PaperlayerView exact revision on arXiv

Source-linked AI summary

Near-Field Integrated Sensing and Communications

Zhaolin Wang, Xidong Mu, Yuanwei Liu

arXiv:2302.01153v5cs.ITeess.SP

TL;DR

Far-field ISAC lacks the distance information available in near-field propagation for both sensing and communications. The paper develops a near-field ISAC framework, derives and optimizes joint distance-angle sensing performance under user-rate constraints, and investigates fully digital and hybrid architectures. Numerical results show that near-field ISAC can estimate target distance and angle, while hybrid antennas trade sensing performance for lower power consumption.

  • Problem

    Far-field ISAC does not exploit the near-field distance dimension, motivating joint distance-angle sensing and communication design for near-field systems.

  • Method

    The paper derives the near-field joint distance-angle sensing CRB and optimizes ISAC waveforms under minimum user-rate constraints for fully digital and hybrid antennas.

  • Results

    Near-field ISAC identifies target distance and angle, while hybrid antennas reduce sensing performance relative to fully digital antennas at the same communication rate but consume less power.

  • Takeaways & Limitations

    Near-field ISAC benefits from the additional distance dimension, and fully digital optimization provides a theoretical performance upper bound for hybrid antennas.

Abstract

from arXiv · show

A near-field integrated sensing and communications (ISAC) framework is proposed, which introduces an additional distance dimension for both sensing and communications compared to the conventional far-field system. In particular, the Cramer-Rao bound for the near-field joint distance and angle sensing is derived, which is minimized subject to the minimum communication rate requirement of each user. Both fully digital antennas and hybrid digital and analog antennas are investigated. For fully digital antennas, a globally optimal solution of the ISAC waveform is obtained via semidefinite relaxation. For hybrid antennas, a high-quality solution is obtained through two-stage optimization. Numerical results demonstrate the performance gain introduced by the additional distance dimension of the near-field ISAC over the far-field ISAC.

I. INTRODUCTION

The paper proposes near-field ISAC, where spherical-wave propagation adds distance information to sensing and communications. It develops channel models and joint distance-angle sensing for fully digital and hybrid antenna architectures.

  • Motivation: Near-field spherical-wave propagation introduces a distance dimension for joint distance-angle sensing and can reduce communication interference.Near-field communication channels depend on both user distance and angle, allowing users in the same direction to be distinguished by distance.
  • Framework: The proposed framework establishes an accurate near-field channel model and jointly optimizes ISAC signals under minimum communication-rate constraints.The framework covers both fully digital and hybrid digital-and-analog antennas.
  • System assumptions: The system assumes users and the sensing target lie within the near-field region defined relative to the array aperture and wavelength.The model uses an N-antenna uniform linear array with aperture D=(N−1)d and Rayleigh distance 2D^2/λ.
  • Channel model: The near-field array response reduces to the far-field response when the array aperture is much smaller than the propagation distance.This reduction follows from a first-order Taylor approximation of the antenna-element distance.
  • Near-field sensing: Near-field sensing uses a round-trip channel containing both target distance and angle, unlike far-field sensing, which only estimates angles.This enables joint distance and angle estimation from the sensing channel.

B. ISAC Model for Fully Digital Antennas

The fully digital ISAC model transmits user-specific information beamformers together with a dedicated sensing signal over a coherent time block.

  • Fully digital architecture: Each fully digital antenna is connected to a dedicated RF chain, and communication channels and target parameters are assumed constant during the coherent time block.The remaining block is used for joint communication and sensing.
  • Transmit signal: The transmitted signal combines user information beamformers with a dedicated sensing signal that provides full sensing degrees of freedom.The user information symbols are independently distributed and have unit power.
  • Signal covariance: The sensing-signal covariance matrix is used to characterize the dedicated sensing component in the fully digital model.

1) Communication Model:

The communication model describes each user’s received signal as desired information, interference from the joint transmit signal, and additive white Gaussian noise, leading to an achievable rate expression.

  • Received signal: User k receives its desired beamformed information signal together with interference from the transmitted sensing and communication signals.
  • Rate model: The communication model uses additive white Gaussian noise and evaluates performance through each user’s achievable communication rate.

2) Sensing Model:

The sensing model uses the received echo signal to estimate target distance and angle, with MUSIC for estimation and the CRB as a closed-form performance bound.

  • Sensing signal: The BS receives a target echo signal through the near-field round-trip channel and collects samples over the coherent time block.
  • Parameter estimation: Near-field MUSIC exploits signal-subspace orthogonality to jointly estimate the target’s distance and angle.The sensing data are formed from the received echo samples across the coherent time block.
  • Performance metric: The Cramér-Rao bound replaces difficult closed-form MSE expressions and provides a lower bound on distance and angle estimation errors.The CRB matrix has a closed-form expression, with detailed entries derived separately.

C. ISAC Model for Hybrid Digital and Analog Antennas

The hybrid architecture combines a large, power-efficient analog phase-shifter component with a low-dimensional digital component, then forms effective transmit and sensing channels through analog beamforming and combining.

  • Hybrid antennas use a large-dimensional analog component realized by power-efficient phase shifters and a low-dimensional digital component.
  • The transmit covariance is constructed from the analog beamformer, digital beamformers, and dedicated sensing-signal covariance.
  • The analog beamformer obeys a unit-modulus constraint on every entry because of phase-shifter hardware limitations.
  • The hybrid user rate is evaluated using the effective beamformer pHB,k = PRFpBB,k.
  • Sensing reception uses an analog combiner subject to the same unit-modulus constraint.
  • A randomly selected analog combiner from the unit circle supports effective-channel sensing when the number of receive antennas is sufficiently large.
  • For M targets, the CRB matrix has dimension 2M × 2M, and the resulting optimization can use the proposed algorithm.

