摘要
具有零相关区的序列集在无线通信以及雷达中具有重要的应用。然而,现有的序列集大都基于数学解析构造方法得到,其参数如序列长度和序列数目等受到一些限制,不能灵活设定,这限制了其在实际场景中的应用。因此,研究具有灵活参数的序列集构造方法成为一个有意义的课题。为得到更多灵活参数的序列集,该文利用牛顿优化方法来进行零相关区序列设计研究,具体提出了非周期零相关区互补序列集和非周期零相关区序列集的优化设计方法,得到的序列集参数可灵活调节。最后,通过互补峰值旁瓣水平(CPSL)和加权峰值旁瓣水平(WPSL)评估了序列集性能。
Objective Sequences with favorable correlation properties are widely applied in radar and communication systems.Sequence sets with zero or low correlation characteristics enhance radar resolution,target detection,imaging quality,and information acquisition,while also improving the omnidirectional transmission capability of massive multiple-input multiple-output(MIMO)systems.Designing aperiodic Zero Correlation Zone(ZCZ)sequence sets with excellent correlation performance is therefore critical for both wireless communication and radar applications.For example,aperiodic Z-Complementary Set(ZCS)sequence sets are often used in omnidirectional precoding for MIMO systems,whereas aperiodic ZCZ sequence sets are employed in integrated MIMO radar-communication systems.These ZCZ sequence sets are thus valuable across a range of system applications.However,most prior studies rely on analytical construction methods,which impose constraints on parameters such as sequence length and the number of sequences,thereby limiting design flexibility and practical applicability.This study proposes a numerical optimization approach for designing ZCS and aperiodic ZCZ sequence sets with improved correlation properties and greater parametric flexibility.The method minimizes the Complementary Peak Sidelobe Level(CPSL)and Weighted Peak Sidelobe Level(WPSL)using Newton’s method to achieve superior sequence performance.Methods This study proposes an optimization-based design method using Newton’s method to construct both aperiodic ZCS sequence sets and aperiodic ZCZ sequence sets with low sidelobe levels and flexible parameters.The optimization objective is first formulated using the CPSL and WPSL.The problem is then reformulated as an equivalent system of nonlinear equations,which is solved using Newton’s method.To reduce computation time,partial derivatives are approximated using numerical differentiation techniques.A loop iteration strategy is employed to address multiple constraints during the optimization process.To ensure algorithmic convergence,Armijo’s rule is used for step size selection,promoting stable descent of the objective function along the defined search direction.Results and Discussions The aperiodic ZCS sequence set is constructed using Newton’s method.As the number of sequences increases,the CPSL progressively decreases,falling below-300 dB when M≥2.The proposed method yields better sidelobe performance than the improved Iterative Twisted Approximation(ITORX)algorithm(Fig.1).The performance of ZCS sequences generated by both methods is evaluated under different ZCZ conditions.While both approaches achieve low CPSL,Newton’s method yields aidelobe levels closer to the ideal value(Fig.2).Convergence behavior is assessed using CPSL and the number of iterations.The improved ITROX algorithm typically requires around 20000 iterations to converge,with increasing iterations as ZCZ size grows.In contrast,Newton’s method achieves rapid convergence within approximately 10 iterations(Figs.3 and 4).The aperiodic ZCZ sequence set constructed using Newton’s method exhibits autocorrelation and cross-correlation peak sidelobe levels below-300 dB within the ZCZ.Moreover,Newton’s method achieves the lowest WPSL,offering the best overall performance among all tested methods(Fig.5).The smooth convergence curves further confirm the algorithm’s stability when applied to aperiodic ZCZ sequence construction(Fig.6).Conclusions This study proposes an optimization-based algorithm for designing aperiodic ZCS and aperiodic ZCZ sequence sets using Newton’s method,aiming to address the limitations of fixed parameters and high peak sidelobe levels found in existing approaches.Two optimization problems are formulated by minimizing the WPSL and CPSL,respectively.To simplify computation,the optimization tasks are converted into systems of nonlinear equations,which are solved using Newton’s method.The Jacobian matrix is computed via numerical differentiation to reduce computational cost.A loop iteration strategy is introduced to meet multiple constraints in the construction of aperiodic ZCZ sequences.Simulation results confirm that the proposed method yields sequence sets with excellent correlation properties and flexible parameter configurations.By tuning the weighting coefficients,low sidelobe levels can be achieved in specific regions of interest,accommodating different application requirements.The combination of flexible design parameters and favorable correlation performance makes the proposed sequences suitable for a wider range of practical scenarios.
作者
呼恩波
刘涛
李玉博
HU Enbo;LIU Tao;LI Yubo(School of Information Science&Engineering,Yanshan University,Qinhuangdao 066004,China;Shenzhen Research Institute of Yanshan University,Shenzhen 518063,China)
出处
《电子与信息学报》
北大核心
2025年第11期4451-4458,共8页
Journal of Electronics & Information Technology
基金
国家自然科学基金(62471427)
河北省中央引导地方科技发展资金项目(246Z0403G)。
关键词
牛顿法
非周期
零相关区
峰值旁瓣水平
Newton’s Method
aperiodic
Zero Correlation Zone(ZCZ)
Peak Sidelobe Level(PSL)
