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.