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Location Sensing and Beamforming Design for IRS-Enabled Multi-User ISAC Systems

Zhouyuan Yu, Xiaoling Hu, Chenxi Liu, Mugen Peng, Caijun Zhong

arXiv:2208.05300v1cs.ITeess.SP

TL;DR

The paper addresses simultaneous multi-user communication and localization with IRSs using shared time-frequency resources. It proposes a distributed semi-passive IRS framework with communication-signal-based sensing and location-informed beamforming, achieving millimeter-level localization and communication performance comparable to perfect-CSI, continuous-phase benchmarks.

  • Problem

    Existing IRS-aided communication and localization designs often treat the functions separately, while joint designs may allocate different time slots; the paper seeks simultaneous operation using the same time-frequency resources.

  • Method

    The paper designs an ISAC/PC transmission protocol, senses user locations from uplink communication signals without dedicated positioning references, and uses those locations for discrete-phase beamforming without CSI acquisition.

  • Results

    The sensing algorithm achieves millimeter-level positioning accuracy, and the proposed beamforming achieves similar performance to a perfect-CSI, continuous-phase benchmark.

  • Takeaways & Limitations

    Sensed location information can support high-accuracy multi-user localization and communication beamforming in the proposed IRS-enabled ISAC framework.

Abstract

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This paper explores the potential of the intelligent reflecting surface (IRS) in realizing multi-user concurrent communication and localization, using the same time-frequency resources. Specifically, we propose an IRS-enabled multi-user integrated sensing and communication (ISAC) framework, where a distributed semi-passive IRS assists the uplink data transmission from multiple users to the base station (BS) and conducts multi-user localization, simultaneously. We first design an ISAC transmission protocol, where the whole transmission period consists of two periods, i.e., the ISAC period for simultaneous uplink communication and multi-user localization, and the pure communication (PC) period for only uplink data transmission. For the ISAC period, we propose a multi-user location sensing algorithm, which utilizes the uplink communication signals unknown to the IRS, thus removing the requirement of dedicated positioning reference signals in conventional location sensing methods. Based on the sensed users' locations, we propose two novel beamforming algorithms for the ISAC period and PC period, respectively, which can work with discrete phase shifts and require no channel state information (CSI) acquisition. Numerical results show that the proposed multi-user location sensing algorithm can achieve up to millimeter-level positioning accuracy, indicating the advantage of the IRS-enabled ISAC framework. Moreover, the proposed beamforming algorithms with sensed location information and discrete phase shifts can achieve comparable performance to the benchmark considering perfect CSI acquisition and continuous phase shifts, demonstrating how the location information can ensure the communication performance.

I. INTRODUCTION

The paper proposes a distributed semi-passive IRS framework for simultaneous multi-user uplink communication and localization using shared time-frequency resources. It combines communication-signal-based sensing with location-informed beamforming under discrete phase shifts.

  • I. INTRODUCTION: The framework uses an ISAC period for simultaneous communication and localization, followed by a pure communication period for uplink data transmission.During the ISAC period, passive reflecting and semi-passive sensing sub-IRSs operate across two time blocks; sensed locations guide later beamforming.
  • I. INTRODUCTION: The sensing algorithm estimates effective AoA pairs and path losses from uplink communication signals, then matches them to determine multiple users’ locations.This removes the need for dedicated positioning reference signals.
  • I. INTRODUCTION: The proposed beamforming algorithms use sensed locations and discrete phase shifts to maximize sum rate without high-overhead CSI acquisition.Separate algorithms are designed for the ISAC and pure communication periods.
  • I. INTRODUCTION: The location sensing algorithm achieves millimeter-level positioning accuracy, while sensing-based beamforming has similar performance to perfect-CSI, continuous-phase benchmarks.These results support the effectiveness of using sensed location information for communication and localization.
  • I. INTRODUCTION: The system model assumes a distributed semi-passive IRS with discrete phase shifts and quasi-static block-fading user-IRS and IRS-BS channels.The IRS comprises passive reflecting elements, and its phase shifts are selected from a finite quantized set.

