Research On Binary Cross Z-complementary Sequence Pairs

Spatial modulation(SM)is a special kind of multiple-input multiple-output(MIMO)technique,in which one transmit antenna is activated during each symbol duration.Recently,cross Z-complementary sequence pairs(CZCPs)have been evolved as a new kind of sequence pair to be used for pilot design in SM over frequency-selective channels.CZCPs are pairs of sequences whose autocorrelation sums and cross-correlation sums are all equal to zero within specific time-shifts.In this paper,we apply GCP Kernels(K2,K10 and K26)and Turyn's Method to propose four constructions of binary CZCPs with new lengths of the form 2?10?26?(??1,?,??0),10?(??1),26?(??1)and 10?26?(??1,??1).The specific recursive method of construction is as follows,(ei,fi)=Turyn(A0,(ei-1,fi-1)),(e0,f0)=B0,where Turyn(A0,(ei-1,fi-1)denotes that A0 and(ei-1,fi-1)are operated by Turyn's Method.By substituting A0,B0 into different GCP Kernels,we can obtain four kinds of binary CZCPs with different lengths.In addition,for binary perfect cross Z-complementary sequence pairs with length 2?10?26?(??1,?,??0),we have also proved that the magnitude of their nonzero aperiodic cross-correlation sums is lower bounded by 4.