## 6 Results
### SDR Performance Evaluations  
The environmental set-up of the SDR transceiver experiment is shown in Figure 11. It consisted of a transmitter, a laptop that controlled the SDR transmitter, a receiver, and a laptop that controlled the SDR receiver. The laptop used an Intel Core i7-8750H processor and 16 GB RAM. The utilized SDRs were Ettus USRP B210. In addition, to minimize the external noise effect, we connected the RF port via a cable during the performance evaluation experiments. The details of the SDR configuration set-up are shown in Table 1.  
We conducted an experiment to compare the theoretical BER and SDR performances for QPSK, 8 PSK, and 16 PSK, which represent up to four different levels of phase-modifying factor. As shown in Figure 12, we confirmed that the trends for theoretical and SDR performance were somewhat similar. However, as the modulation order increased, we observed that the differences between the SDR performance and theory increased. Additionally, at low SNR values (approximately less than 3 dB), SDR performance had more error than the theory. However, as the SNR increased, we observed the SDR performance having similar trends to the theoretical performance. When comparing the lower SNR region performances, the differences between the SDR and theoretical performance decreased, \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Parameter Values** \\ \hline Center frequency & 915 MHz \\ Bandwidth & 1 MHz \\ Data bit & 10,000 \\ Clock rate & 20 MHz \\ Header symbol length & 12 symbols \\ Message & hello world *** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SDR configuration parameters. Figure 11: SDR performance evaluation experiment set-up. Figure 10: BER simulation results (fixed \(I_{p}\) and varying \(I_{m}\)) for (**a**) QPSK, (**b**) 16 QAM, and (**c**) 64 QAM. and the trends were somewhat similar. Therefore, we may expect the SDR performance at a higher SNR region to be similar to that of the theory, especially for the lower modulation scheme, with an adjustment of few dBs. Even though there were some differences observed for the BER performance, the ring-shaped signaling system placed a higher priority on the I/Q constellation shape than on recovered communication performance. As shown in Figure 13, we confirmed that the I/Q constellation forms of QPSK, 8 PSK, and 16 PSK were clearly distinguishable. From this observation, we could define that the SDR system's recovering data function was not perfectly working, even though the I/Q constellation shaping was working properly. As we observed in the BER performance evaluation, the error between the theoretical value and SDR performance according to the modulation order increased, and the I/Q constellation data points' concentrations were more scattered as the modulation order increased. With the confirmed I/Q constellation working properly up to 16 PSK, the ring-shaped signaling system implementation through SDR could function up to \(I_{p}=4\). To evaluate whether the ring-shaped signaling system was functioning properly, we conducted transceiver performance evaluation experiments by varying the phase- and magnitude-modifying factors. As shown in Figure 14a, the performance degraded as the magnitude-modifying factor decreased. As shown in Figure 14b, the performance could be recovered even though different phase-modifying factors were applied. As shown in Figure 14b, in the case of \(I_{p}=4\) for 16 PSK, full recovery was not achieved due to the existence of functional error for the 16 PSK modulation scheme performance in SDR without noise signaling. Therefore, we assumed that if the plain SDR transceiver was properly functioning, perfect performance recovery with different phase-modifying factors  
Figure 12: BER comparison between theoretical values and SDR performance. Figure 13: I/Q constellation shapes of (**a**) QPSK, (**b**) 8 PSK, and (**c**) 16 PSK. could possibly be achieved.