Multi-Frequency Interference Detection and Mitigation Using Multiple Adaptive IIR Notch Filter with Lattice Structure

Radio Frequency Interferences (RFI), such as strong Continuous Wave Interferences (CWI), can influence the Quality of Service (QoS) of communications, increasing the Bit Error Rate (BER) and decreasing the Signal-to-Noise Ratio (SNR) in any wireless transmission, including in a Digital Video Broad-casting (DVB-S2) receiver. Therefore, this paper presents an algorithm for de-tecting and mitigating a Multi-tone Continuous Wave Interference (MCWI) using a Multiple Adaptive Notch Filter (MANF), based on the lattice form structure. The Adaptive Notch Filter (ANF) is constructed using the second-order IIR NF. The approach consists in developing a robust low-complexity algorithm for removing unknown MCWI. The MANF model is a multistage model, with each stage consisting of two ANFs: the adaptive IIR notch filter ( ) l H z and the adaptive IIR notch filter ( ) N H z , which can detect and mitigate CWI. In this model, the ANF ( ) l H z is used for estimating the Jam-ming-to-Signal Ratio (JSR) and the frequency of the interference ( o ω ) by using an LMS-based algorithm. The depth of the notch is then adjusted based on the estimation of the JSR. In contrast, the ANF ( ) N H z is used to mitigate the CW interference. Simulation results show that the proposed ANF is an effective method for eliminating/reducing the effects of MCWI, and yields better system performance than full suppression ( 1 N k = ) for low JSR values, and mostly the same performance for high JSR values. Moreover, the proposed can detect low and high JSR and track hopping frequency interference and provides better Bit error ratio (BER) performance compared to the case without an IIR notch filter.

Simulation results show that the proposed ANF is an effective method for eliminating/reducing the effects of MCWI, and yields better system performance than full suppression ( 1 N k = ) for low JSR values, and mostly the same performance for high JSR values. Moreover, the proposed can detect low and high JSR and track hopping frequency interference and provides better Bit error ratio (BER) performance compared to the case without an IIR notch filter.

Introduction
Many communications systems, such as wireless and satellite communication systems, suffer from Radio Frequency Interference (RFI) thanks to the ever-increasing number of wireless applications in use, as well as human-made RFI. RFI may be unintentional or could be an intentional act, such as jamming. It can also reduce the Signal of Interest (SoI) and result in a degraded QoS, a decrease in SNR, and an increase in BER or a loss of the receiver's communication signal. Various jamming mitigation techniques have been proposed in the literature, and can be classified as adaptive antenna-based techniques (space domain) [1], Time-Frequency Filtering (TFF)-based methods [2] [3], and adaptive filtering-based techniques [4] [5] [6] [7]. The adaptive antenna methods (spatial filtering) are appropriate for Narrow-Band (NB) and wideband (WB) jamming mitigations. The space domain (antenna array) can also achieve a high jammer suppression ratio but is not suitable for mobile devices [8] [9]. The TFF methods remove signal features in both the Time Domain (TD) and the Frequency Domain (FD) simultaneously, but the major concern with the FD method is computational complexity, which arises from FFT and IFFT in hardware. [10]. The methods are appropriate for NB jamming mitigation, such as Short Time Fourier transforms (STFT) [11], bilinear signal distribution [12], filter banks [13], and Wavelet Transforms (WT) [14] [15]. The STFT and the filter bank techniques employ fixed windows, which are useful for analyzing nonstationary signals. The adaptive filtering-based methods are commonly used for narrowband CWI jamming rejection and can be classified into two approaches, namely, TD and FD. For the FD approach, [16] proposed an N-sigma method to reject CWI. Also, [17] [18] proposed methods to detect and mitigate CWI and NB interference. Also, [19] proposed a method to detect and mitigate MCWI using a first-order IIR notch filter based on a simplified Welch algorithm and notch filter. However, the main concerns with the FD approach are computational complexity and higher costs.
Using the Finite Impulse Response (FIR) and the Infinite Impulse Response (IIR) filters to detect and mitigate interference for TD approaches. The papers by [20] [21] [22] present methods for suppressing the CWI in the TD using an ANF based on a lattice form structure. The authors in [23] proposed a method for detecting and mitigating CW interference using two-pole and multiple NF. Also, [9] presented a technique using ANF to detect and mitigate MCWI in GPS. In [10], the ANF is used to mitigate both CWI and NB interference for GNSS. Moreover, the papers by [24] [25] [26] present linear prediction and nonlinear prediction methods. Both methods require longer tap filters to effectively mitigate narrowband interference, which increases the system's complexity [20]. In the literature, NF is used to reduce and remove interference in different applications, such as biomedical applications and [27] and GNSS applications (e.g., DSSS systems and GPS receivers) [20] [23]. The lattice IIR ANF performs better than the direct IIR ANF form [21] [22]. The IIR NF in lattice form is less computationally complex than are direct form implementations [20] [21] [23]. A typical IIR notch digital filter has constrained zeros on the unit circle, which makes the notch more depth "results into infinite" leading to complete removal of the interference. Nevertheless, this method creates self-noise due to the distortion of the data "desired signals" at the notch frequency as the interference is removed [22], called self-noise, as briefly described in [28]. In DSSS systems, Choi [20] proposed a new CWI excision method that uses an ANF to reduce self-noise. The authors in [29] proposed a novel low-complexity anti-jamming filter to reduce the CWI for general wireless communications. With the exception of the works in [20] and [29], these previous works concentrated on detecting and removing CWI and MCWI without focusing on controlling the notch filter's depth. The two divergent papers [20] [29] focused only on the excision of the CWI. The present paper proposes a low-complexity algorithm operating in TD using multiple ANF to detect and mitigate MCWI with considering controlling the notch depth based on an estimation of the interference power, called an anti-jamming receiver system model. This model is constructed using the secondorder IIR NF based on a lattice form structure described in Section 3.
The rest of the paper is organized as follows. The signal model of the transmitted and received signals in the presence of MCWI is described in Section 2.
Section 3 reviews and describes the adaptive IIR NF structure and the proposed adaptation algorithm for mitigating MCWI using MANF. Section 4 describes and defines the optimal notch depth that maximizes the output SNR, while Section 5 presents the simulation performed and discusses the results obtained. Finally, Section 6 concludes the paper.

