###### Abstract  
The removal filter coefficients in this technique are dependent on the jammer's power and its Instantaneous Frequency (IF) information, which can both be obtained in the time-frequency domain (adaptive filtering techniques). The dependence of the removing/reducing filter characteristics on the interference power is critical, as it allows an optimal trade-off between removal interference and the amount of self-noise generated by the filter. This trade-off is bounded by the two extreme cases of no notch filter (no self-noise) and full suppression (\(k_{1}=1\)) for both low- and high-power jammer values. In this paper, a cascade second-order adaptive direct Infinite Impulse Response (IIR) Notch Filter (NF) with a gradient-based algorithm to suppress the Continuous-Wave (CW and MCW) interference is proposed for maximizing the receiver Signal-to-Noise Ratio (SNR) in a Quadrature Phase-Shift Keying (QPSK)-modulated signal. The suppression approach consists of two Adaptive IIR NFs (ANFs) based on a direct-form structure: the \(H_{d1}(z)\) and \(H_{d1}(z)\). The proposal in this work presents a low-complexity Time-Domain (TD) algorithm for controlling the update filter coefficient and notch depth. Simulation results demonstrate that the proposed approach represents an effective method for removing/reducing the impacts of CWI/MCWI, resulting in improved system performance for low- and high-power jammer values when compared with the case of full suppression (\(k_{1}=1\)); furthermore, it also improves the notch filter's output SNR for a given Jamming-to-Signal Ratio (JSR) value and Bit Error Ratio (BER) performance. For example, the SNR output of the proposed IIR NF was enhanced by 7 dB versus the case without a filter when \(E_{b}/N_{o}=15\) dB and JSR \(=-5\) dB. The proposed method can detect and mitigate weak and strong jamming with JSR values ranging from \(-30\) to \(40\) dB, and can track the hopping frequency interference. Moreover, an improved BER performance is seen as compared to the case without an IIR NF. radio frequency interference; Adaptive Notch Filters (ANFs); SNR; BER; Quadrature Phase Shift Keying (QPSK); Jamming-to-Signal Ratio (JSR) +
Footnote †: journal: Applied  
Wireless Networks (MHWNs) [6], and Long-Term Evolution (LTE) cellular communications [7]. In [8], the authors discuss the negative effects of jamming on GNSS receiver performance, and present three types of jamming detection, namely, digital pre-correlation signal processing, post-correlation domain, and Automatic Gain Control (AGC). Several techniques have been developed to mitigate the RFIs that impact the receiver in various areas of telecommunications--especially wireless communications. In GNSS signals [9], interference can be easily detected and mitigated, as the distance between the transmitter and the receiver is too large (around 20,000 Km); thus, the signal is Wideband (WB). Additionally, the GNSS signals from the satellites are below the noise level. Furthermore, a higher Jamming-to-Noise Ratio (JNR) enables easier interference detection [10]. When compared to GNSS signals, the amplitude level of a modulated Narrow-band (NB) signal, as defined by the Digital Video Broadcasting Satellite Second Generation (DVB-S2) standard [11, 12], is significantly higher than the noise. The modulated NB digital communication signal is the main focus of this work. In the literature, most algorithms used in detection and mitigation techniques are in Wideband (WB) signals that do not work directly with NB signals. Therefore, this work utilizes the Jamming-to-Signal Ratio (JSR) instead of JNR in order to mitigate modulated Narrowband (NB) signals. Figure 1 displays the effect of the Power Spectrum (PS) on the received signal with different JSR parameters, and compares the impact of JSR and the energy per bit to the noise power spectral density ratio (\(E_{b}/N_{o}\)) on the effectiveness of detection.