PaperlayerView exact revision on arXiv

Source-linked AI summary

Joint Power Control and Passive Beamforming in IRS-Assisted Spectrum Sharing

Xinrong Guan, Qingqing Wu, Rui Zhang

arXiv:2003.03105v2cs.ITeess.SP

TL;DR

Strong cross-link interference can make SU spectrum sharing ineffective while the PU must meet its QoS target. The paper jointly optimizes SU transmit power and IRS passive beamforming using alternating optimization and successive convex approximation. Simulations show that IRS significantly improves SU rate, including in challenging conventional-CR scenarios where no-IRS designs are ineffective.

  • Problem

    Strong cross-link interference between nearby PU and SU links can severely limit the achievable SU rate while PU quality of service must be preserved.

  • Method

    The paper jointly optimizes SU transmit power and IRS reflection using alternating optimization and successive convex approximation, with heuristic lower-complexity designs.

  • Results

    IRS significantly improves SU rate and handles highly challenging interference scenarios in which conventional no-IRS designs can be ineffective.

  • Takeaways & Limitations

    IRS passive beamforming can reduce severe interference sufficiently for the SU to access shared spectrum while maintaining the PU QoS requirement.

Abstract

from arXiv · show

In cognitive radio (CR) communication systems, achieving high secondary user (SU) rate in the presence of strong cross-link interference with the primary user (PU) is challenging. In this letter, we exploit the emerging intelligent reflecting surface (IRS) technology to tackle this problem. Specifically, we investigate an IRS-assisted CR communication system where an IRS is deployed to assist in the spectrum sharing between a PU link and an SU link. We aim to maximize the achievable SU rate subject to a given signal-to-interference-plus-noise ratio target for the PU link, by jointly optimizing the SU transmit power and IRS reflect beamforming. Since the formulated problem is difficult to solve due to its non-convexity and coupled variables, we propose an efficient algorithm based on alternating optimization and successive convex approximation techniques to solve it sub-optimally, along with some heuristic designs for lower complexity. Simulation results show that IRS is able to significantly improve the SU rate, even for the scenarios deemed most challenging in conventional CR systems without using IRS.

I. INTRODUCTION

The paper addresses strong cross-link interference that limits secondary-user rates in cognitive-radio spectrum sharing. It introduces IRS-assisted passive beamforming jointly with secondary transmit-power control to improve SU communication while preserving the PU QoS target.

  • I. INTRODUCTION: An IRS can adaptively adjust passive reflection coefficients to enhance desired signals and suppress interference through constructive or destructive combining.The IRS is a planar array of passive reflecting elements whose coefficients control reflected-signal combining.
  • I. INTRODUCTION: Strong cross-link interference can severely limit the achievable SU rate when secondary and primary users are nearby.The system includes primary and secondary links sharing spectrum, with nearby transmitters and receivers creating challenging interference conditions.
  • I. INTRODUCTION: The work jointly optimizes SU transmit power and IRS reflection to maximize SU rate subject to a PU SINR-based QoS target.The PU constraint is imposed at the primary receiver, with γth specifying the required PU SINR.
  • I. INTRODUCTION: The considered system contains single-antenna PU and SU links, with an IRS deployed near the primary and secondary transmitters to assist a communication hotspot.The IRS has N reflecting elements and participates in the PT/ST-to-PR/SR composite channels.
  • I. INTRODUCTION: The IRS design assumes perfect knowledge of all involved channel state information at the secondary transmitter and IRS.The paper presents this idealized assumption as providing insights and performance bounds for future systems with partial or imperfect CSI.
  • I. INTRODUCTION: The SU transmitter varies its power up to Pmax while the PU transmit power remains fixed, and the resulting received signals determine the two link SINRs.The PU SINR must satisfy the target constraint before the achievable SU rate can be optimized.

