Markov model based circular frequency feature extraction method for electronic communication signal anti-jamming

With the development of modern information technology, people’s lives are becoming more and more convenient and fast. Electronic communication signals provide important technical support for the exchange and transmission of information between people and people, people and nature. Usually ultra-wideband communication needs to detect and extract the signal, the receiver needs to detect and analyze and obtain the ultra-wideband communication signal on the one hand, and on the other hand, it needs to judge the modulation mode of the communication signal, and then realize the extraction of the transmitted information [1–2]. From the current electronic communication signal extraction methods, mainly including statistical features, likelihood function decision theory and digital signal processing three methods, each with its own advantages and disadvantages, but prone to noise interference, there is a large frequency deviation, timing error and other shortcomings, can not meet the requirements of the electronic communication signal extraction, so the establishment of electronic communication signal anti-interference extraction algorithms are particularly important [3–4]. Markov model is characterized by high accuracy in processing nonlinear dynamic signals and low complexity of the algorithm, so it is suitable for electronic communication signal feature extraction subject to noise interference [5]. The characteristic parameters of electronic communication signals show cyclic changes and have obvious frequency characteristics, so it is especially important to improve the extraction performance from the perspective of cyclic frequency when studying the feature extraction algorithm of electronic communication signals [6–7].

Electronic communication has become one of the most convenient ways of information dissemination and exchange, the whole communication process by detecting and extracting the signal value, after detecting and analyzing the signal, through the adjustment of the electronic communication signal mode, modulation to determine its transmission information. Literature [8] based on symmetric algorithm proposed an electronic communication network transmission signal feature extraction method, through simulation analysis verified that it can effectively extract the transmission signal of the electronic communication network, especially can accurately extract the amplitude and frequency characteristics of the transmission signal under the strong vibration environment. Literature [9] emphasizes the importance of communication signal identification for electronic security in electronic warfare, and develops a communication radiation source individual feature extraction algorithm based on the fractal complexity of the signal, and the feasibility of the algorithm is confirmed by simulation experiments, which provides important technical support for the accurate identification of the fine features of the low signal-to-noise ratio signals in the field of information confrontation. Literature [10] for the existing signal sorting algorithm sorting effect is poor, proposed a multi-parameter five-layer mutual coupling sorting algorithm and a new key feature index extraction method, through a variety of communication signals classification experiments can be seen that the proposed method can be used for the separation of serious overlap and part of the missing data signal, in the mixed electromagnetic signal feature extraction has certain superior performance. Literature [11] proposed a weak signal extraction method based on weak measurements using time-division multiplexing technique, spectral shifting and time-varying phase estimation, and after theoretical analysis and validation experiments, it was proved that the proposed method can extract the weak sensing signals of non-smooth channels with low signal-to-noise ratio. Literature [12] for the extraction of RF signals in modern communication systems, the use of Bayesian neural networks, deep neural networks, long and short-term memory networks to design a specific machine learning model, through the comparison of example studies, the results show that the probability parameters of the Bayesian neural network can significantly improve the feature extraction and signal clarity, which provides a theoretical basis for the study of the RF signal extraction method in the chaotic environment . Literature [13] emphasizes the importance of accurately extracting the features of abnormal communication signals in the network, and proposes a method of feature extraction of abnormal communication signals in the network based on nonlinear techniques, which is tested and verified to be practical, which can have a significant signal noise reduction performance, and can be accurately extracted the features of abnormal signals.

