Weighted Optimization Beamforming Algorithm for Integrated Sensing and Communication in Multi-User Multi-Target Scenarios
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摘要: 无论在军事领域的战术通信和目标探测，还是在无人驾驶技术中实现高效的通信和高精度的环境感知，通信感知一体化都可以显著提升系统性能并大幅提高频谱资源利用率。然而，通信和感知资源分配不均衡问题成为该项技术应用的巨大挑战。针对多目标探测和多用户通信场景，该文提出一种基于Pareto优化框架的发射波束形成设计方法。该方法首先将通感资源优化问题建模为一个非凸优化问题，采用通信性能与雷达性能的加权和作为优化目标，以提高系统的灵活性。为了求解该问题，该文提出改进的加权最小均方误差算法将其转化成一个易于求解的凸问题，通过调整Pareto权重因子权衡通信信干噪比与雷达发射波束图误差，实现在功率约束条件下通感性能的最优化设计，同时通过采用MIMO雷达的方式提高了雷达的自由度。仿真结果验证了所提出波束形成方法的有效性和优越性。Abstract:
Objective The increasing demand for wireless communication has led to a significant scarcity of spectrum resources, while the inherent coupling between communication and sensing systems allows for shared spectrum utilization. Integrated Sensing and Communication (ISAC) thus shows considerable promise for future applications. However, most existing studies focus on optimizing either communication or sensing performance, treating the other as a constraint, which limits system flexibility. This approach becomes particularly problematic in complex multi-user, multi-target scenarios, where balancing both functionalities is essential. Additionally, previous works often assume symmetrically distributed radar targets in small quantities, simplifying optimization but diverging from practical asymmetric and dense target distributions. To address these limitations, this study explores ISAC systems with asymmetric multi-target configurations, aiming to improve flexibility and practicality through joint optimization of communication and sensing performance optimization. Methods This study adopts a MIMO radar framework in which orthogonal transmit signals maximize waveform Degrees of Freedom (DoFs) in proportion to the antenna count. A beamforming matrix is designed to detect targets across multiple directions while allocating distinct waveforms for communication and sensing tasks. In contrast to conventional antenna configurations, the proposed scheme utilizes all antennas for radar detection, enhancing sensing performance. To address the limitations of single-objective optimization, a Pareto optimization framework is introduced, allowing for weighted trade-offs between the communication Weighted Sum Rate (WSR) and radar beam pattern error. This framework is adaptable to dynamic scenarios. To handle the non-convexity of the optimization problem, a hybrid algorithm combining Weighted Minimum Mean Square Error (WMMSE) and Semidefinite Relaxation (SDR) is proposed. Specifically, the WSR and radar error maximization problem is first reformulated as a Mean Square Error (MSE) minimization problem, followed by SDR-based relaxation of constraints for tractable solutions. Results and Discussions As shown in ( Fig. 2 -3 ): (a) The proposed beamforming design demonstrates superior flexibility compared to single-objective optimization, enabling adaptable balancing of communication and sensing performance across scenarios by adjusting the Pareto weight factor. (b) Compared to separated deployment schemes, the proposed method utilizes more antennas for sensing, concentrating transmit power in specific directions to enhance target detection capability. (c) With comparable radar performance, the communication WSR of the proposed scheme shows an 11.6% improvement over shared deployment configurations.(Fig. 4 ) further illustrates the radar detection error under varying SNRs. Regardless of the performance weight values, the radar detection error decreases with increasing transmit power, indicating that higher power improves system performance. Under constant transmit power, a smaller performance weight results in higher radar detection accuracy, as more power is allocated to radar performance optimization. For a more comprehensive comparison, (Fig. 5 ) shows the beamforming patterns under different transmit power levels for the separated deployment scheme. In this scheme, as transmit power increases, the radar detection error actually increases. This occurs because the system optimizes detection performance in a specific direction, achieving optimal precision there. As shown in the figure, as power increases, the antenna power becomes concentrated in the direction of the target at 0°, significantly improving resolution in that direction, while detection performance in other directions deteriorates. This indicates that the separated deployment scheme is limited in its ability to meet detection requirements for multiple targets simultaneously. (Fig. 6 ) demonstrates that, at all transmit power levels, the proposed scheme exhibits clear advantages in communication performance. (Figs. 7 -9 ) analyze the impact of target quantity on radar detection error, confirming robustness in multi-target asymmetric scenarios. When transmit power and weight factors remain unchanged, increasing the number of radar detection targets leads to an increase in radar detection error. This happens because total power remains constant, and adding more detection targets reduces the power allocated to each target. This effect becomes more pronounced as the number of targets grows. However, this error increase can be mitigated by increasing transmit power. Simulation results show that the proposed scheme consistently outperforms other methods under different target numbers, demonstrating its ability to efficiently utilize limited power and maintain low detection errors, even as the number of targets increases. (Fig. 10 ) reveals directional limitations, as beam patterns at edge angles exhibit weak directivity, complicating peripheral target detection. Algorithm convergence curves (Fig. 11 ) and Pareto frontiers for communication-radar trade-offs (Fig. 12 ) confirm the stability and flexibility of the proposed scheme.Conclusions This study addresses the limitations of single-objective optimization (communication or radar performance) and constrained radar degrees of freedom by proposing a weighted joint beamforming design for ISAC. The ground base station, equipped with dual functionalities, optimizes the WSR and radar beam pattern error. By adjusting the Pareto weight factor, flexible performance trade-offs between communication and sensing are achieved, improving adaptability to diverse scenarios. Experimental results demonstrate that, under optimized weights and transmit SNR, the proposed scheme reduces radar detection error by 36.2% and enhances communication SINR by 1 dB compared to separated deployment strategies. These advancements validate the effectiveness of the joint optimization framework in practical asymmetric multi-target environments, providing a robust foundation for next-generation ISAC systems. -
1 多目标联合优化发射波束形成设计
(1) 设置迭代次数$r = 0$ (2) 对${{\boldsymbol{W}}^{\left[ 0 \right]}}$进行初始化 (3) 对于给定的${{\boldsymbol{W}}^{\left[ t \right]}}$，根据式(15)计算$U_k^{[t]}$ (4) 对于步骤(3)所求的$U_k^{[t]}$，根据式(21)和式(22)计算${\boldsymbol{A}}_k^{[t]}$和
${\boldsymbol{B}}_k^{[t]}$(5) 对优化问题${\text{P}}4$进行求解，得到最优的${\boldsymbol{T}}_k^*$ (6) 通过特征值分解或高斯随机化得到近似解${\boldsymbol{\tilde w}}_k^*$ (7) 更新$t = t + 1$ (8) 重复步骤(3-7)直到$\left| {{\text{WS}}{{\text{R}}^{[t - 1]}} - {\text{WS}}{{\text{R}}^{[t]}}} \right| \le \varepsilon $ 
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