Channel estimation using aperiodic binary sequences

Estimating a channel impulse response using a known aperiodic sequence is considered. The problem can be reduced to minimizing the trace of the inverse of a Toeplitz matrix. An efficient algorithm for computing this trace is developed and optimal binary sequences up to length 32 are found and tabulated. The use of complementary sequences in this context is also investigated. It is shown that the eigenvalues of the autocorrelation matrices of a pair of complementary sequences sum to a known constant     

Three-level m sequences

Those properties of 3-level m sequences which are likely to prove useful in the crosscorrelation method of system dynamic analysis are listed. The use of 3-level m sequence signals in the identification of nonlinear systems is discussed, and it is shown that the number of crosscorrelation experiments required to determine the impulse response of the linear channel of a system with an amplitude nonlinearity is reduced by the use of these signals.     

混沌序列与一类基于移位寄存器的非线性序列的性能比较

混沌序列与一类基于移位寄存器的非线性序列非线性前馈逻辑(Non-Linear Feed-ForwardLogic,NLFFL)序列都具有非线性、宽带类噪声、大的码族、长的周期且容易产生的特性,通过对它们在产生方式、相关性能、多址性能以及抗相关攻击能力等方面进行分析和仿真研究,说明混沌序列与该类非线性序列在性能上总体相当,但对于短周期序列(N1023),混沌序列的抗相关攻击、抗干扰能力更强,因此更具有实用价值。     

Huffman sequences with approximately uniform envelopes or cross-correlation functions (Corresp.)

The question of whether uniform Huffman (impulse equivalent) sequences exist is discussed, and some necessary conditions for a Huffman sequence to be uniform are mentioned. A comprehensive search revealed that no uniform Huffman sequences exist from lengths 4 to 17, inclusive. A procedure is described for synthesizing pairs of Huffman sequences whose cross-correlations are approximately uniform and, incidentally, are also themselves Huffman sequences.     

Cascaded GMW sequences

Pseudorandom binary sequences with high linear complexity and low correlation function values are sought in many applications of modern communication systems. A new family of pseudorandom binary sequences, cascaded GMW sequences, is constructed. These sequences are shown to share many desirable correlation properties with the GMW sequences of B. Gordon, W.A. Mills, and L.R. Welch (1962)-for example, high-shifted autocorrelation values and, in many cases, three-valued cross-correlation values with m-sequences. It is shown, moreover, that in many cases the linear complexities of cascaded GMW sequences are far greater than those of GMW sequences     

一类新的宽间隔跳频序列族的构造

基于GF（p)上的m序列构造的最佳跳频序列，提出了一种宽间隔跳频序列族的构造方法。通过理论推导和计算机模拟，表明该宽间隔跳频序列族具有较好的汉明相关性能，略差于最佳跳频序列族。     

Prime-phase sequences with periodic correlation properties better than binary sequences

For the case where p is an odd prime, n>or=2 is an integer, and omega is a complex primitive pth root of unity, a construction is presented for a family of p/sup n/ p-phase sequences (symbols of the form omega /sup i/), where each sequence has length p/sup n/-1, and where the maximum nontrivial correlation value C/sub max/ does not exceed 1+ square root p/sup n/. A complete distribution of correlation values is provided. As a special case of this construction, a previous construction due to Sidelnikov (1971) is obtained. The family of sequences is asymptotically optimum with respect to its correlation properties, and, in comparison with many previous nonbinary designs, the present design has the additional advantage of not requiring an alphabet of size larger than three. The new sequences are suitable for achieving code-division multiple access and are easily implemented using shift registers. They wee discovered through an application of Deligne's bound (1974) on exponential sums of the Weil type in, several variables. The sequences are also shown to have strong identification with certain bent functions.<>     

Analysis of protocol sequences for slow frequency hopping

An error probability bound for protocol sequences is derived for frame asynchronous access on a slow frequency hopping channel. This bound depends on the maximum and average cyclic Hamming correlation properties of the protocol sequences used. Constructions of protocol sequences with good cyclic correlation properties are given.     

