⚡ electrical engineering

Secure Spatial Signal Design for ISAC in a Cell-Free MIMO Network

This paper proposes a secure spatial signal design for cell-free MIMO integrated sensing and communication networks that utilizes artificial noise and semi-definite relaxation to jointly optimize precoding and noise covariance, thereby revealing a unique trade-off where increasing the distance between users and an eavesdropping target paradoxically improves sensing accuracy.

Original authors: Steven Rivetti, Emil Bjornson, Mikael Skoglund

Published 2026-05-26

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CC BY 4.0

Original authors: Steven Rivetti, Emil Bjornson, Mikael Skoglund

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ 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 futuristic city where the streetlights don't just illuminate the road; they also talk to your car and keep an eye on traffic. This is the world of Integrated Sensing and Communication (ISAC). In this paper, the researchers are designing a smarter version of this system using a "Cell-Free MIMO" network.

Here is the simple breakdown of what they did, using everyday analogies:

The Setup: A Team of Smart Streetlights

Instead of having one big, powerful tower sending signals, imagine a neighborhood filled with many small, distributed Access Points (APs) (like smart streetlights).

The Goal: These lights need to do two things at once:
1. Talk to your phone (Communication): Send you data.
2. Watch a specific target (Sensing): Track a vehicle or object.
The Problem: In this scenario, the "target" they are watching is actually a spy (called "Eve"). The spy is trying to listen in on the conversation between the lights and your phone while pretending to be a normal object being tracked.

The Strategy: The "Whisper" and the "Shout"

The researchers designed a special signal that acts like a dual-purpose tool. Think of it as a conversation where the speakers are trying to be heard clearly by their friends but are trying to confuse a spy standing nearby.

The Main Signal (The Shout): This is the data meant for your phone. The network focuses its energy to make sure your phone gets a clear, strong signal.
The Artificial Noise (The Whisper): This is the paper's big innovation. The network generates a special type of "static" or "noise" (called Artificial Noise).
- Where does it go? It is aimed directly at the spy (Eve).
- What does it do? It's like a speaker playing loud static noise right next to the spy's ear. The spy hears a mess and can't understand the conversation, but because the noise is aimed only at the spy, your phone (which is in a different direction) doesn't hear it.

The Balancing Act (The Trade-Off)

The researchers found a tricky balancing act, like trying to tune a radio while also trying to hear a whisper:

If you want the phone to hear perfectly: You have to focus all your energy on the phone. This leaves less energy to confuse the spy, so the spy might hear a little bit more.
If you want to confuse the spy perfectly: You have to blast noise at the spy. This might use up energy that could have helped the phone, making the phone's connection slightly weaker.

The paper proves that you can mathematically calculate the perfect balance. You can set a rule like, "The spy must hear no more than X amount of noise," and the system will automatically adjust the signal to make the spy as confused as possible without ruining the phone's connection.

The "Surprise" Discovery

The researchers found something interesting about how the distance between the phone and the spy affects the system:

When the phone and spy are far apart: The system works great. It can easily aim the "noise" at the spy without bothering the phone.
When the phone and spy are standing right next to each other: The system struggles. Because the noise is aimed at the spy, it inevitably hits the phone too (since they are so close). The researchers found that the closer the spy is to the phone, the harder it is for the system to protect the data, and the "accuracy" of the tracking gets worse.

The Result

By using a complex mathematical method (which they call "Semi-Definite Relaxation"), they proved that the best way to generate this "noise" is to focus it in a single, tight beam directly at the spy.

In summary: The paper shows how a network of smart antennas can talk to your phone and track a spy simultaneously. They figured out how to generate a "noise beam" that jams the spy's ears without hurting your phone's hearing, provided the spy isn't standing right next to you.

Technical Summary: Secure Spatial Signal Design for ISAC in a Cell-Free MIMO Network

Problem Statement
This paper addresses the challenge of securing Integrated Sensing and Communication (ISAC) systems within a cell-free Multiple-Input Multiple-Output (MIMO) network. In such networks, distributed Access Points (APs) jointly serve User Equipments (UEs) while simultaneously sensing a target. The authors posit a security scenario where the sensing target is a malicious eavesdropper (Eve) attempting to intercept confidential communication data embedded within the dual-functional waveform.

Unlike traditional Physical Layer Security (PLS) research, which often assumes independent and identically distributed (i.i.d.) channels for legitimate users and interceptors, ISAC systems face a unique constraint: the sensing channel (often containing a Line-of-Sight component at mmWave frequencies) is inextricably linked to the communication channel. Consequently, the target used for sensing is the same entity potentially intercepting data. The core problem is to design a transmit waveform that maintains high-quality sensing performance (specifically, low estimation error for the target's angle) while ensuring the communication Signal-to-Interference-plus-Noise Ratio (SINR) for UEs and degrading the Eve's Signal-to-Noise Ratio (SNR) to prevent interception.