Signal Model
In this section, Figure 1

Interference Signal Model
Continuous Wave Interference (CWI) is one of the most common sources of interference. CWI can be modeled as a sinusoidal wave in time, such as a single or multi-CWI. A multitoned CWIs is considered in this paper, and can be modeled as: where:  m is the number of CW interferences;

Received Signal Model
The received signal ( ) r t , which is the input signal to the IIR notch filter, is the sum of the QPSK modulated baseband signal ( ) S t , the AWGN, ( ) w t , and the interference signal, ( ) i J t , which can be modeled as: In Section 3, the case of a multitoned CWI is considered, and 2 m = . The input baseband signal to the IIR notch filter ( ) r t given by Equation (2) is then sampled at chip rate to convert it into discrete-time samples for further processing as shown here: For ease of notation, the sampling interval s T will be ignored in the rest of this paper, and Equation (3) will be adopted as:

Proposed Algorithm and Structure of the Filter
This paper proposes using a MANF based on a second-order IIR lattice form structure as an anti-jamming receiver system model, as shown in Figure 2. The model presents as a low-complexity algorithm operating in the TD approach.
The reason the approach operates in TD is to avoid the costs associated with the transfer domain approach. The MANF system model is a multistage model, with each of its stages consisting of two ANFs: the adaptive IIR notch filter

Transfer Function of IIR Notch Filter
A. El Gebali, R. J. Landry Journal of Computer and Communications  where β is the pole radius factor that controls the filter's bandwidth ( 0 1 β < < ); ol k is a coefficient of lattice IIR NF parameter that rejects an unknown CWI, which is defined as

Adaptation of Parameter kol and LMS Adaptive Algorithm
In this subsection, the derivation of the LMS adaptive algorithm is utilized in transversal tapped (IIR) filters with the structure shown in Figure 3. It is as- The cost function of the filter can be given as [30]:   (9) where L is the length of data. The goal of the filter is to adjust the notch parameter o k for minimizing the cost function, and the gradient-based method of steepest descent is used to achieve the goal: The instantaneous value of ( ) o J k is used to replace the ensemble-averaged value as: To simplify, Equation (11) thus becomes: where ( ) ( ) ol g J k is the gradient signal for the adaptation of ol k , and is defined as: Substituting into Equation (13): where µ is the step-size factor that controls the convergence speed and stability, and Equation (14) is a new adaptive algorithm for our proposed ANF that allows and controls the update filter coefficient in this work.
Since the normalized notch frequencies, N f and ol k , are related by where N k is the depth of the NF and is a function of the estimated JSR l . β is the pole radius that controls the bandwidth of the NF. Note that N l = . While many implementation schemes can obtain  of ( ) l H z , which has zero on the unit circle, resulting in an infinite depth of the notch that completely removes the interference [20]. As stated previously, with the NF's infinite depth, the interference is removed completely, but nonetheless creates self-noise at the NF, resulting from the exclusion of some useful signals.
Hence, the depth of the notch N k should thus be adjusted with the interference power to reduce the distortion of the signal. Therefore, the same structure can be used for ANF

Optimal Depth of the Notch that Maximizes SNRout
This section described how the notch's optimal depth maximizes the SNR output of the IIR NF as a function of its parameters [20] [31] [32]. SNR out can be expressed as: where ( ) y n is the output of the ANF. Equation (20) describes SNR out in terms of the filter parameters as given [20]: where 2 σ is the variance of AWGN, and 2 JSR 2 Let us assume that the first part of the Equation (20) From Equation (20), the SNR output is affected by JSR l and D in Equation (21). D shows a large value since N k increases as the notch becomes deeper, whereas JSR l effect indicated by the second part of Equation (20). To maximize SNR out , the optimal value of N k needs to be found in Equation (20). The denominator in Equation (20) can be rewritten after some modification as a function of N k [20]: To find the optimal N k , we differentiate ( ) N f k and solve all possible roots of N k , as shown in Equation (23): Equation (23) has at least one real root in the [0 1] range that gives the optimal N k as a function of JSR l . Figure 6 describes the flow chart for the system model. After a signal is received, the ANF ( ) l H z estimates JSR l and the frequency of the interference ( ol ω ) using Equation (16) and Equation (15)

