A Costas array of size n is an n × n binary matrix such that no two of the $inom{n}{2}$ line segments connecting 1s have the same length and slope. Costas arrays are found by finite-field-based construction methods and their manipulations (systematically constructed) and exhaustive search methods. The arrays found exhaustively, which are of completely unknown origin, are called sporadic. Most studies in Costas arrays have tended to focus on systematically constructed Costas arrays rather than sporadic ones, which reveals the hardness of examining a link between systematically constructed Costas arrays and sporadic ones. This paper introduces a new transformation that preserves the Costas property for some Costas arrays, but not all. We observed that this transformation could transform some systematically constructed Costas arrays to sporadic ones and vice versa. Moreover, we introduce a family of arrays with the property that the auto-correlation of each array and the cross-correlation between any two arrays in this family is bounded above by two.

The calculation of cross-correlation between a sequence with good autocorrelation and its decimated sequence is an interesting problem in the field of sequence design. In this letter, we consider a class of ternary sequences with perfect autocorrelation, proposed by Shedd and Sarwate (IEEE Trans. Inf. Theory, 1979, DOI: 10.1109/TIT.1979.1055998), which is generated based on the cross-correlation between m-sequence and its d-decimation sequence. We calculate the cross-correlation distribution between a certain pair of such ternary perfect sequences and show that the cross-correlation takes three different values.

This paper investigated a Subsample Time delay Estimation (STE) algorithm based on the amplitude of cross-correlation function to improve the estimation accuracy. In this paper, a rough time delay estimation is applied based on traditional cross correlator, and a fine estimation is achieved by approximating the sampled cross-correlation sequence to the amplitude of the theoretical cross-correlation function for linear frequency modulation (LFM) signal. Simulation results show that the proposed algorithm outperforms existing methods and can effectively improve time delay estimation accuracy with the complexity comparable to the traditional cross-correlation method. The theoretical Cramér-Rao Bound (CRB) is derived, and simulations demonstrate that the performance of STE can approach the boundary. Eventually, four important parameters discussed in the simulation to explore the impact on Mean Squared Error (MSE).

Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q2+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.

In this letter, the almost binary sequence (sequence with a single zero element) is considered as a special class of binary sequence. Four new bounds on the cross-correlation of balanced (almost) binary sequences with period Q ≡ 1(mod 4) under the precondition of out-of-phase autocorrelation values {-1} or {1, -3} are firstly presented. Then, seven new pairs of balanced (almost) binary sequences of period Q with ideal or optimal autocorrelation values and meeting the lower cross-correlation bounds are proposed by using cyclotomic classes of order 4. These new bounds of (almost) binary sequences with period Q achieve smaller maximum out-of-phase autocorrelation values and cross-correlation values.

In the letter, two classes of optimal codebooks and asymptotically optimal codebooks in regard to the Levenshtein bound are presented, which are based on mutually unbiased bases (MUB) and approximately mutually unbiased bases (AMUB), respectively.

In this letter, motivated by the research of Tian et al., two constructions of asymptotically optimal codebooks in regard to the Welch bound with additive and multiplicative characters are provided. The parameters of constructed codebooks are new, which are different from those in the letter of Tian et al.

This paper presents an efficient wideband two-dimensional direction-of-arrival (DOA) estimation for an L-shaped microphone array. We propose a way to construct a wideband sample cross-correlation matrix without any process of DOA preliminary estimation, such as beamforming technique, by exploiting sample cross-correlation matrices of two different frequencies for all frequency bins. Subsequently, wideband DOAs can be estimated by using this wideband matrix along with a scheme of estimating DOA in a narrowband subspace method. Therefore, a contribution of our study is providing an alternative framework for recent narrowband subspace methods to estimating the DOA of wideband sources directly. It means that this framework enables cutting-edge techniques in the existing narrowband subspace methods to implement the wideband direction estimation for reducing the computational complexity and facilitating the estimation algorithm. Theoretical analysis and effectiveness of the proposed method are substantiated through numerical simulations and experiments, which are performed in reverberating environments. The results show that performance of the proposed method performs better than others over a range of signal-to-noise ratio with just a few microphones. All these advantages make the proposed method a powerful tool for navigation systems based on acoustic signal processing.

Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.

Let Fpm be the field of pm elements where p is an odd prime. In this letter, binary sequence pairs of period N=pm-1 are presented, where sequences are generated from the polynomial x2-c for any c Fpm{0}. The cross-correlation values of sequence pairs are completely determined, our results show that those binary sequence pairs have optimal three-level correlation.

In this correspondence, two types of multiple binary zero correlation zone (ZCZ) sequence sets with inter-set zero cross-correlation zone (ZCCZ) are constructed. Based on orthogonal matrices with order N×N, multiple binary ZCZ sequence sets with inter-set even and odd ZCCZ lengthes are constructed, each set is an optimal ZCZ sequence set with parameters (2N2, N, N+1)-ZCZ, among these ZCZ sequence sets, sequences possess ideal cross-correlation property within a zone of length 2Z or 2Z+1. These resultant multiple ZCZ sequence sets can be used in quasi-synchronous CDMA systems to remove the inter-cell interference (ICI).

