This letter presents two constructions of Gaussian integer Z-periodic complementary sequences (ZPCSs), which can be used in multi-carriers code division multiple access (MC-CDMA) systems to remove interference and increase transmission rate. Construction I employs periodic complementary sequences (PCSs) as the original sequences to construct ZPCSs, the parameters of which can achieve the theoretical bound if the original PCS set is optimal. Construction II proposes a construction for yielding Gaussian integer orthogonal matrices, then the methods of zero padding and modulation are implemented on the Gaussian integer orthogonal matrix. The result Gaussian integer ZPCS sets are optimal and with flexible choices of parameters.

Based on a perfect Gaussian integer sequence, shift and combination operations are performed to construct Gaussian integer sequences with zero correlation zone (ZCZ). The resultant sequence sets are optimal or almost optimal with respect to the Tang-Fan-Matsufuji bound. Furthermore, the ZCZ Gaussian integer sequence sets can be provided for quasi-synchronous code-division multiple-access systems to increase transmission data rate and reduce interference.

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.