Meanwhile, literature [14] proposed an innovative UAV communication anti-jamming scheme using RF watermarking in order to solve the RF interference problem in the RF communication channel of UAVs, which can strengthen the defense of UAVs against RF interference, and then improve the safety and effectiveness of UAV combat. Literature [15] proposed an intelligent anti-jamming communication algorithm by combining a multi-parameter Markov decision process and a nearest neighbor policy optimization algorithm, and the superior performance of the algorithm was verified by simulation experiments, which can effectively adjust multiple communication parameters simultaneously and help to solve the problem of new threats brought by high-dynamic intelligent jamming. Literature [16] designed an interference source identification method based on support vector machine, and the simulation experiment proved that the method can efficiently identify broadband interference, which helps to guarantee the safety of civil aviation broadband communication. Literature [17] designed an intelligent identification and complex interference parameter estimation method based on joint time-frequency distribution features using the joint algorithm based on YOLOv5 convolutional neural network and interference key parameter estimation algorithm, and verified the scientific and practicality of the method through simulation and actual data, which can improve the performance of complex interference identification and parameter estimation in radar confrontation under low signal-to-noise ratio. Literature [18] proposes a modulation identification method for communication signals based on cyclic spectral features and bagging decision tree, and the proposed method is verified by simulation and analysis that it can improve the identification accuracy of certain modulation types, which provides reference value for the research in the fields of jamming identification, electronic countermeasures, and intelligent modems. Literature [19] proposes a modulation-based non-cooperative communication signal recognition method with low computational cost and good real-time performance, and the feasibility and applicability of the proposed method is verified by Matlab simulation analysis, which can effectively recognize and extract the features of non-cooperative communication signals. Literature [20] in order to improve the security of the electronic communication environment, the use of particle swarm optimization-support vector machine algorithm designed a electronic communication signal anti-jamming cycle frequency feature extraction method, through the experiments show that the method can be more accurate extraction of the signal features, which not only enhances the sensitivity of the anti-jamming cycle frequency features, but also improves the accuracy of the identification of anti-jamming cycle frequency features.

This paper firstly introduces the basic principle of wavelet packet thresholding noise reduction, which removes the wavelet components with a large proportion of noise components by setting the threshold, and then reconstructs the original signal using the wavelet packet reconstruction algorithm, so as to obtain the useful information of electronic communication signals. Then the spectral overlapping signal separation algorithm is proposed, which separates the overlapping signals after adaptive frequency shift filtering and then demodulates the signals. Finally, based on the principle of Hidden Markov Model, the feature extraction of anti-jamming frequency of electronic communication signals is accomplished by inputting sampling data, cyclically detecting the frequency, and calculating the characteristic quantities of BPSK signals. Experimentally verify the rationality and scientificality of the proposed method, which can effectively accomplish the task of extracting cyclic frequency features for anti-jamming electronic communication signals.

2

Wavelet packet thresholding noise reduction algorithm

2.1

Wavelet transform analysis

Wavelet transform can be expressed differently for both continuous and discrete signals. When the signal is continuous, the continuous wavelet transform is used to process it. For the continuous wavelet transform, there exists any function β(x) belonging to the square productible space L²(R), which has the form of $\hat{β} (ω)$ after the Fourier transform, when it satisfies the constant resolution condition, i.e.: 1 $C_{β} = \int_{R} \frac{{| \hat{β} (ω) |}^{2}}{| ω |} d ω < \infty$

β(x) It can be referred to as the wavelet mother function. β(x) After translational and telescopic operations will get the expression of continuous wavelet basis function as: 2 $β_{a, b} (x) = \frac{1}{\sqrt{a}} β (\frac{x - b}{a})$

Where a is the scale factor, which is responsible for the scaling transform of the wavelet basis function, and b is the translation factor, which controls the translation transform of the wavelet basis function.

A continuous wavelet transform is performed on any function F(x) ∈ L²(R), i.e: 3 $W_{F} (a, b) = 〈 F (x), β_{a, b} (x) 〉 = \frac{1}{\sqrt{a}} \int_{R} F (x) β' (\frac{x - b}{a}) d x$ where W_F (a, b) denotes the wavelet transform coefficients and its reconstruction formula, i.e., the inverse transform is: 4 $F (x) = \frac{1}{C_{β}} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \frac{1}{a^{2}} W_{F} (a, b) β (\frac{x - b}{a}) d a d b$

