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Target Sensing with Intelligent Reflecting Surface: Architecture and Performance

Xiaodan Shao, Changsheng You, Wenyan Ma, Xiaoming Chen, Rui Zhang

arXiv:2201.09091v2eess.SP

TL;DR

Conventional sensing can suffer interference, path loss, and blockages, motivating a self-sensing IRS with nearby probing and receiving hardware. The paper combines both direct and IRS-reflected echoes with MUSIC, optimizes passive reflection through received power, and reports stronger sensing performance than benchmarks.

  • Problem

    Conventional wireless sensing faces interference, product-distance path loss, and blockages, while IRS sensing has been studied less for self-localizing nearby targets.

  • Method

    The paper uses an IRS controller to transmit probing signals, dedicated IRS sensors to receive direct and IRS-reflected echoes, and MUSIC with passive-reflection optimization for DOA estimation.

  • Results

    The proposed scheme outperforms benchmark sensing schemes across the transmit-power range in RMSE, while successful-estimation probability increases with transmit power and IRS reflecting elements.

  • Takeaways & Limitations

    Self-sensing hardware at the IRS can estimate nearby-target direction without involving the BS or a mobile device.

Abstract

from arXiv · show

Intelligent reflecting surface (IRS) has emerged as a promising technology to reconfigure the radio propagation environment by dynamically controlling wireless signal's amplitude and/or phase via a large number of reflecting elements. In contrast to the vast literature on studying IRS's performance gains in wireless communications, we study in this paper a new application of IRS for sensing/localizing targets in wireless networks. Specifically, we propose a new self-sensing IRS architecture where the IRS controller is capable of transmitting probing signals that are not only directly reflected by the target (referred to as the direct echo link), but also consecutively reflected by the IRS and then the target (referred to as the IRS-reflected echo link). Moreover, dedicated sensors are installed at the IRS for receiving both the direct and IRS-reflected echo signals from the target, such that the IRS can sense the direction of its nearby target by applying a customized multiple signal classification (MUSIC) algorithm. However, since the angle estimation mean square error (MSE) by the MUSIC algorithm is intractable, we propose to optimize the IRS passive reflection for maximizing the average echo signals' total power at the IRS sensors and derive the resultant Cramer-Rao bound (CRB) of the angle estimation MSE. Last, numerical results are presented to show the effectiveness of the proposed new IRS sensing architecture and algorithm, as compared to other benchmark sensing systems/algorithms.

I. INTRODUCTION

The paper proposes an IRS-self-sensing architecture for nearby-target localization, addressing path loss and interference limitations in conventional sensing systems. It combines IRS-generated probing, dedicated IRS sensors, both echo links, and MUSIC-based DOA estimation.

  • 6G location-aware applications require high-precision sensing alongside stringent wireless communication performance.
  • Conventional BS sensing suffers transmit-receive interference and deteriorating localization performance from product-distance path loss and blockages.
  • The proposed IRS-self-sensing system uses an IRS controller near the reflecting elements to illuminate nearby targets with reflected beams.
  • Dedicated IRS sensors receive both the two-hop IRS-reflected echo and one-hop direct echo, enabling customized MUSIC-based target DOA estimation.
  • The system is designed to improve path loss and DOA resolution while avoiding involvement from a distant BS in the sensing architecture.
  • The modeled IRS contains reflecting elements, a probing controller, and adjacent sensors for estimating target azimuth and elevation angles.

A. Radar Channel Model

The radar channel model represents target echoes, clutter, controller-sensor coupling, and noise for an IRS with controllable reflecting elements and colocated sensing hardware.

  • The controller transmits probing signals over T snapshots while channels remain static, and sensors receive target echoes with and without IRS reflection.
  • The single-target model can extend to multiple sufficiently separated targets, whereas closely located targets require techniques such as spatial smoothing.
  • The IRS-reflected echo follows the controller→IRS elements→target→IRS sensors path and is parameterized by the IRS reflection vector.
  • Each IRS reflection coefficient has unit amplitude and a controllable phase shift, enabling dynamic passive beamforming across reflecting elements.
  • The direct echo follows the controller→target→IRS sensors path, with propagation gains determined by the associated distances and target scattering.
  • The received sensor signals include target and clutter echoes, the controller-to-sensor channel, and additive complex Gaussian noise.

B. Proposed Protocol for IRS-enabled Target Angle Estimation

The protocol estimates the target azimuth from cleaned multi-snapshot sensor observations while coordinating horizontal and vertical IRS reflection vectors. The two echo links share the target angle at the sensors.

  • The signal model focuses on azimuth estimation within a selected range-Doppler bin, with range and Doppler parameters omitted.
  • Offline training estimates static background channels for available reflection patterns, followed by online interference removal and target-angle estimation.
  • The IRS reflection vector is factorized into horizontal and vertical components to facilitate passive-reflection design over space and time.
  • The target DOA θ is estimated from the processed observations across T snapshots using MUSIC.
  • The two echo links arrive from the same echo angle, which supports enhanced DOA estimation compared with conventional radar arrangements.

