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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 Broadcasting (DVB-S2) receiver. Therefore, this paper presents an algorithm for detecting 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
H
_{l}(
z) and the adaptive IIR notch filter
H
_{N}(
z), which can detect and mitigate CWI. In this model, the ANF is used for estimating the Jamming-to-Signal Ratio (JSR) and the frequency of the interference (
w(0)) 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
H
_{N}(
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 (
k_{N}=1) 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.

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) [

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 [

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.

In this section,

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:

J i ( t ) = ∑ i = 1 m A i cos ( 2 π f i t + θ i ) (1)

where:

• m is the number of CW interferences;

• A i is the amplitude of the i^{th} interference signal;

• f i is the frequency of the i^{th} interference signal;

• θ i is the phase delay of the i^{th} interference signal, which is assumed to be a random variable uniformly distributed in the range [ − π , π ] .

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, J i ( t ) , which can be modeled as:

r ( t ) = S ( t ) + w ( t ) + J i ( t ) (2)

In Section 3, the case of a multitoned CWI is considered, and m = 2 . 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:

r ( n T s ) = S ( n T s ) + w ( n T s ) + ∑ i = 1 m A i cos ( 2 π f i n T s + θ i ) (3)

For ease of notation, the sampling interval T s will be ignored in the rest of this paper, and Equation (3) will be adopted as:

r ( n ) = S ( n ) + w ( n ) + ∑ i = 1 m A i cos ( 2 π f i n + θ i ) (4)

where:

• S ( n ) is the desired QPSK modulated signal;

• w ( n ) is the AWGN.

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

into infinite, and leading to the complete removal of the interference and exclusion of some desired signals. To avoid this, the ANF H N ( z ) is added to adjust and control the depth of the notch ( k N ) according to the estimated JSR_{l} in order to reduce the elimination of some useful signals while removing interferences. The adaptive filter can be performed in various structures or realizations. There are two major implementations of an adaptive digital notch filter: the FIR and the IIR. FIR filters are also called moving average (MA) filters, which implement an all-zero transfer function. While the IIR filter has two parts, the auto-regression (AR) and the moving average (MA) (or an ARMA), the filter implements all-pole and all-zero transfer functions. In this work, the IIR filter is used since the IIR NF obtains a frequency response closer to that of the ideal NF than do FIR notch filters of the same length. _{l} and the frequency of the interference ( ω o l ), while the ANF ( H N ( z ) ) is used for interference cancellation. Note that in this work, the number of states is chosen as two (k = 2).

This section introduces the second-order IIR NF transfer function H l ( z ) based on the lattice form structure. A decision was made to use the IIR NF with an LMS algorithm to design and implement the Adaptive Notch Filter (ANF). By indicating the adaptive coefficient of l^{th} ANF by k o l , the second-order IIR NF transfer function H l ( z ) [

H l ( z ) = N l ( z ) D l ( Z ) = 1 + 2 k o l Z − 1 + Z − 2 1 + k o l ( 1 + β ) Z − 1 + β Z − 2 (5)

where β is the pole radius factor that controls the filter’s bandwidth ( 0 < β < 1 ); k o l is a coefficient of lattice IIR NF parameter that rejects an unknown CWI, which is defined as k o l = − cos ( ω o l ) . If the absolute values of both β and k o l are less than 1, the H l ( z ) is stable. Also, in this work, the parameter β is fixed and only adapt k o l to avoid notch too much QPSK signal.

In this subsection, the derivation of the LMS adaptive algorithm is utilized in transversal tapped (IIR) filters with the structure shown in

y ( n ) = u ( n ) + 2 k o l u ( n − 1 ) + u ( n − 2 ) (6)

u ( n ) = r ( n ) − k o l ( 1 + β ) u ( n − 1 ) − β u ( n − 2 ) (7)

The cost function of the filter can be given as [

J ( k o l ) = E { | y ( n ) | 2 } (8)

where E { ∗ } is an expectation operator. Replacing the expectation value in Equation (8) with the ensemble-averaged value as shown in Equation (9), we get:

J ˙ ( k o l ) = 1 L ∑ n = 0 L − 1 y 2 ( n ) (9)

where L is the length of data. The goal of the filter is to adjust the notch parameter k o for minimizing the cost function, and the gradient-based method of steepest descent is used to achieve the goal:

k o l ( n + 1 ) = k o l ( n ) − μ ( d J ˙ ( k o l ) d k o l ( n ) ) (10)

The instantaneous value of J ˙ ( k o ) is used to replace the ensemble-averaged value as:

k o l ( n + 1 ) = k o l ( n ) − μ ( d y 2 ( n ) d k o l ( n ) ) (11)

To simplify, Equation (11) thus becomes:

k o l ( n + 1 ) = k o l ( n ) − μ y ( n ) ( g ( J ( k o l ) ) ) (12)

where g ( J ( k o l ) ) is the gradient signal for the adaptation of k o l , and is defined as:

g ( J ( k o l ) ) = − ( 1 + β ) x ( n − 1 ) (13)

Substituting into Equation (13):

k o l ( n + 1 ) = k o l ( n ) − μ y ( n ) ( ( 1 − β ) x ( n − 1 ) ) (14)

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, f N and k o l , are related by k o l = − cos ( ω o l ) , where ω o l = 2 π f N , at sample n, the estimated frequency is given by:

f ^ N ( n ) = 1 2 π arccos ( k ^ o l ( n ) ) (15)

