Estimating Target Doppler in Unsynchronized Multistatic ISAC Deployments with Mobile Nodes

Technical Summary: Estimating Target Doppler in Unsynchronized Multistatic ISAC Deployments with Mobile Nodes

Problem Statement
Integrated Sensing and Communication (ISAC) is a cornerstone of future 6G networks, yet accurate target characterization in real-world scenarios faces significant hurdles. While monostatic radar systems are well-understood, practical ISAC deployments often rely on bistatic or multistatic configurations involving physically separated Transmitters (TX) and Receivers (RX). These scenarios become particularly challenging when nodes are mobile and unsynchronized.

In such environments, the estimation of the target's Doppler shift is distorted by two primary factors:

1. Clock Asynchrony: The lack of synchronization between the TX and multiple RXs introduces Timing Offsets (TO), Carrier Frequency Offsets (CFO), and Phase Offsets (PO). These act as disturbance terms that obscure the target-induced frequency shift.
2. Node Mobility: When the TX (e.g., a mobile User Equipment) is moving, it introduces an additional, dynamic Doppler component that combines non-trivially with the target's own Doppler shift.

Existing literature has largely addressed these issues separately (e.g., static devices with asynchrony or mobile monostatic radars) or has relied on the presence of Line-of-Sight (LoS) paths alongside external static reflectors to resolve ambiguities. This paper addresses the gap in estimating target Doppler in a mobile, asynchronous, multistatic configuration without leveraging any external reflectors.

Methodology
The proposed method targets a scenario with one mobile TX and multiple static RXs (e.g., sectors of a 5G gNB or Cloud RAN components). The RXs are assumed to be phase-synchronized at baseband but possess independent RF front-ends, resulting in unique CFOs and POs for each receiver. The algorithm operates in four distinct stages:

1. Offset Removal (CFO and PO):
   The method exploits the invariance of CFO and PO across all multipath components received by a single RX. By subtracting the phase of the direct LoS path (from TX to RX) from the phase of the target path (TX to Target to RX) at each RX, the common offset terms ($\Psi^o_n$) are eliminated. This leaves a phase difference dependent only on path geometry and Doppler shifts.

2. Static Phase Term Elimination:
   The remaining phase difference still contains static terms related to path length ($\Delta \angle A_n$). By computing the time-domain difference between consecutive time steps (temporal phase differentiation), these static amplitude-related phase terms are removed, isolating the dynamic Doppler components.

3. Geometric Simplification:
   The resulting system of equations relates the measured phase differences to the velocities of the TX and target, as well as various geometric angles (bistatic angle, velocity vectors relative to the line-of-sight). Initially, this system is underdetermined. The authors reduce the number of unknowns by leveraging known Receiver locations and Angle of Arrival (AoA) measurements:

   • The known RX positions and AoAs allow for the triangulation of the TX and target locations.
   • These estimated locations allow the calculation of bistatic angles ($\beta_n$).
   • Recursive geometric relationships are established between the angles of adjacent RXs ($\zeta_{n+1}$ and $\gamma_{n+1}$), reducing the independent angular unknowns.
   • Key Constraint: Through these simplifications, the system becomes solvable only if at least four RXs ($N_{rx} \ge 4$) are available.

4. Non-Linear Optimization:
   The reduced system, containing four unknowns (TX velocity magnitude, target velocity magnitude, and two initial angles), is solved as a non-linear Least Squares (LS) problem using the Levenberg–Marquardt algorithm. A moving average is applied to the solutions to improve estimation quality.

Key Contributions
The paper claims three primary contributions:

1. First Method for Mobile/Asynchronous Multistatic Doppler: It presents the first technique to estimate target Doppler in a multistatic ISAC scenario where both the TX and the target are moving, and the nodes are unsynchronized, without requiring external reflectors.
2. Realistic Hardware Modeling: The approach explicitly accounts for the challenging but realistic case where each RX exhibits distinct CFOs and POs due to separate RF front-ends, a condition often ignored in theoretical models but critical for sensing accuracy.
3. Validation via Simulation: The solution is evaluated through numerical simulations in various scenarios, demonstrating its validity for estimating Doppler shifts in realistic multistatic deployments.

Simulation Results
The authors evaluated the method using 5G NR Physical Uplink Shared Channel (PUSCH) Demodulation Reference Signals (DM-RS) at 28 GHz. Key findings include:

• AoA Noise Sensitivity: The method is robust to small AoA noise (Standard Deviation $\le 3^\circ$), yielding a Mean Absolute Error (MAE) $\le 100$ Hz. Performance degrades significantly with larger AoA errors ($10^\circ$–$20^\circ$).
• Receiver Spacing: Increased spatial diversity (larger inter-distance between RXs) improves performance. When RXs are too close, path similarities make scene dynamics harder to resolve.
• Range Limitations: With a localized RX deployment (similar to a single gNB sector), the method performs well at short ranges (compatible with narrow street scenarios, e.g., TX distance $\le 10$ m). Performance degrades at longer ranges unless the RXs are distributed over a wider area (e.g., opposite sides of a wide street), which increases spatial diversity but also implementation complexity.
• Speed Invariance: The method's accuracy is invariant to the target's speed, performing consistently across pedestrian, bicycle, and vehicle velocities.

Significance and Claims
The paper modestly claims to provide a valid approach for a previously unsolved problem in ISAC: estimating target Doppler in the absence of synchronization and external reflectors in a mobile multistatic setting. It demonstrates that the problem is mathematically solvable with a minimum of four receivers by exploiting geometric invariances and phase relationships.

The authors position this work as a step toward pervasive radio-based sensing fabrics in 6G, where sensing is embedded directly into communication infrastructure. They acknowledge that while the current localized deployment works well for short-range scenarios, future work is required to optimize RX placement for wider coverage and to experimentally validate the methodology in real-world conditions.