III. IRS PASSIVE REFLECTION DESIGN AND DOA ESTIMATION

The paper applies MUSIC to the IRS sensor covariance structure, using signal and noise subspaces to estimate the target DOA. The estimate is obtained by maximizing the MUSIC spectrum.

  • The received sensor snapshots are stacked into a matrix Y containing the target steering vector, reflection-dependent amplitudes, and noise.
  • The ULA-based azimuth procedure can extend to elevation estimation with a UPA by sequentially fixing one reflection dimension and tuning the other.
  • MUSIC decomposes the covariance matrix into signal and noise subspaces whose orthogonality identifies the target steering direction.
  • The target DOA is estimated by finding the angle that maximizes the MUSIC spectrum.

B. IRS Reflection Design

Because MUSIC angle-estimation MSE is difficult to characterize, the paper designs IRS reflections by maximizing average received echo power without prior target-location knowledge. The optimal design is an orthogonal unit-modulus reflection matrix, exemplified by a truncated DFT matrix that produces an omnidirectional sensing beampattern.

  • Design objective: The reflection design maximizes average received echo power at IRS sensors because MUSIC-based DOA estimation MSE is difficult to characterize directly.The optimization is equivalently formulated as maximizing tr(R_ϕB) under worst-case target-direction uncertainty.
  • Design objective: The optimization seeks passive reflection vectors that maximize tr(R_ϕB) for any target direction while avoiding dependence on prior target-location knowledge.The formulation uses the worst case with respect to B and excludes the trivial B = 0 solution.
  • Optimal reflection: The optimal reflection covariance satisfies R_ϕ = I_N, requiring an orthogonal reflection matrix with unit-modulus entries.This condition is achievable when the reflection matrix has sufficient snapshots and satisfies T ≥ N.
  • Optimal reflection: A truncated T × T DFT matrix with T ≥ N provides one optimal passive reflection matrix under the orthogonality and unit-modulus constraints.The construction concatenates the first N columns of the DFT matrix.
  • Sensing implication: The optimal reflection generates an omnidirectional angular beampattern, enabling target-direction scanning across all possible directions.The random phase difference between IRS-reflected and non-reflected signals does not affect average estimation performance.

IV. PERFORMANCE ANALYSIS

The performance analysis compares the IRS-reflected and direct echo links through their average received powers at IRS sensors. It establishes that the IRS-reflected link grows with the number of reflecting elements and can dominate the direct link when that number is sufficiently large.

  • IRS-reflected versus direct echo links: The analysis characterizes the average received powers of the IRS-reflected and direct echo links at the IRS sensors.These powers are denoted by P_r and P_d, respectively.
  • IRS-reflected versus direct echo links: The average power of the IRS-reflected echo link increases linearly with the number N of IRS reflecting elements.This is the principal scaling result stated by Lemma 1.
  • IRS-reflected versus direct echo links: The IRS-reflected echo link exceeds the direct echo link in average received signal power when the number of IRS reflecting elements is sufficiently large.The threshold condition is stated in Lemma 2, although its explicit expression is not included here.
  • IRS-reflected versus direct echo links: Placing the IRS controller closer to the reflecting elements is desirable because it reduces path loss on the controller-to-IRS-elements link.This placement helps exploit the gain of the IRS-reflected echo link when the reflecting-element count is sufficiently large.

2) IRS controller versus mobile user for sending probing signals:

The paper compares controller-based probing with a mobile-user-assisted IRS sensing system as the user position varies. Controller-based probing avoids the random availability and location of the assisting user, yielding more predictable estimation performance.

  • Controller versus mobile user: The proposed architecture achieves better estimation performance than a benchmark system requiring a nearby mobile user to transmit probing signals.The benchmark’s estimation performance critically depends on the assisting user’s location.
  • User-position dependence: For 0 < d_UI < d_IT, the user-aided system’s combined-channel power includes contributions from both IRS-reflected and direct echo links.The analysis characterizes the effects of d_UI on P_r, P_d, and the combined power P_c.
  • User-position dependence: When the mobile device is near the IRS, IRS passive beamforming makes the IRS-reflected echo link much stronger than the direct echo link on average.When the device is near the target instead, the direct echo link benefits from the shorter user-to-target path while the IRS-reflected link is severely attenuated.
  • Numerical example: For N = 64 and d_IT = 30 m, the two links have equal sensor signal power and equal MSE at d_UI = 0.47 m.As d_UI increases, combined received power first decreases and then increases.
  • Numerical example: The combined received power reaches its minimum at d_UI = 1.7852 m, which also produces the maximum MSE.This result follows by setting the derivative of the combined power to zero.
  • Controller versus mobile user: Using the IRS controller as the probing transmitter avoids dependence on random mobile-user availability and location, offering more predictable estimation performance.This is equivalent to the short user-to-IRS-distance case in the user-aided comparison.

B. Cramer-Rao Bound

The paper derives a CRB for target DOA estimation in the IRS self-sensing system and analyzes how IRS sensors and reflecting elements affect estimation performance.

