PaperlayerView exact revision on arXiv

Source-linked AI summary

Cram\'er-Rao Bound Optimization for Joint Beamforming and Mode Selection in RDARS-Assisted ISAC Systems

Ahmad Reza Hassanshahi, Rouhollah Amiri, Fereidoon Behnia

arXiv:2610.01474v1eess.SP

TL;DR

The paper addresses joint RDARS configuration and beamforming for target-localization accuracy under multi-user communication constraints. It develops an AO-based optimization method and reports that RDARS achieves lower PEB than passive RIS and DAS at the same SINR.

  • Problem

    Prior RDARS-ISAC work had not jointly optimized connected/reflected mode selection and transmit design for position-CRB minimization under multi-user SINR constraints.

    Source: A. Related Works · p. 2

  • Method

    The paper jointly optimizes transmit beamforming and dynamic RDARS mode selection using AO with MM and penalty methods.

    Source: B. Contributions · p. 2

  • Results

    Simulations report lower PEB for RDARS than passive RIS and DAS under the same SINR constraints.

    Source: B. Contributions · p. 2

  • Takeaways & Limitations

    The reported advantage is attributed to RDARS's hybrid distribution and reflection gains.

    Source: B. Contributions · p. 2

Abstract

from arXiv · show

Integrated Sensing and Communication (ISAC) is a foundation of 6G networks, demanding architectures that simultaneously enhance sensing accuracy and communication reliability. This paper presents a Reconfigurable Distributed Antenna and Reflecting Surface (RDARS) aided ISAC framework, where an RDARS overcomes the limitations of conventional passive Reconfigurable Intelligent Surfaces (RIS) and Distributed Antenna Systems (DAS). By enabling each element to dynamically operate in either \textit{reflection} or \textit{connection} mode, RDARS synergistically harnesses reflection gain, distribution gain, and an additional mode-selection gain. We investigate the joint optimization of transmit beamforming at the base station and dynamic mode selection at the RDARS to minimize the sensing performance metric, namely the Cram\'er-Rao Bound (CRB) for target localization, while guaranteeing a minimum required Signal-to-Interference-plus-Noise Ratio (SINR) for multiple communication users. To solve the resulting non-convex and mixed-integer problem, we develop an efficient iterative algorithm based on the Alternating Optimization (AO) framework, effectively leveraging Majorization-Minimization (MM) and Penalty methods. Comprehensive simulations validate the proposed design, demonstrating that the dynamic RDARS configuration achieves a superior trade-off between the Position Error Bound (PEB) and communication SINR, significantly outperforming benchmark passive RIS and DAS systems.

I. INTRODUCTION

The paper targets joint RDARS configuration and transmit-beamforming design for position-CRB minimization under multi-user SINR constraints, a gap in prior RDARS-ISAC work. It proposes an AO-based method and reports lower PEB than passive RIS and DAS at the same SINR.

A. Related Works

  • The joint design minimizes position CRB while ensuring multi-user SINR, addressing a gap left by prior RDARS-ISAC designs.The work distinguishes its position-domain CRB objective from prior work using sensing SINR.Source: A. Related Works · p. 2, B. Contributions · p. 2

B. Contributions

  • The paper provides tractable SINR and CRB expressions as functions of active beamforming, reflection coefficients, and mode selection.These expressions enable a concrete problem formulation.Source: B. Contributions · p. 2
  • An AO-based iterative algorithm decomposes the problem into subproblems, using MM or successive approximation for non-convexities and penalties for SINR and mode-selection consistency.The joint problem has variable coupling and unit-modulus and binary constraints.Source: B. Contributions · p. 2
  • The proposed RDARS outperforms passive RIS and DAS, achieving lower PEB under the same SINR constraints by exploiting hybrid distribution and reflection gains.Simulations evaluate beampatterns, geometry, and the sensing-communication trade-off.Source: B. Contributions · p. 2

C. Outline

  • The paper proceeds from the system model and CRB derivation to joint design and simulation comparisons against benchmarks.The simulations include beampatterns, trade-off analyses, geometric evaluations, and parametric studies.Source: C. Outline · p. 2

A. Scenario Description

  • The system uses MIMO-OFDM to serve K single-antenna users and sense a target, evaluating communication with SINR and sensing with radar CRB.The system model includes the BS, target, and RDARS panel.Source: A. Scenario Description · p. 2
  • RDARS elements switch between reflected and connected modes, combining passive phase shifting with connected elements that act as a distributed antenna system.Only a small subset of elements operates in connected mode for hardware efficiency.Source: A. Scenario Description · p. 2

B. Communication Channel

  • The communication model defines BS-RDARS and BS-user channels, and uses a selection matrix to map connected RDARS elements to the signal dimensions.The channel components follow a general Rician fading model.Source: B. Communication Channel · pp. 2–3

C. Radar Channel

The radar model describes five propagation paths and uses the resulting signal model to derive a position-localization CRB. The CRB is obtained from the Fisher information matrix (FIM), with stated approximations and identifiability conditions delimiting the calculation.

