PaperlayerView exact revision on arXiv

Source-linked AI summary

RIS-Assisted Communication Radar Coexistence: Joint Beamforming Design and Analysis

Yinghui He, Yunlong Cai, Hao Mao, Guanding Yu

arXiv:2201.07399v1cs.ITeess.SP

TL;DR

The paper addresses mutual interference in communication-radar coexistence by introducing a double-RIS system and jointly designing radar and RIS beamforming. It reformulates the nonconvex problem for a PDD-based solution, develops special-case low-complexity designs, and reports improved performance over benchmarks.

  • Problem

    Communication-radar coexistence suffers mutual interference, motivating RIS-assisted enhancement of communication signals while preserving radar detection performance.

  • Method

    The paper jointly optimizes radar and RIS beamforming using an auxiliary-variable reformulation and a double-loop PDD algorithm, with special-case designs for large and low radar power.

  • Results

    The PDD-based and low-complexity algorithms outperform benchmark algorithms in simulations.

  • Takeaways & Limitations

    Two RISs can be used in the studied setting to enhance communication and suppress mutual interference while maintaining radar detection constraints.

Abstract

from arXiv · show

Integrated sensing and communication (ISAC) has been regarded as one of the most promising technologies for future wireless communications. However, the mutual interference in the communication radar coexistence system cannot be ignored. Inspired by the studies of reconfigurable intelligent surface (RIS), we propose a double-RIS-assisted coexistence system where two RISs are deployed for enhancing communication signals and suppressing mutual interference. We aim to jointly optimize the beamforming of RISs and radar to maximize communication performance while maintaining radar detection performance. The investigated problem is challenging, and thus we transform it into an equivalent but more tractable form by introducing auxiliary variables. Then, we propose a penalty dual decomposition (PDD)-based algorithm to solve the resultant problem. Moreover, we consider two special cases: the large radar transmit power scenario and the low radar transmit power scenario. For the former, we prove that the beamforming design is only determined by the communication channel and the corresponding optimal joint beamforming strategy can be obtained in closed-form. For the latter, we minimize the mutual interference via the block coordinate descent (BCD) method. By combining the solutions of these two cases, a low-complexity algorithm is also developed. Finally, simulation results show that both the PDD-based and low-complexity algorithms outperform benchmark algorithms.

I. INTRODUCTION

The paper introduces a double-RIS-assisted communication-radar coexistence system to enhance communication and suppress mutual interference, then develops joint beamforming algorithms under radar-performance constraints.

  • ISAC combines sensing and communication, but coexistence systems suffer communication degradation from mutual interference.
  • Two RISs are placed near the communication transmitter and receiver to reconfigure propagation, enhance communication signals, and suppress interference.
  • The proposed design jointly optimizes radar active beamforming and RIS passive beamforming to maximize communication SINR under radar detection constraints.
  • Auxiliary variables enable an equivalent tractable formulation, which is solved using a double-loop PDD-based algorithm.
  • For large radar power, the joint beamforming solution is closed-form; for low radar power, BCD minimizes mutual interference, enabling a low-complexity combined algorithm.
  • The system and algorithms are evaluated through simulations against conventional systems and benchmark algorithms.

C. Communication Model

The communication model accounts for direct and RIS-assisted desired links, radar interference links, and receiver noise, using average communication SINR as the performance metric.

  • The transmitter reaches the receiver through four direct and RIS-assisted wireless links.
  • Radar interference reaches the communication receiver through the radar–receiver and radar–RIS 2–receiver links.
  • The transmitter–RIS 2–radar link is neglected because its average received power is much lower than the other considered transmitter-to-radar paths.
  • RIS 2 uses a diagonal passive beamforming matrix whose phase shifts satisfy 0 ≤ φ2,n ≤ 2π.
  • The receiver noise is modeled as complex white Gaussian noise with zero mean and variance σ2.
  • Average communication SINR over one radar detection epoch is adopted as the communication-performance metric.

D. Problem Formulation

The paper formulates communication SINR maximization subject to radar detection and transmit-power constraints, then applies a PDD framework to the nonconvex problem.

  • D. Problem Formulation: The objective is to maximize communication performance while guaranteeing radar detection performance in every detection direction.
  • D. Problem Formulation: The radar SINR threshold, total radar-power budget, and RIS uni-modulus constraint define the principal feasibility requirements.
  • D. Problem Formulation: The resulting problem is difficult because its objective and constraints are highly coupled and nonconvex.
  • III. JOINT BEAMFORMING DESIGN ALGORITHM: PDD transforms the original problem into an equivalent formulation using auxiliary variables and equality constraints.
  • A. PDD Framework: The PDD framework uses an augmented-Lagrangian inner loop and an outer loop that updates dual variables or the penalty parameter.
  • A. PDD Framework: The framework applies to continuously differentiable objectives and constraints over a closed convex variable set, with possibly nonconvex inequality constraints.
  • A. PDD Framework: The transformed problem has an identical solution to the original problem, and the penalty parameter and dual variables are updated using constraint violation.

