## 4 Performance with Phase Noise
### Result Analysis  
The consideration of positive phase noise values reflects the voltage-controlled oscillator (VCO) operation at high frequencies, where the phase noise can be exceptionally high. This is not a typical scenario, yet this study aimed to find the operating limits for each system under phase noise. As was mentioned in the introductory part of the section, an obvious application of these systems fits the requirements of multiple narrowband transmission, such as in WSN or 5G technologies. The following Figures 16-19 show the results of the second study case, which took several values of the phase noise to analyze the performance of the systems in the AWGN conditions. The SNR levels on the \(x\)-axis are normalized to set the 0 dB SNR at the BER = \(10^{-3}\) for comparison issues, like in the selective fading section. The BER curves in Figures 16-19 shows system performance decreasing with the decrease of the SNR. However, at certain phase noise levels, the phase noise influence becomes more dominant, and at higher SNR values, system BER performance does not improve; thus, the BER curves diverge. Figure 16: QCPSK system’s AWGN performance for several phase noise levels. Figure 15: SSB phase noise of the SMC100 signal generator [58] (**a**) and generated SSB noise (**b**). For QCPSK and 4-QAM communication systems (Figures 16 and 17), SNR was normalized at BER 10\({}^{-3}\), corresponding to a phase noise of 11 dBc for QCPSK and \(-\)23 dBc for 4-QAM. Increasing the phase noise level by 2 dBc, BER performance reduces to 3.98 \(\times\) 10\({}^{-3}\) for QCPSK and 1.48 \(\times\) 10\({}^{-3}\) for 4-QAM. If phase noise grows by an additional 2 dBc, BER performance for QCPSK and 4-QAM is 1.50 \(\times\) 10\({}^{-2}\) and 2.16 \(\times\) 10\({}^{-3}\), respectively. BER performance for the QCPSK communication system is 4.98 \(\times\) 10\({}^{-2}\), and 4-QAM performance is 3.91 \(\times\) 10\({}^{-3}\) when an additional 2 dBc of phase noise are added to the communication system. Increasing the phase noise by 2 dBc, QCPSK BER performance is 9.96 \(\times\) 10\({}^{-2}\), and 4-QAM performance is 8.20 \(\times\) 10\({}^{-3}\). If the phase noise is increased by 2 dBc, QCPSK and 4-QAM communication systems BER performance is 1.55 \(\times\) 10\({}^{-1}\) and 1.61 \(\times\) 10\({}^{-2}\), respectively. Figure 19: FSK system’s AWGN performance for several phase noise levels. Figure 17: 4-QAM system’s AWGN performance for several phase noise levels. For the FM-CSK and FSK communication systems (Figures 18 and 19), SNR was normalized at BER \(10^{-3}\), corresponding to a phase noise 15 dBc for FM-CSK and 10 dBc for FSK. FM-CSK shows a typical behavior for the systems based on analog frequency modulation [59]. At phase noise levels of 15 dBc and 17 dBc, BER performance is \(10^{-3}\); however, if the phase noise level increases further, the BER of the system is close to 0.50, meaning the system is useless for data transmission. For the FSK communication system, at phase noise levels of 10 14 dBc, BER performance is \(10^{-3}\). Increasing the phase noise to 16 dBc BER performance of the FSK is 1.32 \(\times\)\(10^{-3}\). Adding 2 dBc to the phase noise reduces BER performance to 2.01 \(\times\)\(10^{-3}\). At a 20 dBc phase noise, FSK performance is 5.50 \(\times\)\(10^{-3}\). Comparing QCPSK and FM-CSK communication system performance (Figures 16 and 18) at a phase noise of 15 dBc, QCPSK performance is 1.50 \(\times\)\(10^{-2}\), and FM-CSK performance is 1.00 \(\times\)\(10^{-3}\). If the phase noise is increased to 17 dBc, QCPSK performance is 4.98 \(\times\)\(10^{-2}\), and FM-CSK performance remains unchanged. At phase noise levels higher than 19 dBc, the FM-CSK communication system is useless for data transmission, while the QCPSK communication system is showing better results--at 19 dBc, performance is 9.96 \(\times\)\(10^{-2}\), and at 21 dBc the performance is 1.55 \(\times\)\(10^{-1}\). 4-QAM data transmission system shows a BER decrease with a decrease in phase noise.