An Optimization Design Method for Zero-Correlation Zone Sequences Based on Newton’s Method

HU Enbo; LIU Tao; LI Yubo

doi:10.11999/JEIT250394

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HU Enbo, LIU Tao, LI Yubo. An Optimization Design Method for Zero-Correlation Zone Sequences Based on Newton’s Method[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250394

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HU Enbo, LIU Tao, LI Yubo. An Optimization Design Method for Zero-Correlation Zone Sequences Based on Newton’s Method[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250394

HU Enbo, LIU Tao, LI Yubo. An Optimization Design Method for Zero-Correlation Zone Sequences Based on Newton’s Method[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250394

Citation:

HU Enbo, LIU Tao, LI Yubo. An Optimization Design Method for Zero-Correlation Zone Sequences Based on Newton’s Method[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250394

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An Optimization Design Method for Zero-Correlation Zone Sequences Based on Newton’s Method

doi: 10.11999/JEIT250394 cstr: 32379.14.JEIT250394

1.
School of Information Science & Engineering, Yanshan University, Qinhuangdao 066004, China
2.
Shenzhen Research Institute of Yanshan University, Shenzhen 518063, China

Funds: The National Natural Science Foundation of China(62471427), The S&T Program of HeBei (246Z0403G)

Received Date: 2025-05-08
Rev Recd Date: 2025-07-16

Available Online: 2025-07-25

Abstract

Abstract

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 $M \geqslant 2$. 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.
- Newton’s Method,
- aperiodic,
- Zero Correlation Zone(ZCZ),
- Peak Sidelobe Level(PSL)

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References(23)

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