Complementary sets based on sequences with ideal periodic autocorrelation

A new general construction for the complementary sets of polyphase and ternary sequences is presented. The new construction produces the so-called supercomplementary sets of sequences, with some special additional properties. An important property of these sequences is the ambiguity function complementary property. As a special case, it is shown that the cyclic versions of some famous pulse compression codes, such as Frank, P3 and P4 codes, form the super complementary set of sequences.<>     

Complementary Huffman sequences

The theories of complementary and Huffman sequences have been two distinct areas. It is shown that each Huffman sequence has its complementary pair. In radar applications, these pairs can be used, in the same way as other binary and nonbinary complementary sequences. They have the added advantage of zero autocorrelation sidelobes at all time shifts except the largest one. Even these sidelobes are cancelled if the autocorrelation functions are summed because of the complementarity.<>     

Complementary code sets for OTDR

It is shown that (0, 1) pulse compression code sets with zero resultant correlation sidelobes must comprise at least three codewords and examples of such code sets with word lengths up to 10 bits are given.<>     

Supercomplementary sets of sequences

In the letter we propose a general method for generating a set of complementary sequences with special properties. In addition to autocorrelation function complementarity, these sequences exhibit complementarity of the crosscorrelation between the original sequence and the `deformed? sequence. The consequence of this property is ambiguity function complementarity. Many known complementary sets of sequences are special cases of the presented class of sequences. Properties useful in radar applications are also discussed.     

Odd-Periodic and Periodic Complementary binary sequences

Two or more sequences are called an Odd-Periodic Complementary binary sequences Set (OPCS) if the sum of their respective odd-periodic autocorrelation function is a delta function. In this paper, the definition of OPCS is given and the construction method of OPCS is discussed. The relation of the OPCS with the Periodic Complementary binary sequences Set (PCS) is pointed out, and some new PCSs are obtained based on such relation.     

Complementary sequences for ISI channel estimation

A merit factor based on the sequence autocorrelation function, whose minimization leads to the reduction in the Cramer-Rao lower bound (CRLB) for the variance of “two-sided” intersymbol interference (ISI) channel estimation is introduced. Pairs of binary pilot symbol sequences (a preamble and a postamble) for channel estimation are jointly designed to minimize this merit factor. Given that the number of channel taps is L and the length of a pilot symbol sequence is (N+L-1), where N⩾L, we distinguish between the case when N is even and the case when it is odd. For even N, we show that complementary sequences not only minimize the merit factor, but also the CRLB. For a subset of odd N we construct almost-complementary periodic sequence pairs that minimize the merit factor. The optimal pilot symbol block signaling requires alternating between two (in most cases) different binary sequences that form the merit-minimizing pair     

基于移位多相正交序列的周期完全互补码

对Suehiro提出的多相正交序列的构造方法进行了简要地介绍和分析,通过简化生成矩阵,达到了避免重复,直接产生独立序列的目的。在此基础上,本文通过对该多相序列的循环移位与正交复合,提出了一组新的完全互补码,其方法简单,生成容易,且具有较强的灵活性。     

Orthogonal sets of quadriphase sequences with good correlationproperties

A general construction for orthogonal sets of quadriphase sequences based on the sequence family A discovered by Sole (1989), Boztas, Hammons, and Kumar (1992) is presented. The sequence family A is equivalent to the S(0) family that belongs to a chain of sequence families S(i),i=0,1,2,..., m with each family in the chain containing the preceding family. Therefore, a number of orthogonal subsets can be generated for an arbitrary family S(m). The algorithm for an efficient implementation of the bank of correlators corresponding to any orthogonal subset of family S(m) is derived as well     

Almost difference sets and their sequences with optimalautocorrelation

Almost difference sets have interesting applications in cryptography and coding theory. We give a well-rounded treatment of known families of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplier group of some families of almost difference sets. We also construct six new classes of almost difference sets, and four classes of binary sequences of period n≡0 (mod 4) with optimal autocorrelation. We have also obtained two classes of relative difference sets and four classes of divisible difference sets (DDSs). We also point out that a result due to Jungnickel (1982) can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation     

