rao lower bounds.It examines phase-shifter values and LIS element counts through channel-parameter, PEB, and OEB analyses.
  • I. INTRODUCTION: Numerical results show that LIS-aided mmWave MIMO positioning outperforms the conventional counterpart without a LIS.The comparison concerns a system with a direct link and a non-line-of-sight path.

II. SYSTEM MODEL

The system models a two-dimensional mmWave MIMO positioning scenario with one BS, one MS, and one LIS, where the MS position and orientation are unknown. Its received signal combines a direct path with an LIS-controlled reflection path.

  • II. SYSTEM MODEL: The 2D system contains one multiple-antenna BS, one multiple-antenna MS, and one LIS with ULA elements and analog phase shifters.The BS and LIS are not rotated, while the MS has unknown orientation α.
  • II. SYSTEM MODEL: The propagation channel consists of one direct BS–MS path and one reflection path through the LIS.The LIS reflection is formed by tandem BS-to-LIS and LIS-to-MS channels.
  • II. SYSTEM MODEL: The model defines array responses, path loss, delays, angles, and geometry for the BS, LIS, and MS under far-field constraints.The BS, LIS, and MS centers are denoted by b, l, and m, respectively.
  • II. SYSTEM MODEL: The LIS phase-control matrix is diagonal with constant-modulus entries that encode the elements’ phase shifts.These phase shifts control the reflected signal in the combined channel.
  • II. SYSTEM MODEL: With known BS and LIS positions, the system can be viewed as a two-LoS-aided positioning system.The paper expects better position accuracy than a mixture of one LoS and one NLoS path.

III. PROBLEM FORMULATION

The paper estimates the MS position and orientation through a two-stage procedure based on channel-parameter estimation. It formulates position and orientation accuracy using expected Euclidean distortion and derives theoretically achievable error bounds.

  • III. PROBLEM FORMULATION: The first stage estimates the channel-parameter vector containing delays, angles, and path-loss terms for the direct and LIS-assisted links.The parameter vector is η = [τB,M, θB,M, φB,M, ρB,M, τL,M, φL,M, ρL,M]T.
  • III. PROBLEM FORMULATION: The second stage obtains the MS coordinates and orientation from the estimated channel parameters through their geometric relationship.The mapping is represented by η(m, α).
  • III. PROBLEM FORMULATION: Channel-parameter estimation can use compressive-sensing methods because mmWave MIMO channels are inherently sparse.Examples include OMP, BP, and AMP.
  • III. PROBLEM FORMULATION: The positioning objective minimizes average Euclidean position-estimation distortion.The formulation uses the expectation operator to define the average error.
  • III. PROBLEM FORMULATION: The orientation objective separately minimizes average orientation-estimation distortion.Position and orientation are treated as distinct estimation targets.

IV. CRAM´ER RAO LOWER BOUNDS

The paper derives Cramér–Rao bounds for channel, position, and orientation estimation using Fisher information, revealing separate direct- and indirect-link estimation behavior and an LIS phase condition that optimizes the reflected link.

  • Cramér Rao lower bounds: The Fisher information matrix is transformed from channel parameters to the unknown position and orientation vector to derive theoretical error bounds.The target vector is ζ = [m_x m_y α]^T, and the full FIM aggregates contributions across subcarriers.
  • Cramér Rao lower bounds: Direct-link channel-parameter estimation is independent of the LIS-mediated NLoS path and depends on the precoding matrix F and pilot signals x[n].
  • Cramér Rao lower bounds: Indirect-link channel-parameter estimation is independent of the LoS path and depends on β[n], which is determined by F, x[n], and the LIS phase matrix Ω.
  • Cramér Rao lower bounds: When F and x[n] are fixed, the incremental phase condition ω_i = 2π(i − 1)d/λ[sin(θ_L,M) − sin(φ_B,L)] optimizes indirect-link channel estimation.Under this condition, the reflected-link combining magnitude reaches the LIS-element-scaled maximum described in the supplied derivation.

V. SIMULATION RESULTS

The simulations use a two-dimensional mmWave MIMO positioning setup with a deterministic benchmark containing one LoS and one NLoS path, under specified antenna, bandwidth, frequency, and geometry parameters.

  • Simulation setup: The simulation uses NB = 128, NM = 32, N = 31 subcarriers, B = 100 MHz, and fc = 60 GHz.
  • Simulation setup: The BS, LIS, and MS are positioned at (0, 0), (160/3, 80), and (80, 40), respectively, with MS orientation α = π/10.
  • Simulation setup: The far-field constraint permits at most NL ≤ 138 LIS elements in this configuration.
  • Simulation setup: The benchmark scenario contains one LoS and one NLoS path with a scatterer at (160/3, 80), whose location is deterministic but unknown to the MS.

A. Impact of the LIS: Phase Shifter

The phase-shifter study shows that an incremental LIS phase aligned with the reflected-path geometry improves estimation of reflected-channel parameters over random phases.

  • Impact of the LIS: Phase Shifter: The incremental phase choice makes the diagonal FIM terms attain their maximum value, NL, under the experiment’s fixed random beamforming vector.
  • Impact of the LIS: Phase Shifter: Figure 2 compares phase conditions using the CRB of the standard deviation of reflection-path channel parameters with NL = 100.
  • Impact of the LIS: Phase Shifter: The incremental phase significantly outperforms the random phase, achieving roughly 10 times better performance in the current experiment.Both phase conditions use the same randomly generated f and other parameters; only the LIS phase condition differs.

B. Impact of the LIS: Number of Elements

Increasing the number of LIS elements improves estimation of reflection-path channel parameters, while having little impact on direct-path channel-parameter accuracy.

  • With around 100 LIS elements, reflection-path channel-parameter estimation improves by around 100 times.The affected parameters are τL,M, φL,M, and ρL,M.
  • The CRB of normalized standard deviation for τL,M, φL,M, and ρL,M is inversely proportional to the number of LIS elements.
  • The benchmark scheme’s estimation performance remains unchanged as LIS elements increase because its number of scatterers is fixed.
  • Increasing LIS elements has little impact on direct-path channel-parameter estimation accuracy.

C. PEB and OEB

Increasing the number of LIS elements improves both positioning and orientation performance, with measurable orientation-error gains even from a 40-element LIS.

  • A 40-element LIS achieves around 3 dB gain when the OEB is at the level of 10^-2.
  • Increasing the number of LIS elements improves positioning performance across the PEB and OEB evaluations.The evaluations are presented in Figs. 4 and 5.
  • The performance enhancement mainly comes from improved NLoS propagation via the LIS.
  • The PEB is evaluated as a function of SNR.

VI. CONCLUSIONS

The paper derives fundamental limits for mmWave MIMO positioning aided by a LIS and studies how LIS elements and their phases affect estimation and error bounds.

  • The study investigates how the number and phases of LIS elements affect channel-parameter estimation.
  • These channel-estimation results support analysis of positioning and orientation error bounds.
  • The paper compares positioning systems with and without LIS assistance to assess potential benefits from passive elements.
  • Joint BS beamformer and LIS phase-shifter design is left for future investigation.

APPENDIX A DERIVATION OF FIM

The appendix derives the Fisher information matrix by differentiating channel-array responses with respect to angular parameters and incorporating subcarrier-dependent phase terms.

  • The FIM derivation differentiates channel-array responses with respect to φB,M and φL,M.
  • The appendix presents the derivation of the FIM for the channel parameters.
  • The derivative expressions use diagonal matrices whose entries scale with antenna indices and angular cosine factors.
  • The derivation includes the subcarrier phase term ξ[n] associated with the direct and reflected path delays.
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