In this paper, for an odd prime p, two positive integers n, m with n=2m, and pm≡1 (mod 4), we derive an upper bound on the magnitude of the cross-correlation function between two decimated sequences of a p-ary m-sequence. The two decimation factors are 2 and 2(pm+1), and the upper bound is derived as $rac{3}{2}p^m + rac{1}{2}$. In fact, those two sequences correspond to the p-ary sequences used for the construction of Kasami sequences decimated by 2. This result is also used to obtain an upper bound on the cross-correlation magnitude between a p-ary m-sequence and its decimated sequence with the decimation factor $d=rac{(p^m +1)^2}{2}$.

A chirp spread spectrum (CSS) system uses a chirp signal which changes the instantaneous frequency according to time for spreading a transmission bandwidth. In the CSS system, the transmission performance can be simply improved by increasing the time-bandwidth product which is known as the processing gain. However, increasing the transmission bandwidth is limited because of the spectrum regulation. In this letter, we propose a correlation-based chirp rate allocation method to improve the transmission performance by analyzing the cross-correlation coefficient in the same time-bandwidth product. In order to analyze the transmission performance of the proposed method, we analytically derive the cross-correlation coefficient according to the time-bandwidth separation product and simulate the transmission performance. The simulation results show that the proposed method can analytically allocate the optimal chirp rate and improve the transmission performance.

This paper proposes a new multi-value sequence generated by utilizing primitive element, trace, and power residue symbol over odd characteristic finite field. In detail, let p and k be an odd prime number as the characteristic and a prime factor of p-1, respectively. Our proposal generates k-value sequence T={ti | ti=fk(Tr(ωi)+A)}, where ω is a primitive element in the extension field $F{p}{m}$, Tr(⋅) is the trace function that maps $F{p}{m} ightarrow {p}$, A is a non-zero scalar in the prime field ${p}$, and fk(⋅) is a certain mapping function based on k-th power residue symbol. Thus, the proposed sequence has four parameters as p, m, k, and A. Then, this paper theoretically shows its period, autocorrelation, and cross-correlation. In addition, this paper discusses its linear complexity based on experimental results. Then, these features of the proposed sequence are observed with some examples.

Quadriphase sequences with good correlation properties are required in higher order digital modulation schemes, e.g., for timing measurements, channel estimation or synchronization. In this letter, based on interleaving technique and pairs of mismatched binary sequences with perfect cross-correlation function (PCCF), two new methods for constructing quadriphase sequences with mismatched filtering which exist for even length N ≡ 2(mod4) are presented. The resultant perfect mismatched quadriphase sequences have high energy efficiencies. Compared with the existing methods, the new methods have flexible parameters and can give cyclically distinct perfect mismatched quadriphase sequences.

In this paper, for an odd prime p and i=0,1, we investigate the cross-correlation between two decimated sequences, s(2t+i) and s(dt), where s(t) is a p-ary m-sequence of period pn-1. Here we consider two cases of ${d}$, ${d=rac{(p^m +1)^2}{2} }$ with ${n=2m}$, ${p^m equiv 1 pmod{4}}$ and ${d=rac{(p^m +1)^2}{p^e + 1}}$ with n=2m and odd m/e. The value distribution of the cross-correlation function for each case is completely determined. Also, by using these decimated sequences, two new p-ary sequence families of period ${rac{p^n -1}{2}}$ with good correlation property are constructed.

In this paper, for an odd prime p such that p≡3 mod 4, odd n, and d=(pn+1)/(pk+1)+(pn-1)/2 with k|n, the value distribution of the exponential sum S(a,b) is calculated as a and b run through $mathbb{F}_{p^n}$. The sequence family $mathcal{G}$ in which each sequence has the period of N=pn-1 is also constructed. The family size of $mathcal{G}$ is pn and the correlation magnitude is roughly upper bounded by $(p^k+1)sqrt{N}/2$. The weight distribution of the relevant cyclic code C over $mathbb{F}_p$ with the length N and the dimension ${ m dim}_{mathbb{F}_p}mathcal{C}=2n$ is also derived.

In this paper, we analyze the existing results to derive the cross-correlation distributions of p-ary m-sequences and their decimated sequences for an odd prime p and various decimations d. Based on the previously known results, a methodology to obtain the distribution of their cross-correlation values is also formulated.

Recently, asymmetric zero-correlation zone (A-ZCZ) sequence sets that are composed of several sequence subsets have been proposed. In A-ZCZ sequence sets, the zero-cross-correlation zone (ZCCZ) length between different sequence subsets is larger than the zero-correlation zone (ZCZ) length in each sequence subset. However, the ZCCZ length between different sequence subsets was not precisely shown in previous studies. The present letter shows precisely the ZCCZ length between different sequence subsets. This information is useful for estimating the magnitude of inter-cell interference when designing approximately synchronized code-division multiple-access (AS-CDMA) systems.

In this paper, a new construction method of quaternary sequences of even period 2N having the ideal autocorrelation and balance properties is proposed. These quaternary sequences are constructed by applying the inverse Gray mapping to binary sequences of odd period N with the ideal autocorrelation. Autocorrelation distribution of the proposed quaternary sequences is derived. These sequences can be used to construct quaternary sequence families of even period 2N. Family size and the maximum absolute value of correlation spectrum of the proposed quaternary sequence families are also derived.