Families of polyphase sequences with near-optimal two-valued auto- and crosscorrelation functions

A construction method is proposed for new families of uniform polyphase sequences with near-optimal correlation. These families consist each of N sequences of length N and energy N with the following unique properties: (a) the sidelobes of the periodic autocorrelation functions have constant, nearly perfect magnitude 1; (b) the sequences are orthogonal; (c) all sidelobes of the periodic crosscorrelation functions have the constant magnitude square root (N+1); and (d) the correlation values asymptotically reach the Sarwate bound.<>     

Aperiodic autocorrelation and crosscorrelation of polyphasesequences

A detailed analysis of the maximum aperiodic autocorrelation of the original Chu sequences (equivalently, P3/P4 pulse compression codes) is presented. The result implies the best known upper bound on the minimax aperiodic autocorrelation for polyphase sequences except when the length is very small or a perfect square. It is well known that determining the minimax aperiodic correlation for polyphase sequence sets is an intractable task. The simplest nontrivial cases for Barker and general polyphase sequences are solved for the first time     

Merit factor based comparison of new polyphase sequences

New polyphase sequences, named Px sequences, of a square integer length are found. Standard merit factors of polyphase Frank (1963), P1, P3, P4, Golomb and Chu (1972) sequences are compared with merit factors of Px sequences. It is found that Px sequences have better sidelobe-energy merit factor and not worse maximum-sidelobe merit factor in comparison to all mentioned analytically constructed sequences     

New class of polyphase sequences with two-valued auto- andcrosscorrelation functions

A new class of polyphase sequences with two-valued periodic auto- and crosscorrelation properties is proposed. It is proved that, for a given prime length L>3, the out-of-phase ACFs and CCFs of the sequences are constant and equal to L. It is also shown that sequences of the same length are mutually orthogonal and the correlation values asymptotically reach the Sarwate bound     

Polyphase sequences with low autocorrelation

Low autocorrelation for sequences is usually described in terms of low base energy, i.e., the sum of the sidelobe energies, or the maximum modulus of its autocorrelations, a Barker sequence occurring when this value is /spl les/ 1. We describe first an algorithm applying stochastic methods and calculus to the problem of finding polyphase sequences that are good local minima for the base energy. Starting from these, a second algorithm uses calculus to locate sequences that are local minima for the maximum modulus on autocorrelations. In our tabulation of smallest base energies found at various lengths, statistical evidence suggests we have good candidates for global minima or ground states up to length 45. We extend the list of known polyphase Barker sequences to length 63.     

基于多相互补序列的多载波信号的峰值因子分析

针对具有相同幅度和等频率间隔的许多余弦函数组成的多载波信号，本文首先对它们的峰值因子上界进行了推导，得出它取决于由多载波信号初始相位组成的复序列的幅度谱。然后证明了由多相互补序列对中任-互补序列构成的多载波信号的峰值因子小于或等于6dB。最后，给出了由长度等于10的多相互补序列构成的多载波信号的两个仿真例子，结果表明它们的峰值因子在5-6dB之间，和理论分析相吻合。此外，还发现二进制Golay互补序列能够产生对称的多载波信号，该特性对于某些应用是很有用的。     

A new polyphase sequence with perfect even and good odd cross-correlation functions for DS/CDMA systems

A class of polyphase signature sequences for direct-sequence code-division multiple-access (DS/CDMA) systems is proposed. The proposed class has zero periodic (=even) cross-correlation (CC) function and approximate maximum magnitude N//spl pi/ of odd cross-correlation (OCC), where N is the length of sequences. Although the maximum magnitude is relatively large, it is observed that the maximum magnitude has little effect on the performance of the DS/CDMA system, since its frequency is very low. The performance of the proposed sequence in DS/CDMA systems is investigated and shown to be better than that of other sequences for an asynchronous additive white Gaussian noise channel environment with and without Rayleigh multipath fading.     

Design of Sequences with Specified Autocorrelation and Cross Correlation

A method of designing sequences with specified autocorrelation and cross-correlation properties is presented in this paper. This is based on power residue classification of a prime or a prime power and consists of first finding periodic sequences with acceptable correlation sidelobes and then testing these for aperiodic correlation. Signals considered include binary, polyphase, and frequency-time coded sequences. Computer results for some short length sequences are also given.     

