L2 OSTC-CPM: Theory and design

TL;DR

This paper introduces L2-OSTC-CPM, a novel class of space-time codes combining orthogonality and continuous phase modulation, enabling full rate, full diversity, and low decoding effort for multiple antennas.

Contribution

It generalizes existing two-antenna codes to L2-orthogonal codes for multiple antennas and presents the first L2-orthogonal CPM code for three antennas, enhancing efficiency and performance.

Findings

L2-orthogonal codes achieve full rate and diversity.

Optimization of initial phase improves bit error rate.

Simulation results confirm systemic behavior of proposed codes.

Abstract

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.