New Sets of 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 sequence pair to be used for pilot design in SM over frequency-selective channels. CZCPs are sequence pairs having zero autocorrelation sums and zero cross-correlation sums within specific time-shifts. In this letter, we propose systematic constructions of binary CZCPs with new lengths of the form $2^\alpha 10^\beta 26^\gamma ~(\alpha \geq 1)$ , $10^\beta $ , $26^\gamma $ and $10^\beta 26^\gamma $ . We have also proved that for a specific kind of binary CZCP, the magnitude of non-zero aperiodic cross-correlation sums at each time shift outside the zero cross-correlation zone is lower bounded by 4. Finally, we have compared our proposed constructions with the previous constructions.