💻 computer science

Integrated Sensing and Communications for Unsourced Random Access: Fundamental Limits

This paper introduces the unsourced ISAC (UNISAC) framework, which enables simultaneous message decoding and sensing user detection for massive numbers of uncoordinated users without scheduling, and demonstrates its superior performance over conventional multiple access and interference management schemes through theoretical analysis and numerical simulations.

Original authors: Mohammad Javad Ahmadi, Rafael F. Schaefer, H. Vincent Poor

Published 2026-04-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mohammad Javad Ahmadi, Rafael F. Schaefer, H. Vincent Poor

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 Chaotic Cocktail Party

Imagine a massive, noisy cocktail party where thousands of people are in the room. However, there are two distinct groups of guests:

The Talkers (Communication Users): They want to whisper secret messages to the host.
The Movers (Sensing Users): They aren't speaking; they are just walking around, and the host wants to know where they are and how fast they are moving.

The Problem:
In a traditional setup, the host would have to call out, "Okay, Bob, speak now. Then, Alice, speak now." This is called scheduling. But with thousands of people, this takes forever, wastes energy, and creates a huge bottleneck.

In this paper, the authors propose a new system called UNISAC (Unsourced Integrated Sensing and Communications). Here, everyone shouts their message or moves at the exact same time, all at once, without asking for permission. The host has to listen to the resulting wall of noise and figure out:

What were the secret messages?
Where are the people walking?

The challenge? It's like trying to hear a single conversation in a stadium full of screaming fans while also tracking the movement of a few people in the crowd.

The Core Innovation: The "Magic Codebook"

How does the host make sense of this chaos? The paper proposes a clever trick using a Shared Codebook (think of it as a giant dictionary of unique sound patterns).

The Talkers: Each one picks a unique page from the first half of the dictionary and reads it out loud.
The Movers: Each one picks a unique page from the second half of the dictionary and reads it out loud (even though they aren't sending a message, they use this "sound" to reveal their location).

Because everyone is using the same dictionary, the host doesn't need to know who is speaking (the "unsourced" part). They just need to figure out which pages from the dictionary are being used.

The Two Superpowers

The UNISAC system does two things simultaneously:

Decoding the Messages: It filters out the noise to reconstruct the secret whispers of the Talkers.
Locating the Movers: By analyzing how the sound waves hit the host's microphone array (which is like having ears spaced out in a line), it can calculate the Angle of Arrival (AOA).
- Analogy: Imagine you are in a dark room with a row of microphones. If a sound comes from the left, the left microphone hears it slightly before the right one. The system uses this tiny delay to triangulate exactly where the "Mover" is standing.

The Results: Why UNISAC Wins

The authors compared their new system against old, standard methods:

TDMA (Time Division): Like a strict teacher making students raise their hands one by one. It works for small classes but fails miserably with thousands of students (too slow, too much waiting).
ALOHA: Like a chaotic free-for-all where everyone shouts whenever they want. It works okay for a few people, but with thousands, everyone just drowns each other out (collisions).
TIN (Treat Interference as Noise): The host just ignores the other people and tries to listen to one person, treating everyone else as static. This fails when the crowd is too loud.
MUSIC: A sophisticated listening technique, but it struggles when there are more people than microphones.

The UNISAC Advantage:
The paper shows that UNISAC is like a super-powered noise-canceling headphone combined with a super-vision.

It handles the "crowd" much better than the old methods.
It allows for a massive number of users (thousands) to connect without crashing the system.
It achieves the goal (hearing the messages and finding the people) with much less energy and time than the competition.

The "Mathy" Part (Simplified)

The authors did a lot of heavy math to prove this works. They created a "scorecard" (an achievable bound) that predicts how well the system will perform.

They calculated the probability of missing a person (Misdetection).
They calculated the probability of mixing up two people (Collision).
They calculated how accurate the location estimate is (Mean Squared Error).

Their simulations showed that UNISAC's scorecard is much better (lower error rates) than the old methods, especially when the room is packed with people.

The Takeaway

This paper solves a major problem for the future of 6G networks. As we connect millions of cheap devices (smart sensors, IoT gadgets, autonomous cars), we can't afford to schedule them one by one. We need a system where they can all "scream" at once, and the network can still understand the message and know where the device is.

UNISAC is the solution that turns a chaotic, screaming crowd into a clear, organized conversation, even when thousands of people are talking at the same time.

1. Problem Statement

The paper addresses the challenge of Integrated Sensing and Communications (ISAC) in a massive unsourced random access (URA) scenario.

Context: In next-generation (6G) networks, millions of inexpensive devices connect to a base station (BS), but only a small, sporadic fraction are active at any given time.
The Challenge: Traditional scheduling and user identification introduce excessive signaling overhead and latency. In Unsourced Random Access (URA), the BS must recover transmitted data without identifying which specific user sent it.
The Specific Gap: Existing URA research focuses solely on communication (decoding messages). This paper tackles the dual objective where the system must simultaneously:
1. Decode messages from active communication users.
2. Detect the presence of active sensing users (objects) and estimate their Angles of Arrival (AOA).
Difficulty: All active users transmit simultaneously over a short frame without coordination, creating severe multi-user interference, making signal extraction and parameter estimation extremely difficult.