  • Cramer-Rao Bound: The CRB characterizes a lower bound on the DOA estimation MSE when the MUSIC algorithm’s MSE is difficult to obtain.The analysis also provides insight into the effects of IRS reflecting elements and sensors.
  • Cramer-Rao Bound: The theorem gives the CRB for target DOA estimation in equation (31).The theorem statement introduces the bound whose terms are interpreted through the direct and IRS-reflected echo links.
  • Cramer-Rao Bound: The CRB decreases as the number of IRS sensors M and reflecting elements N increase.The denominator includes contributions from the IRS-reflected echo link, direct echo link, and their combined effect.
  • Cramer-Rao Bound: When |αCIηr|2 is small, a large N is needed to compensate for severe path loss in the two-hop IRS-reflected echo link.Increasing M improves performance by boosting estimation SNR over both echo links.

V. NUMERICAL RESULTS

Numerical results evaluate the IRS self-sensing system against conventional and IRS-assisted benchmarks across transmit power, sensor count, reflecting elements, and sensing distance. The proposed scheme generally benefits from shorter propagation paths, combined echo links, and increasing IRS beamforming gain.

  • Transmit power: The proposed IRS self-sensing scheme achieves superior RMSE performance across the entire transmit-power range.Its shorter controller-to-target-to-sensor path and simultaneous use of direct and IRS-reflected echo links explain the reported advantage over BTB, BITS, BTS, and BITIB.
  • Transmit power: The proposed scheme attains a much higher successful-estimation probability than the benchmark schemes as transmit power increases.Higher transmit power increases received SNR at the BS or sensors.
  • Number of IRS sensors: Increasing the number of IRS sensors M decreases NMSE and increases successful-estimation probability for all schemes.The proposed system requires fewer sensors for high DOA accuracy than BITS, BTS, and MUS, with a threshold beyond which its success probability is higher.
  • Number of IRS reflecting elements: Increasing the number of IRS reflecting elements N decreases the proposed scheme’s NMSE and increases its successful-estimation probability.The proposed scheme first improves rapidly and then more slowly as N becomes sufficiently large, while benchmark gains are limited by path loss.
  • Sensing distance: The proposed scheme maintains small NMSE at long sensing distances, whereas other benchmarks perform poorly when the target is far from the IRS or sensors.The short-distance IRS-controller link supports received power, and the proposed reflection design outperforms random-phase reflection by producing an omnidirectional beampattern.
  • CRB comparison: At sufficiently large transmit power, the MUSIC-based NMSE approaches the CRB obtained in Theorem 1.A notable gap remains in the low-transmit-power regime.

VI. CONCLUSION

The paper concludes that IRS self-sensing can estimate nearby-target DOA using an IRS controller, dedicated IRS sensors, and both direct and IRS-reflected echoes. It optimizes passive reflection for received echo power and derives a corresponding CRB.

  • Conclusion: The proposed architecture uses the IRS controller for probing signals and dedicated IRS sensors for angle estimation without a BS or mobile device.The sensors receive target-reflected signals with and without IRS reflection.
  • Conclusion: The IRS passive reflection matrix is optimized to maximize average received signal power at the IRS sensors, leading to minimum MSE.The paper also derives the CRB for target DOA estimation.
  • Conclusion: The analysis shows benefits from using the IRS controller instead of a helping mobile device at a random location for transmitting probing signals.The conclusion connects this design choice with the proposed system’s analytical performance characterization.

APPENDIX A PROOF OF THEOREM 1

The appendix derives the Fisher information matrix and angle-estimation result by reformulating the received-signal model through sufficient statistics, transformations, and array-response properties.

  • Signal model: The received sensor signal is modeled as an independent CSCG vector whose mean depends on the unknown angle, complex amplitude, and transformed probing signal.The model uses ξα_CIη_r b(θ)q^T(θ)(ϕ[t]+c) as the mean and σ^2I as the covariance.
  • Parameterization: The unknown parameter vector comprises the direction of arrival θ and the real and imaginary parts of the complex amplitude ξ.The amplitude parameter is represented as ¯ξ = [ℜ{ξ}, ℑ{ξ}]^T.
  • Fisher-information derivation: A sufficient-statistic matrix replaces the full log-likelihood to reduce the dimensionality and computational complexity of Fisher-information analysis.The derivation then decomposes the relevant matrix using singular value decomposition into eigenvectors and eigenvalues.
  • Fisher-information derivation: Orthogonality properties are used to calculate the Fisher-information blocks for θ and ¯ξ before substituting them into the target result.The proof evaluates f_θθ, f_θ¯ξ, and f_¯ξ¯ξ and then combines them to obtain the stated theorem expression.
  • Proof completion: The appendix completes the theorem proof by applying transformations and array-response identities involving c, R_ϕ, q(θ), and the angle-dependent functions ς(θ) and ¯ς(θ).The final substitutions into the preceding expressions lead to the desired result in (31).
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