⚡ electrical engineering

Robust Beamforming Design for Secure Uplink NOMA-ISAC

This paper proposes a robust beamforming design for secure uplink NOMA-ISAC systems that jointly optimizes receive combining and transmit beamforming via an alternating optimization algorithm to maximize sum rate and sensing performance while mitigating eavesdropping threats from users with uncertain locations.

Original authors: Azadeh Tabeshnezhad, Milad Tatar Mamaghani, A. Lee Swindlehurst, Tommy Svensson, Erik Ström

Published 2026-06-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Azadeh Tabeshnezhad, Milad Tatar Mamaghani, A. Lee Swindlehurst, Tommy Svensson, Erik Ström

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

The Big Picture: A Two-in-One Super-Tool

Imagine a future mobile network (6G) that doesn't just talk to your phone but also acts like a super-accurate radar. This technology is called Integrated Sensing and Communication (ISAC). It's like having a single flashlight that can both illuminate a room so you can see (sensing) and send a secret message to a friend in the dark (communication).

However, there's a catch. Because this system is doing two things at once, it's harder to keep secrets. A "spy" (called Eve in the paper) might try to listen in on the messages while the system is trying to find them.

This paper solves a specific problem: How do we send messages and find a spy when we aren't 100% sure exactly where the spy is standing?

The Characters and the Setup

The Base Station (The Tower): A powerful tower with many antennas. It acts as a radio station (sending/receiving data) and a radar (looking for targets).
The Users (UEs): Two people trying to send data up to the tower. They are using a clever trick called NOMA, which is like two people speaking at the same time in a crowded room, but one speaks louder than the other so the listener can separate their voices.
The Spy (Eve): A bad actor trying to steal the messages. The tricky part is that the tower only has a rough guess of where Eve is. It's like trying to throw a net to catch a fish when you only know the fish is "somewhere in that pond," not exactly where.

The Problem: Guessing the Spy's Location

In previous research, scientists assumed they knew the spy's location perfectly. But in the real world, radar isn't perfect. It makes small errors in guessing the angle and distance of a target.

If the tower designs its security based on a "perfect guess" but the spy is actually standing a few feet away, the security plan might fail, and the spy could hear everything.

The Solution: A "Robust" Safety Net

The authors created a new design that accounts for these guessing errors. They didn't just guess where the spy is; they calculated the worst-case scenario based on how much the radar might be wrong.

Think of it like this:

Old Way: You build a fence exactly where you think the wolf is. If the wolf moves two steps, it gets in.
This Paper's Way: You build a fence that accounts for the wolf's potential movement. You make the fence slightly wider and stronger to ensure the wolf can't get in, even if your initial guess was slightly off.

How They Did It (The Mechanics)

To make this work, the researchers used a mathematical tool called the Cramér-Rao Bound (CRB).

The Analogy: Imagine you are trying to measure the length of a table with a ruler that is slightly bent. The CRB is like a mathematical rule that tells you, "Based on how bent the ruler is, your measurement could be off by at most X inches."
The Application: The team used this rule to figure out exactly how much the "spy's location" could be wrong. They then used this "error margin" to design the signal beams.

They created a system that does two things simultaneously:

Sends Data: It beams the users' messages to the tower efficiently.
Jams the Spy: It sends a special "noise" signal (a jamming beam) specifically aimed at the area where the spy might be. This noise drowns out the secret messages for the spy, but because the tower knows the noise pattern, it can filter it out and still hear the users clearly.

The "Dance" of Optimization

Because the math for this problem is incredibly complex (like trying to solve a puzzle where every piece changes shape as you move it), the authors developed a step-by-step algorithm.

The Analogy: Imagine tuning a radio. You turn the frequency knob (optimizing the beam direction), then you adjust the volume (optimizing the power), then you go back to the frequency, and so on. You keep doing this "dance" back and forth until the signal is perfect and the static (the spy's ability to listen) is gone.

The Results: What Did They Find?

The authors ran computer simulations to test their idea against two other scenarios:

The "Ideal" Scenario: Where everyone knows the spy's exact location (unrealistic).
The "Non-Secure" Scenario: Where they don't try to protect against the spy at all.

The findings were:

Security: Their "Robust" design kept the spy's ability to hear the messages (SINR) below a dangerous level, even when the spy's location was uncertain. The "Ideal" design was slightly better, but the "Non-Secure" design failed miserably, letting the spy hear everything.
Efficiency: The system managed to keep the communication speed high and the radar sensing accurate, even while spending extra energy to jam the spy.
The Trade-off: As they increased the power sent to the radar (to find the spy better), the spy's ability to listen actually got worse. This is because the "jamming" signal became stronger, effectively blinding the spy.

In a Nutshell

This paper presents a smart, "safety-first" way to use 6G networks that double as radars. It admits that we can't always know exactly where a hacker is standing. Instead of hoping for the best, it builds a mathematical safety net that ensures the hacker stays in the dark, even if our radar is slightly fuzzy. It proves that you can have high-speed internet, accurate radar, and strong security all at the same time, without needing to know the spy's location perfectly.