Simulation and Discussion of Results
The performance of the proposed low-complexity anti-jamming receiver system model of a MANF with MCWI is demonstrated in this section. The system performance is investigated in terms of the BER and the SNR out of the IIR NF for varying JSR and SOI power ( b o E N ). In this work, for the i th jamming signal, the number of CWIs is considered, and thus, noise at the output, but a smaller broadband noise [20]. The BER is measured as JSR changes.
The estimated optimal value of N k vs. JSR is obtained by calculating the roots as JSR is changed, with a different parameter of β and b o E N , as shown in Figure 7. As a result, N k approaches 1 as JSR l increases to a large value. Also, this approach depends on the parameters of ( b o E N ) and β. Therefore, as the parameter of b o E N decrease, JSR l increases as well, as 1 β → .    and a large β. Figure 13 and Figure 14 show the performance of the BER vs.  It can be seen that the proposed algorithm effectively controls the notch depth and obtains better results than in the case of full suppression for a low JSR, and mostly the same for a high JSR.
The performance of the SNR vs. JSR is shown in Figure 18 and Figure 19.
The proposed IIR NF algorithm effectively controls the notch depth, to be deeper for high JSR in each stage. The results show that full suppression achieves better results than does the case without a notch filter for a high JSR. Hence, full suppression is better for a high JSR, and without a notch filter is better for a low Journal of Computer and Communications        JSR. The results also show that the proposed IIR NF at any stage approaches the case of full suppression when the JSR is increasing "high" because the notch depth becomes deeper in this case. So the notch depth becomes smaller for a lower JSR value and deeper for a higher JSR value. Figure 20 shows the received signal of the Power Spectrum (PS) before and after processing by the IIR notch filter. The results show that the proposed IIR NF algorithm is able to detect and mitigate the interference. They also show that with the adjusted depth of the IIR NF, the interference is removed according to the estimated JSR l to avoid the reduction of the Signal of Interest (SoI).
A. El Gebali, R. J. Landry These results will be compared with [19]. [19] proposed a method to detect and mitigate MCWI using a simplified Welch algorithm and notch filter operating in a frequency-domain approach. The approach used a first-order IIR notch filter. Although the CWI has been removed, a portion of the useful signal has been lost, compromising overall signal integrity. Also, the main concerns with the FD approach are computational complexity and higher costs. On the other hand, the proposed method proposes a low-complexity algorithm operating in a time-domain approach using multiple ANF to detect and mitigate MCWI. The approach used the second-order IIR notch filter based on a lattice form structure. The IIR notch depth is adjusted based on interference power estimation. Table 1 shows a comparison between the algorithm proposed in [19] with our proposed algorithm. Table 1. Comparison between the algorithm proposed in [19] with our proposed algorithm. No.
Ref. [19] Proposed algorithm 1 They used QPSK signal They used QPSK signal 2 They proposed a method to detect and mitigate MCWI using a simplified Welch algorithm and notch filter We proposed a low-complexity algorithm to detect and mitigate MCWI using a multiple adaptive notch filter based on the lattice form structure 3 They used a frequency-domain approach We used a time-domain approach 4 They used a first-order IIR adaptive notch filter we used a second-order IIR adaptive notch filter 5 They do not adjust the depth of the notch We adjusted the depth of the notch based on the estimation of the JSR

Conclusion
This paper proposes a novel low-complexity algorithm for mitigating multi-tone continuous wave interference using multiple adaptive notch filters based on a second-order IIR lattice form structure. This structure detects, estimates, and removes the MCWI. The algorithm operates in TD, which reduces hardware costs. Adaptive frequency estimators are used to adjust the notch filter's zeros, placing them on the interference frequency. However, if zeros on the unit circle and has a notch of infinite depth ( 1 N k = ), and leading to the complete removal of the interference and exclusion of some desired signals This causes a reduction of the Signal of Interest (SoI) and results in a degraded QoS, a decrease in SNR, and an increase in BER. The adaptive notch filter algorithm for the given notch filter is thus proposed to adjust the notch depth and frequency. Therefore, the proposed method can effectively detect and mitigate the MCWI and adjust the notch depth for any given value of JSR, and can therefore effectively control the notch depth. It also provides better results than does a full suppression for low JSR values, and mostly the same performance for high JSR values, and provides a better BER performance. Also, the resulting SNR out of the NF is maximized for lower and higher JSR values with different values of ( b o E N ) power. Therefore, this technique can be applied in a DVB-S2 receiver or any other communication and navigation receivers.