TRP-UE Bistatic Sensing for 6G Performance Analysis and Insights

I. INTRODUCTION

• UE participation adds spatial diversity and can improve geometric conditions, but smaller UE apertures, reduced sensing SNR, and waveform-dependent processing losses constrain performance.The paper focuses on passive target positioning through TRP-only, UE-assisted, and hybrid TRP–TRP/TRP–UE sensing.Source: §I · p. 1

A. Existing Studies

• Prior work covers cooperative sensing and PRS-based bounds, but a unified treatment of hybrid TRP–TRP/TRP–UE sensing with realistic arrays, waveform effects, and estimator-aligned bounds remains limited.The cited PRS study does not address communication-waveform reuse or angular estimation.Source: A. Existing Studies · p. 2

B. Contribution and Improvement

• The paper develops an OFDM framework for PRS and communication-waveform reuse, derives delay and angular bounds, and evaluates estimator-aligned PEBs for time–angle and delay-only positioning.It also compares TRP–TRP, TRP–UE, and Hybrid sensing across deployment and waveform conditions.Source: B. Contribution and Improvement · p. 2

1) PRS-Based Sensing Signal Model

• PRS sensing uses known pilot symbols mapped to active resource elements through the configured PRS sequence, allocation, comb size, and symbol-dependent offsets.The model explicitly links the sequence sample and mapping parameters to the active resource grid.Source: A. Sensing Signal Models · p. 3, 1) PRS-Based Sensing Signal Model · p. 3

2) Communication Waveform Reuse Sensing Model

• Communication-waveform reuse treats transmitted data symbols as known at the sensing processor after decoding and reconstruction, and applies the common signal and Fisher-information models to the waveform’s active resource elements.The model retains each active resource element’s frequency and OFDM-symbol reference time.Source: 2) Communication Waveform Reuse… · p. 3

B. URA Antenna and Steering Vectors

• TRPs use 8 × 8 URAs and UEs use 2 × 2 URAs, with half-wavelength element spacing; azimuth and elevation map to x- and y-direction cosines for the array steering vectors.The same URA model applies when a TRP acts as the sensing receiver.Source: B. URA Antenna and Steering Vectors · p. 3

C. Channel Model

• The channel model represents one passive target with separate bistatic and direct-path gains, while accounting for transmit and receive angles, delay, Doppler, and the complex target response.The bistatic power gain excludes the transmit-array factor and receive-array response to avoid counting array gain twice.Source: C. Channel Model · p. 4

D. Received Signal

• PRS pilots and reconstructed data symbols share a normalized observation model, but reciprocal normalization makes QAM noise symbol-dependent and enhances its average variance.For the adopted unweighted receiver, the average shifts are 2.76 dB for 16QAM and 4.29 dB for 64QAM; this is not a fundamental reuse penalty.Source: D. Received Signal · pp. 4–5

A. CRLB Derivation by Likelihood Estimation

• The CRLB derivation uses a likelihood/FIM framework and eliminates the unknown complex target-reflection coefficient by a Schur complement.Bounds are exact for constant-modulus signals and serve as equivalent-noise benchmarks for 16QAM and 64QAM; Monte Carlo methods retain the exact symbol-dependent variances.Source: A. CRLB Derivation by Likelihood… · p. 5

1) Open form of the received signal

• Each active resource element is modeled as a mean signal plus noise, with delay, Doppler, azimuth, and elevation as parameters of interest and the complex reflection coefficient treated as unknown.The model does not assume the echo amplitude or its initial phase is known.Source: 1) Open form of the received signal · p. 5

2) Open form likelihood and log-likelihood function

• For non-constant-modulus QAM, the homogeneous-noise likelihood is a receiver-aligned average-noise model for the adopted unweighted reciprocal processor.The exact conditional noise variances remain symbol-dependent.Source: 2) Open form likelihood and… · p. 5

3) Open form Fisher information matrix (FIM)

• The FIM uses centered coordinates over the actual active resource elements; its delay–Doppler block can be non-diagonal, while centered URA geometry separates that block from the angle block.For NR-mapped PRS, symbol-dependent offsets are retained when computing frequency–time moments.Source: 3) Open form Fisher information matrix… · pp. 5–6

