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arXiv 2510.26147cs.ITeess.SPmath.ITmath.OC
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基于对偶的固定点迭代算法在智能感知与通信系统中的波束成形设计

Duality-Based Fixed Point Iteration Algorithm for Beamforming Design in ISAC Systems

Academy of Mathematics and Systems Science, Chinese Academy of Sciences(中国科学院数学与系统科学研究院);School of Mathematical Sciences, University of Chinese Academy of Sciences(中国科学院大学数学科学学院);Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications(北京邮电大学数学科学学院教育部数学与信息神经网络重点实验室)

Xilai Fan, Ya-Feng Liu

AI总结:

研究ISAC系统波束成形设计问题,通过建立等价关系和对偶公式转化为GDB问题,提出GDB问题有界条件和FPI算法,开发Dual-FPI算法,能实现全局最优解并降低计算复杂度。

摘要:

本文研究智能感知与通信(ISAC)系统中的波束成形设计问题,多天线基站在进行雷达感知时同时为多个通信用户服务。将问题表述为总发射功率最小化,受通信用户的信号与干扰加噪声比(SINR)约束和雷达感知的均方误差(MSE)约束。核心挑战源于通信SINR要求与感知性能指标之间的复杂耦合。首先建立原始ISAC波束成形问题与其半定松弛(SDR)之间的等价关系,推导其拉格朗日对偶公式,并进一步将其重新表述为具有潜在不定加权矩阵的广义下行链路波束成形(GDB)问题。提出GDB问题有界的充要条件和一种定制的高效固定点迭代(FPI)算法。在此基础上开发了基于对偶的固定点迭代(Dual-FPI)算法,仿真结果表明该算法能实现全局最优解且显著降低计算复杂度。

英文摘要:

In this paper, we investigate the beamforming design problem in an integrated sensing and communication (ISAC) system, where a multi-antenna base station simultaneously serves multiple communication users while performing radar sensing. We formulate the problem as the minimization of the total transmit power, subject to signal-to-interference-plus-noise ratio (SINR) constraints for communication users and mean-squared-error (MSE) constraints for radar sensing. The core challenge arises from the complex coupling between communication SINR requirements and sensing performance metrics. To efficiently address this challenge, we first establish the equivalence between the original ISAC beamforming problem and its semidefinite relaxation (SDR), derive its Lagrangian dual formulation, and further reformulate it as a generalized downlink beamforming (GDB) problem with potentially indefinite weighting matrices. Compared to the classical DB problem, the presence of indefinite weighting matrices in the GDB problem introduces substantial analytical and computational challenges. Our key technical contributions include (i) a necessary and sufficient condition for the boundedness of the GDB problem, and (ii) a tailored efficient fixed point iteration (FPI) algorithm with a provable convergence guarantee for solving the GDB problem. Building upon these results, we develop a duality-based fixed point iteration (Dual-FPI) algorithm, which integrates an outer subgradient ascent loop with an inner FPI loop. Simulation results demonstrate that the proposed Dual-FPI algorithm achieves globally optimal solutions while significantly reducing computational complexity compared with existing baseline approaches.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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