C. Radar Channel

  • The radar channel comprises five paths linking the BS, target, RDARS, and BS or RDARS receivers.The paths include direct BS–target–BS propagation and paths involving RDARS connected or reflecting elements.Source: C. Radar Channel · p. 3

D. Performance Metrics

  • The CRB is used as a lower bound on the covariance of an unbiased estimator and on target-position localization MSE.The parameter vector includes target position and the real and imaginary parts of the five path gains.Source: D. Performance Metrics · pp. 3–4

III. CALCULATION OF THE CRB OF TARGET POSITION

  • The closed-form FIM calculation reparameterizes position and path gains using delays, angles, and gains under a resolvable-path and score-orthogonality approximation.If those orthogonality conditions fail, the full FIM is retained and the position EFIM is obtained by a Schur complement.Source: §III · p. 4
  • Nuisance path gains are eliminated by a Schur complement; the position CRB requires a positive-definite EFIM, which can fail when paths are indistinguishable or sensing has a target null.Clutter can be represented as colored noise, while dynamic-RCS chance constraints are identified as future work.Source: §III · p. 4

IV. JOINT BEAMFORMING AND MODE SELECTION

The paper formulates joint beamforming and RDARS mode selection to minimize target-position CRB subject to minimum SINR requirements for multiple users. It addresses the non-convex problem with alternating updates of beamforming and RDARS variables.

A. Problem Formulation

  • The design minimizes target-position CRB while enforcing each communication user's minimum SINR threshold.The jointly optimized variables are the composite transmit beamforming matrix F, reflection matrix Φ, and selection matrices A and Aa.Source: A. Problem Formulation · pp. 4–5
  • The problem is non-convex and is handled by alternating between beamforming optimization and joint reflection-coefficient and mode-selection optimization.The formulation also imposes a total power budget, unit-modulus reflection coefficients, and feasible-set constraints on the selection matrices.Source: A. Problem Formulation · p. 5

B. Transmit Beamforming Matrix Optimization

The solution alternates a transmit-beamforming update with updates to reflection coefficients and RDARS selection matrices. Its subproblems use relaxation, successive approximation, and penalty methods, with acceptance checks for local updates.

B. Transmit Beamforming Matrix Optimization

  • The transmit update combines Dinkelbach's method with successive convex approximation of a lifted transmit-covariance problem.A spectral decomposition majorizes the concave term at the current iterate to form a local convex approximation.Source: B. Transmit Beamforming Matrix… · p. 5
  • The transmit subproblem uses semidefinite relaxation by dropping rank-one constraints, then recovers a beamformer and retains a SINR-feasible candidate with the smallest original CRB.The method makes no global-optimality claim for this relaxation-based update.Source: B. Transmit Beamforming Matrix… · p. 5

C. Reflection Matrix and Selection Matrices Optimization

  • Penalty terms decouple coupled SINR and mode-selection constraints, after which four variable blocks are updated iteratively.For fixed beamforming and RDARS variables, the auxiliary-variable objective separates into independent user subproblems; the stated QCQP can use a Lagrangian dual method when Slater's condition holds.Source: C. Reflection Matrix and Selection… · p. 6
  • The phase update models the CRB through path-3 gain and its angle derivative, then uses a local first-order model and unimodular quadratic majorization.Because the CRB model is local, a candidate is accepted only if it does not increase the original fixed-penalty objective.Source: C. Reflection Matrix and Selection… · p. 6
  • The binary reflected-element selection update majorizes a local quadratic model and chooses the prescribed number of elements from the smallest entries of e.The candidate is retained only if the original fixed-penalty objective decreases.Source: 3) Update · p. 7
  • The connected-element update is a finite assignment problem with distinctness constraints and preserves dependence on the elements' physical locations.The update is accepted only when the original fixed-penalty objective is non-increasing.Source: 3) Update · p. 7
  • The overall method is a local AO/penalty algorithm for a non-convex mixed-integer problem, with no global-optimality guarantee.Source: 3) Update · p. 7

D. Convergence and Complexity Analysis

The convergence claim is limited to objective values within fixed-penalty stages, while the lifted transmit update dominates the stated worst-case per-iteration complexity.

