Based on a ternary perfect sequence and a binary orthogonal matrix, the Z-periodic complementary sequence (ZPCS) sets over the 8-QAM+ constellation are constructed. The resultant sequences can be used in multi-carriers code division multiple access (MC-CDMA) systems to remove interference and increase the transmission rate. The proposed construction provides flexible choice for parameters so as to meet different requirements in the application. A construction of shift sequence sets is proposed and the number of 8-QAM ZPCS sets is extended by changing the parameters of shift sequences. As a result, more users can be accommodated in the system.

Perfect arrays are widely applied to high-dimensional communications, time-frequency-coding, spatial correlation or map matching, built-in tests of VLSI-circuits, radar, and so on. The letter investigates perfect arrays over the 8-QAM+ constellation, and two constructions for yielding such arrays are presented. Furthermore, the family size of the proposed arrays is determined as well.

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.

In this letter, constructions of sequences with perfect odd autocorrelation and sequence sets with zero odd correlation zone (ZOCZ) over the 8-QAM+ constellation are presented. Based on odd perfect ternary sequences, odd perfect sequences and ZOCZ sequence sets over the 8-QAM+ constellation are constructed by using shift vectors and mappings. These odd perfect sequences and ZOCZ sequence sets over 8-QAM+ constellation can be used in communication systems to achieve high transmission data rate (TDR) and low interference.