⚡ electrical engineering

Cooperative OFDM-ISAC Networks: Performance Analysis and Resource Allocation

This paper analyzes the performance and optimizes resource allocation for cooperative OFDM-ISAC networks by comparing signal-level and parameter-level fusion architectures, deriving corresponding Cramér-Rao bounds, and proposing an efficient algorithm for joint resource-element selection and power allocation that balances sensing accuracy, communication rates, and ambiguity suppression.

Original authors: Shoushuo Zhang, Rang Liu, Qian Liu, Ming Li

Published 2026-04-30

📖 5 min read🧠 Deep dive

CC0 1.0

Original authors: Shoushuo Zhang, Rang Liu, Qian Liu, Ming Li

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a city where several cell towers (Base Stations) are trying to do two things at once: talk to your phone (Communication) and act like a giant radar to track moving objects like cars or drones (Sensing). This paper tackles the tricky problem of how to organize these towers so they don't step on each other's toes while doing both jobs efficiently.

Here is a breakdown of the paper's ideas using everyday analogies:

1. The Setup: A Team of Flashlights

Think of the cell towers as a team of people holding flashlights in a dark room. They need to:

Talk: Send messages to people in the room.
See: Shine their lights to spot a moving object and figure out exactly where it is and how fast it's moving.

The problem is that they all share the same "flashlight grid" (the time and frequency slots of the signal). If everyone flashes at the same time, the beams mix up, and you can't tell which beam came from which person.

2. The Solution: The "No-Overlap" Dance

The authors propose a very specific way to coordinate the flashlights. Instead of everyone flashing in big blocks (like a whole minute of talking, then a whole minute of sensing), they use a fine-grained, non-periodic pattern.

The Old Way (1D): Imagine the towers taking turns in big chunks. Tower A talks for a while, then Tower B talks. This is like a relay race where everyone runs a long leg. It's simple, but you lose the ability to see fast movements (Doppler) or distant objects (Range) clearly because you aren't looking long enough or wide enough.
The New Way (2D): The authors suggest a complex dance where Tower A flashes a specific dot here, Tower B flashes a dot there, and Tower C flashes a dot somewhere else, all mixed together in time and frequency. This creates a "net" that covers the whole area without the beams colliding. It preserves the ability to see both fast and far.

3. The Two Ways to Share the News (Fusion Architectures)

Once the towers see the object, they need to tell a central "Brain" (the Fusion Center) what they found. The paper compares two ways of doing this:

Signal-Level Fusion (SLF) – "The Raw Video Feed":
Every tower sends the entire raw video of what it saw back to the Brain.
- Pros: The Brain has all the information. It can calculate the object's position and speed with maximum precision.
- Cons: It requires a massive amount of data to send (heavy traffic on the network cables).
Parameter-Level Fusion (PLF) – "The Summary Note":
Each tower looks at the video, figures out the object's location and speed locally, and sends only a short note with those numbers back to the Brain.
- Pros: Very little data needs to be sent. It's efficient.
- Cons: The tower might have made a small mistake when it calculated the numbers locally, or it might have rounded them off. The Brain loses some detail.

The Paper's Big Finding: The authors did the math to show that the "Summary Note" method (PLF) can only ever be as good as the "Raw Video" method (SLF) if the towers are perfect calculators and the Brain knows exactly how much to trust each note. In the real world, where towers use simpler, faster calculators (like standard FFTs), the "Summary Note" method usually loses a bit of accuracy. The gap between the two methods depends on how the towers are arranged; if they are spread out evenly, the gap is small. If they are clustered weirdly, the gap gets bigger.

4. The Optimization: Playing Tetris with Power

The authors created a smart algorithm to decide:

Who flashes when? (Which time/frequency slot belongs to which tower?)
How bright should the flash be? (How much power to use?)

They had to balance three competing goals:

Sensing Accuracy: Make the radar as sharp as possible.
Communication Speed: Make sure people can still download their emails and stream videos.
Clutter Control: Make sure the radar doesn't get confused by "ghosts" (false alarms) appearing in the wrong places.

They treated this like a game of Tetris. They wanted to fit the "Sensing Blocks" and "Communication Blocks" into the grid so that the Sensing Blocks were scattered perfectly to catch the target, while still leaving enough room for the Communication blocks to work. They also added a rule to ensure the radar didn't have "ghosts" (sidelobes) that could trick the system.

5. The Results

When they tested their new "2D Dance" against the old "Big Block" methods:

Better Tracking: Their method tracked the object's position and speed much better, especially when the signal was weak.
No Ghosts: The "ghosts" (ambiguities) were suppressed, meaning the radar was less likely to get confused.
The Trade-off: They showed that you can increase the internet speed for users without completely destroying the radar's ability to see, provided you use their smart scheduling.

Summary

In short, this paper teaches a group of cell towers how to coordinate their "flashes" in a complex, scattered pattern so they can talk to your phone and track moving objects simultaneously without getting in each other's way. It also proves that while sending a simple summary of the data is efficient, you lose some precision compared to sending the raw data, and the amount you lose depends on how the towers are positioned.

1. Problem Statement

The paper addresses the challenges in Cooperative Integrated Sensing and Communication (ISAC) networks based on Orthogonal Frequency-Division Multiplexing (OFDM). Specifically, it tackles two tightly coupled issues in a multi-Base Station (BS) network:

Transmitter-Side Resource Allocation: How to schedule time-frequency resources (Resource Elements or REs) and allocate transmit power across multiple BSs to simultaneously support high-throughput communication and high-precision sensing, while managing inter-BS interference.
Receiver-Side Performance Characterization: How different fusion architectures impact sensing accuracy. The paper compares:
- Signal-Level Fusion (SLF): Raw echoes are forwarded to a central fusion center (high overhead, high information retention).
- Parameter-Level Fusion (PLF): Only local delay/Doppler estimates and their uncertainty are forwarded (low overhead, potential information loss).