PERFECT PUNCTURED BINARY SEQUENCE PAIRS

This paper presents the definition of perfect punctured binary sequence pair and the combinatorial admissible conditions for searching the perfect punctured binary sequence pairs and proves that all of the pseudo-random binary sequences satisfy these conditions. Computer calculation verifies that the pseudo-random binary sequences with length up to N=127 can be easily turned into perfect punctured binary sequence pairs.     

Optimal phases for a family of quadriphase CDMA sequences

Signature sequences with good even even and odd (or polyphase) correlations are crucial for asynchronous code-division multiple access (CDMA). When the data sequence is random, the even and odd (or polyphase) correlations are equally important. However, for most known signature sequences, only their even correlations were analyzed. It appears that determining the odd (or the polyphase) correlations is generally a very hard problem since the odd (or the polyphase) correlations depend on the phases of the signature sequences. Sole (1989), Boztas, Hammons, and Kumar (1992) found a family of quadriphase sequences that are asymptotically optimal. These sequences gain a factor √2 in terms of their maximum periodic even correlations when compared with the best possible binary phase-shift keying (BPSK) sequences. We find the optimal phases of these sequences. The optimality is in the sense that at these phases, the mean square values of the even, odd, and the polyphase correlations are minimal, and achieve the Welch (1974) bound-equality simultaneously. Furthermore, we show that at these phases, the average user interference of these sequences is always smaller than that of the ideal random signature sequences. Comprehensive analytical and numerical results show that good phase sequences can offer a nonnegligible amount of gain over bad phase sequences at modest and high signal-to-noise ratios     

基于正交矩阵构造非周期组间互补序列集

基于正交矩阵,该文提出一类非周期组间互补序列集的构造法。构造的非周期组间互补序列集的零相关区长度可灵活设定,且参数达到了理论界限。通过选取二元或多相正交矩阵,可以得到二元或多相非周期组间互补序列集。构造的组间互补序列可以用于同步和非同步码分多址通信系统。     

Polyphase Barker sequences

Polyphase sequences are time-discrete complex sequences with constant magnitude and variable phase. In this letter polyphase sequences with aperiodic autocorrelation function (ACF) sidelobes of values less than or equal to 1 are presented. Such sequences are called Barker sequences. Binary Barker sequences with elements 1 or -1 are only known up to 13 elements. Now, with an iteration scheme, polyphase Barker sequences are found up to 25 elements, except for 20 elements.<>     

A signal design without co-channel interference for approximatelysynchronized CDMA systems

A signal design is proposed for a CDMA system that is approximately synchronized. The signals are called pseudoperiodic sequences. The set of pseudoperiodic polyphase sequences are introduced from a set of periodic polyphase sequences with ideal autocorrelation for small shifts and zero cross correlation for all shifts. The system works without cochannel interference, even when the signals are modulated by data     

Modulated filter banks with arbitrary system delay: efficientimplementations and the time-varying case

We present a new method for the design and implementation of modulated filter banks with perfect reconstruction. It is based on the decomposition of the analysis and synthesis polyphase matrices into a product of two different types of simple matrices, replacing the polyphase filtering part in a modulated filter bank. Special consideration is given to cosine-modulated as well as time-varying filter banks. The new structure provides several advantages. First of all, it allows an easy control of the input-output system delay, which can be chosen in single steps of input sampling rate, independent of the filter length. This property can be used in audio coding applications to reduce pre-echoes. Second, it results in a structure that is nearly twice as efficient as performing the polyphase filtering directly. Perfect reconstruction is a structurally inherent feature of the new formulation, even for nonlinear operations or time-varying coefficients. Hence, the structure is especially suited for the design of time-varying filter banks where both the number of bands as well as the prototype filters can be changed while maintaining perfect reconstruction and critical sampling. Further, a proof of effective completeness is given, and the design of equal magnitude-response analysis and synthesis filter banks is described. Filter design can be performed by nonconstrained optimization of the matrix coefficients according to a given cost function. Design and audio-coding application examples are given to show the performance of the new filter bank     