When the signal is discrete, the discrete wavelet transform is used to process the signal. For the discrete wavelet transform, it is necessary to discretize a and b in the wavelet basis function, which are usually taken as $a = a_{0}^{j}$ , $b = k a_{0}^{j} b_{0}$ . The expression for the discrete wavelet basis function is: 5 $β_{j, k} (x) = a_{0}^{- \frac{j}{2}} β (\frac{x - k a_{0}^{j} b_{0}}{a_{0}^{j}}) = a_{0}^{- \frac{j}{2}} β (a_{0}^{- j} x - k b_{0})$

The expression for the discretized wavelet coefficients is then: 6 $W_{j, k} = \int_{- \infty}^{\infty} F (x) β_{j, k} (x) d x = 〈 F (x), β_{j, k} (x) 〉$

Its reconstruction formula is viz: 7 $F (x) = A \sum_{- \infty}^{\infty} \sum_{- \infty}^{\infty} W_{j, k} β_{j, k} (x)$ where A denotes a constant independent of the signal.

A three-layer wavelet decomposition is performed on the signal. The wavelet decomposition does not re-decompose the high-frequency band D1 after the decomposition of the signal S, but only the low-frequency bands A1 and A2 are decomposed layer by layer. The original signal S can be represented after performing the three-layer wavelet decomposition as: 8 $S = A 3 + D 3 + D 2 + D 1$

2.2

Wavelet packet analysis and noise reduction principle

Compared with wavelet analysis, wavelet packet analysis is a more flexible and fine signal analysis method [21], which adopts multi-level division of the signal’s frequency band, further decomposes the high-frequency components that are not involved in the wavelet analysis, and can adaptively select the corresponding frequency bands according to the different characteristics of the signal analyzed, so as to match the signal’s frequency spectrum, and has a higher frequency resolution compared with wavelet analysis. The three-layer wavelet packet decomposition of the signal is performed, and its tree structure is shown in Fig. 1.

The original signal S is subjected to a three-layer wavelet packet decomposition can be expressed as: 9 $\begin{array}{l} S & = A A A 3 + D A A 3 + A D A 3 + D D A 3 \\ + A A D 3 + D A D 3 + A D D 3 + D D D 3 \end{array}$

For wavelet packet analysis, define the orthogonal scale function ϕ(x) and its corresponding wavelet function ψ(x) and set g(k) to represent the high-pass filter coefficients and h(k) to represent the low-pass filter coefficients, while g(k) = (–1)^k h(k–1) needs to be satisfied, i.e: 10 ${\begin{array}{l} ϕ (x) = \sqrt{2} \sum_{k \in Z} h (k) ϕ (2 x - k) \\ ψ (x) = \sqrt{2} \sum_{k \in Z} g (k) ϕ (2 x - k) \end{array}$

Let μ₀ = ϕ(x), μ₁ = ψ(x), then the two-scale equation for the wavelet packet is: 11 ${\begin{array}{l} μ_{2 n} (x) = \sqrt{2} \sum_{k \in ℤ} h (k) μ_{n} (2 x - k) \\ μ_{2 n + 1} (x) = \sqrt{2} \sum_{k \in ℤ} g (k) μ_{n} (2 x - k) \end{array}$

Let the closure space of function μ_n (x) be the subspace $U_{j}^{n}$ and the closure space of function μ_2n (x) be the subspaces $U_{j}^{2 n}$ , $g_{j}^{n} \in U_{j}^{n}$ , then $g_{j}^{n}$ can be expressed as: 12 $g_{j}^{n} = \sum_{l} C_{l}^{j, n} μ_{n} (2^{j} x - 1)$

The wavelet packet decomposition coefficients can be obtained as: 13 ${\begin{array}{l} C_{l}^{j, 2 n} = \sum_{k} h (k - 2 l) C_{k}^{j + 1, n} \\ C_{l}^{j, 2 n + 1} = \sum_{k} g (k - 2 l) C_{k}^{j + 1, n} \end{array}$

The received NLFM-16QAM integrated signal is decomposed into 3-layer wavelet packets, which can reflect the information of the original signal more comprehensively by extracting the coefficient features of each wavelet packet.

