PaperlayerView exact revision on arXiv

Source-linked AI summary

STARS Enabled Integrated Sensing and Communications

Zhaolin Wang, Xidong Mu, Yuanwei Liu

arXiv:2207.10748v3cs.ITeess.SP

TL;DR

The paper addresses sensing in STARS-enabled ISAC despite multi-hop path loss, clutter, and practical phase-shift coupling. It introduces sensing at STARS, derives and optimizes the 2D DOA CRB under communication constraints, and develops PDD-based algorithms for both phase-shift models. STARS outperforms conventional RIS, while coupled phase shifts can approach independent-phase performance in favorable regimes.

  • Problem

    STARS-enabled ISAC must support sensing and communication across separated spaces while mitigating sensing path loss, clutter interference, and practical phase-shift constraints.

  • Method

    The paper installs dedicated sensors at STARS, derives the 2D DOA CRB, reformulates independent-phase optimization through a modified FIM, and applies PDD-based algorithms to both phase-shift models.

  • Results

    STARS significantly outperforms conventional RIS in CRB and 2D DOA estimation, while coupled and independent phase-shift models have similar performance under low communication requirements or sufficient STARS elements.

  • Takeaways & Limitations

    Increasing passive STARS elements is more efficient than increasing sensor elements, and STARS can support high-quality sensing and communication on opposite sides.

Abstract

from arXiv · show

A simultaneously transmitting and reflecting intelligent surface (STARS) enabled integrated sensing and communications (ISAC) framework is proposed, where the whole space is divided by STARS into a sensing space and a communication space. A novel sensing-at-STARS structure, where dedicated sensors are installed at the STARS, is proposed to address the significant path loss and clutter interference for sensing. The Cramer-Rao bound (CRB) of the 2-dimension (2D) direction-of-arrivals (DOAs) estimation of the sensing target is derived, which is then minimized subject to the minimum communication requirement. A novel approach is proposed to transform the complicated CRB minimization problem into a trackable modified Fisher information matrix (FIM) optimization problem. Both independent and coupled phase-shift models of STARS are investigated: 1) For the independent phase-shift model, to address the coupling of ISAC waveform and STARS coefficient in the modified FIM, an efficient double-loop iterative algorithm based on the penalty dual decomposition (PDD) framework is conceived; 2) For the coupled phase-shift model, based on the PDD framework, a low complexity alternating optimization algorithm is proposed to tackle coupled phase-shift constants by alternatively optimizing amplitude and phase-shift coefficients in closed-form. Finally, the numerical results demonstrate that: 1) STARS significantly outperforms the conventional RIS in CRB under the communication constraints; 2) The coupled phase-shift model achieves comparable performance to the independent one for low communication requirements or sufficient STARS elements; 3) It is more efficient to increase the number of passive elements of STARS rather than the active elements of the sensor; 4) High sensing accuracy can be achieved by STARS using the practical 2D maximum likelihood estimator compared with the conventional RIS.

I. INTRODUCTION

The paper proposes STARS-enabled ISAC to divide space into sensing and communication regions while addressing sensing path loss, clutter, and practical phase-shift constraints. It formulates 2D DOA CRB minimization under communication requirements and develops algorithms for independent and coupled phase-shift models.

  • Motivations and Challenges: STARS divides the whole space into sensing and communication half-spaces, allowing sensing targets and communication users to occupy opposite sides of the surface.The BS signal is split at STARS to sense a target in the sensing space and serve users in the communication space.
  • Contributions: The paper derives the 2D DOA CRB and minimizes it under communication SINR constraints for both independent and coupled STARS phase-shift models.The 2D formulation covers azimuth and elevation DOAs rather than azimuth alone.
  • Contributions: For independent phase shifts, an equivalent modified-FIM optimization and a PDD-based iterative algorithm address the coupled waveform and STARS-coefficient design variables.The reformulation makes the CRB problem more trackable.
  • Contributions: For coupled phase shifts, a low-complexity iterative algorithm alternately optimizes STARS amplitude and phase-shift coefficients using closed-form solutions.This addresses the additional nonconvex coupled phase-shift constraints.
  • Contributions: Numerical results show STARS outperforms conventional RIS in ISAC performance, while the two phase-shift models perform similarly under low communication requirements or sufficient STARS elements.Increasing passive STARS elements is reported as more appealing than increasing sensor elements.
  • Motivations and Challenges: A sensing-at-STARS structure mounts dedicated sensors on STARS to address severe multi-hop sensing path loss and clutter from the communication space.The sensor side facing communication users is physically blocked to avoid clutter.

