PaperlayerView exact revision on arXiv

Source-linked AI summary

Joint Transmit Waveform and Passive Beamforming Design for RIS-Aided DFRC Systems

Rang Liu, Ming Li, Yang Liu, Qingqing Wu, Qian Liu

arXiv:2112.08861v2eess.SP

TL;DR

The paper asks how RIS can improve both radar sensing and communication in a shared-hardware DFRC system. It jointly designs the dual-functional waveform and RIS passive beamforming using ADMM and MM, with simulations showing radar gains while maintaining communication QoS. The resulting algorithm provides a locally optimal solution and a lower bound on radar SINR.

  • Problem

    The paper addresses how to exploit RIS in DFRC systems to jointly improve radar sensing and MU-MISO communication while meeting QoS and waveform and RIS modulus constraints.

  • Method

    The paper jointly optimizes the transmit waveform, receive filter, and RIS reflecting coefficients using alternating ADMM and MM updates for the constrained non-convex problem.

  • Results

    Simulation studies show significant radar improvement from RIS, especially when the BS-target direct channel is weak, while the proposed design achieves satisfactory communication QoS.

  • Takeaways & Limitations

    RIS-assisted DFRC can enhance radar sensing and communication together, with the proposed design trading about 0.5dB radar performance against the radar-only system for communication QoS.

  • Takeaways & Limitations

    The proposed algorithm offers only a locally optimal solution, and its obtained radar SINR is a lower bound whose optimality is difficult to prove.

Abstract

from arXiv · show

Reconfigurable intelligent surface (RIS) is a promising technology for 6G networks owing to its superior ability to enhance the capacity and coverage of wireless communications by smartly creating a favorable propagation environment. In this paper, we investigate the potential of employing RIS in dual-functional radar-communication (DFRC) systems for improving both radar sensing and communication functionalities. In particular, we consider a RIS-assisted DFRC system in which the multi-antenna base station (BS) simultaneously performs both multi-input multi-output (MIMO) radar sensing and multi-user multi-input single-output (MU-MISO) communications using the same hardware platform. We aim to jointly design the dual-functional transmit waveform and the passive beamforming of RIS to maximize the radar output signal-to-interference-plus-noise ratio (SINR) achieved by space-time adaptive processing (STAP), while satisfying the communication quality-of-service (QoS) requirement under one of three metrics, the constant-modulus constraint on the transmit waveform, and the unit-modulus constraint of RIS reflecting coefficients. An efficient algorithm framework based on the alternative direction method of multipliers (ADMM) and majorization-minimization (MM) methods is developed to solve the complicated non-convex optimization problem. Simulation results verify the advancement of the proposed RIS-assisted DRFC scheme and the effectiveness of the developed ADMM-MM-based joint transmit waveform and passive beamforming design algorithm.

I. INTRODUCTION

The paper integrates RIS with DFRC to jointly support radar sensing and multi-user communications on a shared BS hardware platform. It formulates a constrained joint design problem and develops ADMM-MM methods for optimizing the transmit waveform and RIS reflection coefficients.

  • I. INTRODUCTION: RIS can manipulate the radio environment, offering additional degrees of freedom for improving wireless transmission quality, coverage, and robustness.The paper motivates RIS as a passive reflecting surface whose elements cooperatively control reflected electromagnetic waves.
  • I. INTRODUCTION: DFRC integrates sensing and communication through shared hardware, frequency bands, and a unified dual-functional waveform, improving hardware, spectrum, and energy efficiency.MIMO and STAP provide spatial and temporal degrees of freedom for radar sensing and multi-user communications.
  • I. INTRODUCTION: Prior RIS-DFRC studies addressed communication interference while preserving radar beampattern or Cramér-Rao-bound performance, leaving RIS effects on radar sensing less fully exploited.The paper therefore targets joint enhancement of radar sensing and communication functionalities.
  • I. INTRODUCTION: The paper jointly designs the transmit waveform, BS receive filter, and RIS reflecting coefficients to maximize radar output SINR subject to communication QoS and modulus constraints.Three communication QoS metrics are considered, while RIS coefficients satisfy unit-modulus constraints.
  • I. INTRODUCTION: ADMM and MM transform the non-convex optimization into tractable subproblems that are solved alternately for the waveform, receive processing, and passive beamforming.The resulting target echo includes direct and RIS-assisted propagation paths, with clutter and noise included in the received signal model.
  • II. SYSTEM MODEL AND PROBLEM FORMULATION: The considered system uses a multi-antenna BS, an N-element RIS, STAP, and a constant-modulus waveform to detect a target amid clutter while serving K single-antenna users.The same transmit waveform carries different information symbols and is designed to manage multi-user interference at the symbol level.

