Design And Research Of Contiguous And Non-contiguous Z-complementary Sequences/Arrays

Orthogonal frequency division multiplexing is the main modulation and demodulation technology used in 5G communication system.The complementary sequence has many applications in infrared spectrum analysis,acoustic devices,pulse radar and navigation,synchronization,channel estimation and spread spectrum communication because of its good autocorrelation.However,the existence space of contiguous complementary sequences is small and the construction of non-contiguous complementary sequences are few.Therefore,it is very important to study and construct contiguous and non-contiguous complementary sequences with good autocorrelation.This paper aims at the design and research of contiguous and non-contiguous Z-complementary sequences,and the specific work is as follows:Firstly,for the finite length of binary Z-complementary sequence pairs,based on onedimensional Boolean function,the direct construction of binary even-length Zcomplementary pairs with zero correlation zone ratio of 6/7 is proposed.By concatenating Golay complementary pairs,the indirect construction of binary and quadriphase even-length Z-complementary sequence pairs with fixed zero correlation zone ratio is proposed.The Kronecker product construction formula for Z-complementary sequence pairs with fixed zero correlation zone ratio is derived.This extends the existence space of Z-complementary sequence pairs.Secondly,aiming at the autocorrelation property of binary Z-complementary array pairs,the lower bound of aperiodic autocorrelation values outside the zero correlation zone of binary Z-complementary array pairs is studied.It is found that the minimum value of the aperiodic autocorrelation sum of the two zones adjacent to the zero correlation zone outside the zero correlation zone is 0,and the minimum modulus of the aperiodic autocorrelation sum of the relative zone of the zero correlation zone is 2 when the zero correlation zone of the Z-complementary array pair with two odd dimensions is the maximum.When one dimension is even,the sum of aperiodic autocorrelation values of Z-complementary array pairs with at least one point has a lower bound of 4;In addition,based on two-dimensional Boolean function,we propose a direct construction of a pair of binary Z-optimal Zcomplementary arrays with two odd dimensions.This provides a theoretical basis for the practical application of two dimensional complementary arrays.Finally,there is a finite length problem for non-contiguous complementary sequences.The non-contiguous complementary sequences are constructed iteratively based on parunitary matrices.The constructed non-contiguous complementary sequences have the optimal autocorrelation and extend the existence space of non-contiguous complementary sequences.Then the instantaneous peak-average power ratio of the non-contiguous complementary sequences is simulated.It is found that the non-contiguous complementary sequences can be used as OFDM code words with low peak-average power ratio transmitted in non-contiguous mode.This provides more choices of non-contiguous sequences for practical communication systems.