Construction Methods of Two-Dimensional Golay-Zero Correlation Zone Array Sets with Flexible Parameters

WANG Meiyue; LIU Tao; CHEN Xiaoyu; LI Yubo

doi:10.11999/JEIT251360

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WANG Meiyue, LIU Tao, CHEN Xiaoyu, LI Yubo. Construction Methods of Two-Dimensional Golay-Zero Correlation Zone Array Sets with Flexible Parameters[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251360

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WANG Meiyue, LIU Tao, CHEN Xiaoyu, LI Yubo. Construction Methods of Two-Dimensional Golay-Zero Correlation Zone Array Sets with Flexible Parameters[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251360

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Construction Methods of Two-Dimensional Golay-Zero Correlation Zone Array Sets with Flexible Parameters

doi: 10.11999/JEIT251360 cstr: 32379.14.JEIT251360

1.
School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
2.
Hebei Province Key Laboratory of Information Transmission and Signal Processing, Qinhuangdao 066004, China
3.
Shenzhen Research Institute of Yanshan University, Shenzhen 518063, China

Funds: The National Natural Science Foundation of China (62501520, 62471427), The Central Guiding Local Science and Technology Development Fund Project of Hebei Province (246Z0403G), The Natural Science Foundation of Hebei Province (F2025203055)

Accepted Date: 2026-02-05
Rev Recd Date: 2026-02-05

Available Online: 2026-02-15

Abstract

Abstract

Objective Sequences with good correlation properties have important applications in wireless communications, cryptography and radar. However, a sequence set cannot simultaneously achieve ideal autocorrelation and ideal cross-correlation. This limitation has driven the study of two signal classes with ideal correlation properties: Zero Correlation Zone (ZCZ) sequences and Golay Complementary Sets (GCS). The Golay-ZCZ sequence set combines their advantages: its constituent sequences exhibit ideal periodic autocorrelation and cross-correlation within the ZCZ, while their aperiodic autocorrelations sum to zero at all non-zero shifts. That is, a Golay-ZCZ set is a ZCZ set and also a GCS. Therefore, it can be used in the original applications of GCSs and those of ZCZ sets. An array set is a two-dimensional extension of a sequence set. Although Golay-ZCZ sequence sets have been extensively constructed and studied, research on Two-Dimensional (2-D) Golay-ZCZ array sets remains relatively limited. This study proposes three constructions of 2-D Golay-ZCZ array sets using 2-D multivariate functions and concatenation operator, which can be applied as precoding matrices for massive Multiple Input Multiple Output (MIMO) omnidirectional transmission. Methods This paper proposes three construction methods for constructing 2-D Golay-ZCZ array sets, including both direct and indirect construction approaches. The parameters of these methods have not been reported in the existing literature. In the first construction, the 2-D Golay-ZCZ array set is generated based on 2-D multivariate functions, with its parameters taking the form of prime powers. This function-based direct construction enables more efficient synthesis of the target arrays. The second and third construction methods generate 2-D Golay-ZCZ array sets by horizontally cascading and vertically cascading two-dimensional complete complementary codes, respectively. The parameters of these indirect construction methods are not restricted to prime powers, thereby broadening the applicability and parametric flexibility of the approaches. Results and Discussions The first construction generates a 2-D Golay-ZCZ array set with array size $ p_{1}^{{m}_{1}}\times p_{2}^{{m}_{2}} $ and ZCZ size $ ({p}_{1}-1)p_{1}^{{\pi }_{1}(2)-1}\times ({p}_{2}-1)p_{2}^{{\sigma }_{1}(2)-1} $ through a direct function-based method, where $ {p}_{1} $ and $ {p}_{2} $ are primes. For ease of understanding, the magnitudes of the 2-D periodic cross-correlation function of the constructed array set in example 1 (Fig. 1). The second construction presents a ZCZ array set with array size $ {L}_{1}\times {N}^{2}{L}_{2} $ and ZCZ size $ ({L}_{1}-1)\times (N-1){L}_{2} $ based the horizontal concatenation of $ (N,N,{L}_{1},{L}_{2}) $ 2-D CCC. The third construction presents a ZCZ array set with array size $ {N}^{2}{L}_{1}\times {L}_{2} $ and ZCZ size $ (N-1){L}_{1}\times ({L}_{2}-1) $based the vertical concatenation of $ (N,N,{L}_{1},{L}_{2}) $ 2-D CCC. An illustrative example for construction 2 is provided. The corresponding correlation magnitudes are detailed accordingly (Figs. 2 and 3). As shown in (Table 1), the construction methods proposed in this paper produce parameters that have not been reported in the existing literature. The constructed array sets exhibit significant flexibility in terms of array dimensions and ZCZ sizes, which is of substantial practical importance for the design of precoding matrices in MIMO omnidirectional transmission systems. In practical implementations, the dimensionality of a precoding matrix is typically determined by the number of transmit antennas, while the size of the ZCZ must align with the maximum multipath delay spread of the channel. Owing to the parameter flexibility, the proposed 2-D Golay-ZCZ array sets facilitate adaptive selection based on diverse antenna configurations and channel conditions. Conclusions This paper proposes three constructions of 2-D Golay-ZCZ array sets, which can provide flexible array size and large ZCZ width. Based on the 2-D multivariable function, the first proposed construction can include the previous result as a special case without utilizing any kernels. The second and third constructions exhibit more parametric flexibility based on concatenation operator. The proposed 2-D Golay-ZCZ arrays have potential applications in MIMO omnidirectional transmission. The parameter-flexible 2-D Golay-ZCZ array set can adaptively select according to different antenna configurations and channel conditions, thereby effectively suppressing multi-antenna interference within the zero-correlation zone while maintaining the uniformity of the transmitted energy.
- 2-D Golay-ZCZ Array Set,
- 2-D Multivariable Function,
- Zero Correlation Zone (ZCZ),
- Omnidirectional Transmission

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References(28)

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