A unified construction for transforming binary sequences of balance or unbalance into quaternary sequences is presented. On the one hand, when optimal and balanced binary sequences with even period are employed, our construction is exactly the same Jang, et al.'s and Chung, et al.'s ones, which result in balanced quaternary sequences with optimal autocorrelation magnitude. On the other hand, when ideal and balanced binary sequences with odd period N are made use of, our construction produces new balanced quaternary sequences with optimal autocorrelation value (OAV), in which there are N distinct sequences in terms of cyclic shift equivalence, and includes Tang, et al.'s and Jang, et al.'s ones as special cases. In addition, when binary sequences without period 2n-1 or balance are employed, the transformation of Jang, et al.'s method is invalid, however, the proposed construction works very good. As a consequence, this unified construction allows us to construct optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences with arbitrary period.

This letter presents three methods for producing 8-QAM+ sequences. The first method transforms a ternary complementary sequence set (CSS) with even number of sub-sequences into an 8-QAM+ periodic CSS with both of the period and the number of sub-sequences unaltered. The second method results in an 8-QAM+ aperiodic CSS with confining neither the period nor the number of sub-sequences. The third method produces 8-QAM+ periodic sequences having ideal autocorrelation property on the real part of the autocorrelation function. The proposed sequences can be potentially applied to suppression of multiple access interference or synchronization in a communication system.

Based on quadriphase perfect sequences and their cyclical shift versions, three families of almost perfect 16-QAM sequences are presented. When one of two time shifts chosen equals half a period of quadriphase sequence employed and another is zero, two of the proposed three sequence families possess the property that their out-of-phase autocorrelation function values vanish except one. At the same time, to the other time shifts, the nontrivial autocorrelation function values in three families are zero except two or four. In addition, two classes of periodic complementary sequence (PCS) pairs over the 16-QAM constellation, whose autocorrelation is similar to the one of conventional PCS pairs, are constructed as well.

This paper improves the family size of quadrature amplitude modulation (QAM) complementary sequences with binary inputs. By employing new mathematical description: B-type-2 of 4q-QAM constellation (integer q ≥ 2), a new construction yielding 4q-QAM complementary sequences (CSs) with length 2m (integer m ≥ 2) is developed. The resultant sequences include the known QAM CSs with binary inputs as special cases, and the family sizes of new sequences are approximately 22·2q-4q-1(22·2q-3-1) times as many as the known. Also, both new sequences and the known have the same the peak envelope power (PEP) upper bounds, when they are used in an orthogonal frequency-division multiplexing communication system.

Sequences that attain the smallest possible absolute sidelobes (SPASs) of periodic autocorrelation function (PACF) play fairly important roles in synchronization of communication systems, Large scale integrated circuit testing, and so on. This letter presents an approach to construct 16-QAM sequences of even periods, based on the known quaternary sequences. A relationship between the PACFs of 16-QAM and quaternary sequences is established, by which when quaternary sequences that attain the SPASs of PACF are employed, the proposed 16-QAM sequences have good PACF.

Based on the non-standard generalized Boolean functions (GBFs) over Z4, we propose a new method to convert those functions into the 16-QAM Golay complementary sequences (CSs). The resultant 16-QAM Golay CSs have the upper bound of peak-to-mean envelope power ratio (PMEPR) as low as 2. In addition, we obtain multiple 16-QAM Golay CSs for a given quadrature phase shift keying (QPSK) Golay CS.

The shift-and-add property (SAP) of a p-ary m-sequence {ak} with period N=pn-1 means that this sequence satisfies the equation {ak+η}+{ak+τ}={ak+λ} for some integers η, τ and λ. For an arbitrarily-given p-ary m-sequence {ak}, we develop an algebraic approach to determine the integer λ for the arbitrarily-given integers η and τ. And all trinomials can be given. Our calculation only depends on the reciprocal polynomial of the primitive polynomial which produces the given m-sequence {ak}, and the cyclotomic cosets mod pn-1.

In an approximately synchronized (AS) code-division multiple-access (CDMA) communication system, zero correlation zone (ZCZ) sequences can be used as its spreading sequences so that the system suppresses multiple access interference (MAI) and multi-path interference (MPI) fully and synchronously. In this letter, the mutually orthogonal (MO) ZCZ polyphase sequence sets proposed by one of the authors are improved, and the resultant ZCZ sequences in each set arrive at the theoretical bound regarding ZCZ sequences under some conditions. Therefore, the improved MO ZCZ sequence sets are optimal.

