## 4 Ring-Shaped Signaling System Algorithm  
A block diagram of the proposed ring-shaped signaling system is shown in Figure 1. After the conventional modulation process of the communication system, a noise-shaping operation is added to modify a signal having the characteristics of a noise. The envelope that is used for the noise-shaping operation is composed of phase and magnitude, and it is possible to control the noise level using different variables. The phase envelope variable rotates the constellation. For example, in a PSK signal, the result of the rotation process is to modify the PSK constellation to a different order of PSK signal that makes it difficult for attackers to interpret the data. The signal looks like a noisier signal when the rotation order increases. The magnitude envelope displaces the original I/Q constellation data points close to the origin point (I/Q = (0,0)). The signal transformed by the magnitude envelope looks more like white noise, and the magnitude modification process lowers the power of the signal, making it difficult to intercept. Figure 1: Ring-shaped signaling system block diagram. The expected modified constellation obtained through the proposed ring-shaped signaling system is shown in Figure 2. With the proposed system, the data points around the origin (I/Q = (0,0)) are displaced to a certain low boundary to form a ring. With the ring-shaped signal, the constellation seems faded or like white noise with a hole at the center. Therefore, eavesdroppers have difficulty interpreting the data because they are unable to determine the modulation scheme. In addition, since the modified signal is similar to noise, the average transmission power of the signal is relatively lower than the original signal. The lower transmission power also enables a decrease in the probability of intercepting the signal. The ring-shaped signaling system converts a conventionally modulated signal as shown in Equation (1) into a modified signal using a magnitude-modifying factor and a phase modifying factor, as shown in Equation (2). The magnitude-modifying factor and the phase-modifying factor can adjust the noise level through independent variables. The covertness performance can be changed according to the modifying factors:  
\[ \begin{array}{l}\text{S}=\chi(\cos\varphi+j\sin\varphi)\\ \chi\text{:magnitude of signal}\end{array}  \tag{1}\]  
\[ \begin{array}{l}S_{n}=\ \chi\text{M}(\cos(\varphi+\theta)+j\sin(\varphi+\theta)) \\ \text{M: magnitude modifying factor}\\ \theta\text{: phase modifying factor}\end{array}  \tag{2}\]  
The phase-modifying factor is generated through the process shown in Figure 3. After generating random number bits \(bn\) with same length as the original data length \(n\), the random bits are added with additional bits, which are same length as \(lp\). The generated random bits, which have a length of \(n+lp\), are grouped with \(lp-1\) number of bits and then converted to a decimal number \(Nn\), which has same length as original data length \(n\). The converted decimal is divided by the value of the power (2) of the intensity level \(lp\). Through this process, the range of \((0,2\pi)\) is divided by a certain resolution according to the intensity level. The modified signal is rotated as shown in Figure 2b. Since the phase rotation process is performed with I/Q data, additional key bits are not required. Thus, the data rate for the intended receiver stays same, while the previous methods [4; 26] that use additional key bits have increased data rates. Figure 2: I/Q constellation (**a**) before signaling process and (**b**) after ring-shaped signaling process. The magnitude-modifying factor is applied to the original signal by multiplying it by a uniformly distributed random number that has a length equal to that of the transmitted data. As shown in Figure 4, when generating the magnitude-modifying factor, the minimum value of the random number is adjusted according to the magnitude intensity level \(I_{m}\) to control the lower boundary, which influences the signal magnitude.