4) Open form CRLBs for delay, Doppler, and angles

• When the delay–Doppler block is invertible, its inverse gives the joint delay and Doppler CRLBs.The exact active-set moments determine the block.Source: 4) Open form CRLBs for delay, Doppler,… · p. 6
• If Doppler is known or compensated, the conditional delay bound reduces to a delay-only expression; contiguous-tone and regular-comb formulas follow from the corresponding frequency moments.For a regular comb, the spacing is Kcomb∆f.Source: 4) Open form CRLBs for delay, Doppler,… · p. 6
• The angle CRLBs are obtained from the azimuth–elevation information matrix, simplifying to separate expressions when its cross-information is negligible.The paper also gives variance-scaling identities for monostatic range and velocity.Source: 4) Open form CRLBs for delay, Doppler,… · pp. 6–7

A. Positioning Algorithms

• The LOS-referenced excess delay is the estimated target-echo delay minus the direct-path delay, and its bistatic range sum equals baseline length plus c∆τ.The direct-path reference forms a synchronization-robust excess-delay measurement.Source: A. Positioning Algorithms · p. 7
• Both methods estimate intermediate excess delay and 3D DoA from active OFDM observations before converting measurements into Cartesian position.DoA uses a 2D MUSIC spectrum over azimuth and elevation; delay processing uses the active set and mapped subcarrier frequencies.Source: A. Positioning Algorithms · p. 7

1) Time-Angle Based Algorithm (Excess Delay + DoA)

• Time–Angle positioning jointly fits selected links’ range-sum and DoA-ray constraints, then refines one common target position rather than averaging pair estimates.The DoA-ray residual avoids the azimuth singularity near vertical directions; the refinement uses a robust, covariance-weighted objective with a geometric safeguard.Source: 1) Time-Angle Based Algorithm (Excess… · pp. 8–9
• For multiple valid links, per-pair position estimates provide an initializer; the final Time–Angle output comes from joint nonlinear fusion.The arithmetic mean of pair estimates is only an initializer, not the final position estimate.Source: 1) Time-Angle Based Algorithm (Excess… · pp. 8–9
• Delay-only positioning treats each measured bistatic range sum as a 3D ellipsoid constraint and minimizes residual mismatch across valid links.At least four non-coplanar links are generally required for unique 3D positioning; the implementation refines candidates using delay-residual cost alone.Source: 1) Time-Angle Based Algorithm (Excess… · pp. 9–10

B. Positioning Error Bounds of Bistatic Modes

• Hybrid scheduling ranks TRP–UE and TRP–TRP link universes separately and partitions the fixed link budget near 50/50, while all modes use the same total number of links.Odd link budgets alternate the ceiling/floor allocation across realizations; the scheduled set uses the same coarse position estimate for each mode.Source: B. Positioning Error Bounds of… · p. 10
• Each scheduled pair contributes a target-echo SNR and active resource-element set to the positioning-bound evaluation.The pair’s receive-array size and waveform/resource configuration are also specified in the section’s model.Source: B. Positioning Error Bounds of… · pp. 10–11
• For higher-order QAM, the effective receiver-noise enhancement ηn is frame-wise or ensemble averaged, so the resulting PEBs remain receiver-aligned.For PRS, BPSK, and QPSK, ηn = 1.Source: B. Positioning Error Bounds of… · p. 10
• The excess-delay bound retains covariance between target and LOS delay estimates because both are estimated from the same normalized OFDM-array observation.The model treats the generally stronger LOS and weaker target echo with separate path powers; in the resolved-path limit, the covariance reduces to an isolated-path check.Source: B. Positioning Error Bounds of… · p. 11

2 SNRq,eff,nNR,n

• For the square half-wavelength URAs used in the paper, the angular cross-term is zero, allowing azimuth and elevation variances to enter the position FIM separately.The resulting open-form PEB applies to the stated symmetric 3 × 3 position-FIM form.Source: §2 · p. 11
• The position-FIM mapping is presented through its six unique entries and an open-form PEB expression.The expression is obtained by substituting the position-FIM entries into the generic mapping.Source: §2 · p. 11
• The main task is deriving position FIMs for the sensing modes and mapping them to 3D PEB through the symmetric-FIM expression.Detailed entry-wise expressions are collected in equations (116)–(127).Source: §2 · p. 11

