Distributed OTFS-ISAC Systems

• Distributed OTFS-ISAC is a framework that employs OTFS modulation on a delay-Doppler grid to enable unified high-mobility communication and precise environmental sensing.
• It utilizes spatially distributed nodes with triangulation and Kalman filtering to achieve robust multi-target localization and tracking under Doppler and multipath effects.
• The system optimizes resource allocation through joint AP mode selection and power control, enhancing spectral efficiency and reducing localization errors compared to traditional OFDM.

Distributed OTFS-ISAC (Orthogonal Time Frequency Space for Integrated Sensing and Communication) systems are high-mobility, fully cooperative architectures that employ OTFS modulation to enable joint communication and environmental sensing across spatially distributed network nodes. In these systems, OTFS waveforms exploit inherent delay-Doppler diversity, enabling robust communication, accurate multi-target localization, and high-resolution tracking, even under significant Doppler and multipath effects. Recent works establish OTFS-ISAC as a foundational framework for next-generation “cell-free” or distributed ISAC with substantial advantages in vehicle-to-everything (V2X), distributed radar, and large-scale mMIMO deployments, where spatial node geometry and adaptive resource allocation critically impact overall performance.

1. Delay–Doppler Domain OTFS Modulation in Distributed ISAC

OTFS modulation is central in distributed ISAC due to its resilience to doubly selective (delay- and Doppler-dispersive) channels. In an OTFS system, information symbols are mapped onto a two-dimensional delay-Doppler (DD) grid, and the transmit sequence is synthesized using the inverse symplectic finite Fourier transform (ISFFT), yielding a time–frequency representation that, after pulse-shaping, is radiated through the channel (Yuan et al., 2021, Rani et al., 20 Sep 2025). The structure is

$s = (F_N^H \otimes P_{\text{tx}}) \, \mathbf{d}$

where $\mathbf{d}$ is the DD-domain data vector and $P_{\text{tx}}$ is the transmit pulse-shaping matrix. At the receiver, demodulation returns the signal to the DD domain, where channel variations are “sparsified”: multipath and Doppler effects become localized shifts rather than spreading across the entire bandwidth. This framework offers a joint basis for distributed communication (data detection) and radar sensing (delay-Doppler estimation), unifying both operations in a single receiver signal model.

2. Spatial Configuration and Node Deployment in Distributed ISAC

The geometric distribution of network nodes is a critical design variable in distributed OTFS-ISAC (Rani et al., 20 Sep 2025). A commonly studied scenario consists of an anchor node $\mathcal{A}_0$ and several spatially dispersed receiver nodes $\mathcal{R}_1, \ldots, \mathcal{R}_Z$, forming a multi-static system for both communication coverage and multi-perspective sensing. Target localization is solved by triangulation: with estimated range measurements $\rho_{i,q}$ (from each node q), the target position $(\alpha, \beta)$ is obtained from equations

$(x_q - \alpha)^2 + (y_q - \beta)^2 = \rho_{i,q}^2$

for $q$ in the set of selected nodes. Pairwise differences, arranged in matrix form, produce a linear system $A [\alpha\,\,\beta]^T = B$, whose solution gives the unique intersection point—provided the area of the triangle spanned by the nodes ($(x_j y_k - x_k y_j)$) is non-zero. The accuracy is mathematically tied to this area: estimation error $$\operatorname{tr}(\operatorname{cov}(\widehat{\alpha}, \widehat{\beta}))$$ decreases with larger triangulation area, favoring deployment along approximately orthogonal axes.

Node deployment also impacts communication reliability through spatial diversity. When multiple antennas are deployed per node, localization errors decrease cubically with the number of antennas (Rani et al., 20 Sep 2025). Thus, spatial planning is a decisive factor for both multi-target sensing performance and bit error rate (BER) in communication.

3. Kalman Filtering and State Tracking for Dynamic Targets

Distributed OTFS-ISAC systems require real-time tracking as targets (e.g., vehicles) move. Kalman filtering (KF) is integrated for sequential state estimation—capitalizing on spatial measurements from multiple nodes and the time-series evolution of the target position and velocity. The target state vector, $$\mathbf{s}_{i,t} = [\alpha_{i,t}, \beta_{i,t}, v_{i,x,t}, v_{i,y,t}]^T$$, evolves according to a discrete-time linear system, capturing correlated random walk (Ornstein-Uhlenbeck) dynamics: $$\mathbf{s}_{i,t+1} = T_i\,\mathbf{s}_{i,t} + \mathbf{n}_t$$ with system matrix $T_i$ determined by mobility parameters ($\delta_i, \omega_i, \psi_i$), and process noise $\mathbf{n}_t$. The KF performs optimal minimum mean-square error prediction and update steps given new measurements, reducing position/velocity RMSE (root mean square error) in both single and multi-target settings (Rani et al., 20 Sep 2025). Closed-form expressions for the covariance of the estimation error under arbitrary node placement further clarify the interplay between geometry, measurement noise, and temporal filter performance.