B. Problem Formulation

The formulation maximizes SU spectral efficiency under a PU SINR constraint, but non-concavity and variable coupling make direct optimization difficult. The proposed solution alternates between power and IRS-reflection updates, supplemented by lower-complexity heuristic designs.

  • B. Problem Formulation: The objective is to maximize Rs = log2(1 + γs) subject to the PU constraint γp ≥ γth and unit-modulus IRS coefficients.The optimization jointly controls SU transmit power and the IRS reflection vector.
  • B. Problem Formulation: The problem is difficult because its objective is non-concave and the transmit-power and reflection variables are coupled.Fixing either ps or v yields a more tractable subproblem.
  • B. Problem Formulation: Alternating optimization iteratively optimizes SU transmit power and IRS reflection with the other variable fixed until convergence.This procedure provides a sub-optimal solution to the original problem.
  • III. PROPOSED SOLUTIONS: The proposed-solutions section first develops an AO-based algorithm and then introduces heuristic designs to reduce complexity and signaling overhead.The heuristics separately simplify passive beamforming and power-control design.
  • A. Alternating Optimization Based Joint Design: For fixed IRS reflection, the power subproblem has an objective monotonically increasing in ps, allowing the optimal SU power to be obtained in closed form.The solution remains subject to the maximum transmit-power budget.

2) Optimizing v for Given ps:

For fixed SU transmit power, the IRS beamforming problem is handled by successive convex approximation, relaxation, and iterative updates that preserve feasibility and converge to an approximate solution.

  • 2) Optimizing v for Given ps:: Successive convex approximation replaces the fractional QCQP with unit-modulus constraints by tractable approximated subproblems using lower bounds on the objective and constraint functions.The method applies a lemma-based lower-bound construction before solving each approximation.
  • 2) Optimizing v for Given ps:: The relaxed convex problem retains an optimal solution satisfying the unit-modulus constraints, making it optimal for the preceding constrained subproblem.This establishes the validity of relaxing |u_n|^2 ≤ 1 before recovering the IRS coefficients.
  • 2) Optimizing v for Given ps:: The beamforming update uses u_n = e^{j∠(w_ss(n)+λ⋆w_pp(n))}, with λ⋆ selected to satisfy the PU SINR constraint when necessary.If the constraint is active, λ⋆ is found by bisection because γ_p(λ) is monotonic; infeasibility occurs when γ_p(∞) < γ_th.
  • 2) Optimizing v for Given ps:: The algorithm successively solves the approximated problem, updates the reference point, and obtains the IRS reflection vector after convergence.The overall procedure is summarized in Algorithm 1 and terminates when the objective value reaches convergence.

3) Overall Algorithm:

The overall alternating-optimization procedure combines iterative SU power and IRS beamforming updates, with complexity dominated by matrix computations and scaling cubically with the IRS dimension.

  • 3) Overall Algorithm:: The overall complexity is O(L2(L1 + 1)(N + 1)^3), where L1 and L2 are the inner and outer convergence iteration counts.The dominant computations involve forming w_pp, d_ss, and d_pp.

B. Low Complexity Two-Stage Designs

The low-complexity designs separate passive beamforming from SU power optimization into two stages, using channel-power maximization or interference-power minimization objectives.

  • B. Low Complexity Two-Stage Designs: The first stage designs passive beamforming to maximize desired equivalent-link gains α_pp and α_ss or minimize interference-link gains α_ps and α_sp.These alternatives target the desired PT–PR/ST–SR links or the interfering PT–SR/ST–PR links, respectively.
  • B. Low Complexity Two-Stage Designs: The second stage optimizes ST transmit power using the same power-optimization procedure as the main design.This decomposition reduces implementation overhead relative to joint iterative optimization.

1) Signal power maximization based designs:

The signal-power designs choose IRS phases to maximize the effective desired PT–PR or ST–SR channel power under unit-modulus reflection constraints.

