并元码研究的新方法

本文提出了一类新的区组设计－－并元设计，给出了并元加集的概念，研究了并元设计，并元加集，并元码之间的关系，为研究并元码提供了新的方法。     

并元加集与二元并元码

本文首先进一步研究了并元加集存在的必要条件，从而提出了二元并元码所具有的长度。然后给出了一系列二元并元码的构造方法。证明了存在长度为２２ｔ＋２的二元并元码，相应地证明了存在参数为（２２ｔ＋２，２２ｔ＋１±２ｔ，２２ｔ±２ｔ）的并元加集。     

具有良好并元相关特性的序列

该文对并元互补码偶族作出进一步的研究。首先提出了新的区组设计的概念一并元加族偶,然后给出了并元互补码偶族与区组设计的等价关系,应用这一等价关系给出了并元互补码偶族存在的必要条件,最后给出了并元互补码偶族的若干构造方法。     

一种新的并元互补码偶族的构造方法

利用并元互补码偶族和准最佳二进阵列的性质,给出了一种构造并元互补码偶族的新方法.使用这种方法,可以用一个长度为、组教为的并元互补码偶族和一个2维的准最佳二进阵列,构造成新的一类长度为、组数为的并元互补码偶族,为实际工作中提供了更多的最佳信号.     

非等周期ZCZ序列偶集合及其谱特性

提出了一种新的序列偶———非等周期ZCZ序列偶的概念。介绍了该序列偶在几种基本变换情况下的性质,在此基础上引入了集合的概念,并介绍了偶集合的基本性质。研究了这种偶的谱特性,应用这些谱特性给出了这中偶的重量分布情况及存在的必要条件。非等周期ZCZ序列偶的提出,为工程应用提供了更广泛的信号选择。     

几乎最佳二进阵列偶理论研究

本文提出了一种新的周期循环相关信号,即几乎最佳二进阵列偶.文中给出了其定义,并研究了它的变换性质,为了减少搜索范围,提高计算机搜索效率,文中研究给出了一些几乎最佳二进阵列偶存在的组合允许条件,在此基础上,利用计算机搜索出了若干小体积的几乎最佳二进阵列偶.搜索结果表明几乎最佳二进阵列偶具有很高的能量效率,因而可以作为同步码或多用户码应用到工程中.     

伪随机二进序列偶研究

提出了一种新的具有良好周期相关特性的离散信号,即伪随机二进序列偶,研究了其性质和组合允许条件,用计算机搜索出若干小体积的伪随机二进序列偶。在此基础上,对伪随机二进序列偶作为同步码在同步检测中的应用进行了研究,并与Barker码进行了性能比较分析。     

伪随机三元阵列偶理论研究

文中提出了一种新的具有良好循环相关特性的离散信号，即伪随机三元阵列偶。首先给出了伪随机三元阵列偶的相关定义；然后研究了伪随机三元阵列偶的变换性质和频谱特性；而且，为了减小搜索范围，提高搜索效率，给出了伪随机三元阵列偶存在的必要条件；最后证明了伪随机三元阵列偶的唯一性，并给出了一种构造伪随机三元阵列偶的方法。     

最佳二元序列偶族的构造方法

文中利用并元变换的不进位性质,给出了一种构造最佳周期互补二元序列偶族的新方法。使用这种方法,可以用已知的最佳周期互补二元序列偶族构造出更多的性能相同的新的最佳周期互补二元序列偶族,如原最佳周期互补二元序列偶族为长度为n,个数为q,则新生成最佳周期互补二元序列偶族的个数为qn,为实际工作中提供了更多的最佳信号。     

互补二进阵列偶的理论研究

具有良好非循环相关特性的序列中,互补序列最具有代表性。提出了一种新的非循环相关信号,即互补二进阵列偶。给出了定义,并研究了其变换性质。同时为了减少搜索范围,提高计算机搜索效率,研究给出了一些互补二进阵列偶的组合允许条件。互补二进阵列偶理论拓宽了互补序列的研究范围,有很好的工程应用背景。     

Research on perfect dyadic binary sequence pair

In this paper, the perfect dyadic binary sequence pair with one-value dyadic correlation functions is presented. That is, the perfect dyadic binary sequence pair is a perfect discrete signal, for its dyadic relative function is δ-function. The transformation features and some existing admissibility conditions of perfect dyadic binary sequence pair are discussed, and the properties for this kind of code in Walsh transformation spectrum and weight spectrum are also analyzed. From above, It is found that the perfect dyadic binary sequence pair can easily differentiate from its dyadic shifting. So these good signals can used in engineering as synchronization code, multi-user code and so on.     