1) Time-Angle Based Algorithm FIM and PEB

• Each pair contributes an excess-delay measurement and AoA azimuth–elevation measurements to the time–angle FIM for each sensing mode.The delay variance follows from the joint two-path covariance, while the angle variances follow from the angular information block.Source: 1) Time-Angle Based Algorithm FIM and… · p. 12
• The time–angle PEB depends on per-pair sensing SNR, delay resolution through ∆f, M, and K, and receive-array geometry.The expression is obtained by substituting the grouped FIM entries into the generic PEB mapping.Source: 1) Time-Angle Based Algorithm FIM and… · p. 12

• The position FIM for delay-only positioning contains only the delay term induced by the excess-delay measurement Jacobian.Source: 2) Delay Based Algorithm · p. 12
• The delay-only PEB makes explicit dependence on bistatic geometry, receive-array size, LOS and target powers, and joint two-path coupling.Source: 2) Delay Based Algorithm · p. 12
• A finite delay-only PEB requires locally identifiable per-link delays and a full-rank position FIM from sufficiently diverse, non-coplanar bistatic pairs.Source: 2) Delay Based Algorithm · p. 12

A. Indoor factory layout and node deployment

• The modeled hall spans 300 × 150 × 10 m, with 18 TRPs on a 6 × 3 grid and 20 UAV targets at 8 m height.The deployment includes 20 active UEs; TRP–UE receivers use 2×2 URAs while TRPs use 8×8 URAs, and the simulations omit multipath, clutter, and multi-target interference.Source: A. Indoor factory layout and node… · p. 12, Figure 2 · p. 12

B. Bistatic sensing modes, links, and sensing pairs

• All modes use the same coarse target estimate and selected-pair count; hybrid sensing applies a near-50/50 TRP–UE and TRP–TRP quota.The scheduling estimate has independent horizontal and vertical standard deviations of 5 m and 2 m, respectively; reported curves use 10 pairs.Source: B. Bistatic sensing modes, links, and… · p. 13

C. Bandwidth, delay resolution, and angular resolution

• Occupied-tone count and frequency aperture are distinct: delay information depends on the active set’s second central frequency moment, not tone count alone.Source: C. Bandwidth, delay resolution, and… · p. 13
• For PRS comb allocations, adjacent active tones are separated by the comb spacing, so treating them as contiguous tones gives an incorrect delay-information moment.The evaluation uses the exact PRS frequency mapping; angular resolving power scales qualitatively with wavelength and effective array aperture.Source: C. Bandwidth, delay resolution, and… · p. 13

D. Target reflectivity and radar cross section (RCS)

• RCS is an effective area measuring backscattered-echo strength, and the reference-SNR convention preserves physical distance and RCS dependence.The reference uses 30 m transmitter and receiver distances and RCS of 1 m^2; the RCS sweep changes received target power linearly with σRCS.Source: D. Target reflectivity and radar cross… · p. 13

E. Key simulation parameters

• The principal simulation settings are summarized in Table 1, with the link-budget convention, noise model, fusion constants, and scheduling rule specified elsewhere.The quantitative evaluation uses a single-target, two-path observation and equal selected-link budgets across sensing modes.Source: E. Key simulation parameters · p. 14, Table 1 · p. 14, B. Quantitative Positioning Results · p. 15

A. Qualitative Signal-Domain Illustrations

• The qualitative delay-domain views distinguish the direct path from the delayed target echo, while their separation motivates excess-delay estimation.The illustrated extra peaks are not included in quantitative PEB comparisons; larger frequency aperture improves peak resolvability and reduces the delay bound.Source: A. Qualitative Signal-Domain… · p. 14

1) 2D DoA estimation using 2D MUSIC Algorithm

• The DoA stage uses 2D MUSIC over azimuth and elevation, with TRP arrays providing narrower mainlobes and higher angular resolution than compact UE arrays.Delay-domain gating associates a selected angular peak with the target echo when an illustrative spectrum has multiple local maxima.Source: 1) 2D DoA estimation using 2D MUSIC… · p. 15, Figure 6 · p. 15

