⚡ electrical engineering

Inference-Optimal ISAC via Task-Oriented Feature Transmission and Power Allocation

This paper proposes a task-oriented ISAC framework that optimizes inference performance by maximizing discriminant gain through closed-form transceiver designs and power allocation, demonstrating superior power efficiency over traditional MSE-based approaches, particularly in low SNR regimes.

Original authors: Biao Dong, Bin Cao, Qinyu Zhang

Published 2026-05-21

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CC BY 4.0

Original authors: Biao Dong, Bin Cao, Qinyu Zhang

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 you have a smart robot that needs to do two things at once: look at an object to figure out what it is (Sensing), and tell a distant computer exactly what it saw (Communication). This is the world of ISAC (Integrated Sensing and Communication).

Usually, engineers treat these two jobs separately. They try to make the "look" as clear as possible and the "tell" as accurate as possible, often by trying to minimize the "blur" or "noise" in the signal. They use a standard rule: "Make the picture as close to the original as possible."

This paper asks a different question: "Does making the picture look exactly like the original actually help the computer guess what the object is?"

The authors say: Not necessarily. Sometimes, a slightly blurry picture that highlights the important parts is better for guessing than a perfectly clear picture that wastes energy on unimportant details.

Here is the breakdown of their idea using simple analogies:

1. The "Compress-and-Check" Strategy

Instead of the robot trying to do complex math to identify the object itself (which uses too much battery), it takes a quick snapshot, picks out the most important features (like "it has wings" or "it is red"), and sends just those features to a powerful computer in the cloud. This is called the Compress-and-Estimate (CE) framework.

2. The Old Way vs. The New Way

The Old Way (MSE-Optimal): Imagine you are sending a photo of a cat to a friend. The old method tries to send the photo with the highest possible resolution, ensuring every whisker is perfect. It spreads its energy evenly to make the whole image "clear."
The New Way (DG-Optimal): The new method asks, "What does my friend actually need to know to tell a cat from a dog?" It realizes that the shape of the ears and the tail are crucial, but the exact shade of fur on the belly doesn't matter. So, it saves energy by ignoring the belly and spends extra energy to make sure the ears and tail are crystal clear.

The authors call this "Discriminant Gain" (DG). It's a measure of how easy it is to tell two things apart.

3. The "Water Filling" Analogy

The paper describes how they decide where to send power using a concept called "Water Filling."

Imagine you have a bucket of water (your total energy budget) and a set of cups (the different features of the object).
The Old Method (MSE): Pours water evenly into all cups until they are full, regardless of whether the cup is big or small.
The New Method (DG): Looks at the cups. Some cups hold "important" information (like the cat's ears), and some hold "useless" information. It pours all the water into the important cups and leaves the useless ones dry. If a feature isn't helpful for telling the difference, it gets zero power.

4. The Big Win: Saving Energy for the "Look"

Here is the clever part. Because the new method is so efficient at sending the "tell" message (it uses less power to get the same result), it saves energy.

Since the robot has a fixed total battery, the energy saved on the "tell" part can be moved to the "look" part.

Result: The robot can use the saved power to take a better, clearer picture of the target in the first place.
Why it matters: This is especially helpful when the signal is weak (like in a foggy room or far away). The old method struggles because it wastes energy on details that don't help the guess. The new method focuses only on what matters, making the whole system smarter and more power-efficient.

5. What the Experiments Showed

The authors tested this with a dataset of human postures (like standing, sitting, or waving).

They found that in low-power situations, their new method was much better at correctly identifying the posture.
The old method (trying to be perfectly clear) often wasted power on features that didn't help distinguish between "sitting" and "standing."
The new method (focusing on what distinguishes them) achieved higher accuracy with less power, leaving more battery for the sensing part.

Summary

Think of this paper as a guide on how to be a smart messenger. Instead of shouting every single detail of a story to ensure accuracy, a smart messenger learns which details are the "plot twists" and focuses their voice on those. By shouting only the important parts, they use less energy, which allows them to listen better to the environment around them.

The paper proves that for machines trying to "guess" what they see, focusing on what makes things different is a better strategy than trying to make everything perfectly clear.

Technical Summary: Inference-Optimal ISAC via Task-Oriented Feature Transmission and Power Allocation

Problem Statement
Integrated Sensing and Communication (ISAC) systems aim to maximize "coordination gain" by jointly optimizing sensing and communication (S&C) resources. While existing literature often focuses on parameter estimation tasks (e.g., angle or velocity) using Estimate-and-Compress (EC) schemes, many complex inference tasks (e.g., pattern recognition) require offloading computation to edge servers due to limited local device capabilities. This necessitates a Compress-and-Estimate (CE) framework where raw or compressed features are transmitted for remote inference.