Asynchronous multicarrier DS-CDMA using mutually orthogonalcomplementary sets of sequences

The use of sets of multiple spreading sequences per user in multicarrier code-division multiple-access (CDMA) is investigated. Each user is assumed to have a distinct set of spreading sequences, with a different spreading sequence for each carrier in each user's set. We show that when these sets of sequences are chosen to be the mutually orthogonal (MO) complementary sets of sequences, multiple-access interference is minimal on a nonfading channel. As a result of the autocorrelation sidelobe cancellation properties of the MO complementary sequences, it is possible to pack symbols more closely together on the nonfading channel, resulting in a higher data rate than in multicarrier CDMA using the same spreading sequence for each carrier. The resulting communication system scheme results in an easily parallelized receiver architecture that may be useful in nonfading coherent channels, such as the optical fiber channel or the Rician channel with a strong line-of-sight component. On the Rayleigh fading channel, the performance of the system is identical to that of multicarrier CDMA employing a single spreading sequence per user, with only a minimal increase in receiver complexity     

两类最优跳频序列集的线性复杂度

利用有限域中的一类不同于幂置换的置换多项式,将两类具有低线性复杂度的跳频序列集变换为具有高线性复杂度的最优跳频序列集。通过理论证明给出了变换以后序列线性复杂度的精确值。所得到的两类新的跳频序列集不仅具有最优的Hamming相关值,而且相对于变换前的序列集具有大的线性复杂度,可以抵抗Berlekamp-Massey算法的攻击。     

Synthesis of uncorrelated and nonsquare sets of multilevel complementary sequences

New techniques for the synthesis of multiple uncorrelated sets of multilevel complementary sequences are described. Application possibilities in the field of radio communications are indicated.<>     

The merit factor of binary sequences related to difference sets

Long binary sequences related to cyclic difference sets are investigated. Among all known constructions of cyclic difference sets it is shown that only sequences constructed from Hadamard difference sets can have an asymptotic nonzero merit factor. Maximal-length shift register sequences, Legendre, and twin-prime sequences are all constructed from Hadamard difference sets. The authors prove that the asymptotic merit factor of any maximal-length shift register sequence is three. For twin-prime sequences it is shown that the best asymptotic merit factor is six. This value is obtained by shifting the twin-prime sequence one quarter of its length. It turns out that Legendre sequences and twin-prime sequences have similar behavior. Jacobi sequences are investigated on the basis of the Jacobi symbol. The best asymptotic merit factor is shown to be six. Through the introduction of product sequences, it is argued that the maximal merit factor among all sequences of length N is at least six when N is large. The authors also demonstrate that it is fairly easy to construct sequences of moderate composite length with a merit factor close to six.<>     

Complementary sequences with high sidelobe suppression factors forST/MST radar applications

Under ideal conditions, complementary code pairs produce no sidelobes. In practice, sidelobes are produced, among other things, when the period of the Doppler frequency shift as well as the time of coherence of clear air turbulence are comparable (or smaller) than the interpulse period. The intensity of sidelobes increases with the radar operating frequency and becomes a real problem in the upper VHF and UHF bands. In this paper, a new technique for reducing sidelobes originating from atmospheric characteristics for clear air radar systems using pulse coding is presented. For this, a generalized analytic expression for a sidelobe suppression factor applicable to any number of binary code sequences is first derived. This is then used to develop the technique, which in the case of complementary codes consists of manipulating the order of transmission of the code sequences. For such codes, improvements in sidelobe suppression of the order of 80 dB on the VHF frequency band are obtained. The modifications required to implement the technique into existing systems are very few and simple     

Spectral efficiency of the feedback receiver for two sets of orthogonal sequences

We present the spectral efficiency analysis of the recently proposed feedback receiver for two sets of orthogonal sequences (TSOS) scheme which is capable of supporting higher number of users than the spreading gain of the DS/CDMA system. The added complexity is minimal compared to the conventional matched filter. We show that in the case of coded system, spectral efficiency of this scheme is close to that of a Gaussian multiple access channel if the incomplete group of orthogonal sequences is detected first. We also discuss the choice of orthogonal sequences that maximizes the spectral efficiency. This analysis is extended for the case of flat fading channels.     