2) PC Period:

The PC period uses all IRS sub-surfaces to assist uplink transmission through a quantized phase-shift design based on the IRS-assisted channel model. Its received-signal and achievable-rate formulations depend on the user-IRS and IRS-BS links.

  • 2) PC Period:: During the PC period, the whole IRS assists uplink transmission using a phase-shift matrix formed from the sub-IRS phase-shift vectors.The phase-shift matrix is defined as Θ = diag(ξ), with ξ concatenating the three sub-IRS beams.
  • C. Channel Model: The channel model represents each IRS-to-BS link through a complex gain and array-response vectors, with effective AoDs and AoA determined by array geometry.The wavelength and adjacent-element spacings determine the effective angular parameters.
  • C. Channel Model: The user-to-sub-IRS and inter-sub-IRS channels are likewise characterized by complex gains and effective elevation/azimuth angles.These links provide the channel components used in the distributed IRS model.

III. MULTI-USER LOCATION SENSING

The sensing algorithm extracts effective AoA pairs from received communication signals at two semi-passive sub-IRSs. It combines FBSS preprocessing, TLS-ESPRIT estimation, and MUSIC-based pairing.

  • III. MULTI-USER LOCATION SENSING: The algorithm estimates effective AoA pairs at two semi-passive sub-IRSs from received communication signals using FBSS, TLS-ESPRIT, and MUSIC.FBSS preprocesses the signals; TLS-ESPRIT estimates AoAs along the two axes, and MUSIC pairs the axis-specific estimates.
  • 1) Preprocess the received signals by using the FBSS technique:: Each micro-surface contains Qy,i × Qz,i semi-passive elements, with shifted micro-surfaces constructed along the z or y direction.The construction provides multiple overlapping micro-surfaces for processing the received signals.
  • 1) Preprocess the received signals by using the FBSS technique:: The received signal at each micro-surface is represented through its auto-correlation matrix before signal-subspace decomposition and effective-AoA estimation.The auto-correlation matrix is defined from the received micro-surface signals, and its eigendecomposition supplies the relevant subspaces.
  • 2) Estimate effective AoAs by using TLS-ESPRIT: Two auxiliary sub-surfaces are constructed for TLS-ESPRIT estimation, each containing (Qy,i −1) × Qz,i semi-passive elements and at least K+2 elements.The auxiliary-sub-surface signal subspace is used to estimate effective AoAs associated with the y-axis.
  • 3) Pair the effective AoAs: A second auxiliary-sub-surface construction estimates effective AoAs along the z axis, after which MUSIC pairs the y- and z-axis estimates.The z-axis construction uses Qy,i × (Qz,i −1) semi-passive elements.

5) Determine the AoA pairs corresponding to the links from users to semi-passive sub-IRSs:

Known BS and sub-IRS locations allow the algorithm to remove the inter-sub-IRS AoA pair and retain the pairs associated with the users.

  • 5) Determine the AoA pairs corresponding to the links from users to semi-passive sub-IRSs:: Because the BS and sub-IRS locations are known, the effective AoAs of the passive-sub-IRS-to-semi-passive-sub-IRS links can be calculated.These known-link AoAs are used to identify the non-user path.
  • 5) Determine the AoA pairs corresponding to the links from users to semi-passive sub-IRSs:: After excluding the AoA pair corresponding to the inter-sub-IRS link, each semi-passive sub-IRS retains K effective AoA pairs corresponding to K users.The retained sets are denoted A_i for i=2,3.

B. Determine users’ locations

User locations are inferred by combining AoA pairs from the two semi-passive sub-IRSs with estimated path losses. The resulting candidate locations are evaluated using a distance-dependent path-loss model.

