Energy-Efficient Index and Code Index Modulations for Spread CPM Signals in Internet of Things

The evolution of Internet of Things technologies is driven by four key demands: ultra-low power consumption, high spectral efficiency, reduced implementation cost, and support for massive connectivity. To address these challenges, this paper proposes two novel modulation schemes that integrate continuous phase modulation (CPM) with spread spectrum (SS) techniques. We begin by establishing the quasi-orthogonality properties of CPM-SS sequences. The first scheme, termed IM-CPM-SS, employs index modulation (IM) to select spreading sequences from the CPM-SS set, thereby improving spectral efficiency while maintaining the constant-envelope property. The second scheme, referred to as CIM-CPM-SS, introduces code index modulation (CIM), which partitions the input bits such that one subset is mapped to phase-shift keying symbols and the other to CPM-SS sequence indices. Both schemes are applied to downlink non-orthogonal multiple access (NOMA) systems. We analyze their performance in terms of bit error rate (BER), spectral and energy efficiency, computational complexity, and peak-to-average power ratio characteristics under nonlinear amplifier conditions. Simulation results demonstrate that both schemes outperform conventional approaches in BER while preserving the benefits of constant-envelope, continuous-phase signaling. Furthermore, they achieve higher spectral and energy efficiency and exhibit strong resilience to nonlinear distortions in downlink NOMA scenarios.