III. PROBLEM FORMULATION AND PROPOSED SOLUTION

The formulation minimizes joint distance-and-angle estimation CRBs while maintaining each user's minimum rate and respecting power and covariance constraints.

  • A. Problem Formulation: The optimization minimizes CRBs for joint distance and angle estimation while guaranteeing each communication user's minimum rate.
  • A. Problem Formulation: Target distance r and angle θ are treated as fixed because target parameters change only slightly between neighboring coherent time blocks.
  • A. Problem Formulation: Rmin,k denotes user k's minimum rate requirement.
  • A. Problem Formulation: Pmax denotes the maximum transmit power.
  • A. Problem Formulation: The formulation includes the constraint Rs = Rx − Pk ⪰ 0.
  • A. Problem Formulation: The hybrid digital-and-analog antenna optimization problem is formulated similarly.

B. Proposed Solution for Fully Digital Antennas

For fully digital antennas, the CRB optimization is reformulated into a tractable convex-relaxation problem whose rank-one solution preserves global optimality.

  • The fully digital optimization is first transformed from the complex CRB form into an equivalent, more tractable formulation.
  • An auxiliary matrix U transforms the non-convex CRB objective into the convex constraint (17b).
  • Semidefinite relaxation addresses the non-convex constraints (16b) and (16d).
  • The auxiliary variables Pk = pkpHk satisfy Pk ⪰ 0 and rank(Pk) = 1.
  • The rate constraint is converted into a convex form using γk = 1 + 1 2Rmin,k −1.
  • Omitting the rank-one constraint yields a convex optimization problem solvable by a standard interior-point algorithm.
  • A rank-one solution can be constructed with the same objective value as the relaxed optimum, making the resulting solution globally optimal.
  • The fully digital solution provides a theoretical performance upper bound for hybrid digital-and-analog antennas.

C. Proposed Solution for Hybrid Digital and Analog Antennas

The hybrid solution designs the analog beamformer in a first stage and then optimizes digital transmission and sensing components; numerical results evaluate this framework under specified system settings.

  • C. Proposed Solution for Hybrid Digital and Analog Antennas: The hybrid method uses two-stage optimization: analog beamforming first, followed by digital beamformer and dedicated sensing-signal optimization.
  • C. Proposed Solution for Hybrid Digital and Analog Antennas: The analog beamformer is designed to maximize array gain at communication users and the sensing target.
  • C. Proposed Solution for Hybrid Digital and Analog Antennas: After analog design, the remaining digital optimization has the same form as problem (16) and can be solved by the fully digital algorithm.
  • IV. Numerical Results: The numerical setup uses a 65-antenna ULA at 28 GHz with 0.5 m aperture and Rayleigh distance 46.73 m.
  • IV. Numerical Results: The experiment includes four communication users and one sensing target in the near-field region, with target location (20 m, 45°).
  • IV. Numerical Results: Figure 2 reports RCRB versus minimum communication rate, while Figure 3 reports normalized MUSIC spectrum for Rmin = 5 bit/s/Hz.
  • IV. Numerical Results: The hybrid configuration uses NRF = 5 RF chains, equal user rate requirements, and the labels FD, HB, and RCRB denote fully digital, hybrid, and root of CRB.

A. RCRB Versus Minimum Communication Rate

The RCRBs reveal a sensing–communication tradeoff: increasing the minimum communication rate worsens distance and angle estimation, while near-field ISAC retains low RCRBs. Near-field sensing also gains distance information absent from far-field sensing, though this advantage decreases with target distance.

  • Higher minimum communication rates increase the RCRBs for both distance and angle estimation, demonstrating a sensing–communication tradeoff.Even at considerably high communication rates, the RCRB remains low.
  • Near-field ISAC estimates both target distance and angle, whereas far-field ISAC produces equal spectrum maxima along the target direction.At Rmin = 5 bit/s/Hz, near-field MUSIC estimates 19.952 m and 45° for the target.
  • As target distance increases, near-field distance-estimation accuracy decreases because the sensing channel approaches its far-field form and loses distance information.
  • Near-field angle-estimation RCRB decreases with target distance and approaches the far-field RCRB as echo directions become more similar across antennas.
  • The paper concludes that enlarging the near-field region is an important direction for improving near-field ISAC benefits.

APPENDIX A MUSIC ALGORITHM FOR NEAR-FIELD SENSING

The MUSIC procedure estimates near-field target distance and angle by exploiting orthogonality between signal and noise subspaces. It selects the location minimizing the target steering vector’s projection onto the noise subspace.

  • MUSIC obtains signal and noise subspaces from the received-echo covariance matrix through eigenvalue decomposition.The signal subspace uses the M largest eigenvalues and eigenvectors, while the remaining components form the noise subspace.
  • For one target, the signal subspace is spanned by the steering vector a(r_s, θ_s), and the noise-space projection operator is formed from the noise eigenvectors.
  • The MUSIC spectrum approaches zero only at the target’s true distance and angle because the signal and noise subspaces are orthogonal there.
  • The estimated target parameters are obtained by minimizing the projection metric p(r, θ) over candidate distance–angle pairs.
  • The sensing formulation derives the Fisher information and CRB for the target parameters from the received echo signal model.

J11 J12 JT

The CRB for joint distance and angle estimation is constructed from the Fisher information matrix and the channel derivatives with respect to distance and angle.

  • The channel matrix is differentiated with respect to target distance and angle to form the quantities used in the Fisher-information-based CRB.
  • The CRB matrix for estimating target distance and angle is obtained by inverting the relevant Fisher information matrix block.
Loading 2302.01153v5…