## 3 Methodology and Solution  
### General Solution  
In this section, a detailed structure of the detector and interference mitigation system is presented. Figure 2 displays the proposed design based on downsampling and notch filtering. Based on this structure, the input signal passes through two different paths. The first path directly goes to the chain of adaptive notch filters, which their center frequencies and bandwidths are adjusted by the detector. This paper focuses on the narrowband digital communication signals. Usually in a digital receiver, an analog to digital converter (AD) samples the input RF signal with a sample rate several time faster than the largest maximum frequency component. A faster sample rate is necessary for fulfilling the symbol time recovery (STR), which extracts symbols with maximum power from input samples [9]. Thus, as it can be seen in Figure 1, the desired signal power spectrum is located in a narrow bandwidth of all frequency interval. The target is to detect and remove the in-band interferences. In this way, the detector does not need to investigate all frequency bandwidth and by zooming on the useful interval, it can obtain better and more accurate results. One of the common ways for zooming in frequency domain is downsampling. To avoid aliasing before downsampling, the input signal is passed through a low-pass filter, which removes the extra bandwidth and avoids folding [31]. The downsampling rate must be chosen based on the signal bandwidth and sample rate of analog to the digital converter of the receiver. Consider that AD samples the RF signal with sample rate \(F_{s}\) and input signal has the maximum bandwidth \(BW\). Based on the Nyquist theorem, maximum downsampling factor must be smaller than \(\frac{F_{s}}{BW}\). After downsampling, the signal passes through the detector itself to extract the main characteristic of each interference and carry this information over to the filters. In the frequency domain, an effective narrowband interference can be considered as an abnormality on top of the desired signal spectrum power. One can describe this abnormality with three main factors: center frequency, bandwidth, and power. The main job of the detector bank is to group the abnormalities as individual interferences and estimate these three parameters for each detected interference. An adaptive notch filter is a band-stop filter where its center frequency and its bandwidth are adjustable based on the situation. Detector bank estimates the characteristics of each interference and adjusts the center and bandwidth of each notch for optimum quality of service (QoS). Notch filter also removes a part of the useful spectrum of the signal, thus it is necessary to activate the mitigation system when the interference is detected and remove the notch filter from the receiving chain when there is no interference. In other words, the number of utilized notch filters must be equal to the observed interferences. The detector handles this important duty with the help of the multiplexer. Each multiplexer has two inputs: the signal that passed through to the last notch and the signal that does not go to the notch. Figure 2: General block diagram of the proposed detector. Based on the selection process, the detector selects one of these two signals by the help of the \"select\" signal. When all \"select\" pins are zero, no filtering is applied to the input signal. This helps to have several notches in the chain of the receiver and utilize as much as required based on the current situation. The high-power level of the modulated signal makes the detection process difficult; however, for a narrowband signal, when the interference center frequency is out of the interest bandwidth, it cannot affect the receiver's performance. In other words, if a detection algorithm tries to find the interference in the entirety of the interval \([-\pi\pi]\), its efficiency will be negatively impacted. The easiest way to increase the resolution in the frequency domain is to downsample the input signal before detection.