Perfect 8-QAM+ Sequences

This letter investigates the construction methods of perfect 8-QAM+ sequences, which relate to one of three open problems proposed by Boztas and Parampalli in 2010, and two constructions that transform the known perfect ternary sequences (PTSs) into the required sequences are presented. The resultant sequences and the employed sequences have the same period, or the former´s length is twice as long as the latter´s, depending on the differently proposed methods. In addition, the simulation results by a computer show that energy efficiency of the proposed sequences in Construction 2 is higher than that of the employed PTSs. Incidentally, one of our constructions can also produce a family of almost perfect 8-QAM+ sequences with only two nonzero nontrivial autocorrelation values.