# Effects of Interference and Mitigation Using Notch Filter for the DVB-S2 Standard
## 3 The Effects of Interference
### Symbol Timing Recovery
For frame synchronization, there are two states: 1-correct detection (or successful detection), if the start of frame detected is exactly equal to the position of the frame header, then the data can be retrieved from the packet. Two-error detection: any deviation, even one symbol from the exact position of the header causes the packet loss. If the number of \(Np\) packets is received, then successful frame synchronization is equal to the percentage of the packet that the receiver detected the header position:  
\[\textit{Probability of successful frame synchronization}\ =\ \frac{N_{success}}{N_{p}}\]  
where \(N_{success}\) is the number of packets that the receiver successfully detected the position of the header in the packet. Because it is a two states event, the probability of error is equal to:  
\[\textit{Probability of synchronization error (packet lost Probability)}=1-\textit{Probability of successful frame synchronization}\]  
Figure 11 displays the probability of successful frame synchronization in the presence of CWI with JSR = -7 dB based on the simulation results. The block performance completely changes as the center frequency varies. With some center frequencies, the probability of correct detection can decrease to less than 85% which means 18% of packets are lost, which will cause large distortion in all the system (One example of minimum points can be seen between frequency 0.02 to 0.04). Thus, the frame synchronization process is vulnerable to CWI. Extra terms distort the differential correlation process in two ways:  
1. At some frequency, it damages the shape of the differential coefficients \(C_{SOF}^{m}\), therefore, peak amplitude, which indicates the start of the frame, decreases severely. Figure 12 represents the peak amplitude based on the CWI center frequency. Peak amplitude fluctuates between highly detectable amplitudes and critically low amplitudes for detection depending on the CWI center frequency as shown in Figure 12. Where the peak amplitude has its local minimums, correct detection probability is decreased as described in Figure 11.
2. Another important factor for correct detection is the result of correlation with other samples. The structure of SOF in the DVB-S2 packet is in the way that, correlation with other samples is not large, thus, the start of the frame can be found by the receiver even in noisy conditions. In performed simulations, we observe that in normal situations, the result of correlation for other samples (rather than the header) is under 25 that displayed in Figure 10 as a red line. After repeating the simulation, in the same situation with a CWI with an JSR = -7 dB, it was observed that this amount is increased by 50%. In DVB-S2 standard a pilot symbol \(P_{i}\) has the following imaginary and real parts:  
\[f_{j}<\frac{BW}{2}\ \Rightarrow\ f_{j}\times T<\frac{BW.T}{2}\ <\frac{1+\beta}{2N_{up}} \tag{13}\]0  
DVB-S2 system benefits from Luise and Reggiannini (L&R) algorithm [26]. This method estimates the frequency offset \(f_{d}\) based on the following equation:  
\[ \begin{array}{c}f_{d}=\frac{1}{\pi T_{s}(N+1)}arg\left[\sum\limits_{m=1}^{N}R (m)\right]\\ R(m)=\frac{1}{L_{p}-m}\sum\limits_{k=m}^{L_{p}-1}z^{p}(k)z^{p^{\prime}}(k-m) \end{array}  \tag{19}\]  
In the above equations, \(z^{p}(k)\) shows the received pilot samples, in the DVB-S2 system \(L_{p}=36\) is the number of pilots, and N is the correlation interval. Consider that the channel influences the transmitted signal S with the Doppler Effect \(f_{d}\). In normal conditions, without any interference, the first group of received pilots can be expressed as the following:  
\[z^{p}(k)=\frac{1}{\sqrt{2}}(1+j)exp\Big{(}2\pi j\Big{(}n_{p}+k\Big{)}f_{d} \Big{)} \tag{20}\]  
In Equation (20) above, \(n_{p}=16\times 90\) that is the number of symbols before the pilots.