D. Convergence and Complexity Analysis

  • Within fixed penalty parameters, accepted updates are non-increasing and the penalized objective sequence converges in value, but no KKT point or global optimum is guaranteed.Monotonicity is claimed only within each fixed-penalty stage, not across the continuation of penalty parameters.Source: D. Convergence and Complexity Analysis · p. 7
  • The lifted transmit update dominates worst-case per-iteration complexity, with generic interior-point scaling O(IIPK^3d^6).Here, d = M + a; phase updating costs O(N^3), and connected-element assignment is negligible when a ≪ N compared with the SDP step.Source: D. Convergence and Complexity Analysis · p. 7

V. SIMULATION RESULTS

Numerical simulations evaluate the proposed approach, with the main simulation parameters listed in Table I.

V. SIMULATION RESULTS

  • Numerical simulations evaluate the proposed approach.Source: §V · p. 7
  • Table I lists the main simulation parameters.Source: Table I · p. 7

A. Beampatterns

The simulations show that dynamic RDARS configuration balances localization accuracy and communication SINR, outperforming passive RIS and DAS in the reported comparisons. The results also show that beam steering and target geometry affect localization accuracy, while system parameters shape PEB.

B. ISAC Trade-off Analysis

A. Beampatterns

  • The optimal phase design achieves a 5.48 m PEB, while target-focused steering reaches 2.150 m PEB but only 21.8 dB SINR versus 30.9 dB for the optimal design.The optimal design balances sensing and communication under the stated constraints.Source: A. Beampatterns · p. 8, Figure 2 · p. 8

C. Geometric Analysis

  • PEB is lowest between the BS and RDARS, rises away from that region, and is high along the half-line extending from the RDARS.The paper attributes the high-error half-line to tangential direct- and indirect-path fixed-delay contours, and reports relatively lower PEB along diagonal paths between the RDARS and users.Source: Figure 6 · p. 8, C. Geometric Analysis · p. 9

D. Analysis of System Design Parameters

  • PEB decreases as bandwidth, BS antenna count, total RDARS elements, and transmit power increase; about 40 connected elements yields the lowest reported PEB, though this may be cost-ineffective.The reported gains over passive RIS and DAS remain substantial as BS antennas and RDARS elements increase, with few active RF chains.Source: Figure 7 · p. 8, D. Analysis of System Design Parameters · p. 9, Figure 8 · p. 10

VI. CONCLUSION

  • The study jointly optimizes BS beamforming and RDARS mode selection to minimize localization CRB under user-SINR constraints, using an iterative AO algorithm with MM and penalty techniques.The conclusion identifies multi-target localization, imperfect channel state information, and multiple RDARS panels among future research directions.Source: §VI · p. 9

APPENDIX A CALCULATION OF THE FIM

Appendix A derives the position-related Fisher information from the signal model’s parameter derivatives, then expresses it as an effective FIM through a parameter transformation.

APPENDIX A CALCULATION OF THE FIM

  • The FIM elements are obtained from partial derivatives of the signal model with respect to delays, angles, and path losses.The derivation also specifies the geometric position gradients and the Jacobian transforming the parameter vector.Source: Appendix A · p. 10
  • Under the stated resolvable-path/score-orthogonality approximation, the FIM reduces to block-diagonal delay, angle, and path-loss components.Its diagonal elements follow by substituting the signal-model partial derivatives into the Slepian–Bangs expression.Source: Appendix A · p. 10
  • Transforming the parameter-domain FIM yields a position-related effective FIM, whose entries are collected as linear functions of the feasible covariance vector.The appendix defines the effective FIM after forming the transformed FIM.Source: Appendix A · pp. 10–11
  • The effective-FIM coefficient matrix includes cross terms between r1 and r2 and is not assumed positive semidefinite, motivating the spectral split in Section IV-B.The off-diagonal blocks explicitly generate the cross terms.Source: Appendix A · p. 11

APPENDIX B CALCULATION OF THE CRB IN TERMS OF ϕ

Appendix B expresses how the phase vector affects the position effective FIM through Path 3 and specifies the local approximation and acceptance rule used in Section IV-C.

APPENDIX B CALCULATION OF THE CRB IN TERMS OF ϕ

  • For fixed A and Aa, the phase vector affects the radar FIM through Path 3, with delay and θ1 information affine in S0 and θ2 information affine in S1.These dependencies make the position-EFIM entries affine in the phase-dependent quantities.Source: Appendix B · pp. 11–12
  • At each iteration, Section IV-C forms its local SCA model from a first-order expansion around the current phase vector.The expansion uses the current values of S0 and S1 and their derivatives.Source: Appendix B · p. 12
  • The acceptance rule evaluates the original fixed-penalty objective rather than treating the local expansion as a global MM upper bound.Source: Appendix B · p. 12

Related papers

Loading 2610.01474v1…