This paper investigates construction methods of perfect 16-QAM sequences and arrays, since such sequences and arrays play quite an important role in synchronization of communication systems making use of 16-QAM signals. The method used for obtaining the results is to establish a relationship between the known perfect quaternary sequences/arrays and the required ones so that the former is transformed into the latter. Consequently, the sufficient conditions for implementing the required transformations are derived, and several examples are given. Our methods can provide perfect 16-QAM sequences with lengths 2, 4, 8, and 16, which are given in Table A·1 and infinite families of perfect 16-QAM arrays, whose existing sizes up to dimension 5 and volume 2304 are listed in Tables A·2 and A·3.

In an orthogonal frequency division multiplexing (OFDM) communication system, two users use the same frequencies and number of sub-carriers so as to increase spectrum efficiency. When the codewords employed by them form a Golay complementary sequence (CS) mate, this system enjoys the upper bound of peak-to-mean envelope power ratio (PMEPR) as low as 4. This letter presents a construction method for producing S16-QAM and A16-QAM Golay CS mates, which arrives at the upper bound 4 of PMEPR. And when used as a Golay CS pair, they have an upper bound 2 of PMEPR, which is the same ones in both [18] and [17]. However, both cannot produce such mates.

This letter presents a framework, including two constructions, for yielding several types of sequences with optimal autocorrelation properties. Only by simply choosing proper coefficients in constructions and optimal known sequences, two constructions transform the chosen sequences into optimally required ones with two or four times periods as long as the original sequences', respectively. These two constructions result in binary and quaternary sequences with optimal autocorrelation values (OAVs), perfect QPSK+ sequences, and multilevel perfect sequences, depending on choices of the known sequences employed. In addition, Construction 2 is a generalization of Construction B in [5] so that the number of distinct sequences from the former is larger than the one from the latter.

Based on the number of cyclotomy of order eight, a class of balanced almost 8-QAM sequences with odd prime periods is presented. The resultant sequences have low two-level nontrivial autocorrelation values, and their distribution is determined. Furthermore, the smallest possible absolute sidelobes (SPASs) of autocorrelation functions of balanced almost 8-QAM sequences are derived. Compared with the obtained SPASs, some of the proposed sequences is optimal or suboptimal.

The approximately synchronized code-division multiple-access (CDMA) communication system, using the QAM sequences with zero correlation zone (ZCZ) as its spreading sequences, not only can remove the multiple access interference (MAI) and multi-path interference (MPI) synchronously, but also has a higher transmission data rate than the one using traditional ZCZ sequences with the same sequence length. Based on Gray mapping and the known binary ZCZ sequences, in this letter, six families of 16-QAM sequences with ZCZ are presented. When the binary ZCZ sequences employed by this letter arrive at the theoretical bound on the binary ZCZ sequences, and their family size is a multiple of 4 or 2, two of the resultant six 16-QAM sequence sets satisfy the bound referred to above as well.

A novel construction of complementary sequences with multi-width zero cross-correlation zone (ZCCZ) is presented based on the interleaving iteration of a basic kernel set. The presented multi-width ZCCZ complementary (MWZC) sequences can be divided into multiple sequence groups, the correlation functions of which possess one-width intragroup ZCCZ and multi-width intergroup ZCCZ. When an arbitrary orthogonal sequence set with set size equal to sequence length is used as a basic kernel set, the constructed MWZC sequence set and the combination sets of specific subsets with each subset including several groups can be optimal with respect to the theoretical bound on set size. In addition, the MWZC sequence set includes complementary sequence sets with one-width or two-width ZCCZ as special subsets, and allows a more flexible choice of sequence parameters.

In an OFDM communication system using quadrature amplitude modulation (QAM) signals, peak envelope powers (PEPs) of the transmitted signals can be well controlled by using QAM Golay complementary sequence pairs (CSPs). In this letter, by making use of a new construction, a family of new 16-QAM Golay CSPs of length N=2m (integer m≥2) with binary inputs is presented, and all the resultant pairs have the PEP upper bound 2N. However, in the existing such pairs from other references their PEP upper bounds can arrive at 3.6N when the worst case happens. In this sense, novel pairs are good candidates for OFDM applications.

In contemporary communications, Golay, periodic and Z- complementary sequence sets play a very important role, since such sequence sets possess impulse-like or zero correlation zone (ZCZ) autocorrelation. On the other hand, the advantages of the signals over the quadrature amplitude modulation (QAM) constellation are more and more prominent. Hence, the design of such sequence sets over the QAM constellation has turned into one of the all-important issues in communications. Therefore, the construction methods of such sequence sets over the 16-QAM constellation are investigated, in this letter, and our goals are arrived at by the known quaternary Golay, periodic and Z- complementary sequence sets. Finally, many examples illuminate the validity of the proposed methods.