B. Quantitative Positioning Results

• Hybrid reaches the low-error regime earliest and has the smallest high-SNR floor, while TRP–UE is intermediate and TRP–TRP remains higher.The TRP–TRP gap is attributed to poorly conditioned geometry; UE-assisted and Hybrid viewpoints improve position-FIM rank and conditioning.Source: B. Quantitative Positioning Results · pp. 15–16, Figure 7 · p. 16
• PRS and BPSK reuse nearly overlap, whereas 16QAM and especially 64QAM require larger SNR for the same error under the adopted receiver.The shift is a robustness cost of unweighted reciprocal normalization in the transition region, not a fundamental penalty of reuse or higher-order QAM.Source: B. Quantitative Positioning Results · p. 16, Figure 8 · p. 16
• Larger SCS increases frequency span and improves delay resolution, with the strongest reported gains for Hybrid and TRP–UE sensing.At 240 kHz those modes reach low-meter accuracy, while at 30 kHz they remain bandwidth-limited even at high SNR; TRP–TRP retains a higher floor.Source: B. Quantitative Positioning Results · pp. 16–17, Figure 9 · p. 17
• Stronger RCS shifts the performance transition to lower SNR, and Hybrid remains most robust, followed by TRP–UE and then TRP–TRP.The ordering holds for the considered layout, array sizes, scalar gains, and equal-budget scheduler; PRS and BPSK reuse remain close.Source: B. Quantitative Positioning Results · p. 17, Figure 10 · p. 17

1) Dependence on hardware and deployment

• The reported ordering is conditional on 2×2 UE and 8×8 TRP arrays, half-wavelength spacing, an 18-TRP layout, and equal selected-link budget Npair = 10.Larger apertures or stronger TRP receive gain can alter the relative value of the receiver types.Source: 1) Dependence on hardware and deployment · p. 18
• TRP density improves delay-only bounds only when scheduled pairs add sufficiently distinct range-gradient directions; clustered or regular layouts can remain poorly conditioned.Distributed TRPs, favorable baseline orientations, or alternative pair scheduling may improve TRP–TRP performance and alter the baseline ordering.Source: 1) Dependence on hardware and deployment · p. 18

2) Failure-aware interpretation

• Reliability and successful-estimate accuracy must be read jointly: Fig. 12’s conditional median excludes failures, so Pfail is evaluated separately.The 40 m-penalized means in Figs. 7–11 are distinct from conditional-CDF and penalty-free conditional-accuracy measures.Source: 2) Failure-aware interpretation · p. 18

A. Summary of Contributions and Key Findings

• Hybrid sensing ranks best on penalized-mean and conditional-CDF errors in the evaluated deployment, but this ordering is configuration-specific.The comparison uses a fixed near-50/50 TRP–UE/TRP–TRP composition, not an unrestricted union search.Source: A. Summary of Contributions and Key… · p. 19, B. Implications and Future Directions · p. 19
• The revised positioning comparison uses joint nonlinear multi-link fusion, with Time–Angle performance shaped by delay/angle quality, aperture, outlier robustness, and geometry.Compact UE arrays can limit DoA benefits; the paper does not claim delay-only positioning is inherently superior.Source: A. Summary of Contributions and Key… · p. 19

B. Implications and Future Directions

• For the tested deployment, hybrid fusion and increased effective bandwidth are identified as practical routes to improved positioning accuracy, with conclusions bounded by the tested arrays, gains, scheduler, and layout.Future work includes adaptive pair selection and fusion, richer multipath, clutter and multi-target modeling, and experimental validation under hardware and synchronization impairments.Source: B. Implications and Future Directions · pp. 19–20

Appendix: Detailed Open-Form FIM Entries

• Appendix A expands the Time–Angle FIM in (87), used to evaluate PEBTA,m in (104).This expansion supplies detailed open-form entries for the Time–Angle position FIM.Source: Appendix: Detailed Open-Form FIM Entries · p. 20
• Appendix B expands the delay-only FIM in (105), used to evaluate PEBD,m in (107).Its entries support the delay-only 3D positioning pipeline.Source: Appendix: Detailed Open-Form FIM Entries · p. 20
• Appendix B expands the delay-only FIM in (105), used to evaluate PEBD,m in (107); the excess-delay variance σ2∆τ,n is supplied by the joint LOS–target covariance in (98).Source: Appendix: Detailed Open-Form FIM Entries · p. 20
• The expansions make position-FIM entries explicit for TRP–TRP, TRP–UE, and Hybrid modes.These entries are given in the appendix’s delay-only expansion.Source: Appendix: Detailed Open-Form FIM Entries · p. 20