⚡ electrical engineering

Efficient Feedback Design for Unsourced Random Access with Integrated Sensing and Communication

This paper proposes a novel dual-purpose feedback signal design for unsourced random access systems that simultaneously announces user decoding status and enables target sensing, utilizing a modified projected gradient descent algorithm to optimize performance and balance the trade-off between communication and sensing capabilities.

Original authors: Mohammad Javad Ahmadi, Mohammad Kazemi, Rafael F. Schaefer

Published 2026-08-04

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CC BY 4.0

Original authors: Mohammad Javad Ahmadi, Mohammad Kazemi, Rafael F. Schaefer

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 bustling city where millions of tiny, invisible messengers are trying to shout their short messages to a central tower. In the old days, every messenger had to raise their hand, wait for a nod, and say their name before speaking. But with millions of devices, that line would never move. So, engineers invented a chaotic but clever system called "Unsourced Random Access." Here, everyone just shouts their message at once using a shared codebook. The tower doesn't care who shouted; it just wants to hear what was said. It's like a crowded party where the DJ only cares about the song lyrics, not which guest is singing them.

But there's a catch: in this chaotic shouting match, the messengers have no idea if the DJ heard them. Did their message get lost in the noise? Should they shout again? Without a "thumbs up" or "thumbs down" from the tower, they might keep shouting unnecessarily or give up too soon. Meanwhile, the tower is also trying to do something else: it wants to act like a radar, listening for echoes to figure out where objects (like drones or cars) are hiding in the city. The big question is: Can the tower send a single "reply" signal that tells the messengers if they were heard and helps the tower map out the surroundings, all without getting confused?

This paper proposes a clever new way to design that reply signal. The authors, Mohammad Javad Ahmadi, Mohammad Kazemi, and Rafael F. Schaefer, suggest a "dual-purpose" feedback system. Instead of just sending a simple "yes" or "no," the tower sends a sophisticated signal that acts like a Swiss Army knife. It tells the users if their message was decoded correctly so they know whether to retransmit, and at the same time, it bounces off nearby targets to help the tower estimate their angles (directions).

To make this work, the team had to solve a tricky balancing act. They used a mathematical tool called a "modified projected gradient descent" algorithm. Think of this like a hiker trying to find the perfect spot on a mountain ridge. If they walk too far toward the "Communication" peak, they might fall off the "Sensing" cliff, and vice versa. The algorithm helps them find the sweet spot where both tasks are performed well. They tested this idea using computer simulations (virtual experiments) rather than building a physical tower in a real city.

The results of these simulations were quite promising. The new design significantly outperformed the current best method (called HashBeam) in helping users know if their messages were heard. It reduced the number of "wrong decisions" where a user thinks they were heard when they weren't, or vice versa. Furthermore, the paper illustrates a clear trade-off: if you tune the signal to be perfect for communication, the sensing ability drops a bit, and if you tune it for sensing, communication suffers. However, by adjusting a specific "knob" (a weighting factor called $\mu$ ), the system can be tuned to prioritize one task over the other or find a middle ground. The simulations showed that by increasing the length of the feedback signal (denoted as $L$ ), both communication and sensing performance could be boosted simultaneously.

In short, this paper suggests that by carefully designing the "shout back" from the tower, we can make our future wireless networks smarter. They can not only handle millions of chaotic messages more reliably but also act as a built-in radar, all while saving energy and bandwidth. While these findings are currently based on simulations, they offer a vivid blueprint for how 6G networks might one day juggle talking and listening with the same signal.

Technical Summary: Efficient Feedback Design for Unsourced Random Access with Integrated Sensing and Communication

Problem Statement
Unsourced Random Access (URA) is a paradigm designed for massive machine-type communication (IoT), where a large pool of users transmits sporadic, short packets without prior scheduling or identification. While URA reduces signaling overhead, traditional schemes lack downlink feedback, preventing users from knowing if their messages were successfully decoded. This absence can lead to unnecessary retransmissions or data loss. Furthermore, the emerging Integrated Sensing and Communication (ISAC) paradigm seeks to unify communication and sensing functions to share resources like spectrum and hardware. However, existing URA feedback mechanisms, such as the state-of-the-art HashBeam scheme, focus primarily on communication and do not inherently support sensing capabilities like target angle estimation. This paper addresses the challenge of designing a feedback signal in a URA system that simultaneously informs users of decoding status (communication task) and enables the base station (BS) to estimate the directions of sensing targets (sensing task).