Blind equalization by direct examination of the input sequences

This paper presents a novel approach to blind equalization (deconvolution), which is based on direct examination of possible input sequences. In contrast to many other approaches, it does not rely on a model of the approximative inverse of the channel dynamics. To start with, the blind equalization identifiability problem for a noise-free finite impulse response channel model is investigated. A necessary condition for the input, which is algorithm independent, for blind deconvolution is derived. This condition is expressed in an information measure of the input sequence. A sufficient condition for identifiability is also inferred, which imposes a constraint on the true channel dynamics. The analysis motivates a recursive algorithm where all permissible input sequences are examined. The exact solution is guaranteed to be found as soon as it is possible. An upper bound on the computational complexity of the algorithm is given. This algorithm is then generalized to cope with time-varying infinite impulse response channel models with additive noise. The estimated sequence is an arbitrary good approximation of the maximum a posteriori estimate. The proposed method is evaluated on a Rayleigh fading communication channel. The simulation results indicate fast convergence properties and good tracking abilities     

非线性扩频序列的Hamming相关特性

本文讨论了两类非线性扩频序列（Ｎｏ序列和Ｋａｓａｍｉ序列）的Ｈａｍｍｉｎｇ相关特性,求出了这两类扩频序列的Ｈａｍｍｉｎｇ相关函数值,就Ｈａｍｍｉｎｇ相关特性而言,这两类序列不具有最佳相关性能。     

Crosscorrelation properties of pseudorandom and related sequences

Binary maximal-length linear feedback shift register sequences (m-sequences) have been successfully employed in communications, navigation, and related systems over the past several years. For the early applications, m-sequences were used primarily because of their excellent periodic autocorrelation properties. For many of the recent systems applications, however, the crosscorrelation properties of such sequences are at least as important as the autocorrelation properties, and the system performance depends upon the aperiodic correlation in addition to the periodic correlation. This paper presents a survey of recent results and provides several new results on the periodic and aperiodic crosscorrelation functions for pairs of m-sequences and for pairs of related (but not maximal-length) binary shift register sequences. Also included are several recent results on correlation for complex-valued sequences as well as identities relating the crosscorrelation functions to autocorrelation functions. Examples of problems in spread-spectrum communications are employed to motivate the choice of correlation parameters that are considered in the paper.     

二相与四相无限折叠混沌扩频序列的相关特性分析

本文利用无限折叠迭代混沌映射产生二相与四相混沌扩频序列。分析了序列轨迹点具有的分布律与相关特性,模拟结果表明它们分别能获得比同等长度的二相与四相Logistic序列、四相Chebyshev序列、m序列、Gold序列更好的自相关与互相关性能,有利于解决CDMA移动通信中对相关性要求很严格的抗多址（多径）干扰、多用户检测等关键问题。     

多相序列长度改造的研究

CDMA系统中，多址的实现是靠具有特定相关性要求的扩频序列来完成的，而扩频序列越长，其自相关函数的主峰和旁瓣的比值就越大，相关性能就越好。由Suehim构造的多相序列其长度等于相数的平方，相数小时，序列长度满足不了系统对处理增益的要求。为此，引入了伪周期序列的概念，对多相序列的长度进行了改造，提高了多相序列在实际应用中的可行性。     

Chaotic frequency hopping sequences

This letter describes a novel family of frequency hopping sequences generated by chaotic systems. The sequences give a uniform spread over the entire frequency bandwidth. In addition to having good Hamming correlation properties, they possess ideal linear span. The sequences produce almost as good performance as random hopping patterns when used in frequency hopping code-division multiple-access (FH/CDMA) systems. Many numerical examples based on a digital chaos generator are presented     

Balanced nonbinary sequences with good periodic correlationproperties obtained from modified Kumar-Moreno sequences