The generalized lapped pseudo-biorthogonal transform: oversampled linear-phase perfect reconstruction filterbanks with lattice structures

We investigate a lattice structure for a special class of N-channel oversampled linear-phase perfect reconstruction filterbanks with a decimation factor M smaller than N. We deal with systems in which all analysis and synthesis filters have the same finite impulse response (FIR) length and share the same center of symmetry. We provide the minimal lattice factorization of a polyphase matrix of a particular class of these oversampled filterbanks (FBs). All filter coefficients are parameterized by rotation angles and positive values. The resulting lattice structure is able to provide fast implementation and allows us to determine the filter coefficients by solving an unconstrained optimization problem. We consider next the case where we are given the generalized lapped pseudo-biorthogonal transform (GLPBT) lattice structure with specific parameters, and we a priori know the correlation matrix of noise that is added in the transform domain. In this case, we provide an alternative lattice structure that suppress the noise. We show that the proposed systems with the lattice structure cover a wide range of linear-phase perfect reconstruction FBs. We also introduce a new cost function for oversampled FB design that can be obtained by generalizing the conventional coding gain. Finally, we exhibit several design examples and their properties.     

Family of uncorrelated binary ZCZ sequence pairs with mismatched filtering

A family of uncorrelated binary sequence pairs of length N=4(p^m+1) with zero correlation zone (ZCZ) (N/4) -1 and mismatched filtering is proposed. The sequence pairs are derived from almost- perfect binary and ternary sequences and possess energy efficiency close to 1 as N becomes large. They can be used in quasi-synchronous code division multiple access and radar systems to reduce interference.     

新的完备高斯整数序列的构造方法

该文提出了新的偶数周期的完备高斯整数序列构造方法。以整数集上的多电平完备序列为基础,并根据其周期的奇偶性,分别利用不同的组合和映射关系构造出完备高斯整数序列,所得到的完备高斯整数序列的周期等于或者2倍于多电平完备序列的周期。利用该方法可以得到新的完备高斯整数序列,从而实现了对现有完备高斯整数序列数量的扩展。     

Synthesis of power efficient multitone signals with flat amplitudespectrum

It is shown that, generally, any binary or polyphase sequence belonging to a pair of complementary sequences can be used to construct the initial phases of tones forming a multitone signal with the crest factor less than or equal to 6 dB. The previously proposed Shapiro-Rudin sequences are representatives of a much larger family of binary Golay complementary sequences. Numerical investigations show that the values of the crest factors obtained by applying complementary sequences (binary or polyphase) are between 5 and 6 dB, regardless of the number of tones     

Sampling rate conversion systems using a new generalized form ofthe discrete Fourier transform

A recursive factorization of the polynomial 1-z^N leads to an efficient algorithm for the computation of the discrete Fourier transform (DFT) and the cyclic convolution. The paper introduces a new recursive polynomial factorization of the polynomial when N is highly composite. The factorization is used to define a generalized form of the DFT and to derive an efficient algorithm for the computation. The generalized form of the DFT is shown to be closely related to the polyphase decomposition of a sequence, and is applied for the design of sampling rate conversion systems, it gives not only alternative derivations for the polyphase interpolation and the polyphase decimation by an integer factor, but also a new sampling rate conversion system by a rational factor, which is more efficient than the known rational polyphase implementation when the filter length is large     

Implementation and perfect reconstruction of a maximally decimatedFIR filter bank using parallel module decomposition

This paper discusses an implementation and the perfect reconstruction (PR) of an M-channel maximally decimated FIR fitter bank. Using the polynomial module arithmetics, the filter bank is decomposed into a set of module filter banks of size M, independent of the filter length. When the filter bank is uniform, the computational cost is the same as the polyphase/FFT implementation. When it is not uniform, in which case the polyphase/FFT implementation is not applicable, the computational cost is still reduced by sharing among channel filtering computations. The parallel module configuration is favorable for hardware implementation because decomposing a large system into small subsystems is generally advantageous for many realizations. The PR analysis is greatly simplified by working on the module filter banks as well