Finally, the wavelet packet reconstruction formula is derived as: 14 $C_{t}^{j + 1, n} = \sum_{k} [h (l - 2 k) C_{l}^{j, 2 n} + g (l - 2 k) C_{l}^{j, 2 n + 1}]$

The basic principle of wavelet packet thresholding is based on the original signal and noise in various scales of the wavelet packet coefficients show different characteristics, that is, the mode of the wavelet packet coefficients of the noise is much smaller than the mode of the wavelet packet coefficients of the effective signal, will be in the various scales of the wavelet component, especially the noise component accounts for a large proportion of the scale of the wavelet component, through the setting of thresholding to remove it, and the remaining wavelet packet coefficients are basically the original signal wavelet packet coefficients. The wavelet packet coefficients that remain are basically the wavelet packet coefficients of the original signal. Finally, the wavelet packet reconstruction algorithm is applied to reconstruct the original signal to obtain the desired useful information.

2.3

Basic wavelet packet thresholding noise reduction process

1)

Wavelet packet decomposition of the signal: determine the number of decomposition layers, and then carry out wavelet packet decomposition of the noise-bearing radar communication integration received signal with the corresponding number of layers;

2)

Determine the optimal wavelet packet basis: for the known entropy criterion, solve the optimal wavelet packet tree according to the binary tree search method, so as to solve the optimal wavelet packet basis;

3)

Threshold quantization: this paper chooses Stein’s unbiased likelihood estimation threshold, and threshold quantization deals with the coefficients of each wavelet packet decomposition;

4)

Wavelet packet reconstruction of the signal: according to the quantization coefficients and the wavelet packet decomposition coefficients of the last layer of the wavelet packet reconstruction of the processed signal, to obtain the integrated signal of radar communication after noise reduction.

The expression of the NLFM-16QAM signal after the wavelet packet noise reduction module is: 15 $y_{l} (t) \approx A_{m} (t - τ) \exp [j (2 π f_{c} (t - τ) + φ (t - τ) + θ_{m} (t - τ))]$

3

Self-extraction of anti-jamming cyclic frequency features for electronic communication signals

3.1

Spectrum Overlap Signal Separation Algorithm

The algorithm for spectrally overlapping signal separation is discussed below, using DSSS as an example. There are both useful and interfering signals with BPSK modulation [22], and both signals have cyclic smoothness, i.e., both have spectral correlation. The input signal r(n) at the receiver side is in discrete form, which will be demodulated after separating the overlapping signals by adaptive frequency shift filtering. The system model is shown in Fig. 2, where the last 2 boxes of Fig. 2 represent the cumulative and sampling judgments, respectively, which result in the best estimated signal.

Let the discrete form of the input signal at the receiver be: 16 $r (n) = s (n) + i (n) + w (n)$ where s(n) and i(n) are the useful and interfering signals, respectively; and w(n) is Gaussian white noise [23], assumed to be independent of each other.

For the case where the input is a complex signal r(t), the output of the frequency shift filter is given as: 17 $s (t) = \sum_{p} h^{α_{p}} (t) \otimes [r (t) e^{i 2 π a_{p}^{t}}] + \sum_{q} h^{β_{p}} (t) \otimes [r^{*} (t) e^{k π β_{q}^{t}}]$ where α_p and β_q are the frequency shifts of inputs r(t) and r*(t), respectively.

According to Eq. (17), the frequency shift filter can be viewed as two side-by-side systems excited by r(t) and r*(t), which are frequency shifted by α_p or β_q, respectively, and then sent to a finite impulse response (FR) filter with impulse responses of h_αp(t) and h_βη(t), respectively, and finally summed to obtain the output result. This leads to the basic structure of the frequency shift filter, where the input signal is in complex form and the frequency shift filter structure includes a frequency shift part and a conjugate frequency shift part.

