In this letter, we give a new construction of a family of sequences of period pk-1 with low correlation value by using additive and multiplicative characters over Galois rings. The new constructed sequence family has family size (M-1)(pk-1)rpkr(e-1) and alphabet size Mpe. Based on the characters sum over Galois rings, an upper bound on the correlation of this sequence family is presented.

A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).

For an odd prime p and a positive integer k ≥ 2, we propose and analyze construction of perfect pk-ary sequences of period pk based on cubic polynomials over the integers modulo pk. The constructed perfect polyphase sequences from cubic polynomials is a subclass of the perfect polyphase sequences from the Mow's unified construction. And then, we give a general approach for constructing optimal families of perfect polyphase sequences with some properties of perfect polyphase sequences and their optimal families. By using this, we construct new optimal families of pk-ary perfect polyphase sequences of period pk. The constructed optimal families of perfect polyphase sequences are of size p-1.

This letter proposes a class of polyphase zero correlation zone (ZCZ) sequence sets with low inter-set cross-correlation property. The proposed ZCZ sequence sets are constructed from DFT matrices and r-coincidence sequences. Each ZCZ sequence set is optimal, and the absolute value of the cross-correlation function of sequences from different sets is less than or equal to $rsqrt{N}$, where N denotes the length of each sequence. These ZCZ sequence sets are suitable for multiuser environments.

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.

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.

Based on the known quadriphase zero correlation zone (ZCZ) sequences ZCZ4(N,M,T), four families of 16-QAM sequences with ZCZ are presented, where the term "QAM sequences" means the sequences over the quadrature amplitude modulation (QAM) constellation. When the quadriphase ZCZ sequences employed by this letter arrive at the theoretical bound on the ZCZ sequences, and are of the even family size M or the odd width T of ZCZ, two of the resulting four 16-QAM sequence sets satisfy the bound referred to above. The proposed sequences can be potentially applied to communication systems using 16-QAM constellation as spreading sequences so that the multiple access interference (MAI) and multi-path interference (MPI) are removed synchronously.

Aperiodic quadriphase Z-complementary sequences, which include the conventional complementary sequences as special cases, are introduced. It is shown that, the aperiodic quadriphase Z-complementary pairs are normally better than binary ones of the same length, in terms of the number of Z-complementary pairs, and the maximum zero correlation zone. New notions of elementary transformations on quadriphase sequences and elementary operations on sets of quadriphase Z-complementary sequences are presented. In particular, new methods for analyzing the relations among the formulas relative to sets of quadriphase Z-complementary sequences and for describing the sets are proposed. The existence problem of Z-complementary pairs of quadriphase sequences with zero correlation zone equal to 2, 3, and 4 is investigated. Constructions of sets of quadriphase Z-complementary sequences and their mates are given.

A new construction method for polyphase sequences with two-valued periodic auto- and crosscorrelation functions is proposed. This method gives L families of polyphase sequences for each prime length L which is bigger than three. For each family of sequences, the out-of-phase auto- and crosscorrelation functions are proved to be constant and asymptotically reach the Sarwate bound. Furthermore, it is shown that sequences of each family are mutually orthogonal.

In this paper we introduce new M-ary sequences of length pq, called generalized M-ary related-prime sequences, where p and q are distinct odd primes, and M is a common divisor of p-1 and q-1. We show that their out-of-phase autocorrelation values are upper bounded by the maximum between q-p+1 and 5. We also construct a family of generalized M-ary related-prime sequences and show that the maximum correlation of the proposed sequence family is upper bounded by p+q-1.

We propose the P-SLM (Partitioned-SeLected Mapping) scheme with low complexity for PAPR reduction of OFDM signals. In the proposed scheme, a symbol sequence in the frequency domain is partitioned into several sub-blocks which are multiplied by different orthogonal phase sequences whose length and number are shorter and smaller than those used in the conventional SLM. Then, among various sequences in the time domain generated after the IFFT for the SLM sub-blocks, the sub-block combination with the lowest PAPR is selected and transmitted. Simulation results show that the proposed P-SLM scheme significantly reduces the number of IFFT calculation and multiplication than the conventional SLM without loss of PAPR reduction performance.

We propose an adaptive SLM scheme based on peak observation for PAPR reduction of OFDM signals. The proposed scheme is composed of three steps: peak scaling, sequence selection, and SLM procedures. In the first step, the peak signal samples in the IFFT outputs of the original input sequence are scaled down. In the second step, the sub-carrier positions where the power difference between the original input sequence and the FFT output of the scaled signal is large, are identified. Then, the phase sequences having the maximum number of phase-reversed sequence words only for these positions are selected. Finally, the generic SLM procedure is performed by using only the selected phase sequences for the original input sequence. Simulation results show that the proposed scheme significantly reduce the complexity in terms of IFFT and PAPR calculation than the conventional SLM, while maintaining the PAPR reduction performance.

In our previous work, we have proposed a method for constructing ZCZ sequence sets. The method proposed by the previous work is based on perfect sequences and unitary matrices. This method can generate ZCZ sequence sets which possess a good feature concerning the length of zero-correlation zones. In this letter, we propose a new method for constructing ZCZ sequence sets by improving the previous method. The proposed method can generate new ZCZ sequence sets which can not be obtained from the previous method. These ZCZ sequence sets also possess the good feature concerning the length of zero-correlation zones.

This paper proposes a new class of polyphase ZCZ (zero-correlation zone) sequence sets which satisfy a mathematical upper bound. The proposed ZCZ sequence sets are obtained from DFT matrices and unitary matrices. In addition, this paper discusses the cross-correlation property between different ZCZ sequence sets which belong to the proposed class.

Recently, a family of 4-phase sequences (alphabet {1,j,-1,-j}) was discovered having the same size 2r+1 and period 2r-1 as the family of binary (i.e., {+1, -1}) Gold sequences, but whose maximum nontrivial correlation is smaller by a factor of 2. In addition, the worst-case correlation magnitude remains the same for r odd or even, unlike in the case of Gold sequences. The family is asymptotically optimal with respect to the Welch lower bound on Cmax for complex-valued sequences and the sequences within the family are easily generated using shift registers. This paper aims to provide a more accessible description of these sequences.