B. Communication Model

The communication model supports MU-MISO transmission through three QoS metrics that differ in how they handle multi-user interference (MUI), trading communication strictness for radar waveform flexibility.

  • The BS transmits information symbols to K single-antenna users while designing waveforms that enable receivers to decode their intended PSK symbols.
  • The model evaluates communication QoS using zero-forcing (ZF)-type, minimum mean square error (MMSE)-type, and constructive interference (CI)-type metrics.QPSK is used as an illustrative modulation example in the complex plane.
  • ZF-type communication metric: ZF-type QoS eliminates MUI by forcing the received noise-free signal to match a scaled desired symbol, imposing the strictest waveform restriction.
  • MMSE-type communication metric: MMSE-type QoS permits bounded squared error around the scaled desired symbol, creating a larger feasible signal region and more radar-design flexibility than ZF-type QoS.
  • CI-type communication metric: CI-type QoS permits MUI that pushes received signals away from decision boundaries, providing the largest waveform-design flexibility.
  • For the same SNR requirement, ZF-type solutions offer the best communication performance but worst target detection, whereas CI-type solutions show the opposite trade-off.

C. Problem Formulation

The paper formulates joint design of the BS transmit waveform, receive filter, RIS coefficients, and scaling factors to maximize radar output SINR under communication and modulus constraints.

  • The optimization jointly designs the transmit waveform x, scaling factor α, receive filter w, and RIS reflecting coefficients φ.
  • The objective is to maximize radar output SINR while satisfying one of the three communication QoS metrics, constant-modulus waveform constraints, and unit-modulus RIS constraints.
  • With x, α, and φ fixed, optimizing the receive filter w reduces to a minimum variance distortionless response (MVDR) problem.
  • The resulting problem is complicated and non-convex because of its bivariate objective and constant-modulus constraints on both waveform and RIS coefficients.

III. JOINT TRANSMIT WAVEFORM AND PASSIVE BEAMFORMING DESIGN

The design introduces auxiliary variables and an indicator function to handle modulus and feasibility constraints within an ADMM augmented-Lagrangian formulation.

  • Two auxiliary vectors y and ϕ are introduced to transform the non-convex constant-modulus constraints.
  • An indicator function imposes the transformed problem’s feasibility constraints by assigning zero to feasible points and infinity otherwise.
  • The constrained problem is recast through an augmented Lagrangian with penalty parameter ρ and dual variables μ1 and μ2.
  • ADMM removes selected equality constraints and makes the resulting minimization more tractable, while the remaining non-convex function motivates MM-based surrogate minimization.

B. MM-based Transformation

The MM transformation replaces the difficult augmented-Lagrangian objective with an upper-bounding surrogate, enabling alternating updates of the design variables and convex waveform subproblems.

  • MM constructs a tractable surrogate at the current iterate that upper-bounds the augmented-Lagrangian objective for minimization at the next iteration.
  • An affine relationship and a quadratic surrogate are used to express the transformed augmented-Lagrangian function.
  • The surrogate is minimized by alternating updates of x, α, y, φ, ϕ, μ1, and μ2.
  • For all three communication QoS constraints, the transmit-waveform and scaling-factor subproblem is convex and can be solved optimally using existing algorithms or CVX.

D. Update y

The reflecting-coefficient update is reformulated into an explicit problem because RIS-dependent functions and Kronecker-product terms hinder direct optimization.

  • The RIS variable φ is embedded in nonlinear functions and Kronecker-product terms that are not directly amenable to optimization.
  • The reformulation introduces v = φ ⊗φ and exposes the resulting objective terms for subsequent treatment.
  • The transformed problem remains non-convex because its objective contains quadratic and coupled terms involving v and φ.
  • A positive-semidefinite matrix property is used to construct a surrogate for the term v^H F_v,t v.

2) MM-based Transformation:

The MM transformation replaces difficult non-convex RIS-dependent terms with tractable surrogate functions, ultimately yielding a convex update problem under communication constraints.

  • The trace of F_v,t is used as an efficient upper bound on its eigenvalues, avoiding eigendecomposition of an N^2 × N^2 matrix.Because F_v,t contains Q rank-one matrices, its trace can be obtained directly without forming the full matrix.
  • A lower-dimensional construction of eF_v,t avoids computing the N^2 × N^2 matrix F_v,t explicitly.
  • The real-valued RIS objective is converted to a real-valued variable representation and treated with a second-order Taylor expansion to derive a convex surrogate.
  • A surrogate is also derived for the coupled term ℜ{v^H L_t φ}, contributing to the surrogate objective for the RIS update.
  • The resulting RIS subproblem is convex under any one of the three communication constraints and can therefore be solved efficiently.

