⚡ electrical engineering

Low-Complexity Tensor-Based Monostatic Sensing for IRS-Assisted Communication Systems

This paper proposes a low-complexity, higher-order singular value decomposition-based tensor algorithm that jointly estimates target delay, Doppler, and angular information in IRS-assisted monostatic sensing systems, achieving performance comparable to baseline methods while significantly reducing computational cost through parallel processing.

Original authors: Kenneth B. A. Benício, Bruno Sokal, André L. F. de Almeida, Fazal-E-Asim, Behrooz Makki, Gábor Fodor

Published 2026-05-29

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CC BY 4.0

Original authors: Kenneth B. A. Benício, Bruno Sokal, André L. F. de Almeida, Fazal-E-Asim, Behrooz Makki, Gábor Fodor

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 Smart Mirror for Radar

Imagine you are trying to find a lost object in a dark room using a flashlight (the radar). Usually, if there is a wall blocking your view, you can't see the object.

This paper introduces a smart mirror (called an Intelligent Reflecting Surface or IRS) that can be stuck on a wall. This mirror isn't just a piece of glass; it's made of thousands of tiny, programmable tiles. Each tile can twist the light (or radio waves) hitting it in a specific direction.

The goal of this research is to use this smart mirror to help a single device (like a base station) both talk to a phone and find a target (like a car or a person) at the same time. This is called "Integrated Sensing and Communications" (ISAC).

The Problem: The "Search" is Too Slow

To find the target, the system sends out a signal, the signal bounces off the mirror, hits the target, bounces back to the mirror, and returns to the base station. The base station then has to analyze this returning echo to figure out three things:

How far away is the target? (Delay)
How fast is it moving? (Doppler)
Where is it located? (Angle)

In previous methods (the "baseline" mentioned in the paper), the computer had to check every possible combination of distance, speed, and angle all at once.

The Analogy: Imagine trying to find a specific book in a library. The old method is like checking every single shelf, every single row, and every single book on that row, one by one, to see if it's the right one. If the library is huge, this takes forever.

The Solution: A "Tensor" Approach

The authors propose a new way to organize the data. Instead of looking at the signal as a messy pile of numbers, they treat it like a 3D block of data (a "tensor").

The Analogy: Imagine the library again. Instead of checking every book individually, the new method organizes the books into three separate, neat stacks: one stack for "Distance," one for "Speed," and one for "Location."
Because the data is organized this way, the computer can look at the "Distance" stack, the "Speed" stack, and the "Location" stack independently and at the same time (in parallel).

They use a mathematical tool called HOSVD (Higher-Order Singular Value Decomposition). Think of this as a super-efficient librarian who can instantly sort the 3D block of data into those three neat stacks without having to read every single book.

The Results: Faster, Not Slower

The paper compares their new "Smart Librarian" method against the old "Check Every Book" method.

Accuracy: The new method finds the target just as accurately as the old method. The "distance," "speed," and "location" estimates are nearly identical.
Speed (Complexity): This is the big win. The new method is 10 times faster (less computationally complex) than the old one.
- Why? The old method had to do a massive calculation where the difficulty grew by multiplying the number of distance options by the number of speed options. The new method breaks this apart, so the difficulty only grows by adding them together.
- The Analogy: If the old method took 10 hours to search the library, the new method does it in 1 hour, with the same result.

A Small Catch

The paper notes that in extremely noisy conditions (like trying to hear a whisper in a hurricane), the new method is slightly less accurate than the old one. However, in normal conditions, they perform the same, and the new method is much faster.

Summary

The paper presents a clever mathematical trick to organize radar data. By treating the signal as a 3D block and sorting it into separate categories, the system can find targets much faster than before, without losing accuracy. This makes it much more practical to use these smart mirrors in future 6G networks to both communicate and sense the environment simultaneously.

Technical Summary: Low-Complexity Tensor-Based Monostatic Sensing for IRS-Assisted Communication Systems

Problem Statement
The paper addresses the challenge of parameter estimation in Integrated Sensing and Communications (ISAC) systems assisted by Intelligent Reflecting Surfaces (IRS). Specifically, it focuses on a monostatic sensing scenario where a base station (BS) transmits an Orthogonal Frequency Division Multiplexing (OFDM) waveform, which reflects off an IRS, bounces off a target, and returns to the BS. The objective is to jointly estimate the target's delay ( $\tau$ ), Doppler shift ( $\nu$ ), and angular information (Angle of Departure, $\theta$ ).