B. Signal Model

The signal model uses a joint BS transmission containing communication streams and a dedicated sensing signal. STARS splits the incident signal toward users and sensing targets, while sensor echoes and user receptions are modeled over a coherent block.

  • Signal Model: The BS transmits a joint signal comprising communication information streams and a dedicated sensing signal.The communication streams use beamforming, while the sensing signal supports full sensing degrees of freedom.
  • Signal Model: The communication transmit covariance combines the beamformed communication signals with the covariance of the dedicated sensing signal.Communication signals are independent unit-power Gaussian streams, and the sensing signal is generated by pseudo-random coding.
  • Signal Model: The received signal at each communication user is modeled through the BS–STARS and STARS–user channels with multiuser interference and additive Gaussian noise.The model includes desired signal, inter-user interference, and user noise.
  • Signal Model: Sensors receive the target echo over a coherent block of length L, with the model depending on target amplitude, azimuth and elevation DOAs, steering vectors, and sensor noise.The sensing target is observed through STARS and the dedicated sensor array.
  • Signal Model: The sensing model assumes planar-wave steering vectors and specified STARS and sensor array geometries, while direct BS–sensor interference is omitted after offline elimination.Range and Doppler are omitted because the echo is modeled in a specific range-Doppler bin.

C. Performance Metrics for Communication and 2D Sensing

Communication is evaluated through per-user SINR, while sensing targets 2D DOA estimation and optimizes its CRB under communication requirements. Proposition 1 replaces the complicated CRB objective with a modified FIM optimization, including a multiple-target extension.

  • Per-user SINR is used as the communication metric because it determines achievable rate.
  • The sensing task estimates azimuth and elevation DOAs from coherent-block observations using maximum likelihood estimation.
  • The CRB provides a closed-form lower bound for 2D DOA estimation MSE, making it tractable to optimize instead of MSE directly.
  • The design minimizes the CRB trace while guaranteeing each communication user's minimum SINR.
  • Proposition 1 equivalently converts trace-CRB minimization into a modified FIM optimization using an auxiliary positive semidefinite matrix.
  • For multiple targets, the same reformulation applies with a 2Q × 2Q CRB and auxiliary semidefinite matrix.
  • The resulting problem remains difficult because transmit waveform matrices and STARS coefficients are highly coupled in non-convex constraints.

B. PDD Framework for Solving Problem P

The PDD framework solves the reformulated problem through an augmented-Lagrangian procedure with inner block-coordinate updates and outer dual-variable and penalty updates. Its constraint violation is driven toward zero as the penalty factor decreases sufficiently.

  • PDD constructs an augmented-Lagrangian problem and optimizes it by block coordinate descent in an inner loop.
  • The outer loop updates Lagrangian dual variables and penalty factors after inner-loop optimization.
  • The optimization variables are χ = {U, P, Rs, F, θt, θr}, while the augmented Lagrangian incorporates equality-constraint penalties.
  • Algorithm 1 alternates optimization and updates until the constraint violation falls below a predefined threshold.
  • When the penalty factor ρ is sufficiently small, both the penalty term and constraint violation reduce to zero, satisfying the equality constraint.

C. Proposed BCD Algorithm for Solving AL Problem (26)

The augmented-Lagrangian problem is solved by alternating between waveform-related variables and STARS coefficients. SDR makes the waveform block convex, while rank-one recovery introduces a practical convergence caveat.

