# Effects of Interference and Mitigation Using Notch Filter for the DVB-S2 Standard
## 4 Proposed Solution and Efficiency Analysis
### Notch Filter  
A notch filter is a narrow band stop filter that rejects part of the signal located in a very specific frequency band. The gain drops and rises very quickly. The notch filter is utilized as a solution by filtering a single-tone CWI frequency and letting all other frequencies pass. It can also be used in multi-tone CWI mitigation by employing multi-notch filters in cascade. This greatly improves the reception performance at the cost of a slight loss of information, since a frequency band of the original signal is removed as well.  
The transfer function of an IIR M-order notch filter can be expressed as following [34]:  
\[H(z)=\ \frac{\prod_{i=1}^{M}\left(1-e^{i\omega_{i}}z^{-1}\right)}{\prod_{i=1}^{M }\left(1-re^{i\omega_{i}}z^{-1}\right)} \tag{33}\]  
Each \(\omega_{i}\) represents the frequency of each gap in the notch filter and pole radius r (restricted as \(0<r<1\) for stability) controls the bandwidth of each notch. By inserting M = 1, Equation (33) is simplified as the first order complex notch filter:  
\[H(z)=\ \frac{1-e^{i\omega_{0}}z^{-1}}{1-re^{i\omega_{0}}z^{-1}} \tag{34}\]  
where \(w_{0}\) is the center frequency of the adaptive notch filter. Figure 19 shows the frequency response of three notch filters with different r values and different center frequencies. For a lower value of r, the attenuation is much stronger, and the gap bandwidth is larger.  
The IIR notch filter is used very often in narrowband interference mitigation, especially for GNSS receivers. It has a very simple structure that makes it suitable for practical implementation. Compared with the FIR filter with many taps and coefficients, the IIR notch filter has a simpler structure and is the heart of many narrowband interference mitigation systems because of this unique structure. The most important feature is that both center frequency and bandwidth can be adjusted adaptively by adjusting only two parameters. For the FIR filter, to adaptively remove a hopping CWI, one has to reproduce all filter taps based on the desired center and bandwidth and then change the coefficients of the filter also FIR filters have a longer convergence time. The IIR notch filter also has a linear frequency response in all of the bandwidth except in its gap bandwidth (Figure 19b). However, non-linearity in the gap is not important because this bandwidth is supposed to be removed from the signal. The general drawback of the notch filter on system performance is explained based on the SNR reduction and BER curve. The described system performance reduction is general, thus, it covers all the effects like: removed information from the original signal and effect of phase non-linearity in the frequency gap. In other  
Figure 18: Block diagram of the generic solution.  
words, the system performance study shows the system degradation after the notch filter puts all its effects on the desired signal that contains both amplitude and phase. Both the amplitude and phase of the signal are affected by the notch filter, then the SNR and BER after filtering are calculated. In this case, the system performance study covers both amplitude gap and phase behavior.