# Effects of Interference and Mitigation Using Notch Filter for the DVB-S2 Standard
## 3 The Effects of Interference
### Symbol Timing Recovery
It also confirms that the Gardner algorithm is robust against the CWI interference. As it can be seen, detected timing error converges to half of the symbol period even in the presence of powerful interference. Symbols are discovered correctly, however, because of the interference power, for each point of the signal constellation, symbols are distributed on the circle with a radius proper to the interference power. inserts 90 symbols at the beginning of a frame, called a physical layer (PL). Those symbols are not part of the data, but they can help to recognize the boundaries of a packet [6]. The start of frame (SOF) is 25 special symbols that the DVB-S2 transmitter inserts at the beginning of a frame. With those symbols, the receiver can find the start of the frame based on the correlation of the input frame with the SOF vector. Both the receiver and the transmitter are aware of the symbols in the header. The receiver correlates the input frame with the SOF symbols. After correlation, the position of SOF will appear in the detector as a peak and this peak shows the position of the frame start point. Figure 9 presents the structure of the frame in standard DVB. SOF has a special characteristic that allows the detector to utilize differential correlation. Deferential coefficients are obtained by multiplying each SOF symbol by the conjugate of the next SOF symbol [25]:  
\[C_{SOF}^{m}=SOF_{m}SOF_{m+1}^{*}=\pm j,\ m=1,2,\ldots 25 \tag{14}\]  
\(C_{SOF}^{m}\) are differential coefficients of the SOF, \(SOF_{m}\), is the mth symbol of SOF in a packet and \(SOF_{m}^{*}\) is the conjugate of that. Thus, inside the receiver, a correlator utilizes these 25 differential coefficients to obtain the start point of the frame [25]:  
\[\Lambda^{SOF}=\sum_{i=1}^{25}r_{i}r_{i+1}^{*}C_{SOF}^{i} \tag{15}\]  
In Equation (15) above, \(r_{i}\) shows the ith received symbols. \(\Lambda^{\text{SOF}}\) is the result of the differential correlation of the input symbols and SOF symbols in the receiver. The position of the highest peak in \(\Lambda^{\text{SOF}}\) displays the start of the frame. After correlation because of similarity, at the position of SOF, a large peak will be obtained. All steps of frame synchronization are implemented in Matlab and results are explained in Figures 10-12. Figure 10 displays a typical response of the correlator. The Gardner algorithm downsamples the output of the analog to digital converter to the symbol. Thus, the timing delay is an integer multiplied by the symbol period. Because of satellite movement and random distance between the satellite and the receiver, the start point of the frame is a variable. In our simulation, we consider that there is a delay equal to the 300 of symbol time in the received packet. In this figure, received frames have a delay equal to the 300 th symbol time, thus, a large peak is located at the 300 th symbol. Distance between peak amplitude and correlation results with other samples determines the system's robustness. The larger this distance is, the easier the SOF can be  
Figure 8: STR of a QPSK with JSR = \(-\)4 dB, fj = 0.095 (\(\times\)\(\pi\) rad/samp), CWI effect on (**a**) convergence curve and (**b**) output symbols. Figure 9: Structure of PL header in standard DVB-S2. where \(DC=\ a^{2}exp\left(-2\pi j\! :\!f_{j}T\right)\) and the term \(a.\left\{r_{i}\times\exp\left(-2\pi j\!:\!f_{j}T\!\cdot\! (n+1)\right)+r_{i+1} \times\exp\left(2\pi j\! :\!f_{j}T\!\cdot\!n\right)\right\}\) is the CWI effect. As it can be seen here, term \(a.\left\{r_{i}\times\exp\left(-2\pi j\!:\!f_{j}T\!\cdot\! (n+1)\right)+r_{i+1} \times\exp\left(2\pi j\! :\!f_{j}T\!\cdot\!n\right)\right\}\) is the CWI effect. Here, n is the symbol index in the DVB-S2 standard frame. CWI center frequency, \(f_{j}\), is multiplied by the symbol index and can go up to 32000. Multiplying CWI center frequency by a large number makes the response behavior sensitive to frequency and generates harmonics and periodic behavior with a small change in center frequency (Figure 12).