Near-Field Integrated Sensing and Communications

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.Source: §I · p. 1, A. Near-field Channel Model for ISAC · p. 2

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.Source: §I · p. 1

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.Source: §II · p. 1

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.Source: A. Near-field Channel Model for ISAC · p. 2

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.Source: A. Near-field Channel Model for ISAC · p. 2

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.Source: B. ISAC Model for Fully Digital Antennas · p. 2

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.Source: B. ISAC Model for Fully Digital Antennas · p. 2

Signal covariance

• The sensing-signal covariance matrix is used to characterize the dedicated sensing component in the fully digital model.Source: B. ISAC Model for Fully Digital Antennas · p. 2

Received signal

• User k receives its desired beamformed information signal together with interference from the transmitted sensing and communication signals.Source: 1) Communication Model · p. 2

Rate model

• The communication model uses additive white Gaussian noise and evaluates performance through each user’s achievable communication rate.Source: 1) Communication Model · p. 2

Sensing signal

• The BS receives a target echo signal through the near-field round-trip channel and collects samples over the coherent time block.Source: 2) Sensing Model · p. 2

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.Source: 2) Sensing Model · p. 2

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.Source: 2) Sensing Model · p. 3

• Hybrid antennas use a large-dimensional analog component realized by power-efficient phase shifters and a low-dimensional digital component.Source: C. ISAC Model for Hybrid Digital and… · p. 3
• The transmit covariance is constructed from the analog beamformer, digital beamformers, and dedicated sensing-signal covariance.Source: C. ISAC Model for Hybrid Digital and… · p. 3
• The analog beamformer obeys a unit-modulus constraint on every entry because of phase-shifter hardware limitations.Source: C. ISAC Model for Hybrid Digital and… · p. 3
• The hybrid user rate is evaluated using the effective beamformer pHB,k = PRFpBB,k.Source: 1) Communication Model · p. 3
• Sensing reception uses an analog combiner subject to the same unit-modulus constraint.Source: 2) Sensing Model · p. 3
• A randomly selected analog combiner from the unit circle supports effective-channel sensing when the number of receive antennas is sufficiently large.Source: 2) Sensing Model · p. 3
• For M targets, the CRB matrix has dimension 2M × 2M, and the resulting optimization can use the proposed algorithm.Source: 2) Sensing Model · p. 3

A. Problem Formulation

• The optimization minimizes CRBs for joint distance and angle estimation while guaranteeing each communication user's minimum rate.Source: A. Problem Formulation · p. 3
• Target distance r and angle θ are treated as fixed because target parameters change only slightly between neighboring coherent time blocks.Source: A. Problem Formulation · p. 3
• Rmin,k denotes user k's minimum rate requirement.Source: A. Problem Formulation · p. 3
• Pmax denotes the maximum transmit power.Source: A. Problem Formulation · p. 3
• The formulation includes the constraint Rs = Rx − Pk ⪰ 0.Source: A. Problem Formulation · p. 3
• The hybrid digital-and-analog antenna optimization problem is formulated similarly.Source: A. Problem Formulation · p. 3

• The fully digital optimization is first transformed from the complex CRB form into an equivalent, more tractable formulation.Source: B. Proposed Solution for Fully Digital… · p. 3
• An auxiliary matrix U transforms the non-convex CRB objective into the convex constraint (17b).Source: B. Proposed Solution for Fully Digital… · p. 3
• Semidefinite relaxation addresses the non-convex constraints (16b) and (16d).Source: B. Proposed Solution for Fully Digital… · p. 3
• The auxiliary variables Pk = pkpHk satisfy Pk ⪰ 0 and rank(Pk) = 1.Source: B. Proposed Solution for Fully Digital… · p. 3
• The rate constraint is converted into a convex form using γk = 1 + 1 2Rmin,k −1.Source: B. Proposed Solution for Fully Digital… · p. 4
• Omitting the rank-one constraint yields a convex optimization problem solvable by a standard interior-point algorithm.Source: B. Proposed Solution for Fully Digital… · p. 4
• A rank-one solution can be constructed with the same objective value as the relaxed optimum, making the resulting solution globally optimal.Source: B. Proposed Solution for Fully Digital… · p. 4
• The fully digital solution provides a theoretical performance upper bound for hybrid digital-and-analog antennas.Source: B. Proposed Solution for Fully Digital… · p. 4

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.Source: C. Proposed Solution for Hybrid… · p. 4
• The analog beamformer is designed to maximize array gain at communication users and the sensing target.Source: C. Proposed Solution for Hybrid… · p. 4
• After analog design, the remaining digital optimization has the same form as problem (16) and can be solved by the fully digital algorithm.Source: C. Proposed Solution for Hybrid… · p. 4

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.Source: §IV · p. 4
• The experiment includes four communication users and one sensing target in the near-field region, with target location (20 m, 45°).Source: §IV · p. 4
• Figure 2 reports RCRB versus minimum communication rate, while Figure 3 reports normalized MUSIC spectrum for Rmin = 5 bit/s/Hz.Source: Figure 2 · p. 4, Figure 3 · p. 4
• 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.Source: §IV · p. 4

• 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.Source: A. RCRB Versus Minimum Communication… · p. 4
• 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.Source: B. Spectrum of MUSIC · pp. 4–5
• As target distance increases, near-field distance-estimation accuracy decreases because the sensing channel approaches its far-field form and loses distance information.Source: C. RCRB Versus Distance · p. 5
• Near-field angle-estimation RCRB decreases with target distance and approaches the far-field RCRB as echo directions become more similar across antennas.Source: C. RCRB Versus Distance · p. 5
• The paper concludes that enlarging the near-field region is an important direction for improving near-field ISAC benefits.Source: §V · p. 5

• 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.Source: Appendix A · p. 5
• 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.Source: Appendix A · p. 5
• The MUSIC spectrum approaches zero only at the target’s true distance and angle because the signal and noise subspaces are orthogonal there.Source: Appendix A · p. 5
• The estimated target parameters are obtained by minimizing the projection metric p(r, θ) over candidate distance–angle pairs.Source: Appendix A · p. 5
• The sensing formulation derives the Fisher information and CRB for the target parameters from the received echo signal model.Source: Appendix B · p. 5

• The channel matrix is differentiated with respect to target distance and angle to form the quantities used in the Fisher-information-based CRB.Source: J11 J12 JT · p. 5
• The CRB matrix for estimating target distance and angle is obtained by inverting the relevant Fisher information matrix block.Source: J11 J12 JT · p. 5