  • B. Determine users’ locations: The method combines AoA pairs from the two semi-passive sub-IRSs to calculate possible user locations and their corresponding path losses.For each AoA pairing, the location equations yield a candidate position whose path loss can be computed.
  • 1) Estimate the path loss corresponding to each pair of effective AoAs:: The received signal model separates passive-sub-IRS interference, user-to-semi-passive-sub-IRS signals, and additive white Gaussian noise.This decomposition supports path-loss estimation from the received-signal statistics.
  • 1) Estimate the path loss corresponding to each pair of effective AoAs:: The signal vector contains K user symbols and a final constant component representing the passive-sub-IRS contribution.The diagonal covariance terms correspond to the user-link and passive-sub-IRS path-loss magnitudes.
  • 2) Estimate all possible users’ locations and their corresponding path losses:: For each candidate location, the algorithm calculates distance-dependent path loss using the log-distance model with path-loss exponent ǫU2I.The reference distance d0 and user-to-IRS path-loss exponent are model parameters.

3) Simultaneous multi-user location sensing through AoA matching:

AoA matching pairs the user-related estimates from the two semi-passive sub-IRSs by comparing estimated and candidate path losses. The sensed locations then support sensing-based beamforming.

  • 3) Simultaneous multi-user location sensing through AoA matching:: The AoA matching algorithm pairs effective AoAs from the two semi-passive sub-IRSs so that each pair corresponds to the same user.It compares estimated path losses with path losses calculated for candidate locations.
  • 3) Simultaneous multi-user location sensing through AoA matching:: After K iterations, the matching procedure outputs the estimated locations of all K users.Each selected match is removed from the remaining candidate index set before the next iteration.
  • IV. SENSING-BASED JOINT ACTIVE AND PASSIVE BEAMFORMING: The sensed locations are used to design beamforming for both the ISAC and pure-communication periods, avoiding high-overhead channel estimation.The ISAC-period design uses MRC at the BS and a cross-entropy algorithm for the passive-sub-IRS phase shifts.
  • 3) Simultaneous multi-user location sensing through AoA matching:: The complete sensing procedure estimates AoAs, estimates their path losses, generates candidate user locations, and selects the final locations through AoA matching.These stages are summarized in Algorithm 2.

1) BS combining vectors optimization:

The ISAC-period design first derives BS combining vectors using MRC, then optimizes discrete IRS phase shifts using sensed user locations and iterative candidate selection.

  • BS combining vectors optimization:: MRC derives the combining vector for each user, reducing the original problem to optimizing the IRS phase-shift matrix.The resulting combining matrix simplifies the subsequent optimization to the IRS phase-shift design.
  • BS combining vectors optimization:: The second ISAC time block designs phase shifts using user locations sensed in the first time block.The first time block initializes the phase-shift design because location information is unavailable initially.
  • BS combining vectors optimization:: The algorithm randomly generates discrete ISAC phase-shift candidates, evaluates their sum rates, and retains elite samples.Their probability matrix is updated iteratively until the rate range falls below threshold κ.
  • BS combining vectors optimization:: Algorithm 3 outputs the optimized phase-shift matrix after the probability distribution stabilizes.The procedure repeatedly samples candidates and updates the probability matrix during the second ISAC time block.

B. PC Period

During the PC period, all sub-IRSs assist uplink transmission while the system estimates phase ambiguities from early received-signal-strength measurements before optimizing sum rate.

  • B. PC Period: The PC period formulates joint active and passive beamforming as maximizing the users’ sum rate over BS combining and IRS phase shifts.The objective is represented by optimization problem (P2).
  • B. PC Period: During the first C PC time slots, fixed combining and randomly generated phase-shift beams provide received-signal-strength measurements.The number of measurement slots is much smaller than the PC-period duration, C ≪ T2.
  • B. PC Period: Measured and candidate received signal strengths are compared to remove channel-gain phase ambiguity before remaining-period beamforming.This enables sum-rate calculation in the remaining PC time slots.
  • B. PC Period: The algorithm enumerates 4Kb_Δ possible relative phase configurations and calculates the corresponding BS received signal strength.The configurations use discrete phase shifts from F_Δ under the continuous-phase approximation for sufficiently large quantization.

2) Joint active and passive beamforming:

The PC beamforming algorithm samples discrete IRS phase-shift matrices, computes ZF combining and sum rates, retains elite candidates, and iteratively updates their probability distribution.