Kumar and Moreno (see ibid., vol.37, no.3, p.603, 1991) presented a new family of nonbinary sequences which has not only good periodic correlation properties but also the largest family size. First, the unbalanced properties for Kumar-Moreno sequences are pointed out. Second, a new family of balanced nonbinary sequences obtained from modified Kumar-Moreno sequences is proposed, and it is shown that the new family has the same optimal periodic nontrivial correlation as the family of Kumar-Moreno sequences and consists of the balanced nonbinary sequences. It is also shown that the cost of making sequences balanced is a decrease of the family size in addition to the condition that n is an even number. In particular, let the length of Kumar-Moreno sequences and the new sequences be the same and equal to pⁿ-1 with n even, then the family size of the new sequences is p^n/2 which is much smaller than pⁿ, that of Kumar-Moreno sequences     

Bounds on partial correlations of sequences

Two approaches to bounding the partial auto- and crosscorrelations of binary sequences are considered. The first approach uses the discrete Fourier transform and bounds for character sums to obtain bounds on partial autocorrelations of m-sequences and on the partial auto- and crosscorrelations for the small Kasami sets and dual-BCH families of sequences. The second approach applies to binary sequences obtained by interleaving m-sequences. A bound on the peak partial correlation of such sequences is derived in terms of the peak partial autocorrelation of the underlying m-sequences. The bound is applied to GMW, No (1987), and other families of sequences for particular parameters. A comparison of the two approaches shows that the elementary method gives generally weaker results but is more widely applicable. On the other hand, both methods show that well-known sequence families can have favorable partial correlation characteristics, making them useful in certain spread-spectrum applications     

Bent-function sequences

In this paper we construct a new family of nonlinear binary signal sets which achieve Welch's lower bound on simultaneous cross correlation and autocorrelation magnitudes. Given a parameternwithn=0 pmod{4}, the period of the sequences is2^{n}-1, the number of sequences in the set is2^{n/2}, and the cross/auto correlation function has three values with magnitudesleq 2^{n/2}+1. The equivalent linear span of the codes is bound above bysum_{i=1}^{n/4}left(stackrel{n}{i} right). These new signal sets have the same size and correlation properties as the small set of Kasami codes, but they have important advantages for use in spread spectrum multiple access communications systems. First, the sequences are "balances," which represents only a slight advantage. Second, the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly "hopped" from sequence to sequence for code division multiple access operation. Most importantly, the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it. This high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing.     

New constructions of quaternary low correlation zone sequences

In this paper, given a composite integer n, we propose a method of constructing quaternary low correlation zone (LCZ) sequences of period 2/sup n/-1 from binary sequences of the same length with ideal autocorrelation. These new sequences are optimal with respect to the bound by Tang, Fan, and Matsufuji. The correlation distributions of these new quaternary LCZ sequences constructed from m-sequences and Gordon-Mills-Welch (GMW) sequences are derived.     

Generalized construction of binary bent sequences with optimal correlation property

We generalize the construction method of the family of binary bent sequences introduced by Olsen, Scholtz, and Welch (1982) to obtain a family of generalized binary bent sequences with optimal correlation and balance property by using the modified trace transform. Then, the conventional binary bent sequence becomes a special case of our construction method. Several families of the generalized binary bent sequences are constructed by using the bent functions on the intermediate field. Using some of the generalized binary bent sequences, new families of binary sequences with optimal correlation and balance property can be constructed by the lifting idea similar to No (1988) sequences, which are referred to as binary bent-lifted sequences.     

Product sequences with good correlation properties

The structure of the autocorrelation function of sequences which are the products of factor sequences with known autocorrelation functions is investigated. A means of constructing binary sequences with good correlation properties is presented. It is also shown that this procedure, when applied to sets of sequences, preserves the cross-correlation properties of the factor sequences. The results are also extended to the non-binary case where it is also demonstrated that sequences with similar segmentation and correlation structures to q-ary m-sequences can be constructed which have lengths other than q ⁿ ? 1.