# Data-Aided and Non-Data-Aided SNR Estimators for CPM Signals in Ka-Band Satellite Communications
## 3 System Model  
The Ka-band satellite channel can be simulated by a multiplicative interference vector \(C(t)\) and \(z(t)\) from Section 2. The schematic of the system can be established as shown in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Weather Conditions** & \(m_{1}\) & \(\sigma_{1}^{2}\) & \(m_{2}\) & \(\sigma_{2}^{2}\) \\ \hline Clear/cloudy & 0.455 & 0.00056 & 0.0079 & 0.00381 \\ Cumulus cloud & 0.346 & 0.00272 & 0.0154 & 0.00864 \\ Light rain & 0.483 & 0.00003 & 0.0088 & 0.00546 \\ Thunder shower & 0.436 & 0.01386 & 0.0068 & 0.00414 \\ Blowing snow & 0.500 & 0.00021 & 0.0089 & 0.00435 \\ Ice pellets & 0.482 & 0.00062 & 0.0094 & 0.00544 \\ Rain & 0.662 & 0.02000 & \(-\)0.0089 & 0.03077 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ka-band satellite channel envelope and phase model. Figure 1: Ka-band satellite channel statistical model. Figure 2: Schematic of the system. The data source produces a binary sequence. The data symbol generated at any time is independent of the previous symbol. The probability of the two symbols is the same. The information was sequenced through the CPM modulator and transmitted to the Ka-band fading channel. Gaussian Processes 1 and 2 in Figure 2 are considered as two independent stochastic processes with a mean of zero, and the variances are \(\sigma_{1}\) and \(\sigma_{2}\). Gaussian process 1 and the real constant generator 1 are added to generate the Gaussian stochastic process \(\alpha\). Gaussian stochastic process \(\theta\) can be generated in the same way. \(\theta\) is sent to the exponential generator and multiplied with \(\alpha\) to obtain the multiplicative interference vector \(C(t)=\alpha\exp(j\theta)\). Different weather conditions only need to change the variance and the mean of \(\alpha\) and \(\theta\). The received signal can be represented as \(r(t)\) (the expression is shown in follows) after the Ka-band fading channel. The SNR is estimated according to the received signal and the SNR estimators are shown in Section 4. A suitable coded modulation scheme is selected in the feedback link according to the value of SNR and the ACM schemes switching standards (Since the emphasis of this paper is on SNR estimators, we do not introduce too many coding process). The data is transmitted to the Ka-band fading channel according to the selected coded modulation scheme and the received signal is processed by Viterbi algorithm. Transmitting terminal uses a complex-valued low-pass CPM signal, which is given by  
\[\mathbf{s}(t,\mathbf{a})=\exp\{j\phi(t,\mathbf{a})\}, \tag{13}\]  
where, for \(nT\leq t\leq(n+1)T\)  
\[\phi(t,\mathbf{a})=2\pi h\sum_{i=0}^{n}a_{i}q(t-iT), \tag{14}\]  
where \(T\) is the symbol time, \(\mathbf{a}=(a_{0},a_{1}\cdots)\) is the transmitted information sequence, \(h=K/P\) is the modulation index, where \(K\) and \(P\) are the coprime integer, and \(q(t)\) is the phase pulse and is a continuous monotone function  
\[q(t)=\left\{ \begin{array}{cc}0&\qquad\qquad\quad t\leq 0\\ 1/2&\qquad\qquad\quad t>LT\end{array} \right.. \tag{15}\]  
The CPM signal can be obtained by integrating the rectangular pulse (LREC) with a duration of \(LT\), the raised cosine pulse (LRC), or the Gaussian minimum shift keying (GMSK) pulse and expressed as  
\[q(t)=\int_{-\infty}^{t}g(\tau), \tag{16}\]  
where \(g(t)\) is the pulse shaping function and is nonzero in \(0\leq t\leq LT\). \(g(t)\) is a full response when \(L~{}=~{}1\) and a partial response when \(L>1\). The received signal is given by  
\[r(t)=As(t)+z(t), \tag{17}\]  
where \(A\) is the true amplitude of the received signal, \(s(t)\) is the CPM modulation signal, and \(z(t)\) is additive Gaussian white noise with the variance of \(\delta^{2}\). This paper aims to estimate the SNR according to the received signal. The signal fading caused by the envelope plays a decisive role, and signal fading caused by the phase is almost negligible. Therefore, the mean value of the envelope can be approximated as the multiplicative fading in the channel.