The estimated JSR_{l} can be calculated by subtracting the output of the NF y ( n ) from the received signal, r ( n ) , and is given by:

JSR l dB = 10 log 10 { | r [ n ] − y [ n ] | 2 } (16)

The transfer function of the ANF H N ( z ) [

H N ( z ) = N N ( z ) D N ( Z ) = 1 + K 0 l ( 1 + K N ) Z − 1 + K N Z − 2 1 + K 0 l ( 1 + β K N ) Z − 1 + β K N Z − 2 (17)

where k N 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 H N ( z ) , this work, however, implements H N ( z ) by cascading the lattice IIR NF model [

of H l ( z ) , which has zero on the unit circle, resulting in an infinite depth of the notch that completely removes the interference [_{l}, k o l and k N , are needed to design the IIR notch filter H N ( z ) to maximize the output SNR at H N ( z ) .

The IIR NF H N ( z ) output can be defined as:

y ( n ) = H N ( z ) r ( n ) ≜ S o ( n ) + w o ( n ) + J o ( n ) (18)

where S o ( n ) , w o ( n ) and J o ( n ) are the output components of the desired QPSK modulated signal, the white Gaussian noise, and the MCWI.

This section described how the notch’s optimal depth maximizes the SNR output of the IIR NF as a function of its parameters [_{out} can be expressed as:

SNR out = E [ S 2 ( n ) ] E [ ( y ( n ) − S ( n ) ) 2 ] (19)

where y ( n ) is the output of the ANF. Equation (20) describes SNR_{out} in terms of the filter parameters as given [

SNR out = 1 ( 1 + σ 2 ) ( ( 1 + k N 2 − 2 β k N 2 ) 1 − β 2 k N 2 ) + JSR l ( ( 1 − k N ) 2 ( 1 − β k N ) 2 ) − 1 (20)

where σ 2 is the variance of AWGN, and JSR l = A i 2 2 .

Let us assume that the first part of the Equation (20) denominator is D, called self-noise, as shown in Equation (21)

D = ( 1 + σ 2 ) ( 1 + k N 2 − 2 β k N 2 1 − β 2 k N 2 ) (21)

From Equation (20), the SNR output is affected by JSR_{l} and D in Equation (21). D shows a large value since k N 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 k N needs to be found in Equation (20). The denominator in Equation (20) can be rewritten after some modification as a function of k N [

f ( k N ) = ( 1 + k N 2 − 2 β k N 2 1 − β 2 k N 2 ) + G l ( ( 1 − k N ) 2 ( 1 − β k N ) 2 ) − 1 1 + σ 2 (22)

where G l = JSR l 1 + σ 2 .

To find the optimal k N , we differentiate f ( k N ) and solve f ′ ( k N ) = 0 for all possible roots of k N , as shown in Equation (23):

f ′ ( k N ) = β 2 G l k N 3 + [ 2 β G − β 2 G l + β 2 − β ] k N 2 + [ 1 − β + G l − 2 β G ] k N − G l = 0 (23)

Equation (23) has at least one real root in the [0 1] range that gives the optimal k N as a function of JSR_{l}. _{l} and the frequency of the interference ( ω o l ) using Equation (16) and Equation (15), respectively. Next, and based on the estimation of JSR_{l} and f ^ N ( n ) , the estimated frequency f ^ N ( n ) is used to place the notch by calculating k o l = − cos ( 2 π f ^ N ) , and then using Equation (23) to calculate the optimal value of k N to maximize SNR_{out}. Then, these parameters are used to design the IIR notch filter H N ( z ) as described by Equation (17).

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 ( E b / N o ). In this work, for the i^{th} jamming signal, the number of CWIs is considered, and thus, m = 2 with center frequencies ( f 1 = 0.03 and f 2 = 0.08 ) in Equation (2) and with equal magnitude in the input. However, frequencies could be any value in the [0 - 1] range. The simulation was run for 1e7 data bits for the MCWI. β is chosen to be 0.98 to give more satisfactory results for various situations. As β is chosen, there is a trade-off between some properties of ANF H l ( z ) and ANF H N ( z ) . A large β value gave more accurate JSR_{l} and frequency estimates, but slower convergence and tracking [

The estimated optimal value of k N vs. JSR is obtained by calculating the roots as JSR is changed, with a different parameter of β and E b / N o , as shown in _{l} increases to a large value. Also, this approach depends on the parameters of ( E b / N o ) and β. Therefore, as the parameter of E b / N o decrease, JSR_{l} increases as well, as β → 1 .

The performance of the SNR vs. JSR is shown in

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.

_{l} to avoid the reduction of the Signal of Interest (SoI).

These results will be compared with [

No. | Ref. [ | 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 |

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 ( k N = 1 ), 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 ( E b / N o ) power. Therefore, this technique can be applied in a DVB-S2 receiver or any other communication and navigation receivers.

The work reported in this paper was done under the AVIO 601-Interference Mitigation in Satellite Communication Project of the LASSENA Lab, École de Technologie Supérieure (ÉTS). This research was also supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Thales, Telesat, Vigilant Global, CRIAQ, and Atem Canada.

The authors declare no conflicts of interest regarding the publication of this paper.

El Gebali, A. and Landry, R.J. (2021) Multi-Frequency Interference Detection and Mitigation Using Multiple Adaptive IIR Notch Filter with Lattice Structure. Journal of Computer and Communications, 9, 58-77. https://doi.org/10.4236/jcc.2021.95005