Quadriphase Cross Z-Complementary Pairs for Pilot Sequence Design in Spatial Modulation Systems

Cross Z-complementary pairs play an instrumental role in the design of optimal spatial modulation (SM) to service optimal channel estimation over frequency-selective channels. By selecting a binary Golay complementary pair (BGCP) of length
$N$
as a seed, eight constructions for quadriphase cross Z-complementary pairs (QCZCPs) of lengths
$3N$
,
$7N$
,
$9N$
,
$11N$
,
$12N$
,
$14N$
,
$18N$
, and
$24N$
are presented, respectively. The resultant pairs have not only large cross Z-complementary ratios, but also lots of new lengths which can not be produced by existing known constructions. The proposed constructions can provide more QCZCPs of flexible lengths for applications to broadband SM systems.