Walsh Functions and Gray Code

Gray code is a natural way of ordering binary vectors in dyadic space, hence it appears frequently in connetion with Walsh functions. In Paley's definition of Walsh functions their sequencies are arranged in Gray code. Gray code also appears in a new Walsh function generation algorithm which obtains a function by locating all its sign changes. There are certain computational advantages in using Gray code rather than sequency ordering. Examples in fast Walsh transform, dyadic convolution and digital filtering are given. Methods of Gray code to binary conversion are discussed.     

并元互补二元序列族的布尔函数刻划

本文首先给出了并元互补二元序列族与一类布尔函数族的等价关系，然后采用布尔函数族对并元互补二元序列族进行了研究     

Time-Shift Theorems for Walsh Transforms and Solution of Difference Equations

Several time-shift theorems for Walsh transforms of functions subject to nondyadic as well as dyadic time displacements are presented. Spectrum-conversion matrices are defined and a relation between a function with an ordinary shift and that with a dyadic shift is established. Procedures for solving difference equations by Walsh transformation are given.     

差集偶与最佳二进阵列偶的组合研究方法

本文提出了一类新的区组设计——差集偶的概念. 研究了差集偶的性质,给出了差集偶与最佳二进阵列偶之间的关系. 为应用差集偶这种区组设计的方法研究最佳二进阵列偶提供了理论依据.     

Group Codes and Walsh Functions

The set of Walsh functions, wal(j,?), is the character group of the dyadic group. For O?j?2k it is shown that they may also be derived from the character table of the abstract Abelian group Ck generated by k elements of order two. The method uses Slepians modular representation table[3] to compute the 2k irreducible representations (each of degree one) of Ck. The character table, K, is a 2kx2k square array of +1's and -l's and, considered as a matrix, the orthogonality relationships for characters show that K has the Hadamard property, [K][K]T = 2K [I]. In fact, for the proper ordering of the group elements in the construction of the modular representation table it is the Hadamard matrix, the entries of whose ith row take on the values of the Walsh function wal (i,?) in each of ?/2k subintervals. In a similar way other permutations of the modular representation table define different functions taking on the values +l, -l, also orthogonal and in a one to one relationship to the Walsh functions. Since an n place binary group code with k information places is isomorphic to Ck,[3] each code can thus be used to generate real functions orthogonal over a given interval or period ?. In the special case of cyclic codes where the elements of the code interpreted as polynomials form an ideal in a polynomial ring of characteristic two, the group operation used in deriving the character table is of course, addition.     

Walsh-Transform Analysis of Discrete Dyadic-Invariant Systems

This short paper shows how the sampled output of a dyadic-invariant linear system with a given sequency-domain transfer function, in response to a sampled input, can be determined by 1) a term-wise multiplication of the sampled transfer function and the discrete Walsh transform of the sampled input function, followed by an inverse Walsh transform, or 2) a discrete dyadic convolution of the sampled impulse response and the sampled input directly in the time domain. Functions in both time and sequency domains are represented by column matrices, and discrete Walsh transformation is effected simply by the multiplication with a Walsh matrix. An example is included to illustrate both procedures. The validity of the solutions is further verified by showing that the governing dyadic differential equation of the system is satisfied.     

BER Performance of Walsh–Hadamard Like Kronecker Product Codes in a DS-CDMA and Cognitive Underlay System

Walsh–Hadamard transform, a discrete unitary transform is widely used in many applications such as signature codes in the current wireless standards IS-95 CDMA, WCDMA, CDMA2000 and image transform applications. It is simple to implement this transform since they can be generated by a single Kronecker product recursion formula. In this paper, a new set of binary code families similar to Walsh codes are obtained based on the concept of code concatenation and permutation. It is shown that these codes can be generated by reconfiguring the Walsh–Hadamard code generator. Hence it can be utilized in reconfigurable radios such as underlay cognitive radio (UCR). Theoretical results showing the BER performance due to MAI between primary users and secondary users in an UCR is also obtained. Simulation results showing the BER performance of these codes in a direct sequence spread spectrum system and UCR system with quadrature multiplexing operating in the individual decoding mode under AWGN plus flat fading Rayleigh channel conditions is also obtained.     

伪随机屏蔽二进阵列偶理论研究

 提出一种新的最佳相关信号,即伪随机屏蔽二进阵列偶,研究了其变换性质、Fourier频谱特性和存在的组合允许条件,运用这些性质和条件可以缩小伪随机屏蔽二进阵列偶的搜索范围,提高计算机搜索的效率.在此基础上编写了计算机搜索算法,搜索出若干体积的伪随机屏蔽二进阵列偶.搜索结果表明伪随机屏蔽二进阵列偶具有较大的存在空间,因而可以应用到工程中.