  • BCD divides χ into {U, F, P, Rs} and {θt, θr}, then optimizes the two blocks iteratively.
  • {U, F, P, Rs} block: The waveform-related block is handled through SDR, whose relaxed formulation is a convex SDP with an efficiently obtainable global optimum.
  • {U, F, P, Rs} block: For the communication subproblem, Proposition 2 shows that a global optimum can be obtained by solving the SDR-based problem and then calculating Rs.
  • {θt, θr} block: The θt and θr block is updated as the second alternating subproblem after transforming the objective and SINR into tractable forms.
  • {U, F, P, Rs} block: Rank-one recovery uses eigenvalue decomposition or Gaussian randomization, with sufficient randomization providing at least a π/4-approximation for problem (40).
  • Using AltMin for the STARS-coefficient block guarantees convergence to a stationary point in polynomial time.
  • The rank-one recovery step cannot theoretically guarantee monotonic objective reduction, although eigenvalue decomposition or Gaussian randomization generally converges in practice.

IV. CRB OPTIMIZATION DESIGN WITH COUPLED T&R PHASE-SHIFT

For coupled STARS phase shifts, the PDD-based design addresses additional hybrid continuous-discrete constraints through a low-complexity alternating procedure. Amplitude and phase-shift coefficients are updated alternately in closed form.

  • A PDD-based algorithm is developed to handle the coupled T&R phase-shift constraints.
  • The proposed low-complexity iteration alternates amplitude and phase-shift coefficient updates using closed-form solutions.
  • The coupled phase-shift model makes CRB optimization more complex by imposing hybrid continuous and discrete control.
  • Some transmission phase shifts vary continuously over [0, 2π], whereas corresponding reflection shifts are restricted to a discrete set.

B. PDD Framework for Solving Problem ˜P

The coupled phase-shift problem is reformulated within a PDD framework using auxiliary variables, relaxed constraints, and alternating block optimization. The resulting algorithm combines SDR-based subproblem solutions with closed-form updates for coupled phase shifts and amplitudes.

  • PDD reformulation: The coupled T&R phase-shift constraints are relaxed for the original variables and retained for auxiliary variables linked by equality constraints.Lagrangian dual variables are introduced for these additional equalities to form the augmented-Lagrangian problem.
  • Block coordinate descent: The BCD procedure divides the augmented-Lagrangian variables into {U, F, P, Rs}, {θt, θr}, and {˜θt, ˜θr}.Each block is optimized through its corresponding subproblem before updating the penalty parameters and checking constraint violation.
  • SDR subproblem: The SDR approach approximately solves the homogeneous quadratic subproblem by introducing positive-semidefinite rank-one auxiliary matrices.Eigenvalue decomposition or Gaussian randomization can provide approximate rank-one solutions, although rank-one construction does not theoretically guarantee monotonic objective improvement during BCD.
  • Closed-form alternating optimization: For fixed amplitudes, the phase-shift entries are selected from two closed-form solution pairs, while fixed phase shifts yield closed-form amplitude updates.These results are stated in Propositions 3 and 4 and iterated until the fractional objective reduction falls below a threshold.
  • Overall algorithm: Algorithm 5 applies BCD within PDD and can theoretically converge to a stationary point when the penalty-based AltMin method is used for the phase-shift block.The complexity includes interior-point costs for the main subproblems and the update costs of Algorithm 4.
  • Closed-form alternating optimization: The subproblem for {˜θt, ˜θr} is handled by alternating amplitude and phase-shift updates with closed-form solutions.This alternating optimization is summarized in Algorithm 4, and each step obtains an optimal solution for its current block.

V. NUMERICAL RESULTS

The numerical evaluation uses Monte Carlo simulations under a Rician communication-channel model and compares STARS with reflecting-only and transmitting-only RIS baselines. Results are averaged over random channel realizations under specified geometric and algorithmic settings.

  • Simulation setup: The evaluation assumes a BS 40 m from STARS, users 20–50 m from its transmission side, and a sensing target 30 m from its reflection side.Communication channels follow a Rician model with deterministic line-of-sight and Rayleigh non-line-of-sight components.
  • Simulation setup: All communication users share the same SINR requirement, γk = γ, with PDD and BCD convergence thresholds set to 10^-4 and 10^-3.Convex subproblems are solved using the CVX toolbox.
  • Baseline and averaging: The baseline uses adjacent conventional reflecting-only and transmitting-only RISs, each with N/2 elements, at the same location as STARS.Its fixed amplitude coefficients make it a special case of STARS, so the baseline optimization is solved using the proposed PDD algorithm.
  • Baseline and averaging: The reported numerical results are averaged over 50 random channel realizations unless otherwise specified.This averaging is applied after evaluating the compared system configurations.

