  The combination of space-time coding (STC) and continuous phase modulation
(CPM) is an attractive field of research because both STC and CPM bring many
advantages for wireless communications. Zhang and Fitz [1] were the first to
apply this idea by constructing a trellis based scheme. But for these codes the
decoding effort grows exponentially with the number of transmitting antennas.
This was circumvented by orthogonal codes introduced by Wang and Xia [2].
Unfortunately, based on Alamouti code [3], this design is restricted to two
antennas. However, by relaxing the orthogonality condition, we prove here that
it is possible to design L2-orthogonal space-time codes which achieve full rate
and full diversity with low decoding effort. In part one, we generalize the
two-antenna code proposed by Wang and Xia [2] from pointwise to
L2-orthogonality and in part two we present the first L2-orthogonal code for
CPM with three antennas. In this report, we detail these results and focus on
the properties of these codes. Of special interest is the optimization of the
bit error rate which depends on the initial phase of the system. Our simulation
results illustrate the systemic behavior of these conditions.