Existing approaches, such as the baseline method in [11], rely on Generalized Likelihood Ratio Test (GLRT) detectors that require computationally intensive multi-dimensional peak searches (specifically a four-dimensional search over delay, Doppler, azimuth, and elevation). While effective, these methods suffer from high computational complexity, particularly when the search grids for delay and Doppler are coupled, leading to a complexity proportional to the product of the grid sizes ( $R_\tau R_\nu$ ).

Methodology
The authors propose a low-complexity solution that reinterprets the received echo signal as a third-order rank-one tensor. The core methodology involves the following steps:

System Modeling and Signal Recasting: The received signal is modeled considering the BS-IRS-Target-IRS-BS link. To decouple the angular parameters from the Doppler parameter, the authors employ a repetition-based IRS phase-shift protocol. The IRS phase-shift pattern is repeated over a block of $Q$ OFDM symbols and varied across $L$ blocks (total symbols $M=QL$). This structure allows the time-domain steering vector to be decomposed into Kronecker products of vectors related to the block index and the intra-block index.
Tensor Formulation: By exploiting this repetitive structure, the received signal matrix is reformulated as a third-order rank-one tensor $\mathcal{Y} = c(\tau) \circ d_Q(\nu) \circ \beta(\theta, \nu) + \mathcal{Z}$ , where $\circ$ denotes the outer product. This formulation separates the delay vector $c(\tau)$ , the Doppler vector $d_Q(\nu)$ , and the combined angle-Doppler vector $\beta(\theta, \nu)$ .
HOSVD-Based Estimation: The parameter estimation problem is solved using Higher-Order Singular Value Decomposition (HOSVD). The algorithm computes the Singular Value Decomposition (SVD) for the three matrix unfoldings of the received signal tensor. The dominant left singular vectors from these decompositions provide estimates for the delay, Doppler, and angle components.
Peak Search Decoupling: Following the HOSVD stage, the algorithm performs one-dimensional peak searches to estimate delay ( $\tau$ ) and Doppler ( $\nu$ ) independently. The angular estimation ( $\theta$ ) is then performed via a two-dimensional search, utilizing the previously estimated Doppler to simplify the search space.

Key Contributions

Tensor-Based Reformulation: The paper introduces a novel tensor-based representation of the monostatic IRS-assisted sensing signal, transforming a complex multi-dimensional optimization problem into a rank-one tensor approximation problem.
Complexity Reduction: By leveraging the HOSVD algorithm, the proposed method decouples the estimation of delay and Doppler. This allows these parameters to be estimated in parallel via separate one-dimensional searches, breaking the computational bottleneck of the coupled search found in baseline methods.
Algorithm Design: The authors provide a complete algorithm (Algorithm 1) detailing the HOSVD-based parameter estimation process, including specific cost functions for delay, Doppler, and angle estimation.

Results
Simulation results comparing the proposed tensor-based method with the baseline GLRT detector from [11] yield the following findings:

Performance Accuracy: In terms of Root Mean Squared Error (RMSE), the proposed method achieves performance comparable to the baseline.
- For delay and Doppler estimation, the proposed method performs similarly to the baseline at SNR levels higher than -5 dB, with a slight performance degradation observed only in very low SNR regimes.
- For angular estimation, both methods achieve identical RMSE performance across all tested SNR levels, as both utilize a maximum likelihood criterion for the final angle search.
Computational Complexity: The proposed method offers a drastic reduction in computational complexity.
- The baseline complexity scales with the product of the grid sizes ( $R_\tau R_\nu$ ), whereas the proposed method scales with the sum of these sizes ( $R_\tau + R_\nu$ ) due to the decoupling.
- Simulation curves indicate that the baseline method is approximately 10 times more complex than the proposed tensor-based solution. This complexity advantage holds across varying numbers of subcarriers and grid points.

Significance and Claims
The paper claims that its primary contribution is providing a low-complexity alternative to existing high-performance sensing algorithms without sacrificing estimation accuracy in practical SNR ranges. The authors emphasize that their tensor-based solution "drastically reduces the computational complexity" while maintaining "the same performance as the reference method" in terms of RMSE for delay, Doppler, and angle estimation.

The significance lies in the scalability of the solution for future 6G networks, where the integration of sensing and communication requires efficient processing of large datasets. By exploiting the intrinsic multilinear structure of the received signal, the proposed method enables parallel computation, making it a viable candidate for real-time implementation in IRS-assisted ISAC systems. The authors modestly note that the method is slightly more sensitive to very high noise levels but assert that the trade-off is favorable given the substantial gains in computational efficiency. Future work is suggested to investigate the method's performance under the intrinsic self-interference conditions of monostatic sensing, which was excluded from the current scope.