Taking the discrete form for equation (17), the output of the frequency shift filter is: 18 $\begin{array}{l} s (n) & = \sum_{p = 1}^{p} \sum_{m = 0}^{L_{p} - 1} h^{α_{p}} (m) r (n - m) e^{j π α_{p} (n - m)} \\ + \sum_{q - 1}^{0} \sum_{m = 0}^{M - 1} β^{β η} (m) r^{*} (n - m) e^{i k x_{n} (n - m)} \end{array}$ where L_p and M_q are the lengths of FIR filters h^a_p (k) and h^βη(k), respectively. Eq. (18) can be expressed in matrix form as: 19 $\hat{s} (n) = h^{H} (n) r (n)$

Among them: 20 $r (n) = {r^{α_{1}} (n), \dots, r^{α_{p}} (n), r^{β_{1}} (n), \dots, r^{β Q} (n)}^{r}$ 21 $h (n) = {h^{α_{1}} (n), \dots, h^{α_{p}} (n), h^{β_{1}} (n), \dots, h^{β Q} (n)}^{r}$

They are both K -dimensional vectors and have: 22 $K = \sum_{p - 1}^{p} L_{p} + \sum_{q - 1}^{0} M_{q}$ where the frequency shift portion of the filter is: 23 $r^{α p} (n) = {\begin{matrix} r (n) e^{j_{2} π σ_{p}^{n}} \\ r (n - 1) e^{j_{2} π σ_{p} (n - 1)} \\ ⋮ \\ r (n - L_{p} + 1) e^{j_{2} π σ_{p} (n - L_{p} + 1)} \end{matrix}}$ 24 $h^{α p} (n) = {\begin{matrix} h^{α p} (0) \\ ⋮ \\ h^{α p} (L_{p} - 1) \end{matrix}}$

The conjugate frequency shift portion of the filter is: 25 $r^{β q} (n) = {\begin{matrix} r (n) e^{i 2 π β_{q}^{n}} \\ r (n - 1) e^{j 2 π β q (n - 1)} \\ ⋮ \\ r (n - M_{q} + 1) e^{j 2 π β q (n - M_{q} + 1)} \end{matrix}}$ 26 $h^{β q} (n) = {\begin{matrix} h^{β q} (0) \\ ⋮ \\ h^{β q} (M_{q} - 1) \end{matrix}}$ h vector can be solved according to the classical Wiener filtering method, which is obtained by optimizing under the time-averaged minimum mean square error: 27 $h_{q p 1} = R_{r t}^{- 1} R_{t s}$

Where R_r is the autocorrelation matrix of the received signal; R_rs is the inter-correlation matrix of the received signal and the filtered signal; h_op1 is the multidimensional optimal weights of the frequency shift filter.

In order to minimize the mean square error, the LMS adaptive algorithm can be used to realize the determination of the above K -dimensional weights parameters: 28 $e (n) = d (n) - h^{H} (n - 1) r (n)$ 29 $h (n) = h (n - 1) + μ (n) r (n) e^{*} (n)$ where $e (n) = s (n) - \hat{s} (n)$ is the error; d(n) is the training sequence; and μ(n) is the convergence step.

3.2

HMM Fundamentals

The HMM consists of two sequences of random variables [24]: an unobservable Markov chain {q_t ≥ 0} called the Hidden Markov Chain, and an observable random sequence {o_t ≥ 0} called the Observation Chain.

The HMM consists of the following main elements:

Hidden state space S = {s₁, s₂, ⋯, s_N} where, q_t ∈ {s₁, s₂, ⋯, s_N} q_t denote the state at the moment of t, and N denotes the number of hidden states.

Observation sequence state space V = {v₁, v₂, ⋯, v_M}, where M denotes the number of different symbols for each state.

