An Algebraic Framework for Digital Envelope Modulation

Abstract

Sub-THz communications based on coherent re-ceivers suffer from strong phase impairments issued by oscillators. Envelope detection, inherently robust to this impairment, is hence considered for the design of sub-THz systems. This paper proposes an algebraic framework for envelope modulation. In the first place, we introduce a Hilbert space to represent waveforms with non-negative real values. This space is defined by transport of structure of the usual signal-space L2. So, existing schemes developed for real-valued signals can be exploited upon envelope modulation. In the second place, it is shown that the proposed framework provides powerful tools to design new envelope modulation schemes. To do so, we present the transmission of an Inphase Quadrature signal upon an envelope modulation to prevent the impact of phase noise on communication performance. We also demonstrate that constraints on embedded analog-to-digital converters can be relaxed with the use of orthogonal non-negative waveforms.