2. Methodology and System Model

The authors propose a system model called UNISAC (Unsourced Integrated Sensing and Communications).

System Setup:
- A BS equipped with an $M$ -element Uniform Linear Array (ULA).
- Two types of users: Communication users (transmitting bit sequences) and Sensing users (transmitting signals for detection/AOA estimation).
- Codebook Structure: A shared codebook $A$ is used. Communication users select rows from the first $2^{B_c}$ rows; sensing users select rows from the last $2^{B_s}$ rows.
- Transmission: All active users transmit simultaneously over a frame of length $n$ .
Signal Model: The received signal $Y$ is a superposition of steering vectors (dependent on AOA) multiplied by codewords, plus additive Gaussian noise.
Performance Metrics:
- Per-User Probability of Error ( $\epsilon$ ): A composite metric including missed detection, collisions, and decoding errors for both user types.
- Mean Squared Error of AOA ( $\Delta$ ): The estimation error for the angles of detected sensing users.

3. Key Contributions

The paper derives approximate achievable bounds for the performance of the UNISAC system and validates them against conventional approaches.

A. Theoretical Derivation (Proposition 1)

The authors derive upper bounds for the error probability ( $\epsilon$ ) and AOA estimation error ( $\Delta$ ) based on three primary error sources:

Power Constraint Violation ( $P_{cons}$ ): Probability that a user's signal exceeds power limits.
Collision ( $P_{coll}$ ): Probability that multiple users select the same codeword.
Missed Detection ( $P_{md}$ ): Probability that the decoder fails to identify active users due to interference.

Decoding Strategy: The receiver employs a Maximum Likelihood (ML)-like approach (approximated via least squares) to identify the set of active codewords that minimizes the projection of the received signal onto the null space of the candidate codewords.
AOA Estimation: Once active signals are detected, the system uses a Least Squares (LS) estimator to estimate the steering vectors, from which the AOA is derived.
Bounds: The paper provides closed-form approximations for the probability of missed detection and collision, utilizing random coding arguments and Chernoff bounds. It also derives an upper bound for the MSE of AOA estimation, showing how it scales with the number of antennas ( $M$ ) and signal-to-noise ratio.

B. Comparative Analysis

The proposed UNISAC model is benchmarked against four conventional strategies:

TDMA (Time Division Multiple Access): Users transmit in separate time slots.
TIN (Treat Interference as Noise): Users transmit simultaneously, but the receiver treats all other signals as noise.
ALOHA: Users randomly select time slots; collisions result in packet loss.
TDMA-MUSIC: A hybrid where communication uses TDMA and sensing uses the MUSIC algorithm for AOA estimation.

4. Numerical Results

Simulations were conducted with parameters: $B_c=100$ bits, $M=5$ antennas, and $n=5000$ channel uses. The target was a per-user error probability of $\epsilon_0 = 0.1$ and AOA MSE of $\Delta_0 = 5 \times 10^{-4}$ .

Energy Efficiency: The UNISAC model requires significantly lower $E/N_0$ (energy per bit to noise density) compared to TDMA, ALOHA, TIN, and TDMA-MUSIC as the number of active users increases.
Scalability:
- TDMA-MUSIC fails when the number of sensing users exceeds the number of antenna elements ( $M$ ), as the MUSIC algorithm cannot resolve more sources than sensors.
- ALOHA and TIN suffer from dense collisions and high interference in massive access scenarios, leading to poor performance.
- UNISAC effectively mitigates collisions and interference by leveraging the structure of the unsourced codebook and joint processing, allowing it to support a much larger number of active users.
AOA Estimation: The derived achievable bound for AOA MSE closely matches the "optimistic" lower bound, indicating that the UNISAC scheme operates near the theoretical capacity limit for angle estimation in this regime. Increasing the number of antennas ( $M$ ) significantly improves AOA estimation accuracy.

5. Significance and Conclusion

Theoretical Advancement: This work establishes the first fundamental limits for ISAC in an unsourced random access setting, bridging the gap between communication theory and radar/sensing theory in massive IoT scenarios.
Practical Impact: It demonstrates that joint ISAC processing is superior to separating sensing and communication tasks (e.g., via TDMA) or treating them independently. This is crucial for 6G networks where spectrum efficiency and low latency are paramount.
Robustness: The UNISAC model proves robust against the "curse of dimensionality" in massive access, offering a viable solution for connecting millions of devices without the overhead of user scheduling or identity management.

In summary, the paper proves that UNISAC is a superior architecture for future massive networks, capable of simultaneously decoding data and sensing the environment with higher spectral efficiency and lower energy consumption than traditional multiple-access schemes.