## 5 Results and Discussion
### Impact of PNC Receiver Design  
Consider an ideal implementation of the PNC receiver which comprises an ideal carrier filter, with bandwidth \(2B\). This filter is used to isolate the mm-wave carrier generated through the heterodyne process, and whose phase noise is characterized by a 3-dB linewidth value \(LW_{dec}\). SNR, arising from the presence of phase noise only, can be approximated (conservatively), as follows (see Appendix A):  
\[\text{SNR}\approx\frac{2B}{LW_{dec}}\enspace, \tag{4}\]  
It should be noted that this relationship only holds when the PNC's signal filter bandwidth is sufficient to allow the information signal and associated phase noise component to pass without curtailment. Here, an SNR of 1 indicates that the filter bandwidth is equal to the 3-dB linewidth of the mm-wave carrier component. Practically speaking, this scenario equates to the case where the mm-wave carrier spectrum is band-limited, such that only half of its spectral power can be used for the phase noise cancellation step at the IF down-conversion stage. Considering the high-order Gaussian filter design used in this work (with a bandwidth of \(F_{3 dB}\)), and the fact that the generated mm-wave  
Figure 5: Received OFDM constellations with the (**a**) external LO based receiver and (**b**) PNC receiver when the optical linewidths are set to 12 kHz; and received APSK constellations with the (**c**) external LO based receiver and (**d**) PNC receiver when the optical linewidths are set to 40 kHz. carrier linewidth is equal to the summation of the independent optical carrier linewidths (given by the term \(LW_{opt}\) in Equation (2)), the above relationship can be extended as follows:  
\[\text{SNR}\approx\frac{F_{3 dB}}{2\times LW_{opt}}\enspace, \tag{5}\]  
Given that SNR is related to the root mean square EVM performance metric through the following equation:  
\[\text{SNR}=\left(\frac{1}{\text{EVM}}\right)^{2}\enspace, \tag{6}\]  
an approximate expression for EVM can also be given as:  
\[\text{EVM}\left(\%\right)\approx\sqrt{\frac{2\times LW_{opt}}{F_{3 dB}}}\cdot 1 00\enspace. \tag{7}\]  
In order to minimize EVM, the expression (7) indicates that \(F_{3 dB}\) should be as large as possible. However, as this filter is required to isolate the mm-wave carrier term only, a large value of \(F_{3 dB}\) effectively precludes the use of frequencies around the carrier (i.e., within the carrier filter pass-band) for data modulation. In other words, relatively large IFs must be selected for optical modulation if \(F_{3 dB}\) is large--leading to a wider frequency separation between carrier and signal (sideband) terms in both the optical and mm-wave domains. Considering that the PNC based system which hinges on the co-transmission of both the carrier and signal sideband terms, the requirement for a large frequency separation between these terms is clearly sub-optimal from the perspective of spectral usage. A significant motivating factor for reducing the frequency separation between these components is the ease of compatibility with integrated photonic beam-forming networks (e.g., [35]), whose complexity can be reduced, and achievable mm-wave beam steering angle increased, with narrow-band operation [36]. In essence, when it comes to determining the filter criteria, a trade-off exists between performance optimization through wide-band filtering of the mm-wave carrier, and the efficient use of mm-wave spectrum. Figure 6a shows the performance of the proposed system using the PNC receiver with OFDM modulation, where the bandwidth of the mm-wave carrier filter is varied from 0.1-500 MHz. For optical linewidth values of 10 and 100 kHz (which equates to mm-wave carrier linewidths/phase-noise of 20 kHz (blue curve) and 200 kHz (red curve), respectively), performances improve with increased carrier filter bandwidth, until the performance floor is reached. These scenarios can be observed for bandwidth values of around 30 and 200 MHz, for the blue and red curves.