A. Convergence Performance of the Proposed Algorithms

Algorithms 1 and 3 converge well for the independent and coupled phase-shift models. At γ = 0 dB, Algorithm 3 nearly converges in its first PDD iteration because the coupled and independent models are nearly identical.

  • Convergence behavior: Algorithms 1 and 3 converge well in terms of root CRB and constraint violation for both independent and coupled phase-shift models.The root CRB is converted from radians to degrees for intuitive interpretation of DOA-estimation accuracy.
  • Convergence behavior: At γ = 0 dB, Algorithm 3 almost converges at the first PDD iteration.Its initialization uses Algorithm 1's output, which is nearly optimal when the coupled model closely matches the independent model.

B. Root CRB Versus Communication SINR Threshold

The root CRB increases as communication requirements become more demanding, while STARS consistently outperforms conventional RIS. More passive elements improve sensing and reduce the impact of communication constraints, and passive-element deployment is more effective than adding sensor elements under a fixed total.

  • Higher communication SINR requirements reduce sensing performance because communication consumes power and degrees of freedom.
  • STARS achieves lower CRB than conventional RIS for both independent and coupled phase-shift models.Conventional RIS is nearly infeasible for K = 6 and γ > 5dB.
  • More passive elements decrease root CRB and make communication SINR requirements less influential.Additional elements provide degrees of freedom for directional sensing beams and flexible communication-channel tuning.
  • At γ = 15dB, coupled and independent phase-shift models converge as N increases, while at γ = 0dB their performance remains comparable.
  • With N + Ns = 20, the best sensing performance occurs at N = 14 and Ns = 6, favoring passive elements over sensor elements.Passive elements provide full-space degrees of freedom, whereas sensor elements only increase the sensing-signal dimension.
  • The practical 2D MLE yields a concentrated spectrum for STARS but a broad, low-resolution spectrum for conventional RIS.At γ = 0dB, STARS estimates near (120°, 30°); at γ = 20dB, its brightest region remains relatively small.

APPENDIX A MAXIMUM LIKELIHOOD ESTIMATE OF DOAS

The appendix derives a practical maximum-likelihood estimator for the target's horizontal and vertical DOAs from Gaussian sensor observations. It estimates the complex target response for each candidate angle pair and searches a fine two-dimensional grid.

  • The transmit signal X and channel G are assumed known at the sensors through the wired BS–STARS control link.
  • The sensor observation is modeled as a Gaussian vector with mean αδ(φh, φv) and covariance σs^2INsL.The steering-related vector is δ(φh, φv) = vec(b(φh, φv)a^T(φh, φv)ΘrGX).
  • For each candidate pair of DOAs, the complex response α is estimated from the likelihood model.
  • The DOAs are obtained by exhaustively searching φh and φv over fine grids.The stated search ranges are [0, π] and [−π/2, π/2], respectively.
  • The Fisher information matrix is formed from derivatives of the Gaussian mean with respect to the unknown parameters.The derivation partitions the DOA-related block Jφφ and computes its entries from the corresponding derivatives.

APPENDIX C PROOF OF PROPOSITION 3

The proposition's proof exploits separability in the coupled phase-shift optimization. It alternates between phase variables and amplitudes, reducing each element-wise subproblem to a closed-form unit-circle optimization.

  • For fixed amplitudes, optimizing the transmission and reflection phase variables becomes separable across element pairs.
  • The coupled constraint restricts each element pair to [q̃r]n = j[q̃t]n or [q̃r]n = −j[q̃t]n.
  • Each phase subproblem is simplified to minimizing a real-valued objective subject to |q̃t,n| = 1.
  • Matching the optimal phase solution across the two allowed coupling cases yields the stated phase-shift solutions.
  • For fixed phases, amplitude optimization is likewise separable over transmission and reflection coefficients.
  • Parameterizing amplitudes as β̃t,n = sin ωn and β̃r,n = cos ωn converts each subproblem to minimizing sin(ωn + ψn) over a unit-circle interval.
  • The minimizing angle ωn directly provides the optimal transmission and reflection amplitudes in closed form.
Loading 2207.10748v3…