Phase-Coherent Multistatic Sensing under Phase Noise in Distributed ISAC

1. INTRODUCTION

• Phase-coherent processing preserves carrier-phase relationships across APs, allowing their spatial separation to form an extremely large effective sensing aperture.This is particularly attractive in bandwidth-limited sub-6 GHz deployments with few antennas per AP.Source: §1 · p. 1
• A shared oscillator gives each receiver the same phase-noise process with a link-specific delay, correlating differential phase noise across receivers through bistatic propagation delays.The resulting joint space-time statistics depend on the unknown target location.Source: §1 · p. 1
• Prior work has studied phase noise in radar and monostatic or bistatic OFDM sensing, but lacks a unified characterization for shared-LO multistatic OFDM distributed ISAC.The paper identifies the effect of this statistical structure on phase-coherent multistatic location estimation as unexplored.Source: §1 · p. 1
• The paper derives location-dependent differential phase-noise statistics under a Wiener model and analyzes deterministic, hybrid, and misspecified CRBs for three receiver models.The analysis covers PN-free, PN-aware, and PN-ignorant localization for isotropic and non-isotropic targets.Source: §1 · p. 1

2.1. Scenario Description

• The system has one single-antenna transmit AP and R single-antenna receive APs sharing a common LO; the target location is unknown and AP locations are fixed.The transmit AP sends an OFDM downlink signal, and the receive APs jointly process target echoes for phase-coherent multistatic sensing.Source: §2.1 · pp. 1–2

2.2. Transmit Signal Model

• The transmit AP sends an OFDM symbol over N subcarriers, with data symbols known to the receiving APs.The symbol uses subcarrier spacing 1/T and a cyclic prefix; its total duration is the useful duration plus the prefix duration.Source: §2.2 · p. 2

2.3. Receive Signal Model at Sensing RX APs

• Each receive AP observes a delayed target echo with a link-specific phase-noise process after downconversion through the shared noisy LO.The bistatic delay depends on target position, and the model assumes all delays of interest fall within one cyclic prefix of the earliest arrival to preserve subcarrier orthogonality. The sampled vector model includes AWGN and distinguishes isotropic from non-isotropic scattering; isotropic scattering shares a phase across receivers, whereas non-isotropic scattering has receiver-specific unknown phase absorbed into the channel gain.Source: §2.3 · p. 2

2.4. Problem Formulation

• The goal is to estimate target location from the R receive observations while accounting for their common-LO phase-noise vectors.The vectors are coupled through the unknown target location, making their joint statistics location-dependent and a priori unknown.Source: §2.4 · p. 2

3.1. Statistics of Differential Phase Noise Process

• Under the free-running oscillator model, the differential PN process is stationary, with statistics that depend on propagation delay.The Wiener PN variance is 4πf3dB|τ|.Source: §3.1 · p. 2

3.2. Location-Dependent PN Covariance

• The covariance of the discrete-time PN samples depends on target location through the bistatic delays of the receive links.The result extends delay-dependent PN covariance from monostatic to multistatic sensing.Source: §3.2 · pp. 2–3
• Mean accumulated PN variance varies substantially with target location for the illustrated oscillator bandwidth and AP deployment.Fig. 1 plots the mean over N samples and R receivers as 1/(NR)tr(R(p)).Source: §3.2 · p. 3, Figure 1 · p. 3

4.1. PN-Free Bound: Deterministic CRB

• The PN-free deterministic CRB uses an ideal LO and derives a location bound for isotropic and non-isotropic scattering models.The unknown parameter vectors differ between the scattering models.Source: §4.1 · p. 3

4.2. PN-Aware Bound: Hybrid CRB

• The PN-aware hybrid CRB treats position, gain, and phase as deterministic unknowns and PN as a random process with known statistics.The bound combines prior and observation Fisher information.Source: §4.2 · p. 3

4.3. PN-Ignorant Bound: Misspecified CRB

• The PN-ignorant misspecified CRB measures loss when a receiver assumes a PN-free model despite PN in the true observations.The non-isotropic case lacks the coherent sum because scattering prevents phase-coherent processing.Source: §4.3 · p. 3

5. SIMULATION RESULTS

• Simulations use Table 1 defaults and Fig. 3 geometry, QPSK symbols, bistatic-radar channel gains, and sweeps over transmit power, LO quality, and deployment.The PN-ignorant bound is averaged over 300 phase-noise realizations.Source: §5 · p. 3, Table 1 · p. 4, Figure 3 · p. 4

5.1. Impact of Transmit Power

• At high transmit power, the PN-ignorant bound reaches a performance floor as phase noise dominates AWGN; PN-aware recovery is larger for non-isotropic than isotropic targets.The carrier-phase information for isotropic targets is more sensitive to residual phase perturbations from phase noise.Source: §5.1 · p. 4, Figure 2 · p. 4

5.2. Impact of Oscillator Quality

• As LO bandwidth f3dB increases, PN-aware bounds stay near the PN-free baseline for non-isotropic scattering, while isotropic bounds rise abruptly under severe phase noise.For isotropic scattering, PN-induced shifts of the pseudo-true position produce above-1 m outliers whose percentage increases with f3dB.Source: §5.2 · p. 4, Figure 2 · p. 4, Table 2 · p. 4

5.3. Impact of Deployment

• Expanding the AP deployment shifts PN-ignorant bound values higher for both scattering models; isotropic scattering also develops a meter-level upper tail.The expansion lengthens bistatic delays, increasing differential phase-noise variance; some isotropic cases lose the carrier-phase localization advantage.Source: §5.3 · p. 4, Figure 2 · p. 4

• The study characterizes location-dependent phase-noise statistics and evaluates localization accuracy with PN-free, PN-aware, and PN-ignorant bounds.Source: §6 · p. 4
• Under phase noise, PN-ignorant processing exhibits error floors, and severe phase noise can erase carrier-phase accuracy gains for isotropic targets.Source: §6 · p. 4
• PN-aware bounds indicate significant mitigation potential; future work will consider phase-locked loops and joint location-velocity estimation with multiple symbols.Source: §6 · p. 4