摘要
最佳离散信号在雷达、声纳、导航、遥测遥控、信号处理、信息加密、扩频通信等领域得到了广泛的应用。在过去的几十年里,众多学者对它进行了深入的研究。最佳离散信号偶是最佳离散信号的一个新的研究方向,因此,对最佳离散信号偶的研究具有重要的理论意义和应用意义。
本文在最佳二进阵列偶、几乎最佳二进阵列偶、最佳屏蔽二进阵列偶等具有良好相关特性的离散信号研究的基础上,对最佳离散信号偶进行了深入的研究。
针对二进序列偶的唯一接收问题,提出并证明了低相关区序列偶的唯一性问题。并将零相关区序列偶、几乎最佳自相关序列偶作为特例进行研究,证明二者也满足唯一性。此外,还提出并证明了伪随机二进序列偶、几乎最佳屏蔽二进序列偶、最佳屏蔽二进序列偶、伪随机屏蔽二进序列偶的唯一性问题。从理论上保证了上述序列偶信号在应用时的唯一接收。
提出了二维零相关区序列偶,研究了二维二进零相关区序列偶的变换性质及存在的必要条件;研究给出了二维零相关区序列偶的理论界,并给出扩展零相关区序列偶集和二维零相关区序列偶集的方法。
提出了二维零相关区互补序列偶,研究了二维二进零相关区互补序列偶的变换性质,研究给出了二维零相关区互补序列偶的理论界,给出了一种利用二维二进零相关区互补序列偶集构造二维三元零相关区互补序列偶集的方法。提出了二维零相关区互补序列偶族,研究了二维二进零相关区互补序列偶族的变换性质,研究给出了二维零相关区互补序列偶族的理论界;给出一种利用二维二进零相关区互补序列偶族集构造二维三元零相关区互补序列偶族集的方法。
提出了二维零相关区周期互补序列偶,研究了二维二进零相关区周期互补序列偶的变换性质,研究给出了二维零相关区周期互补序列偶的理论界,给出了一种扩展二维零相关区周期互补序列偶集的方法;提出了二维零相关区周期互补序列偶族,研究了二维二进零相关区周期互补序列偶族的变换性质,研究给出了二维零相关区周期互补序列偶族的理论界,给出一种扩展二维零相关区周期互补序列偶族集的方法。
提出了二值自相关二进阵列偶,研究了它的变换性质、频谱特性及存在的必要条件,给出了二值自相关二进阵列偶与二值自相关二进序列偶及二值自相关二进阵列偶与二值自相关二进阵列偶之间的折叠构造方法。
提出了二值自相关屏蔽二进阵列偶,研究了它的变换性质、频谱特性及存在的必要条件,给出了二值自相关屏蔽二进阵列偶与二值自相关屏蔽二进序列偶及二值自相关屏蔽二进阵列偶与二值自相关屏蔽二进阵列偶之间的折叠构造方法。
针对二进阵列偶的唯一接收问题,提出并证明了二值自相关二进阵列偶的唯一性问题,将伪随机二进阵列偶作为其特例证明也满足唯一性;此外还提出并证明了几乎最佳二进阵列偶、最佳屏蔽二进阵列偶的唯一性问题。从理论上保证了上述阵列偶信号在应用时的唯一接收。
The perfect discrete signal has been widely employed in radar, sonar, navigation, telemetry and remote control, signal processing, information encryption, spread spectrum communication and so on. In the past several decades, many researchers devoted to the study of the perfect discrete signal. The perfect discrete signal pair is a new researching direction of the perfect discrete signal, so the research on the perfect discrete signal pair has important theory significance and application significance.
Based on the study of discrete signals with good correlation, such as perfect binary array pair, almost perfect binary array pair, perfect punctured binary array pair, some in-depth studies of the perfect discrete signal pair have been developed.
Aiming at the unique receiving of binary sequence pair, the uniqueness of low correlation zone sequence pair is put forward and proved. And, the uniqueness of zero correlation zone sequence pair and almost perfect autocorrelation sequence pair is proved as the specific cases of low correlation zone sequence pair. Moreover, the uniqueness of pseudorandom binary sequence pair, almost perfect punctured binary sequence pair, perfect punctured binary sequence pair and pseudorandom punctured binary sequence pair is proved. The unique receiving is guaranteed in theory, when the sequence pairs mentioned above are applied.
Two-dimension sequence pair with zero correlation zone is proposed. The transformation properties and existence conditions of two-dimension binary sequence pair with zero correlation zone are studied. The bound on two-dimension sequence pair with zero correlation zone is given. And methods of extension of set size of sequence pair set with zero correlation zone and two-dimension sequence pair set with zero correlation zone are presented.
Two-dimension complementary sequence pair with zero correlation zone is proposed. The transformation properties of two-dimension binary complementary sequence pair with zero correlation zone are studied. The bound on two-dimension complementary sequence pair with zero correlation zone is given. And the method of construction of two-dimension ternary complementary sequence pair set with zero correlation zone is presented based on two-dimension binary complementary sequence pair set with zero correlation zone. Two-dimension complementary sequence pair family with zero correlation zone is proposed. The transformation properties of two-dimension complementary sequence pair family with zero correlation zone are studied. The bound on two-dimension complementary sequence pair family with zero correlation zone is given. And the method of construction of two-dimension ternary complementary sequence pair family set with zero correlation zone is presented based on two-dimension binary complementary sequence pair family set with zero correlation zone.
Two-dimension periodic complementary sequence pair with zero correlation zone is proposed. The transformation properties of two-dimension binary periodic complementary sequence pair with zero correlation zone are studied. The bound on two-dimension periodic complementary sequence pair with zero correlation zone is given. And the method of extension of set size of two-dimension periodic complementary sequence pair set with zero correlation zone is presented. Two-dimension periodic complementary sequence pair family with zero correlation zone is proposed. The transformation properties of two-dimension binary periodic complementary sequence pair family with zero correlation zone are studied. The bound on two-dimension periodic complementary sequence pair family with zero correlation zone is given. And the method of extension of set size of two-dimension periodic complementary sequence pair family set with zero correlation zone is presented.
Binary array pair with two-level autocorrelation is proposed. The transformation properties, Fourier spectrum characters and existence conditions of binary array pair with two-level autocorrelation are studied. Folding construction between binary array pair with two-level autocorrelation and binary sequence pair with two-level autocorrelation, and folding construction among binary array pairs with two-level autocorrelation are given.
Punctured binary array pair with two-level autocorrelation is proposed. The transformation properties, Fourier spectrum characters and existence conditions of punctured binary array pair with two-level autocorrelation are studied. Folding construction between punctured binary array pair with two-level autocorrelation and punctured binary sequence pair with two-level autocorrelation, and folding construction among punctured binary array pairs with two-level autocorrelation are given.
Aiming at the unique receiving of binary array pair, the uniqueness of binary array pair with two-level autocorrelation is put forward and proved. And, the uniqueness of pseudorandom binary array pair is proved as the specific case of binary array pair with two-level autocorrelation. Moreover, the uniqueness of almost perfect binary array pair and perfect punctured binary array pair is proved. The unique receiving is guaranteed in theory, when the array pairs mentioned above are applied.
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