The core challenge addressed in this work is the design of S&C transceivers under the CE framework to maximize inference performance. Directly optimizing inference metrics (such as classification error probability) is analytically intractable. Consequently, prior works often rely on surrogate metrics like Mean Squared Error (MSE). This paper investigates whether maximizing MSE is optimal for inference tasks or if a metric specifically tailored to classification, such as Discriminant Gain (DG), yields superior performance and resource efficiency.

Methodology
The authors propose a system model where an ISAC device transmits probing signals to detect a target, extracts features from the echo, and forwards these features to a receiver for classification. The system operates under a total power constraint shared between sensing ( $P_r$ ) and communication ( $P_c$ ).

System Modeling:
- Sensing: The device uses Frequency-Modulated Continuous-Wave (FMCW) signals. The echo is processed via pulse compression and Short-Time Fourier Transform (STFT) to generate a time-frequency matrix.
- Feature Extraction: Principal Component Analysis (PCA) is applied to extract a feature vector $\tilde{x} = x + d$ , where $x$ is the ground-truth feature and $d$ is sensing noise. The features are modeled as following a multivariate Gaussian distribution.
- Transmission: Features are transmitted over a block-fading channel using parallel subcarriers. The received signal is scaled to recover the features.
Inference Metric Characterization:
- The paper establishes that the inference error probability ( $P_e$ ) is lower-bounded by a monotonic function of the minimum Discriminant Gain ( $DG_{min}$ ) between classes.
- $DG$ is defined as the Mahalanobis distance between class distributions, normalized by variance. The authors prove that minimizing the error bound is equivalent to maximizing $DG_{min}$ .
Transceiver Design and Optimization:
- Single-Carrier Case: The authors derive closed-form solutions for both MSE-optimal and DG-optimal transceiver designs. They demonstrate that for a single feature dimension, both criteria yield identical performance.
- Multi-Carrier Case: The analysis is extended to multiple feature dimensions ( $M > 1$ $M > 1$ ). The optimization problems for both MSE and DG are formulated as convex problems.
  - MSE-Optimal: Results in a water-filling structure that allocates power based on channel conditions and feature variance.
  - DG-Optimal: Introduces an additional weighting term based on the class separability ( $|\mu_{0,n} - \mu_{1,n}|$ ). This leads to a "selective" power allocation strategy, particularly in low Signal-to-Noise Ratio (SNR) regimes, where power is concentrated on highly discriminative features while potentially turning off uninformative ones.
Joint Power Allocation:
- The paper formulates a joint optimization problem for $P_r$ and $P_c$ . Since maximizing DG is equivalent to maximizing effective sensing power in FMCW systems, the authors propose a one-dimensional search along the power constraint line to find the optimal split between sensing and communication power.

Key Contributions

Theoretical Characterization: The work provides a theoretical analysis linking inference error probability bounds directly to Discriminant Gain, establishing DG as a tractable and relevant metric for ISAC inference tasks.
Closed-Form Solutions: The authors derive explicit transceiver designs for both DG-optimal and MSE-optimal criteria. These solutions reveal water-filling-type structures and highlight the explicit trade-offs between S&C resources.
Power Efficiency Insight: A primary contribution is the revelation that DG-optimal design is more power-efficient than conventional MSE-optimal design, especially in low-SNR regimes. By selectively allocating power to informative features, the DG-optimal approach saves transmit power.
Resource Coordination: The paper demonstrates that the power saved through DG-optimal communication can be reallocated to the sensing function, thereby enhancing the overall coordination gain of the ISAC system.

Results
Numerical experiments were conducted using human posture recognition datasets with Multi-Layer Perceptron (MLP) and Support Vector Machine (SVM) classifiers.

Performance Comparison: In low-SNR regimes, the DG-optimal design significantly outperforms the MSE-optimal design in terms of inference accuracy. The DG-optimal approach achieves higher accuracy with less communication power.
Feature Selection: The results confirm that DG-optimal designs selectively allocate power to features with high discriminative gain, whereas MSE-optimal designs tend to distribute power more uniformly, potentially wasting resources on uninformative features.
Confusion Matrices: DG-optimal designs yield more balanced classification accuracy across different categories compared to MSE-optimal designs.
Power Trade-off: As communication SNR increases, the marginal gain of additional communication power diminishes, and the optimal strategy shifts power toward sensing. The performance gap between DG and MSE designs narrows at high SNR, consistent with theoretical expectations.

Significance
The paper claims that optimizing ISAC systems for inference tasks requires a shift from traditional MSE-based criteria to task-oriented Discriminant Gain maximization. The significance lies in demonstrating that this shift enables more efficient use of the shared power budget. By reducing the power required for communication to achieve a target inference accuracy, the system can allocate the saved power to sensing, thereby improving the overall system performance. This work provides a foundational framework for "inference-oriented" ISAC design, offering closed-form solutions that facilitate practical transceiver implementation and resource management in 6G networks.