# Effects of Interference and Mitigation Using Notch Filter for the DVB-S2 Standard
## 3 The Effects of Interference
### Symbol Timing Recovery
For simplicity \(z^{p}(k)\) is multiplied by \(\Big{(}\sqrt{2}/2\Big{)}\times\ (1+j)\), then it can be rewritten as:  
\[z^{p}(k)=exp\Big{(}2\pi j\Big{(}n_{p}+k\Big{)}f_{d}\Big{)} \tag{21}\]  
Calculation of \(R(m)\) involves \(L_{p}-1-m\) multiplication of \(z^{p}(k)z^{p^{\prime}}(k-m)\):  
\[u^{p}(k)=z^{p}(k)z^{p^{\prime}}(k-m)=exp(2\pi jmf_{d}) \tag{22}\]  
When the signal is distorted by CWI, received pilots have an extra part:  
\[ \begin{array}{c}z^{p}_{Interference}(k)=z^{p}(k)+CWI\\ =\ exp\Big{(}2\pi j\Big{(}n_{p}+k\Big{)}f_{d}\Big{)}+\ \alpha\times exp\Big{(}2\pi j \Big{(}n_{p}+k\Big{)}f_{j}\Big{)}\end{array}  \tag{23}\]  
CWI effect can be discovered by replacing a new number of pilots in [22]:  
\[ \begin{array}{c}u^{p}_{Interference}(k)=\left\{exp\Big{(}2\pi j\Big{(}n_{p }+k\Big{)}f_{d}\Big{)}+\ \alpha\times exp\Big{(}2\pi j\Big{(}n_{p}+k\Big{)}f_{j}\Big{)}\right\}\times\\ \left\{exp\Big{(}-2\pi j\Big{(}n_{p}+k-m\Big{)}f_{d}\Big{)}+\alpha\times exp \Big{(}-2\pi j\Big{(}n_{p}+k-m\Big{)}f_{j}\Big{)}\right\}\end{array}  \tag{24}\]  
Consider that CWI center frequency has distanced \(\Delta\) from Doppler frequency:  
\[ \begin{array}{c}f_{j}=f_{d}+\Delta,\ \Delta=f_{j}-\ f_{d}\\ u^{p}_{Interference}(k)=u^{p}(k)(1+A)(1+B)\end{array}  \tag{25}\]  
Figure 13: Complete frame structure in DVD-S2 system. where:  
\[ \begin{array}{l}A=\alpha.\textit{exp}\big{(}2\pi\gamma\big{(}n_{p}+k\big{)} \Delta\big{)},\\ B=\alpha.\textit{exp}\big{(}2\pi\gamma\big{(}n_{p}+k-m\big{)}\Delta\big{)}\end{array}  \tag{26}\]  
The term \((1+A)(1+B)\) states deviation from the correct value. Since \(R(m)\) is dependent on the phase of \(u^{p}(k)\), the phase of this term cumulatively distorts the \(R(m)\) from its correct value. From this, it is understood that the deviation term depends on the amplitude of CWI and the distance between the CWI's center frequency and the Doppler frequency. Figure 14 shows the percentage of error from the correct value with JSR = \(-8\) dB based on the simulation result. This figure supports the theoretical result and depicts the direct effect of \(\Delta\) on the system performance. When the CWI is near the Doppler frequency, conventional algorithms are affected severely. As the center frequency takes distance from the Doppler frequency, its disturbing effect is decreased. It should be mentioned that if the coarse step does not remove the main part of the carrier offset correctly, the next block, fine carrier recovery cannot fulfill its duty. A 15% deviation is enough to stop fine carrier recovery steps; thus, the CR process is vulnerable to the CWI effect. Figure 15 displays the deviation from the correct value as a function of the JSR. Here again, the amount of distortion depends on the distance \(\Delta\). In both curves, stronger CWI will cause more distortion. When distance \(\Delta~{}=~{}0.1\), almost for all JSR, the error is below 3%. However, in the case with distance \(\Delta~{}=~{}0.003\), error dramatically increases for larger JSR. Figure 14: Effect of CWI on the CR algorithm based on the \(\Delta\) parameter. Figure 15: Percentage of error in Doppler estimation based on JSR. This section presented the effect of a CWI on the CFR based on the (L&R) algorithm. The closer the Doppler frequency is from the CWI's center frequency; the more errors occur. A smart jammer can stop the receiver with low power CWI that has a center frequency close to the Doppler value.