## 3 Waveforms for Millimetre-Wave Mobile Communications  
As well as defining initial frequency bands of operation, 5G NR also specifies the use of the OFDM waveform for system deployments, with increased signal bandwidths and subcarrier spacings compared to 4G long-term evolution (LTE). For operation in the FR2 band, ref. [1] defines OFDM bandwidths up to 400 MHz and subcarrier spacings of 60/120/240 kHz. In hybrid photonic/mm-wave systems using MCM schemes, such as OFDM, our previous work [5] has shown that the phase noise of the heterodyne mm-wave carrier relative to the subcarrier spacing/baud rate is of critical importance. This ultimately leads to the requirement for ultra-low linewidth optical sources in the sub-kHz to kHz range, greatly hindering the wide-scale deployment of such systems. Our recent work [11; 29] has focused on developing phase noise robust photonic/mm-wave systems, which help to ease these laser linewidth restrictions and enable the use of lower cost commercially available devices--which typically exhibit a higher linewidth.  
APSK is a highly popular modulation format for satellite communications. The single-carrier modulation format was first adopted for satellite digital TV through the Satellite Digital Video Broadcasting (DVB-S) open standards. Today, DVB-S2 (up to 32-APSK), and optional extension DVB-S2X (64/128/256-APSK) have been widely adopted to encapsulate satellite broadband traffic, including transmission in the Ka band [30]. DVB-S' popularity stems from its relatively high spectral efficiency and inherent robustness against nonlinear distortion, which can be attributed to its unique APSK constellation. The ideal 32-APSK constellation (which is presented later in Section 4.2) consisting of three concentric rings is shown in Figure 3b. The absence of a wide range of symbol amplitudes results in a reduced peak-to-average power ratio (PAPR) compared to the equivalent quadrature amplitude modulation (QAM) constellation--making APSK more resilient to nonlinear distortions introduced by high-power amplifiers (HPAs). Furthermore, the ratio of the APSK ring radii can be varied in order to tailor the waveform PAPR for a given channel, at the cost of altering the Euclidean distance between constellation points.  
It is worth noting that, although OFDM exhibits relatively high levels of PAPR, its advantages in terms of subcarrier flexibility, spectral efficiency and inherent compatibility with terrestrial broadband and 5G networks have led to its inclusion in discussion around next generation waveforms for satellite broadband applications [3; 31; 32]. Adaptations to OFDM's basic form, in order to limit PAPR and out-of-band (OOB) emission, may be required for satellite communications [32], but its key potential benefits are clear; the provision of a ubiquitous 5G networking platform and the ease of interaction with terrestrial systems.  
With the aims of demonstrating the proposed hybrid system's relevance to the networking applications outlined in Section 2, and providing a comparative study of single-carrier and multi-carrier modulation performances in the presence of mm-wave phase in such a system, both 32-APSK and 32-QAM OFDM are applied in the simulation platform which is outlined in the following section.