## 5 Functions Required for SDR Implementation  
We implemented the ring-shaped signaling system through SDR. Due to several configurational complexities, we focused only on the PSK transmitting and receiving communication system, evaluating whether an effectively covert QPSK system could be implemented without performance degradation. We used Ettus USRP B210 for SDR and Matlab for the software. When the ring-shaped signaling system is implemented through SDR, there are several important functions. Because the conventional QPSK signal shape changes to a signal with a different modulation order due to the phase-modifying factor, any frequency-related functions are required among the transceiver. For data recovery, accurately extracting the envelope is necessary. To accurately eliminate the envelope values for each piece of data, accurate synchronization between the transmitted and received data is needed to align the data in the correct order. For accurate synchronization, pre-processes with an RF signal, performed using certain information such as the modulation, the sample rate of the transmitted signal, or the data header are required. Within the RF signal pre-processing, we considered the required functions that were affected according to the modulation scheme types, which were the carrier synchronizer function and frequency offset estimator function. The carrier synchronizer function uses the Phase-Locked Loop (PLL) method, Direct Digital Synthesizer (DDS), and a phase error detector. Through the phase error calculation [27, 28], which depends on the modulation schemes, the calculated phase error sends through DDS and uses phase shifting to correct for the frequency offset. The frequency offset estimator function uses a frequency offset estimator which estimates the frequency offset by the auto-correlation and frequency offset corrector, which corrects the frequency based on the estimated offset value [29]. Since the PLL method depends on a different step of the phase error value, the transceiver must share the phase information of the same MPSK modulation order to correctly estimate the phase error step. In the case of using the ring-shaped signaling system, the received RF signal is changed to a certain order of MPSK, which is varied by the phase-modifying factor. Since the order can be flexibly changed by the phase modifying factor, the PLL setting of the receiver must match with the order of MPSK. For the same reason, the frequency offset estimator function must also be adjusted to the changed PSK order. The carrier synchronizer function and frequency offset estimator function are shown in Figure 6a,b below. In a conventional communication system, the symbol length depends on the type of modulation scheme and is calculated as shown in Figure 7, dividing the bit length by \(\log_{2}\) of the modulation scheme. This calculation process is also applied to the header, data, and tail bits. The converted symbol is used to form RF signals in the transceivers. In the conventional communication system, the symbol form of the header uses the input for the carrier synchronizer and frequency offset estimator functions. In general, if the length of the header changes, it is difficult to find the exact starting point of the data, and so accurate alignment is not possible. Therefore, we propose a symbol generation process that generates symbol forms of the data and header independently as shown in Figure 8. The process first uses a conventional symbol data transformation process only for the data bit part, generating predefined header symbols and then merging the two-part symbol data to generate a full form of symbol data. For accurate synchronization, symbols 180\({}^{\circ}\) apart were chosen as the symbol form of the header. The separately generated symbol form header could have the same length no matter what phase modifying factor was used.