Technical Summary: Robust Beamforming Design for Secure Uplink NOMA-ISAC

Problem Statement
This paper addresses the security challenges inherent in Integrated Sensing and Communication (ISAC) systems, specifically within an uplink Non-Orthogonal Multiple Access (NOMA) framework. While ISAC offers spectral efficiency by sharing resources for radar sensing and data communication, this joint usage increases vulnerability to eavesdropping. The authors focus on a scenario where a Base Station (BS) simultaneously receives uplink user data and senses a potential eavesdropper (Eve) with an uncertain location.

A critical gap identified in existing literature is that most secure ISAC designs assume perfect Channel State Information (CSI) regarding the eavesdropper or treat sensing estimation errors as isolated metrics. In reality, sensing parameters (such as Angle of Arrival and time delay) are estimated with error, and these uncertainties propagate into the communication and eavesdropping channel models. The paper aims to design a robust beamforming strategy that maximizes the sum rate of users and sensing performance while guaranteeing physical-layer security against an eavesdropper whose location is known only with estimation uncertainty.

Methodology
The proposed solution involves a three-stage approach: modeling, uncertainty analysis, and joint optimization.

System Modeling: The system consists of a monostatic BS with separate transmit and receive arrays, two multi-antenna users, and a single-antenna eavesdropper. The BS transmits a sensing signal to jam and sense Eve while receiving uplink NOMA signals. The received signal at the BS includes communication signals, the radar echo, self-interference (SI), and noise.
Uncertainty-Aware Analysis: The authors derive a framework based on the Cramér-Rao Bound (CRB) to quantify the estimation errors in the target's angle and delay. Using first-order Taylor approximations, they model the actual eavesdropping channels as stochastic perturbations around the estimated values. This allows for the derivation of tractable Signal-to-Interference-plus-Noise Ratio (SINR) expressions for communication, sensing, and eavesdropping that explicitly account for these estimation errors.
Joint Optimization: A non-convex optimization problem is formulated to maximize a weighted utility function of the communication sum rate and sensing performance, subject to power constraints and a secrecy constraint (limiting Eve's SINR).
- Algorithm: An Alternating Optimization (AO) algorithm is developed to solve the problem.
- Subproblem 1: The receive combining vectors are optimized in closed form using Generalized Eigenvalue Decomposition (GEVD).
- Subproblem 2: The transmit beamforming matrices and sensing power are jointly optimized. This is handled via Semidefinite Relaxation (SDR) to relax the rank-1 constraint and Successive Convex Approximation (SCA) using a quadratic transform technique to handle the non-concave objective function. The resulting convex subproblem is solved iteratively until convergence.

Key Contributions
The paper claims the following specific contributions:

Uncertainty-Aware Model: Development of a model for uplink NOMA-ISAC that characterizes how sensing-estimation errors (angle and delay) propagate to affect communication, sensing, and eavesdropping performance metrics.
Tractable SINR Approximations: Derivation of analytical SINR expressions for the communication, sensing, and eavesdropping channels that incorporate the CRB-induced uncertainty.
Joint Optimization Framework: Formulation of a joint beamforming and sensing-power optimization problem that maximizes a weighted utility while enforcing security constraints.
Efficient Algorithm: Proposal of an iterative AO-SCA algorithm that decomposes the non-convex problem into tractable subproblems, with provided convergence and complexity analysis.
Robustness Demonstration: Simulation results showing that the proposed design maintains Eve's SINR below a prescribed threshold under location uncertainty, outperforming non-secure baselines and maintaining performance close to ideal (perfect CSI) benchmarks.

Simulation Results
Numerical simulations were conducted using parameters typical for 6G scenarios (e.g., 6 GHz carrier frequency, 8 BS antennas). The proposed "Proposed" scheme was compared against an "Ideal" scheme (assuming perfect Eve location knowledge) and a "Non-secure" scheme (ignoring the secrecy constraint).

Performance vs. Sensing Power: As the sensing power budget increases, the communication and sensing sum rate improves. The proposed scheme achieves performance very close to the Ideal scheme, while the Non-secure scheme offers higher rates but fails to guarantee secrecy.
Secrecy Constraint: The proposed and Ideal schemes successfully keep Eve's aggregate SINR below the threshold ( $2\gamma_{th}$ ) across all sensing power levels. The proposed scheme maintains a slightly lower SINR for Eve than the Ideal scheme due to the conservative uncertainty margin, ensuring robustness.
Secrecy Rate: The proposed design maintains a high secrecy rate even as the distance between the BS and Eve increases (and thus estimation uncertainty grows). In contrast, the Non-secure scheme's secrecy rate collapses at larger distances where uncertainty is highest.

Significance and Claims
The authors assert that their work demonstrates that CRB-aware robust design is an effective approach for secure uplink NOMA-ISAC. The paper claims that ignoring sensing-induced uncertainty can lead to overly optimistic and potentially insecure system designs. By integrating estimation-theoretic uncertainty directly into the beamforming design, the proposed method ensures that security constraints are met even when the eavesdropper's location is not perfectly known. The study highlights the fundamental coupling between CRB-driven sensing errors and system-level metrics like SINR and secrecy capacity, suggesting that future designs must account for this propagation of error to be truly robust.