最佳离散信号及应用研究
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摘要
近几十年来具有优良相关特性的时间离散信号在需要从接收信号中提取所要信息的测试、数字通信和连续波雷达等应用领域得到了广泛应用。具有优良相关特性的序列是信息理论中备受关注和深入研究的热点问题之一。本文对几种具有优良相关特性的序列偶和失配信号进行了研究。
对最佳四相周期信号进行了研究,提出了最佳周期几乎四相序列偶的概念,并研究了其性质、存在空间和构造方法;研究了一种只有一个非单位根的最佳四相序列偶的构造方法,由此可以产生更多长度的最佳周期四相信号;对最佳周期三元序列偶的构造方法进行了研究,给出了一种利用相关恒等变换设计最佳周期三元序列偶的方法。
研究了ZCZ序列偶集的构造方法,提出了采用最佳序列偶的移位序列与酉矩阵利用相关积构造零相关区序列偶集的方法,通过对一个最佳序列偶特定的移位序列和特定阶数的酉矩阵进行相关积运算,构造出了准最优ZCZ序列偶集及最优ZCZ序列偶集。
研究了扩展ZCZ序列偶集零相关区及容量的方法,提出了两种利用已有的ZCZ序列偶集,构造更宽零相关区ZCZ序列偶集的方法,和四种利用已有的ZCZ序列偶集,构造更宽零相关区和更大容量ZCZ序列偶集的方法。通过对原始序列偶集进行特殊移位运算,再和相应阶数的酉矩阵进行相关积运算,构造出了序列偶的长度更长,零相关区更宽,序列偶集的容量更大的ZCZ序列偶集。对周期和奇周期四相失配阵列信号进行了研究,分析了两种失配阵列信号的存在条件,给出了利用折叠法和周期乘法构造这两种失配阵列的构造过程,由此构造的失配阵列信号不仅实现了其周期或奇周期相关函数的所有旁瓣为0,在实际应用中能够完全消除旁瓣对系统性能的影响,而且扩展了四相阵列信号的体积。
研究了序列偶扩频通信系统的性能,从理论上分析推导了在单音连续波干扰条件下不同的序列偶对扩频通信系统的性能影响,并仿真验证了的不同的序列偶扩频方案的性能,为序列偶的实际应用提供了依据。将设计的ZCZ序列偶集应用于QS-CDMA系统进行了仿真,验证了其在实际系统中的可行性。
研究了OFDM系统信道估计的方法,将失配序列和最佳序列偶应用于OFDM系统进行信道估计,可以简化估计算法,提高估计的准确度。
Time-discrete signal with good autocorrelation properties are used in various application in measurement, digital communications and continuous– wave (CW) radar, where the desired information is extracted from the received signal using the periodic autocorrelation in recent several decades. Discrete signal with good correlation properties is an important problem paid eagerly attention and researched deeply in the field of information theory. Several sequence pairs and mismatched filtering signals are researched in this paper.
First, a new periodic correlation discrete signal is proposed, which can be called as perfect almost-quadriphase sequence pairs. The transformation properties and existing condition of the perfect almost-quadriphase sequence pairs are presented. A kind of constructing method of perfect quadriphase sequence pair with only one nonuniform element is given, and the length of the signals can be extended. From the result above two, we can design more length perfect quadriphase signals. A constructing method of ternary sequence pairs by using correction identity is presented.
Two new methods for constructing sets of zero-correlation zone (ZCZ) sequence pair are proposed. Almost optimal or optimal ZCZ sequence pairs set can be generated from the correlation product of special unitary matrices and difference shifted sequence of perfect sequence pair.
Based on known ZCZ sequence pair set, two new methods of constructing ZCZ sequence pairs set with wide zero correlation zone and four kinds of methods of constructing ZCZ sequence pairs with both large family size and wide zero correlation zone are proposed. They can be generated from the correlation product of special unitary matrices and the difference shifted form of original ZCZ sequence pairs set. The researching result enriches the theory of ZCZ sequence pairs set.
Periodic and odd-periodic quadriphase mismatched filtering arrays are proposed. Exiting conditions and construction methods of folding and periodic multiplication for periodic and odd-periodic quadriphase arrays are presented. All sidelobe of above periodic or odd-periodic correlation arrays converges to zero so their influences vanished with quadriphase array size is enlarged.
The influence of CW interference in direct sequence spread system (DSSS) based on sequence pair is derived, and simulation verification is given later. The ZCZ sequence pair designed above was applied to quasi-synchronous code division multiple access (QS-CDMA) system, simulation results show that they can satisfy the demand of the real system.