B. Problem Transformation and AL Problem

Auxiliary variables decouple the fractional objective and coupled constraints, allowing a PDD augmented-Lagrangian problem to be solved through CCCP and BCD updates.

  • The original problem is difficult because its objective contains a fractional coupling term and a highly coupled constraint.
  • An auxiliary variable v reformulates the objective equivalently without affecting optimality.
  • Auxiliary variables xk and yk convert the highly coupled inequality into equality constraints suitable for PDD treatment.
  • Dualizing and penalizing the introduced constraints yields the augmented-Lagrangian problem for the inner loop.
  • The transformed problem is equivalent to the original as the penalty parameter approaches zero, while the remaining nonconvex constraint is linearized using CCCP.
  • The linearized subproblem is convex and produces feasible iterates that converge to a stationary point of the corresponding problem.
  • BCD successively updates four variable blocks, including v, radar variables, and the two RIS phase vectors, using closed-form subproblem solutions.

D. Summary of the Proposed PDD-based Algorithm

The proposed PDD-based algorithm solves the augmented optimization problem through nested inner and outer loops, combining CCCP updates with dual-variable and penalty-factor updates. It converges to a stationary point while requiring computational work from both loops.

  • The inner loop solves the augmented-Lagrangian problem using a CCCP-based algorithm.The outer loop then updates dual variables or the penalty factor.
  • The penalty factor decreases by a constant c with 0 < c < 1, while dual variables are updated according to constraint violations.
  • The outer loop terminates by comparing the constraint violation indicator h(X) with an accuracy tolerance.
  • The PDD-based algorithm converges to a stationary point of the communication SINR maximization problem.
  • The algorithm uses double loops with maximum outer and inner iteration numbers I_o^max and I^max, respectively.Each inner iteration consists of four computational steps.
  • Its total computational complexity combines terms involving K, N_1, N_2, M, logarithmic bisection cost, and the outer and inner iteration counts.

IV. SPECIAL CASE ANALYSIS AND LOW-COMPLEXITY ALGORITHM

The special-case analysis links radar power to communication interference and SINR, then develops separate designs for large- and low-radar-power regimes. These cases support a lower-complexity beamforming strategy.

  • The analysis first studies how the radar power budget affects interference from the radar to the communication receiver.
  • Under fixed RIS beamforming, radar transmit and receive vectors are designed to avoid interference while satisfying radar requirements.
  • As radar power increases, radar-to-receiver interference decreases and communication SINR increases; with sufficiently large power, interference becomes zero.
  • The optimal radar beamforming combines the steering vector a*(θ_k) with e_k, whose component is orthogonal to a*(θ_k) and reduces communication interference.
  • The large-power and low-power regimes differ because interference vanishes in the former but dominates communication SINR in the latter.

B. Special Case 1: Large Radar Power

When radar transmit power is sufficiently large, radar interference at the communication receiver is zero, so RIS phases can focus on enhancing the communication signal. Closed-form beamforming results then enable comparison with a conventional system.

  • With sufficiently large radar power, the radar-to-receiver interference is zero and RIS beamforming maximizes communication SINR alone.
  • Ignoring the transmitter–RIS 1–RIS 2–receiver link, the optimal RIS phase shifts have closed-form expressions under the condition ||H_tr|| ≪ ||f_tr||.
  • The complete closed-form solution uses Lemma 2 for radar beamforming and Lemma 3 for the RIS passive beamforming vectors.
  • The proposed double-RIS system has higher performance than the conventional no-RIS system in the sufficiently-large-radar-power regime.
  • Under independent Rayleigh RIS-related links, the performance gap quadratically increases with the number of reflecting elements as min(N_1, N_2) grows.

C. Special Case 2: Low Radar Power

When radar transmit power is low, interference dominates communication SINR, so the RIS phases are optimized to reduce interference. Combining this design with the large-power solution yields a lower-complexity algorithm.

  • In the low-radar-power regime, high interference dominates communication SINR performance.
  • The RIS phases are optimized to reduce interference between the communication transmitter and radar, and between radar and communication receiver.
  • A BCD method sequentially optimizes each element of the two RIS phase vectors, then radar beamforming follows Lemma 2.
  • The low-complexity algorithm computes SINR for the large- and low-power cases, obtains their beamforming solutions, and selects the final design by comparing SINR values.
  • Algorithm 3 has lower complexity than the PDD-based algorithm, with performance verified through simulations.

