## 5 Results and Discussion  
### OFDM Versus APSK  
The simulated photonic/mm-wave test-bed outlined in the previous section was firstly evaluated in terms of the tolerance of both waveforms to mm-wave phase noise produced through the heterodyne process. Figure 4a shows the system performance, in terms of EVM, for both mm-wave receivers, as the linewidths of the optical sources were varied. It should be noted that the independent optical phase noise terms are set to have the same linewidth value. After the photo-mixing of these two carriers at the PD, the resultant 60 GHz mm-wave carrier and mm-wave data signal will possess a phase noise, characterized by a linewidth value which is the summation of the optical linewidths. In the case where the standard external LO based receiver is used, Figure 4a shows that OFDM reception is highly sensitive to increased optical linewidth. This is as a direct result of OFDM's MCM FFT-based implementation, which requires strict alignment of orthogonal subcarriers in the frequency domain, as discussed in [5]. Here, the perturbation of the 244 kHz bandwidth data-carrying subcarriers through the introduction of phase noise leads to severe degradation, where EVMs above 10% can be observed for optical source linewidths of just a few kHz. It should be noted that 5G NR specifies an EVM limit \begin{table}
\begin{tabular}{l l l l} \hline \hline
**S.No.** & **Property** & **APSK** & **OFDM** \\ \hline
1. & Total Data Rate & 1 Gb/s & 0.98 Gb/s \\
2. & Bandwidth & 200 MHz (3-dB) & 195.2 MHz \\
3. & Modulation Order & 32 & 32 \\
4. & Phase Tracking/EQ & LMS & Single-Tap FDE \\
5. & No. Subcarriers & - & 800 \\
6. & FFT Size & - & 1024 \\
7. & Subcarrier Spacing & - & 244 kHz \\
8. & CP & - & 6.25\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Waveform Parameters. Figure 3: **(a)** IF 200 MHz bandwidth 32-QAM OFDM spectrum, **(b)** Ideal 32-APSK constellation diagram and **(c)** IF 200 MBaud 32-APSK spectrum. of 8% and 12.5% for 64-QAM and 16-QAM, respectively, but does not specify for 32-QAM to date. An EVM target of 10% is discussed in this work as it is sufficient to obtain a bit error rate (BER) below the 7% forward error correction (FEC) limit of \(3.8\times 10^{-3}\). Figure 5a shows the received 32-QAM OFDM constellation (EVM = 21%), where optical source linewidths are both set to 12 kHz. For all OFDM results, channel estimation, as well as single-tap frequency domain equalization, was performed. For the same external LO-based receiver, the figure shows that APSK exhibits a higher tolerance to phase noise compared to OFDM. APSK's single-carrier implementation means that the information to be transmitted is spread across the entire APSK signal bandwidth (400 MHz). This effectively lowers the relative impact of a given level of mm-wave phase noise, compared to that experienced by a single OFDM subcarrier (244 kHz in this case). However, the results show that the level of performance improvement achieved by using APSK does not depend exclusively on the ratio of carrier modulation bandwidth to phase noise, but also on the application of receiver phase error correction. The cyan colored curve in Figure 4a represents the performance of APSK, where a blind least mean square (LMS) algorithm is used to estimate and correct phase offsets in the received constellation. Compared to the case where no phase tracking is applied (pink curve), a much improved performance, close to the system error floor, can be observed for optical source linewidth values up to 30 kHz--equating to 60 kHz of mm-wave phase noise. For higher linewidth values, the greater levels of phase noise variance become impossible to track, and this leads to the convergence of the APSK curves in the figure. Figure 5c shows the received 32-APSK signal in this case, where the optical linewidths are set at 40 kHz. It is possible that the inclusion of more advanced phase correction techniques [34] may help to sustain acceptable APSK performance beyond the 30 kHz limitation shown in Figure 4a.