Pinching-Antenna Assisted ISAC: A CRLB Perspective

• Pinching antennas provide strong LoS links, flexible array topology, and low-cost implementation.Activating antennas close to users can mitigate large-scale path loss and LoS blockage, while antenna locations and counts can be adjusted.Source: §I · p. 1
• Prior work has extensively studied pinching-antenna communication functions, including activation, array architecture, array gains, placement, and throughput.Source: §I · p. 1
• The sensing impact of pinching antennas remains incompletely characterized in existing literature.Source: §I · p. 1
• The letter derives and compares CRLBs for pinching and conventional antennas to assess positioning accuracy in ISAC networks.It also examines placement effects, CRLB local maxima, and flexible user-centric positioning.Source: §I · p. 1

• The system activates N pinching antennas on NWG waveguides to serve M single-antenna users.The n-th antenna has location ψPin_n, with its vertical coordinate determined by the waveguide height.Source: §II · p. 1
• The service area A is rectangular, centered at (0, 0, 0), with side lengths DW and DL.Source: §II · p. 1
• Users are uniformly distributed in A, and user Um is located at ψm = (xm, ym, 0).Source: §II · p. 1
• The distance dmn from pinching antenna n to user m is used to model range estimates for localization.Source: §II · p. 1
• The range-estimation noise wmn is zero-mean Gaussian with distance-dependent variance governed by system parameter KE.Source: §II · p. 1

• The joint probability density of the estimated distances conditioned on the true distances provides the starting point for CRLB derivation.Source: A. CRLB Achieved by Pinching-Antenna… · p. 2
• The conditioned distance density is converted into a log-likelihood function for the localization parameters.Source: A. CRLB Achieved by Pinching-Antenna… · p. 2
• The CRLB for estimating user coordinates xm and ym is obtained from the corresponding Fisher information matrix Jm.The coordinate estimates are denoted by x̂m and ŷm.Source: A. CRLB Achieved by Pinching-Antenna… · p. 2
• The expectation of the second derivative of the log-likelihood yields the Fisher-information terms for the x-coordinate.The zero-mean range-estimation error is used in this calculation.Source: A. CRLB Achieved by Pinching-Antenna… · p. 2
• The analogous y-coordinate expression combines with the x-coordinate result to form the CRLB for estimating each user’s location.Source: A. CRLB Achieved by Pinching-Antenna… · p. 2

Performance benchmark

• The conventional-antenna benchmark uses a circular array centered in the service area with radius λ/2.Source: 1) Performance Gain over Conventional… · p. 2

Performance comparison

• The performance gain compares pinching-antenna and conventional-antenna CRLBs under uniformly distributed users.The comparison is evaluated through the CRLB expressions and computer simulations.Source: 1) Performance Gain over Conventional… · p. 2
• Conventional antennas can exhibit a CRLB singularity because their elements are clustered near the service-area center, especially at high carrier frequencies.The relevant condition is |yConv_n| → 0 as the wavelength becomes small.Source: 1) Performance Gain over Conventional… · p. 2
• Pinching antennas do not suffer the singularity issue experienced by conventional antennas.Source: 1) Performance Gain over Conventional… · p. 2
• A finite upper bound can always be obtained for the pinching-antenna CRLB by selecting a suitable antenna index among the N antennas.Source: 1) Performance Gain over Conventional… · pp. 2–3

Positioning accuracy

• The case study indicates that pinching antennas can offer uniform positioning accuracy between users, unlike conventional antennas.Source: 1) Performance Gain over Conventional… · p. 3

System model and placement

• The analysis places pinching antennas on waveguides and considers equally spaced antennas activated in a square area centered on the user.The simplifying setup uses Δx = Δy = Δ and assumes the relevant antenna count is even.Source: 2) Flexible User-Centric Positioning · p. 3
• The simplified CRLB is used to design antenna placement by selecting the spacing Δ that minimizes positioning error.Source: 2) Flexible User-Centric Positioning · p. 3

Optimal spacing

• For N = 4, the CRLB is analyzed through its derivatives to obtain an explicit spacing optimization problem.The special case is highlighted as practically relevant because fewer antennas can reduce system overhead.Source: 2) Flexible User-Centric Positioning · p. 3
• The CRLB is a convex function of Δ, so convex optimization solvers can efficiently find the minimizing spacing.Source: 2) Flexible User-Centric Positioning · p. 3
• The optimal antenna spacing is not obtained by placing all antennas arbitrarily close to the user; it depends on the waveguide height.The paper identifies the intuition Δ* → 0 as incorrect for this setting.Source: 2) Flexible User-Centric Positioning · p. 3

Local-Maximum Property

• A local maximum of CRLB exists around each pinching antenna location.The analysis establishes this behavior through the derivatives with respect to both user coordinates.Source: 3) Local-Maximum Property of CRLB · pp. 3–4

Analysis Setup

• The analysis uses users near the first pinching antenna and assumes equal antenna spacings that are much larger than dH.Under these assumptions, the CRLB expressions are simplified to expose the local-maximum behavior.Source: 3) Local-Maximum Property of CRLB · pp. 3–4

Local-Maximum Property

• When the user lies directly underneath a pinching antenna, positioning accuracy can degrade despite potentially improved communication performance.The paper identifies this location as a local-maximum case for the CRLB.Source: 3) Local-Maximum Property of CRLB · p. 4

Implication

• The local-maximum property demonstrates that antenna placement is important in pinching-antenna-assisted ISAC networks.Placement must account for both communication and sensing objectives.Source: 3) Local-Maximum Property of CRLB · p. 4

Averaged CRLB

• Pinching antennas achieve a significant averaged-CRLB performance gain over conventional antennas across antenna counts and excluded-area sizes.The comparison assumes users are uniformly deployed, while conventional antennas exclude a square region because of singularity.Source: §IV · p. 4

Position-Dependent Accuracy

• Conventional antennas can provide extremely poor positioning accuracy for users far from the service-area center.This behavior is associated with the conventional-antenna singularity issue.Source: §IV · p. 4
• Pinching antennas provide reasonably accurate positioning for users near both the service-area center and its edge.The results also indicate fairer positioning accuracy in multi-user scenarios.Source: §IV · pp. 4–5
• CRLB local maxima are visible near pinching antennas, confirming the analytical local-maximum result.The numerical pattern matches the analysis in the local-maximum section.Source: §IV · p. 5

User-Centric Positioning

• Reconfiguring the number and locations of pinching antennas enables different focal points for flexible user-centric positioning.Activating antennas near intended user locations gives nearby users high positioning accuracy.Source: §IV · p. 5, Figure 3 · p. 5

Conclusions

• The letter derives the CRLB for pinching antennas and compares it with the CRLB of conventional antennas.Both analytical and simulation results are used in the evaluation.Source: §V · p. 5
• Pinching antennas significantly reduce CRLB and thereby enhance sensing capability.This is the principal conclusion of the analytical and simulation studies.Source: §V · p. 5
• The low-cost and reconfigurability features of pinching antennas support flexible user-centric positioning.The conclusion links these hardware features to the positioning application.Source: §V · p. 5