  • 1) Signal power maximization based designs:: The IRS phase vector is optimized to maximize α_pp for the primary desired link, subject to |v_n| = 1.The resulting phase aligns the reflected and direct components for the PT–PR path.
  • 1) Signal power maximization based designs:: The corresponding optimal design for α_ss is obtained similarly by applying the same phase-alignment principle to the secondary desired link.The cited formulation states that the optimal v maximizing α_ss can be obtained analogously.

2) Interference power minimization based designs:

The interference-minimization designs distinguish cases where IRS reflection can or cannot completely cancel interference, then solve the resulting phase optimization through semidefinite relaxation.

  • When the reflected ST-IRS-PR channel cannot exceed the direct ST-PR channel, interference cannot be completely canceled.
  • The optimal reflection coefficients are obtained from the interference-minimization formulation for this constrained case.
  • For the alternative case, lifting produces a positive semidefinite matrix with a rank-1 constraint that is relaxed using SDR.
  • The relaxed problem is convexly solvable; rank-1 solutions yield exact coefficients, while others use Gaussian randomization for recovery.

IV. SIMULATION RESULTS

Simulations compare IRS beamforming and no-IRS designs across three deployments, showing that IRS substantially improves SU access under strong interference while performance depends on beamforming objectives and coverage.

  • The evaluation uses three deployments with an IRS illustrated in the simulation setup and compares AO, four low-complexity IRS designs, and two no-IRS baselines.The IRS has 6 rows and 10 columns, and the comparisons include no-IRS operation with and without SIC.
  • In Setup (1), no-IRS with SIC and IRS minimizing αps saturate for Pmax ≥20 dBm, whereas AO and minimizing αsp continue increasing with Pmax.Reducing ST-PR interference through IRS permits higher ST transmit power and SU rate.
  • Low-complexity designs incur substantial rate loss relative to AO in Setup (1), indicating that IRS benefits involve multiple signal and interference links.
  • In Setup (2), IRS with AO always outperforms no-IRS with SIC, while minimizing αps nearly matches the no-IRS benchmark and other low-complexity designs achieve zero SU rate.AO both cancels PT-SR interference and enhances the desired ST-SR signal.
  • In Setup (2), AO eventually saturates because IRS coverage cannot reduce interference from ST to PR.
  • IRS-based designs enable higher SU rates in the most challenging setup, where no-IRS designs are ineffective because the SU must remain silent to protect the PU.The proposed AO and interference-minimization designs reduce ST-PR interference, allowing increased SU transmit power.

V. CONCLUSION

The paper jointly optimizes SU transmit power and IRS reflection beamforming for SU-rate maximization, and simulations show effectiveness in challenging interference scenarios.

  • The paper studies SU-rate maximization through joint transmit power control and IRS reflect beamforming.
  • An alternating-optimization algorithm efficiently solves the problem, and simulations show IRS improves SU rate in challenging conventional-CR scenarios.

APPENDIX A

The appendix derives an upper-bound-based convexification using Taylor expansion and Lagrangian optimality conditions for the subproblem solution.

  • Because f(x,y)=|x|2/y is jointly convex, its first-order Taylor expansion at (x0,y0) is used in the derivation.
  • An upper bound on ˜vHB˜v is substituted into the Taylor-based expression to obtain the target constraint.
  • The Lagrangian dual function is finite only when µn > 0, and the optimal primal and dual variables satisfy the KKT conditions.
  • The first-order condition gives u⋆n=(wss(n)+λwpp(n))/µn, while |u⋆n|=1 completes the optimality proof.

APPENDIX C

Appendix C establishes that the function a(n) increases strictly with λ under the stated nondegeneracy condition.

  • a(n) is defined through the cosine of the phase-angle difference between wss(n)+λwpp(n) and wpp(n).
  • The derivation rewrites γp(λ) as a weighted sum involving |wpp(n)|a(n) plus dpp.
  • Under x2y1 ≠ x1y2, a(n) strictly increases as λ increases for all λ > 0.This completes the appendix proof.
Loading 2003.03105v2…