# Data-Aided and Non-Data-Aided SNR Estimators for CPM Signals in Ka-Band Satellite Communications
## 5 Numerical Results and Analysis  
The length of the source information sequence is set to 1000 bits, and the sampling points per symbol are set to IPOINT = 20. For the CPM modulator, the modulation index is set to h = 1/4, the pulse shaping function is set to GMSK, L = 2, and the modulation order is set to \(M\) = 8. The average value of the SNR estimators is calculated with 1000 frames. The SNR fitting curve of the DA ML and M\({}_{2}\)M\({}_{4}\) estimators are shown in Figure 3. The horizontal axis in the figure is shown as the actual SNR, which is the assumed value in the MATLAB simulation and is the channel environment in the actual communication. The ordinate is the SNR estimated by the Formulas (28) and (35) in Section 4. The horizontal and ordinate of the truth values are all the actual values of SNR and the true values are the standard used to measure the offset of estimate SNR and actual SNR. The DA ML estimator can be approximated as unbiased when SNR is less than 5 dB. The estimation error is large in the case of medium and high SNR. The estimation bias increases with the increase of SNR. The M\({}_{2}\)M\({}_{4}\) estimator can be approximated as unbiased when SNR is medium (near 5 dB), but the estimation error is significantly large at low and high SNRs. The NMSE of the DA ML and M\({}_{2}\)M\({}_{4}\) estimators are shown in Figure 4. The DA ML estimator has the best performance when SNR is approximately 0 dB, but the performance becomes worse with the increase of SNR. The M\({}_{2}\)M\({}_{4}\) estimator has the best estimation performance when SNR is near 7 dB. The performance curve of the M\({}_{2}\)M\({}_{4}\) estimator is similar to a parabola, and the performance is poor at low SNR. The performance becomes worse with the increase of SNR after 7 dB. The two estimators cannot achieve the Cramer-Rao bounds and the existence of the SNR node. The performance worsens with the increase of SNR after the node because the non-CM characteristics introduced by the fading factor. When the SNR is low, the noise power is the main factor affecting the estimation performance due to the large noise power, while the signal power is the main factor affecting the estimation performance in the medium to high SNR. In the process of signal power estimation, it is necessary to do the division of the mean of the fading factor as in Formulas (18). The difference between the estimated value and actual value of the signal power is greater with the increase of SNR, which will lead to the worse performance. The DA ML estimator displays better performance than the M\({}_{2}\)M\({}_{4}\) estimator, especially in the low SNR. The performance gap between the two estimators is reduced gradually when the SNR is medium or high. The two estimators are close to each other in practical applications when the channel environment is good. Thus, the M\({}_{2}\)M\({}_{4}\) estimator can be used to reduce the complexity. The DA ML estimator can be used to improve the estimation performance when the channel environment is poor, and the transmitter information sequence is known. Figure 4: NMSE comparison of DA ML and M\({}_{2}\)M\({}_{4}\) in Ka-band fading channel. Figure 3: Estimated SNR comparison of DA ML and M\({}_{2}\)M\({}_{4}\) in Ka-band fading channel. Three parameters affect the estimation performance by setting the different values of the parameters. These parameters include the number of sampling points per symbol, the length of the transmitted information sequence, and the modulation order. The common parameters are the same as the previous settings. The NMSEs of DA ML and M\({}_{2}\)M\({}_{4}\) for IPOINT = 10, 20, 40 are plotted in Figure 5. The estimation performance improves with the increase in the number of sampling points per symbol. The NMSEs of DA ML and M\({}_{2}\)M\({}_{4}\) for the length of transmission information for 1000, 2000, and 4000 bits are plotted in Figure 6. The estimation performance improves the longer the transmitted information.