  Spatial modulation (SM) is a new paradigm of multiple-input multiple-output
(MIMO) systems, in which only one antenna at the transmitter is activated
during each symbol period. Recently, it is observed that SM training sequences
derived from corss Z-complementary pairs (CZCPs) lead to optimal channel
estimation performance over frequency-selective channels. CZCPs are special
form of sequence pairs which have zero aperiodic autocorrelation zones and
cross-correlation zone at certain time-shifts. Recent paper by Liu \textit{et
al.} discussed only perfect CZCPs. In this paper, we focus on non-perfect
CZCPs. We introduce the term cross Z-complementary ratio and re-categorise the
CZCPs, both perfect and non-perfect, based on that. We propose a systematic
construction of CZCPs based on generalised Boolean functions (GBFs). We further
extend the lengths of the CZCPs by using the insertion method. The proposed
CZCPs are all of new lengths of the form
$2^\alpha10^\beta26^\gamma+2~(\alpha\geq1)$, $10^\beta+2$, $26^\gamma+2$ and
$10^\beta 26^\gamma+2$. Finally we propose a construction of optimal binary
CZCPs having parameters $(12,5)$ and $(24,11)$ from binary Barker sequences.
These CZCPs are also extended to $(12N,5N)$- CZCPs and $(24N,11N)$- CZCPs,
where $N$ is the length of a binary Golay complementary pair (GCP). During the
proof, we also found a new structural property of binary CZCPs and concluded
all binary GCPs are CZCPs too. Finally, we give some numerical simulations to
confirm that depending on the number of multi-paths, the proposed CZCPs can be
used to design SM training matrix which attains the minimum mean square error.
