L2-Orthogonal ST-Code Design for CPM

Non-linear modulations, like the Continuous phase modulation (CPM) with its constant envelope property, have been appealing for energy efficient communication systems. In parallel, linear orthogonal Space-Time block codes (STBC) have emerged as a simple way of achieving spectral efficiency by full diversity and simple decoupled maximum-likelihood decoding. However, linear codes rely on pointwise orthogonality which leads to a well-known degradation of data rate for more than two antennas. In this paper, we introduce the concept of L²-orthogonality for non-linear Space-Time codes (STC). Our approach generalizes code design based on pointwise orthogonality. Namely, we are able to derive new codes with the same advantages as pointwise orthogonal STBC, i.e. low decoding complexity and diversity gain. At the same time, we are no longer limited by the restrictions of pointwise orthogonal codes, i.e. the reduction in data rate. Actually, we show how to construct full rate codes for any arbitrary number of transmit antennas. More precisely, a family of codes for continuous phase modulation (CPM) is detailed. The L²-orthogonality of these codes is ensured by a bank of phase correction functions which maintains the phase continuity but also introduces frequency offsets. We prove that these codes achieve full diversity and have full rate. Moreover, these codes don´t put any restriction on the CPM parameters.