# Effects of Interference and Mitigation Using Notch Filter for the DVB-S2 Standard
## 3 The Effects of Interference
### Symbol Timing Recovery
#### 3.4.2 Blind Carrier Recovery  
The DVB-S2 transmitter has a special mode with a higher bit rate when the channel is under good communication conditions. In this mode, the pilots can be turned off and be replaced by user data for less redundancy and faster transfer speeds. In this situation, the non-data-aided algorithm or blind carrier offset recovery must be utilized for Doppler compensation to fulfill the basic operation of the digital receiver. The most used synchronizer is PLL. The symbolic structure of this synchronizer is displayed in Figure 16a.  
The numerical control oscillator is the heart of almost all synchronization algorithms. It generates a frequency proper to the detected error. The phase error detector calculates the degree of rotation from the original points of the signal constellation. Considering that we have two vectors: V1 and V2, the phase between two vectors: \(\Delta\varphi\), can be calculated with the use of the cross product (Figure 16b) [26, 27]:  
\[\Delta\varphi=\angle V_{2}-\angle V_{1}=\angle\big{(}V_{2}^{*}\oplus V_{1} \big{)}=\angle\big{(}(I_{1}I_{2}+Q_{1}Q_{2})+j(I_{1}Q_{2}-I_{2}Q_{1})\big{)} \tag{27}\]  
where \(\oplus\), is the symbol of the cross product. It can be seen that \(\Delta\varphi\) is proportional to the imaginary part of the cross product:  
\[\Delta\varphi\propto(I_{1}Q_{2}-I_{2}Q_{1}) \tag{28}\]  
The target is to calculate the phase error from the original points of the 4 QAM signal constellation (Figure 16c). Thus, V2 is equal to the received symbol and V1 is equal to the nearest point from the  
Figure 16: Phase synchronizer based on PLL and the cross-product phase detector. (**a**) General block diagram (**b**) The phase error between two vectors (**c**) The phase rotation in 4 QAM signal constellation (**d**) The deviation from original phase error in the presence of CWI.  
QAM signal constellation to the symbol (in the case that the rotation is smaller than \(\pi\)/4). For each received symbol, V1 is equal to the summation of real sign and imaginary sign (Figure 16c):  
\[V_{1}=sign(Q_{2})+jsign(I_{2})=\hat{Q}_{2}+j\hat{I}_{2} \tag{29}\]  
Thus, for input symbol \(S=Q+j.I\), the phase error \(\Delta\varphi\) is estimated based on the following cross-product phase detector [26, 27]:  
\[\Delta\varphi\propto\ I\hat{Q}-Q\hat{I}\sim sin(\Delta\varphi) \tag{30}\]  
For simplicity, consider that the point is located in the first quarter, then:  
\[V_{1}=1+1j\Rightarrow\Delta\varphi\propto\ I-Q \tag{31}\]  
Figure 16d represents the phase error calculation in the presence of CWI. Based on the previous discussions, the symbols start to circle around the original point by the radius of a. In this situation, deviation from the original phase error \(\Delta\varphi\) is estimated based on the following equation:  
\[\begin{array}{c}S^{\prime}=\left(Q+acos\Big{(}2\pi f_{j}t\Big{)}\Big{)}+j \left(I+asin\Big{(}2\pi f_{j}t\Big{)}\right)\Rightarrow\\ \Delta\varphi^{\prime}=\ \left(I-Q\right)+\ a\left(cos\Big{(}2\pi f_{j}t \Big{)}+sin\Big{(}2\pi f_{j}t\Big{)}\right)\end{array} \tag{32}\]  
Based on the above equations and Figure 16d, it can be seen that the maximum deviation depends on the power of the interference. A similar model of the blind carrier phase detector is implemented in Matlab Simulink and the effects of CWI with different power are studied in Figure 17. In our simulations, we utilized different center frequencies that change from frequencies close to Doppler value to frequencies far from it. However, the obtained results were similar to a negligible difference. Based on the simulation performed with the phase detector, its behavior under interference is almost independent of the center frequency of the CWI and is more dependent on its power. Compared to the data-aided algorithm, blind phase detectors work independently of the center frequency and are more robust against CW interferences.