In this letter, based on cyclic difference sets with parameters $(N,rac{N-1}{2},rac{N-3}{4})$ and complex transformations, a method for constructing degree-4 perfect Gaussian integer sequences (PGISs) with good balance property of length $N'equiv2( ext{mod}4)$ are presented. Furthermore, the elements distribution of the proposed Gaussian integer sequences (GISs) is derived.

In this letter, a construction of asymmetric Gaussian integer zero correlation zone (ZCZ) sequence sets is presented based on interleaving and filtering. The proposed approach can provide optimal or almost optimal single Gaussian integer ZCZ sequence sets. In addition, arbitrary two sequences from different sets have inter-set zero cross-correlation zone (ZCCZ). The resultant sequence sets can be used in the multi-cell QS-CDMA system to reduce the inter-cell interference and increase the transmission data.

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 letter, several new families of binary sequence pairs with period N=np, where p is a prime and gcd(n,p)=1, and optimal correlation values 1 and -3 are constructed. These classes of binary sequence pairs are based on Chinese remainder theorem. The constructed sequence pairs have optimum balance among 0's and 1's.

A new class of almost quadriphase sequences with four zero elements of period 4N, where N ≡ 1(mod 4) being a prime, is constructed. The maximum nontrivial autocorrelations of the constructed almost quadriphase sequences are shown to be 4.

In this letter, we propose a novel direct construction of three-phase Z-complementary triads with flexible lengths and various widths of the zero-correlation zone based on extended Boolean functions. The maximum width ratio of the zero-correlation zone of the construction can reach 3/4. And the proposed sequences can exist for all lengths other than powers of three. We also investigate the peak-to-average power ratio properties of the proposed ZCTs.

In this letter, a new class of almost binary sequence pairs with a single zero element and three autocorrelation values is presented. The new almost binary sequence pairs are based on cyclic difference sets and difference set pairs. By applying the method to the binary sequence pairs, new binary sequence pairs with three-level autocorrelation are constructed. It is shown that new sequence pairs from our constructions are balanced or almost balanced and have optimal three-level autocorrelation when the characteristic sequences or sequence pairs of difference sets or difference set pairs are balanced or almost balanced and have optimal autocorrelations.

In this letter, a generic method to construct mutually orthogonal binary zero correlation zone (ZCZ) sequence sets from mutually orthogonal complementary sequence sets (MOCSSs) with certain properties is presented at first. Then MOCSSs satisfying conditions are generated from binary orthogonal matrices with order N×N, where N=p-1, p is a prime. As a result, mutually orthogonal binary ZCZ sequence sets with parameters (2N2,N,N+1)-ZCZ can be obtained, the number of ZCZ sets is N. Note that each single ZCZ sequence set is optimal with respect to the theoretical bound.

This letter presents a novel tensor voting mechanism — analytic tensor voting (ATV), to get rid of the difficulties in original tensor voting, especially the efficiency. One of the main advantages is its explicit voting formulations, which benefit the completion of tensor voting theory and computational efficiency. Firstly, new decaying function was designed following the basic spirit of decaying function in original tensor voting (OTV). Secondly, analytic stick tensor voting (ASTV) was formulated using the new decaying function. Thirdly, analytic plate and ball tensor voting (APTV, ABTV) were formulated through controllable stick tensor construction and tensorial integration. These make the each voting of tensor can be computed by several non-iterative matrix operations, improving the efficiency of tensor voting remarkably. Experimental results validate the effectiveness of proposed method.

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.

A novel class of signal of perfect Gaussian integer sequence pairs are put forward in this paper. The constructions of obtaining perfect Gaussian integer sequence pairs of odd length by using Chinese remainder theorem as well as perfect Gaussian integer sequence pairs of even length by using complex transformation and interleaving techniques are presented. The constructed perfect Gaussian integer sequence pairs can not only expand the existence range of available perfect Gaussian integer sequences and perfect sequence pairs signals but also overcome the energy loss defects.

The concept of Gaussian integer sequence pair is generalized from a single Gaussian integer sequence. In this letter, by adopting cyclic difference set pairs, a new construction method for perfect Gaussian integer sequence pairs is presented. Furthermore, the necessary and sufficient conditions for constructing perfect Gaussian integer sequence pairs are given. Through the research in this paper, a large number of perfect Gaussian integer sequence pairs can be obtained, which can greatly extend the existence of perfect sequence pairs.

This letter provides a direct construction of binary even-length Z-complementary pairs. To date, the maximum zero correlation zone ratio of Type-I Z-complementary pairs has reached 6/7, but no direct construction of Z-complementary pairs can achieve the zero correlation zone ratio of 6/7. In this letter, based on Boolean function, we give a direct construction of binary even-length Z-complementary pairs with zero correlation zone ratio 6/7. The length of constructed Z-complementary pairs is 2m+3 + 2m + 2+2m+1 and the width of zero correlation zone is 2m+3 + 2m+2.

Two new families of balanced almost binary sequences with a single zero element of period L=2q are presented in this letter, where q=4d+1 is an odd prime number. These sequences have optimal autocorrelation value or optimal autocorrelation magnitude. Our constructions are based on cyclotomy and Chinese Remainder Theorem.

In this letter, two new families of quaternary sequences with low four-level or five-level autocorrelation are constructed based on generalized cyclotomy over Z2p. These quaternary sequences are balanced and the maximal absolute value of the out-of-phase autocorrelation is 4.