F. Update ϕ

With the other variables fixed, the auxiliary variable ϕ is updated using a procedure analogous to the update for y.

  • Fixing x_t, α_t, y_t, φ_t, μ_1, and μ_2, the auxiliary variable ϕ is updated similarly to y.

G. Update µ1 and µ2

The algorithm alternates updates of the waveform, auxiliary variables, RIS coefficients, and dual variables until convergence, using initialization procedures designed to improve starting quality.

  • The dual variables μ_1 and μ_2 are updated after obtaining the current waveform, auxiliary variables, RIS coefficients, and auxiliary ϕ.
  • RIS initialization maximizes target and user channel gains while reducing clutter-source channel gains under unit-modulus reflecting coefficients.
  • The RIS initialization problem is a non-convex smooth quadratic optimization over a Riemannian manifold and can be solved by manifold optimization.
  • Waveform initialization maximizes the minimum user QoS using available transmit power, with a relaxed convex power constraint for ZF/MMSE-type metrics.
  • The method provides a locally optimal solution and a lower bound of radar SINR because global optimality is difficult to prove.

IV. SIMULATION STUDIES

Simulations evaluate convergence and radar SINR under varying transmit power, RIS size, communication QoS, antenna count, path loss, and RIS-target distance. RIS improves radar performance, particularly with weak direct channels, while communication QoS introduces a limited trade-off under extreme requirements.

  • Convergence: All three ADMM-MM schemes monotonically increase radar SINR with iterations, and configurations with fewer reflecting elements converge faster.The faster convergence is attributed to a lower-dimensional optimization variable.
  • Transmit power: About 4dB radar performance improvement is achieved with RIS compared with systems without RIS across DFRC and radar-only benchmarks.DFRC systems satisfy communication QoS under all three proposed metrics.
  • RIS size: A 100-element RIS provides about 8dB radar performance gain over schemes without RIS because it creates additional configurable propagation paths and degrees of freedom.Radar SINR increases as the number of reflecting elements N grows.
  • Communication QoS: Radar SINR is nearly unaffected when Γ is between 10dB and 20dB, but a trade-off with radar performance appears at Γ = 35dB.The strong radar-oriented waveform readily satisfies practical communication QoS requirements within the lower range.
  • Antenna count: More transmit/receive antennas improve radar SINR by providing additional spatial degrees of freedom, waveform diversity, and beamforming gains.The antenna-count evaluation uses M as the varying parameter with N = 64, P = 20dBW, and Γ = 10dB.
  • Propagation conditions: RIS benefits become more pronounced as the direct BS-target channel worsens, reaching about 25dB radar-sensing gain at αt = 4, while higher gains occur when RIS is closer to the target.The RIS impact becomes negligible when the direct channel is sufficiently strong, such as αt = 2.

APPENDIX A

Appendix A reformulates RIS-dependent objective and communication QoS expressions using Kronecker-product transformations, enabling an equivalent optimization formulation. The derivation also reduces computational burden by avoiding large intermediate matrices.

  • Objective reformulation: Kronecker-product transformations extract the RIS variable φ from eHq(φ)x and rewrite the expression using reshaped matrices Xq.Xq is defined as the reshaped version of Jrqx satisfying Jrqx = vec{Xq}.
  • Objective reformulation: The same transformations explicitly rewrite the objective terms f2(φ) and eH0(φ)x with respect to φ.The reformulated expressions are substituted into the objective to obtain a concise form.
  • Complexity reduction: The derivation avoids computing and storing the N^2 × L matrix Cq and the ML × N^2 matrix Dq for all q, reducing computational complexity.The intermediate variables are eliminated before subsequent derivations.
  • QoS reformulation: Communication QoS constraints are transformed through the reshaped matrix eGk, where Gkx = vec{eGk}, and the elements egk,l are defined for concise notation.The transformed constraints are then combined with the reformulated objective.

APPENDIX B

Appendix B continues the reformulation of vector and matrix expressions using a stated transformation, producing concise forms for the relevant terms.

  • Vector reformulation: The re-formulated version of Fv,t is used to derive an expression for the vector efv,t.Equation (78b) follows by applying the cited transformation.
  • Matrix reformulation: Combining the re-formulated fv,t with efv,t yields the matrix expression eFv,t.The matrix version is formed as efv,t + fv,t.
Loading 2112.08861v2…