A new approach which using mismatched filtering sequence and sequence pair to channel estimation in orthogonal frequency division multiplexing (OFDM) systems is proposed. Theoretical analysis and simulation results show that the new method has good property of low complexity, accurate estimation and better BER performance.
对最佳四相周期信号进行了研究,提出了最佳周期几乎四相序列偶的概念,并研究了其性质、存在空间和构造方法;研究了一种只有一个非单位根的最佳四相序列偶的构造方法,由此可以产生更多长度的最佳周期四相信号;对最佳周期三元序列偶的构造方法进行了研究,给出了一种利用相关恒等变换设计最佳周期三元序列偶的方法。
研究了ZCZ序列偶集的构造方法,提出了采用最佳序列偶的移位序列与酉矩阵利用相关积构造零相关区序列偶集的方法,通过对一个最佳序列偶特定的移位序列和特定阶数的酉矩阵进行相关积运算,构造出了准最优ZCZ序列偶集及最优ZCZ序列偶集。
研究了扩展ZCZ序列偶集零相关区及容量的方法,提出了两种利用已有的ZCZ序列偶集,构造更宽零相关区ZCZ序列偶集的方法,和四种利用已有的ZCZ序列偶集,构造更宽零相关区和更大容量ZCZ序列偶集的方法。通过对原始序列偶集进行特殊移位运算,再和相应阶数的酉矩阵进行相关积运算,构造出了序列偶的长度更长,零相关区更宽,序列偶集的容量更大的ZCZ序列偶集。对周期和奇周期四相失配阵列信号进行了研究,分析了两种失配阵列信号的存在条件,给出了利用折叠法和周期乘法构造这两种失配阵列的构造过程,由此构造的失配阵列信号不仅实现了其周期或奇周期相关函数的所有旁瓣为0,在实际应用中能够完全消除旁瓣对系统性能的影响,而且扩展了四相阵列信号的体积。
研究了序列偶扩频通信系统的性能,从理论上分析推导了在单音连续波干扰条件下不同的序列偶对扩频通信系统的性能影响,并仿真验证了的不同的序列偶扩频方案的性能,为序列偶的实际应用提供了依据。将设计的ZCZ序列偶集应用于QS-CDMA系统进行了仿真,验证了其在实际系统中的可行性。
研究了OFDM系统信道估计的方法,将失配序列和最佳序列偶应用于OFDM系统进行信道估计,可以简化估计算法,提高估计的准确度。
Time-discrete signal with good autocorrelation properties are used in various application in measurement, digital communications and continuous– wave (CW) radar, where the desired information is extracted from the received signal using the periodic autocorrelation in recent several decades. Discrete signal with good correlation properties is an important problem paid eagerly attention and researched deeply in the field of information theory. Several sequence pairs and mismatched filtering signals are researched in this paper.
First, a new periodic correlation discrete signal is proposed, which can be called as perfect almost-quadriphase sequence pairs. The transformation properties and existing condition of the perfect almost-quadriphase sequence pairs are presented. A kind of constructing method of perfect quadriphase sequence pair with only one nonuniform element is given, and the length of the signals can be extended. From the result above two, we can design more length perfect quadriphase signals. A constructing method of ternary sequence pairs by using correction identity is presented.
Two new methods for constructing sets of zero-correlation zone (ZCZ) sequence pair are proposed. Almost optimal or optimal ZCZ sequence pairs set can be generated from the correlation product of special unitary matrices and difference shifted sequence of perfect sequence pair.
Based on known ZCZ sequence pair set, two new methods of constructing ZCZ sequence pairs set with wide zero correlation zone and four kinds of methods of constructing ZCZ sequence pairs with both large family size and wide zero correlation zone are proposed. They can be generated from the correlation product of special unitary matrices and the difference shifted form of original ZCZ sequence pairs set. The researching result enriches the theory of ZCZ sequence pairs set.
Periodic and odd-periodic quadriphase mismatched filtering arrays are proposed. Exiting conditions and construction methods of folding and periodic multiplication for periodic and odd-periodic quadriphase arrays are presented. All sidelobe of above periodic or odd-periodic correlation arrays converges to zero so their influences vanished with quadriphase array size is enlarged.
The influence of CW interference in direct sequence spread system (DSSS) based on sequence pair is derived, and simulation verification is given later. The ZCZ sequence pair designed above was applied to quasi-synchronous code division multiple access (QS-CDMA) system, simulation results show that they can satisfy the demand of the real system.
A new approach which using mismatched filtering sequence and sequence pair to channel estimation in orthogonal frequency division multiplexing (OFDM) systems is proposed. Theoretical analysis and simulation results show that the new method has good property of low complexity, accurate estimation and better BER performance.
引文
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