State transfer probability distribution A = (a_ij), where: 30 $a_{i j} = p (q_{t + 1} = s_{j} | q_{t} = s_{i}), 1 \leq i, j \leq N$

Probability distribution B = [b_i (k)] of the observation sequence in state i, where: 31 $b_{i} (k) = p (o_{t} = v_{k} | q_{t} = s_{i}), 1 \leq k \leq M, 1 \leq i \leq N$ o_t denotes the observation whose state is s_i at moment t;

The initial state distribution π = [π_i], where: 32 $π_{i} = p (q_{i} = s_{i}), 1 \leq i \leq N$

An HMM can be completely determined using A, B, and π. It is common to shorthand an HMM as a triple λ= (A, B, π).

Applying an HMM to practice requires solving the following 3 basic problems:

Problem 1, knowing observation sequence O = o₁, o₂, ⋯, o_T and model λ = (A, B, π), given model λ, how to efficiently compute the conditional probability of generating observation sequence O, i.e., compute P(O|λ).

Problem 2, knowing the observation sequence O = o₁, o₂, ⋯, o_T and the model λ = (A, B, π), how to choose the state sequence that is optimal in some sense (i.e., that best explains the observation sequence).

Problem 3, how to adjust model parameter λ=(A, B, π) to maximize conditional probability P(O|λ).

The first problem is the probability finding problem during model parameter training, and the common method currently used is the forward-one-backward algorithm; the second problem is the feature extraction problem, and the common method currently used is the Viterbi algorithm; the third problem is the model parameter training problem, and the common method currently used is the Baum-Welch algorithm.

3.3

Signal Feature Recognition and Extraction

Based on the complexity of the electromagnetic environment, signal modulation needs to be accurately identified during signal processing, and the dimensional signals are processed using time-frequency transform analysis, which is transformed into color time-frequency images, and the image features are extracted using the convolutional neural network structure. Based on the characteristics of the cyclic frequency in the communication channel, it can complete the extraction of two-phase phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), offset four-phase phase-shift keying (OQPSK), and the minimum frequency-shift keying (MSK) signals, to ensure that the signal extraction accuracy. Since the channel mixed signal y(t) has a certain degree of variability in different signal frequency bands, the received signal frequency sets Ay2.0, Ay2.1, and Ay4.0 are designed, and the cyclic frequency information of different signals are on this set.

Theoretically speaking, the channel mixing signal in different signal frequency bands and the modulating signal is difficult to one-to-one correspondence, but due to the unique frequency structure of the modulating signal, such as the BPSK signal can be described as positive and negative symmetric cyclic frequency, the representation of the method is Cx2.1, its second-order cyclic frequency is ±1/T, including three equally spaced frequencies, a feature that is unique to the BPSK signal. If the combination of cyclic frequencies matches the above constraints, then the judgment of the received signal can be realized, and it is clear whether there is a BPSK signal or not. The second-order cyclic frequency is used to detect the BPSK signal of a mixed signal, and each cyclic frequency has its own advantages. After the exclusion of BPSK, the remaining cycle frequencies are all derived from QPSK signals, MSK and OQPSK are the same in terms of second-order cycle frequencies, but there are some differences in terms of fourth-order cycle frequencies, so it is necessary to identify the received signals MSK and OQPSK signals in order.

Under the effect of feature quantity A₁, it is possible to realize the classification of 2ASK, 4ASK, and 8ASK signals, and then use A₂ classification to identify 4ASK signals and 8ASK signals. For 2PSK, 4PSK, and 8PSK signals, their fourth-order cumulative quantity features can be defined as follows: 33 $P = [p_{1}, p_{2}]$

Among them: 34 ${\begin{array}{l} p_{1} = | C_{50} | / | C_{50} | \\ p_{2} = | C_{41} | / | C_{42} | \end{array}$

In classifying the MPSK signals, the following decision criterion is used, mainly utilizing the feature vector P with the Euclidean distance classification method: 35 $\hat{M} = \arg \min_{M = 2, 4.8} ({‖ P_{r} - P ‖}^{2})$