Methodology
The authors propose a system model where a BS equipped with a Uniform Linear Array (ULA) detects pilots from active users and estimates their channel coefficients. The BS then transmits a downlink feedback signal $V$ over $L$ channel uses. This signal serves a dual purpose:

Communication: Users correlate the received signal with their known hash codes to determine if their message was decoded ( $s_i = 1$ ) or failed ( $s_i = -1$ ).
Sensing: The BS utilizes the signal reflected by targets in the environment to estimate their angles of arrival/departure.

To design the optimal feedback signal $V$ , the authors formulate a joint optimization problem that minimizes a weighted sum of two error metrics:

Communication Error ( $e_c$ ): The probability of incorrect decision regarding the decoding status. This is derived based on the Q-function of the real part of the correlation between the received signal and the user's hash code.
Sensing Error ( $e_s$ ): The Root Mean Squared Error (RMSE) of angle estimation, approximated using a lower bound derived from the Cramér-Rao bound.

The optimization problem is non-trivial due to the non-linear Q-function and the inverse relationship in the sensing error bound. To make the problem tractable, the authors introduce a modified projected gradient descent algorithm. Key simplifications include:

Approximating the Q-function with a linear term ( $-x$ ) for values above a specific threshold, allowing the algorithm to prioritize users with higher error probabilities.
Using a first-order Taylor expansion for the $1/x$ term in the sensing error cost function.
Iteratively updating the signal matrix $V$ by calculating gradients for both communication and sensing components, normalizing them by their Frobenius norms to ensure stable step sizes, and projecting the result onto the power constraint sphere.

Key Contributions

Dual-Purpose Feedback Design: The paper introduces a novel feedback signal design for URA that simultaneously supports decoding status notification and target angle estimation, bridging the gap between URA and ISAC.
Optimization Framework: A weighted optimization problem is formulated to balance communication reliability and sensing accuracy, controlled by a trade-off parameter $\mu$ .
Algorithmic Innovation: A modified projected gradient descent algorithm is proposed to solve the non-convex optimization problem efficiently. The algorithm dynamically adjusts gradients based on the current error probabilities of users, focusing computational effort on those most likely to benefit from the feedback.
Performance Analysis: The study provides a theoretical analysis of the communication error probability and an approximate lower bound for the sensing angle estimation MSE.

Results
Numerical results obtained via Monte Carlo simulations demonstrate the efficacy of the proposed scheme:

Communication Performance: When prioritizing communication ( $\mu = 1$ ), the proposed scheme significantly outperforms the HashBeam scheme (the state-of-the-art for URA feedback) in terms of detection error probability across various numbers of users ( $K$ ) and feedback signal lengths ( $L$ ). The improvement is attributed to the problem-specific optimization and the utilization of information from both successfully and unsuccessfully decoded users, whereas HashBeam relies only on successfully decoded users.
Sensing-Communication Trade-off: The Pareto frontier analysis reveals a clear trade-off: increasing the weight on communication ( $\mu$ ) improves decoding reliability but degrades sensing accuracy (increased RMSE), and vice versa.
Scalability: Increasing the feedback signal length $L$ leads to significant improvements in both communication and sensing performance.

Significance
The paper claims that its proposed feedback design offers a valuable solution for next-generation 6G networks where URA and ISAC converge. By enabling a single feedback signal to serve both reliable communication (via retransmission triggers) and environmental sensing, the approach improves spectral and hardware efficiency. The work provides a flexible mechanism to balance these competing objectives, offering insights into how system parameters can be tuned to meet specific application requirements without sacrificing the fundamental benefits of unsourced access.

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