V. SIMULATION RESULTS

Simulations evaluate convergence, radar beampattern preservation, communication SINR, feasibility, complexity, RIS size and placement, radar location, and phase quantization. The proposed algorithms generally improve coexistence performance, with PDD strongest at low radar power and the low-complexity method strongest at high radar power.

  • Algorithm Investigation: The PDD-based algorithm converges within about 10 outer-loop iterations, while constraint violation decreases to around 10^-10 and later below 10^-14.These values confirm feasibility to the original problem and indicate fast convergence.
  • Algorithm Investigation: The proposed radar beamforming designs retain nearly the same main lobes as a conventional radar while changing sidelobes to suppress radar-to-communication interference.The reported beampattern comparison indicates little radar beamforming loss.
  • Performance Comparison: Communication-centric design performs well with large radar power, interference-cancellation design with low radar power, and the combined low-complexity algorithm performs well across radar power budgets.The PDD-based algorithm is best under low Pmax, whereas the low-complexity algorithm is best under high Pmax.
  • Performance Comparison: The PDD-based algorithm has the highest successful feasible-solution probability, followed by the low-complexity algorithm, and feasibility probability increases with Pmax.Higher radar power makes the radar SINR requirement easier to satisfy.
  • Performance Comparison: The proposed algorithms significantly outperform benchmark algorithms in achieved communication SINR, and the low-complexity algorithm requires less running time than the PDD-based algorithm.The comparison uses N1 = 40 and reports low running time for all evaluated algorithms.
  • Performance Comparison: With more reflecting elements, the double-RIS system increasingly outperforms single-RIS and conventional systems, while receiver-side RIS placement is more efficient than transmitter-side placement.The receiver-side RIS directly reduces radar interference at the communication receiver.
  • Performance Comparison: Communication SINR increases with radar distance D under Rayleigh fading, and the performance gap between the two proposed algorithms decreases as interference weakens.Under Rician fading, distance and azimuth angle both affect the interference channel and SINR trend.
  • Performance Comparison: Discrete RIS phase shifts approach continuous-phase performance as quantization bits increase, with nearly identical performance beyond 3 bits.This supports practical implementation with finite phase resolution.

VI. CONCLUSION

The paper develops a double-RIS-assisted communication radar coexistence system and algorithms to enhance communication while suppressing interference, then identifies a single-antenna scope limitation.

  • Two RISs are placed near the communication transmitter and receiver to enhance communication signals and suppress interference.
  • Numerical results verify the effectiveness of the proposed system and both algorithms.Figure 12 examines communication SINR as a function of quantization bits b.
  • The communication SINR is maximized subject to radar SINR and radar transmit-power constraints using a double-loop PDD-based algorithm.The inner loop solves the augmented-Lagrangian problem via CCCP, while the outer loop updates multipliers or the penalty factor.
  • Large- and low-radar-power cases yield a closed-form joint beamforming design and a BCD-based interference-minimization method, respectively.Combining these cases produces a low-complexity algorithm.
  • The study considers one transmitter and one receiver, each with a single antenna, leaving multiuser and multiantenna joint beamforming for future work.

APPENDIX A DETAILS OF CCCP ALGORITHM

The appendix derives solutions for two subproblems using Lagrangian analysis, KKT conditions, complementary slackness, and bisection searches when constraints are active.

  • The Lagrange function of subproblem (26) is formed with multiplier µ_k for constraint (22), followed by KKT-based solution analysis.
  • The solution to subproblem (26) is discussed according to the value of the optimal multiplier µ⋆_k.
  • When equality holds in constraint (22), the relevant solution parameter is obtained by bisection search.
  • The Lagrange function of subproblem (27) uses multiplier ˜λ for constraint (10c), and its solution is likewise separated by multiplier values.
  • For the nonzero-multiplier case, the optimal solution satisfies the stated power relation and can be obtained by bisection search.

APPENDIX B PROOF OF LEMMA 2

The proof derives the optimal solution for the radar beamforming subproblem through Rayleigh-quotient and KKT analysis, then relates the multiplier to radar power and communication interference.

  • The radar beamforming vector w_k is optimized first because it appears only in constraint (10b), with its optimum derived using Rayleigh-quotient maximization.
  • The original problem is equivalently transformed before expressing u_k as a linear combination of a(θ_k), e_k, and r_k.
  • Lagrange-multiplier and KKT analysis yields the optimal solution, with ˆλ⋆ satisfying complementary slackness for constraint (69c).
  • When P_max is large enough, interference from the radar to the communication receiver decreases to zero, establishing the communication-SINR relationship with the radar power budget.
  • As P_max increases, ˆλ⋆ decreases and becomes zero when the radar power is sufficiently large.
Loading 2201.07399v1…