4. Joint Sensing and Communication Algorithms

Distributed OTFS-ISAC requires algorithms for simultaneous (joint) target parameter estimation and reliable communications. Three principal algorithmic modes emerge:

• Active Sensing: When receiver nodes have full knowledge of both pilot and data, maximum likelihood (ML) estimation is achieved via direct correlation for delay and Doppler parameters, followed by closed-form channel gain computation. This is suitable for coordinated network scenarios or dedicated radar periods.
• Passive/Joint Sensing–Communication: When only the pilot is known, initial channel estimation treats data as noise; iterative joint detection/refinement alternates between estimating the data via regularized LS and refining the channel estimate. The pipeline repeats until convergence, balancing sensing accuracy and communication reliability.
• KF-Assisted Iterative Estimation: Both preceding algorithms benefit from follow-up Kalman filtering, leveraging prior state knowledge and cross-node fusion to track the target’s movements over time.

Algorithmic trade-offs involve initialization conditions (pilot/data ratio), computational complexity, and rates of convergence. Optimality is governed both by the spatial (geometry) and adaptive allocation of information across RF, time, and spectrum.

5. System Optimization: Resource Allocation and Mode Selection

In cell-free mMIMO OTFS-ISAC, overall system performance critically depends on the joint configuration of node (access point—AP) operational modes (sensing/communication) and transmit power allocation (Fan et al., 9 Sep 2025). The resource management task is formulated as a mixed-integer, non-convex optimization: maximize the minimum user spectral efficiency (SE) while ensuring that the position error bound (PEB, a function of the Cramér-Rao lower bound) for target estimates is below a set threshold. The selection vector (AP mode: transmitter/receiver) is iteratively “learned” along with continuous power variables by temporally relaxing the integer constraints and imposing penalty terms; successive convex approximations (SCA) and first-order relaxations (e.g., $x^2 \geq x_0(2x - x_0)$) drive convergence toward binary solutions.

A decomposition strategy splits the task into (i) geometric selection (e.g., choosing the closest APs for sensing based on the “hotspot” zone), and (ii) continuous convex optimization of the power allocation for the fixed AP configuration. This reduces computational load with only marginal performance loss—facilitating scalability to networks with large numbers of APs or receivers.

In numerical evaluations, this framework achieves a nearly twofold gain in spectral efficiency relative to OFDM under identical PEB constraints for target localization—a direct consequence of the distributed OTFS-ISAC approach and spatial diversity in the cell-free mMIMO regime (Fan et al., 9 Sep 2025).

6. Impact, Trade-Offs, and Practical Considerations

Distributed OTFS-ISAC exhibits significant performance advantages in both sensing and communication over conventional monostatic or OFDM-based ISAC:

• Localization and Tracking Accuracy: Kalman-filtered, triangulation-based node deployments substantially reduce localization RMSE and velocity estimation errors, efficiently supporting high-mobility V2X and multi-target scenarios (Rani et al., 20 Sep 2025).
• Spectral Efficiency: Joint AP mode selection and power optimization maximize fairness across users without violating sensing error constraints, making the approach viable in dynamic and heterogeneous networks (Fan et al., 9 Sep 2025).
• Communication Reliability: The delay-Doppler sparsification and coherence of OTFS significantly mitigate BER, even as the number of cooperating antennas increases; optimal triangular and orthogonal deployments confer further BER reduction.
• Algorithmic Trade-Offs: There exists a balance between maximizing triangulation area (estimation accuracy), computational complexity (full vs. decomposed/approximate optimization), and operational practicality (binary AP roles, pilot-data balance).

Current research points to several key future challenges: robust extension to non-ideal synchronization, explicit multi-target disambiguation in high-density environments, adaptive resource management under limited backhaul, and the integration of emerging paradigms such as Reconfigurable Intelligent Surfaces in distributed OTFS-ISAC topologies.

7. Summary and Outlook

Distributed OTFS-ISAC provides a rigorous, geometry- and state-aware approach to joint sensing and communication in dynamic wireless networks. The synergy of delay-Doppler modulation, triangulation-based node placement, Kalman filtering for state tracking, and adaptive resource allocation yields robust performance against Doppler and mobility-induced impairments, outperforming legacy ISAC designs in both high-mobility localization and multi-user communication reliability. The framework has direct implications for next-generation vehicle networks, cell-free architectures, and cooperative distributed radar—emphasizing the critical role of physical geometry and state prediction in system design and optimization (Rani et al., 20 Sep 2025, Fan et al., 9 Sep 2025).

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References:

(Yuan et al., 2021, Fan et al., 9 Sep 2025, Rani et al., 20 Sep 2025)