  • Joint active and passive beamforming:: For each sampled PC phase-shift matrix, the algorithm forms the effective channel and computes BS combining vectors using ZF.It then evaluates the corresponding sum rate for that candidate.
  • Joint active and passive beamforming:: The algorithm selects PC candidates with the largest sum rates and updates the phase-shift probability matrix from those elite samples.This sampling-and-update process is repeated across iterations.
  • Joint active and passive beamforming:: Iterations stop when the difference between the maximum and minimum candidate sum rates falls below κ, producing Θopt(t) and Wopt(t).Algorithm 4 specifies the stopping condition and outputs the selected phase shifts and combining matrix.
  • Joint active and passive beamforming:: The proposed ISAC- and PC-period beamforming algorithms use sensed locations instead of perfect CSI, avoiding high channel-estimation overhead.This is the stated distinction from CSI-dependent IRS-aided beamforming.

V. SIMULATION RESULTS

The simulations evaluate multi-user location sensing and joint beamforming in a three-sub-IRS geometry with users distributed across a ninety-degree floor sector.

  • V. SIMULATION RESULTS: The simulation places K users in a ninety-degree horizontal-floor sector, with the BS 20 m above the floor and sub-IRSs 5 m, 7 m, and 9 m high.These parameters define the main three-dimensional deployment geometry.
  • V. SIMULATION RESULTS: Fig. 5 depicts the simulation setup from a top view.The figure provides the spatial layout used for the numerical evaluation.

A. Performance of Multi-User Location Sensing

The proposed multi-user location sensing algorithm improves localization with greater transmit power or sensing time, while additional users and longer user–IRS distances reduce accuracy. With 400 semi-passive elements, it achieves millimeter-level localization accuracy with 90% probability.

  • Transmit power and user count: Localization accuracy improves as transmit power increases but decreases sixfold when the user count rises from 2 to 3.More users require the semi-passive IRS to distinguish more user–IRS paths, reducing effective AoA estimation accuracy.
  • Sensing time and distance: Increasing sensing time reduces location RMSE, while longer user–IRS distances degrade accuracy.When dU2I,2 increases from 10 m to 15 m, increasing τ1 from about 20 to 90 keeps RMSE at 10^-2.
  • CDF-based accuracy: With 400 semi-passive elements, the proposed algorithm achieves millimeter-level localization accuracy with 90% probability.Across all tested element configurations, at least 3 cm accuracy is achieved with 90% probability.

B. Performance of the Proposed Sensing-Based Beamforming Algorithms

The sensing-based beamforming algorithms use sensed locations and discrete phase shifts to approach perfect-CSI continuous-phase benchmarks, while performance depends on IRS resources and time allocation. Higher transmit power favors shorter sensing periods because adequate localization accuracy is reached sooner.

  • Beamforming comparison: The proposed discrete-phase beamforming with sensed locations achieves comparable sum-rate performance to perfect-CSI continuous-phase AO and outperforms random phase shifts.This comparison is reported for both the ISAC and PC periods as IRS reflecting elements increase.
  • Beamforming comparison: The PC-period sum rate is much larger than the ISAC-period sum rate because more distributed sub-IRSs assist uplink transmission in the PC period.The additional assisting sub-IRSs provide a larger spatial multiplexing gain.
  • User-number sensitivity: All evaluated beamforming algorithms degrade as the number of users increases under fixed total transmit power.For AO and random phase shifts, the degradation is attributed to increased inter-user interference.
  • ISAC-period time allocation: The optimal sensing-block fraction decreases with transmit power because higher power provides sufficient positioning accuracy in less time.Too little sensing time still degrades communication by reducing localization accuracy for subsequent beamforming.
  • Whole-period time allocation: The optimal ISAC-period fraction decreases from about 1 at −5 dBm to 0.2 at 5 dBm and approaches 0 at 25 dBm.At low power, sensing and communication should occupy the whole transmission period; at high power, adequate sensing accuracy is achieved quickly.
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