Methodology
The proposed solution involves a joint design of transmit precoding and Artificial Noise (AN) covariance matrices in a cell-free MIMO architecture consisting of $M$ APs and $K$ UEs.

System Model:
- The network employs $M$ APs, each equipped with a Uniform Linear Array (ULA) of $N$ transmit and receive antennas.
- The transmitted waveform from each AP includes information streams for $K$ UEs, one dedicated sensing stream, and an AN vector.
- The system utilizes a Central Processing Unit (CPU) that collects observations from all APs via error-free backhaul links to compute optimal transmission strategies.
- Multistatic sensing is implemented, where every AP receives echoes from its own transmissions as well as reflections from other APs.
Optimization Framework:
- Objective: Minimize the Cramer-Rao Bound (CRB) on the estimation of the target's angle of arrival (AoA), which serves as a proxy for maximizing sensing accuracy.
- Constraints:
  - Minimum SINR requirements for all communication UEs.
  - Maximum allowable SNR for the Eve (to limit interception capability).
  - Total transmit power limits per AP.
- Formulation: The problem is initially non-convex due to quadratic terms in the SINR and SNR constraints. The authors reformulate it as a Semi-Definite Program (SDP) by introducing rank-1 matrix variables ( $W_s = f_s f_s^H$ ) and relaxing the rank constraint.
- Solvability: The paper proves that the semi-definite relaxation (SDR) is tight for the specific scenario, meaning the optimal solution to the relaxed problem naturally yields rank-1 matrices, allowing for the direct retrieval of optimal precoding vectors without additional approximation.

Key Contributions
The paper makes the following specific contributions:

Novel Waveform Model: Proposes a transmit waveform model for distributed ISAC APs in a cell-free network that integrates Artificial Noise (AN) specifically designed to degrade the Eve's channel quality while serving communication users.
Optimal Waveform Calculation: Derives the optimal transmit waveform by solving a constrained CRB minimization problem. The authors provide a proof that the semi-definite relaxation of this problem is tight for the considered scenario.
AN Structure Characterization: Analytically characterizes the optimal AN covariance matrix, demonstrating that it is rank-1 and directed specifically towards the Eve's location.
Trade-off Analysis: Through numerical simulations, the paper quantifies the inherent trade-off between sensing and communication performance and investigates the impact of the spatial proximity between UEs and the Eve on system performance.

Simulation Results
The authors evaluate the proposed strategy using a network with $M=2$ APs and $K=4$ UEs. Key findings include:

Sensing-Communication Trade-off: There is a direct proportionality between the required UE SINR ( $\gamma$ ) and the achieved CRB. Stricter SINR requirements force the system to allocate more resources to communication, thereby degrading sensing accuracy (increasing CRB).
Security vs. Sensing Trade-off: Stricter constraints on the Eve's maximum SNR ( $\psi$ ) lead to a slight increase in CRB. However, the results indicate that reducing the allowed Eve SNR by 3–5 dB results in negligible degradation of sensing performance, suggesting that strong security constraints can be imposed with minimal cost to sensing.
Optimal AN Properties: The simulations confirm that the optimal AN covariance matrix is rank-1. The resulting beampattern exhibits a sharp peak directed precisely at the Eve, with power levels dropping significantly (below -15 dB) in other directions.
Proximity Effect: A critical finding is the relationship between UE-Eve proximity and the CRB. When UEs are located close to the Eve (within the main lobe of the AN beam), the system's ability to maintain low CRB degrades. This degradation is more pronounced as the SINR requirement ( $\gamma$ ) increases, as the system has fewer resources available to compensate for the interference caused by the proximity.
Relaxation Tightness: The simulations verify that the optimal matrices for communication streams are rank-1, and the sensing stream effectively becomes superfluous (rank-almost-zero) in the optimal solution, confirming the tightness of the SDR.

Significance and Claims
The paper claims that the proposed design strategy is highly efficient for limiting the impact of an eavesdropper that is physically separated from legitimate communication users. By leveraging the angular directionality of the Artificial Noise, the system can effectively protect confidential data without completely sacrificing sensing capabilities.

The authors emphasize that the inverse proportionality between the UE-Eve distance and the optimal CRB magnitude is a surprising and significant result. It highlights that the system's performance is most robust when the eavesdropper is spatially distinct from the users, as the AN can be focused precisely on the threat without disrupting the communication links. The work provides a theoretical foundation for secure ISAC waveform design in future 6G cell-free networks, demonstrating that physical layer security can be integrated with sensing functions through careful co-design of precoding and noise covariance.

The Setup: A Team of Smart Streetlights

The Strategy: The "Whisper" and the "Shout"

The Balancing Act (The Trade-Off)

The "Surprise" Discovery

The Result

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