DS/CDMA with two sets of orthogonal spreading sequences anditerative detection

In this letter we introduce a direct-sequence code-division multiple access (DS/CDMA) concept which accommodates a higher number of users than the spreading factor N. Each of the available orthogonal spreading sequences of length N is assigned to one of the first N users which employ a common pseudonoise (PN) scrambling sequence. When the number of users K exceeds N, say K=N+M with MN. The proposed technique thus accommodates N users without any mutual interference and a number of additional users at the expense of a small signal-to-noise ratio penalty     

TCM/SSMA communication systems with cascaded sequences and PAM/QAMsignal sets

An expression in matrix form for the multiple-access interference (MAI) in an asynchronous direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system with cascaded sequences (CVs), arbitrary chip waveforms, and trellis-coded modulation (TCM) with a pulse amplitude modulation (PAM) or quadrature amplitude modulation (QAM) signal set is obtained. TCM provides significant coding gain while the CVs decrease the correlation between the MAI of adjacent data intervals. The expression is used to calculate arbitrarily accurate probability density functions (PDFs) of the MAI in the TCM system and to derive an accurate approximation of the MAI variance. It also helps illustrate some properties of the MAI by separating contributing parameters into different matrices. We derive an approximation of the upper union bound on the bit-error probability and investigate its applicability. The results show that CV schemes can greatly reduce the pairwise error probabilities (PEPs) until the length of the CV becomes greater than that of the error weight sequence (EWS) under consideration     

Decoding beyond the BCH bound using multiple sets of syndrome sequences (Corresp.)

Many cyclic codes are generated by polynomials possessing more than one set of consecutive roots. Thus more than one set of syndrome sequences are available for decoding. In this correspondence, a decoding method based on Berlekamp's iterative algorithm is presented which makes use of the multiple sets of syndrome sequences for decoding such cyclic codes beyond the BCH bound.     

Bounds on the sizes of irredundant test sets and sequences for combinational logic networks

We present a method of determining lower and upper bounds on the number of tests required to detect all detectable faults in combinational logic networks. The networks are composed of AND, OR, NAND, NOR, and XOR gates. The fault model assumes that single stuck-at-zero faults occur on the lines of the networks, with the additional requirement that XOR gates be tested with all possible input combinations. The goal is to provide a simple and efficient implementation that processes the fanout-free subnetworks separately, and then combines the results without the need to consider the effects of reconvergent fanout. We introduce the concepts of irredundant test sets, where no test can be deleted regardless of the order of test application, and irredundant test sequences, where every test detects at least one additional fault when tests are applied in order. Identifying and differentiating between these types of collections of tests allows us to understand more precisely the mechanisms and expected performance of test generation and test compaction methods. We apply our test counting technique and two other published procedures to a set of benchmark circuits. Our bounds are shown to compare favorably to the results obtained by the other published approaches. We obtain minimal and maximal test sets and test sequences using a greedy optimization technique. Our bounds are shown to produce tight bounds for the smaller circuits; they grow more conservative as the size of the circuits increase.     

A technique for deriving sets of orthogonal sequences from binaryparents which preserves auto-correlation properties

Binary-valued Barker sequences have close to ideal autocorrelation (AC) properties but are extremely rare. The 11-chip Barker sequence is fundamental to the performance of the IEEE 802.11 WLAN standard. This letter presents a method of deriving new sets of sequences from a binary "parent" using a generalization of the technique derived previously by the author (see IEEE Trans. Commun., vol.45, p.1379-80, Nov. 1997). The method maintains the AC properties of the original binary source and can be used to produce sequence sets orthogonal to the original. This technique is applied to produce orthogonal sets of sequences with Barker-like AC properties