The core challenge is that conventional 1D orthogonal schemes (e.g., Time-Division or Frequency-Division blocks) suffer from a trade-off between resolution and ambiguity (e.g., losing effective bandwidth or coherent processing interval). The paper seeks a unified framework to analyze these fusion architectures and design an optimal, fine-grained 2D resource allocation strategy.

2. Methodology

A. System Model

Network: $P$ Transmit BSs and $Q$ Receive BSs cooperatively serve $K$ users and sense a moving target.
Coordination: The paper enforces network-wide RE-level orthogonality, meaning each RE is assigned to at most one BS for either sensing or communication. This suppresses interference and simplifies multistatic processing.
Signal Model: The system uses a common OFDM frame. The received echo at each Rx-BS is modeled as a sum of delayed and Doppler-shifted signals from all Tx-BSs, plus noise.

B. Performance Analysis (SLF vs. PLF)

The authors derive performance bounds to quantify the trade-offs between fusion architectures:

Signal-Level Fusion (SLF):
- Derives the Cramér–Rao Bound (CRB) for joint target position and velocity estimation based on raw frequency-domain observations.
- Uses the Fisher Information Matrix (FIM) and Schur complement to eliminate nuisance parameters (reflection coefficients), resulting in a centralized CRB metric.
Parameter-Level Fusion (PLF):
- Develops a Two-Stage CRB-like metric (TS-CRB).
- Stage 1 (Local): Characterizes the uncertainty of local delay/Doppler extraction. Two modes are considered:
  - Practical: FFT-based extraction (lossy due to grid discretization).
  - Oracle: Continuous-parameter Maximum Likelihood (ML) extraction (asymptotically lossless).
- Stage 2 (Fusion): Propagates local uncertainties through geometric fusion using Weighted Least Squares (WLS).
- Key Finding: The paper proves that only an "Oracle ML-based PLF" (using continuous parameters and exact covariance) can asymptotically approach the SLF CRB under restrictive conditions. Practical FFT-based PLF incurs inherent information loss due to grid quantization.

C. Resource Allocation Design

Objective: Minimize the SLF CRB (position and velocity estimation error).
Constraints:
- Network-wide RE exclusivity (orthogonality).
- Per-BS power budgets.
- Minimum communication sum-rate.
- Sidelobe-Amplitude Constraint: A novel constraint to suppress off-peak ambiguity peaks in the delay-Doppler ambiguity function, preventing false alarms.
Algorithm:
- The problem is non-convex due to binary RE selection and the inverse CRB objective.
- Schur Complement Reformulation: Transforms the inverse CRB objective into a Linear Matrix Inequality (LMI) constraint.
- Penalty-Based Alternating Optimization:
  - Relaxes binary constraints to continuous variables.
  - Uses a concave penalty function to encourage binary solutions.
  - Applies Majorization-Minimization (MM) to handle the non-convex penalty term.
  - Alternates between optimizing power allocation and RE selection until convergence.

3. Key Contributions

Fine-Grained 2D Orthogonal Coordination: Proposes a non-periodic 2D resource allocation pattern that avoids the resolution-ambiguity trade-offs of conventional 1D schemes (TDB, FDB, TDI, FDI) by preserving both effective bandwidth and coherent processing interval.
Unified Performance Framework: Establishes a rigorous comparison between SLF and PLF. It clarifies that PLF performance is highly dependent on the local extraction method (FFT vs. ML) and fusion weighting, and that practical PLF often suffers significant gaps compared to SLF, especially in asymmetric geometries.
Joint Optimization Algorithm: Develops an efficient algorithm for joint RE selection and power allocation that simultaneously optimizes sensing accuracy (via CRB), communication throughput, and ambiguity suppression (via sidelobe constraints).
Geometry-Dependent Insights: Reveals that the performance gap between SLF and PLF is strongly geometry-dependent; PLF performs well in balanced deployments but degrades significantly in asymmetric regions where local estimation errors are amplified by poor geometric conditioning.

4. Simulation Results

Sensing Accuracy: The proposed 2D allocation significantly outperforms TDB, FDB, and random allocation baselines in both position and velocity RMSE, closely matching the theoretical CRB.
SLF vs. PLF Gap:
- Practical PLF (FFT-based) shows a noticeable performance loss compared to SLF, primarily due to finite-resolution grid effects.
- The gap widens at high SNR (where grid mismatch dominates) and in asymmetric deployments.
- Oracle ML-based PLF can asymptotically match SLF performance.
Sensing-Communication Tradeoff: The proposed scheme maintains low sensing bounds even as communication rate requirements increase, whereas 1D baselines degrade rapidly.
Ambiguity Control: The sidelobe-amplitude constraint effectively suppresses off-peak ambiguity ridges without significantly sacrificing the mainlobe sharpness (local CRB), enhancing robustness against false alarms.

5. Significance

This paper provides a critical theoretical and practical foundation for next-generation 6G ISAC networks.

Theoretical: It bridges the gap between raw signal processing and compressed parameter fusion, offering a clear mathematical characterization of the "cost" of fronthaul compression in cooperative sensing.
Practical: The proposed resource allocation algorithm offers a blueprint for network operators to dynamically schedule resources in multi-BS environments, balancing the competing demands of high-speed data and precise environmental perception.
Design Insight: It highlights that while PLF is attractive for scalability, system designers must carefully account for local extraction fidelity and network geometry to avoid significant sensing performance degradation. The inclusion of ambiguity sidelobe constraints ensures that the system remains robust in real-world, cluttered environments.