Research On Constructions Of Z-Complementary Pairs

If the sum of the aperiodic autocorrelation functions of two sequences is zero everywhere within a certain delay range,the sequence pair is said to be a Zcomplementary pair.Z-complementary pairs have similar autocorrelation as Golay complementary pairs,but the form of the sequence length is far more flexible than Golay complementary pairs and can better me et the application requirements.Therefore,Z-complementary pair is widely used in C DMA systems,wireless broadband communication systems and OFDMA systems by its advantages to suppress the interference generated in communication.Hence,it is of great significance to optimize the parameters of Z-complementary pairs and improve their autocorrelation.This paper focuses on the constructions of 1D Zcomplementary pairs and 2D Z-complementary array pairs.Firstly,three constructions of Type-Ⅱ odd-length Z-optimal complementary pairs are proposed.Based on the constraints among sequence values of Golaycomplementary sequence pairs,the ideal cross-correlation between Golay complementary sequence pair and their Golay complementary mate,using the Golay complementary pair and Golay complementary mate as the seed sequences,applying the cascade interpolation method,by changing the interpolation position and cascade way,three constructions of Type-Ⅱ odd-length Z-optimal complementary pairs are proposed respectively.The zero correlation zone width of the generated sequence reaches the theoretical limit.The proposed constructions have flexible interpolation positions,enrich the number of odd-length Z-optimal complementary pairs,and extend the existing design of Z-complementary sequence pairs.Secondly,two constructions of Type-Ⅱ even-length Z-complementary pairs with large zero correlation zone are proposed.Firstly,the GDJ sequence is obtained based on the generalized Boolean function,and then the GDJ sequence is truncated to construct Type-Ⅱ even-length Z-complementary pairs.Construction 2obtains Type-Ⅱ even-length Z-complementary pairs with large zero correlation zone width by interpolation cascade method.Compared with the existing literature,the proposed Type-Ⅱ even-length Z-complementary pairs have larger width of zero correlation zone,and the zero correlation zone can reach the theoretical bound under certain conditions.In addition,th e new sequence has lower peak-to-average envelope power ratio and higher ratio of zero correlation zone.More sequences with good performance are provided for MC-CDMA system.Finally,two constructions of Z-complementary array pairs are proposed.In the first construction,Z-complementary array pair is constructed by using the vertical connection.When the used base sequence is Golay complementary sequence pair,the zero correlation zone of the proposed Z-complementary array pair is the largest.In the second construction,the Kronecker product and the horizontal cascade method are combined to obtain the Z-complementary array pair.When the base sequence used is an odd-length Z-optimal complementary pair,the proposed array pair is Z-optimal complementary array pair.When the base sequence used is a Golay complementary sequence pair,the propo sed array pair is Type-Ⅱ Z-complementary array pair with a large zero correlation zone.The proposed two constructions can construct Z-optimal complementary array pairs,make the size of the rectangular zero correlation zone of the sequence pair reach the theoretical limit,and enrich the number of existing Z-optimal complementary array pairs.