When seeking the first-order derivative, the noise-containing MFSK will be transformed into a signal containing amplitude information through modulation, and after the calculation of the signal accumulation method after derivation, the first-order derivative can be sought for its model as: 36 ${S^{'}}_{k} = \sqrt{E} \sum_{n} [e^{j (M_{n} k + θ)} δ (k) + w_{n} g (k - n T_{s}) e^{j (M_{n} k + θ + π / 2)}] + n^{'} (k)$

To eliminate the effect of δ(k), the signal can be obtained by finding the second-order derivative of the median filter, calculated as: 37 ${S^{″}}_{k} = \sqrt{E} \sum_{n} w_{n} e^{j (m n k + θ + π / 2)} + n^{″} (k)$

After the change, the MFSK signal accumulation shows obvious variability, so the baseband signal is first differentiated and the 4th order accumulation is calculated, which can help to differentiate between 2FSK, 4FSK, and 8FSK, and its eigenvolume is defined as: 38 $F = | {C^{'}}_{42} | / {| {C^{'}}_{21} |}^{2}$

Communication signal anti-jamming cyclic frequency feature extraction can be summarized as follows: first of all, the input sampling data, and then, the cycle detection frequency, the calculation of the BPSK signal feature quantity, when the calculation result is 1, it means that the signal cyclic frequency is removed after extraction, and the corresponding BPSK signal feature quantity has been extracted. According to the same method to calculate the QPSK signal feature quantity, if it is 1, it means that such signal frequency is removed, and complete the electronic communication signal anti-jamming frequency feature extraction.

4

Experimental results

4.1

Experimental results of noise reduction algorithm

Most of the previous signal analysis is done in the time domain, the innovation of this paper is to put the signal through the wavelet transform noise reduction, the signal is decomposed with wavelet packet in the high frequency and low frequency parts at the same time to extract the feature details. The signals used in this paper were captured during the actual recording. The original signal acquired is shown in Fig. 3, and the result after extracting the feature details with wavelet packet decomposition in the high-frequency and low-frequency parts at the same time is shown in Fig. 4, and it can be seen from the figure that the signal after noise reduction with wavelet transform has a clear envelope and contains detailed information, which achieves the expected effect of noise reduction.

4.2

Filter Application and Simulation

Matched filters can be used for signal detection, i.e., given a signal, we can construct a matched filter when a mixed signal into the filter according to the output can be determined in the mixed signal whether there is a matched filter corresponds to that signal. The criterion for determination is to see if there is a maximum value of the signal waveform at the output of the filter, if there is a maximum value, it means that there is a corresponding signal in the mixed signal, i.e., the mixed signal is matched with the filter. If not, it means that there is no corresponding signal, i.e., the mixed signal and the filter are not matched. The BPSK signal is selected for the experiment, the sampling frequency is 100MHz, the carrier frequency is 25MHz, the code rate is 6.25MHz, the cycle frequency is selected as the code rate, the noise is Gaussian white noise, and the signal-to-noise ratio is selected as -15dB. Figure 5 shows a pure BPSK signal.

Add the signal-to-noise ratio of -15dB Gaussian white noise, the band noise signal as shown in Figure 6, this band noise signal as input, the output of the loop matched filter as shown in Figure 7, you can see that the signal at the value of 0 there is a maximum value, indicating that in the case of the signal- to-noise ratio of -15dB, the loop matched filter can be detected the signal.

Circulating filter output(-15dB)Continuing to reduce the signal-to-noise ratio, Figure 8 shows the output of the loop matched filter when the signal-to-noise ratio is -50dB, and it can be seen that the output waveform does not take the maximum value at the moment of 0 value, which indicates that the detection fails in this case.

We compared the performance of the cyclic correlation matched filter with that of the matched filter for monitoring the desired signal at different signal-to-noise ratios. We conducted 300 independent experiments for different SNRs, and then calculated the monitoring success rate of each filter in determining the presence or absence of the signal as shown in Table 1. From the experimental results, it can be learned that the signal detection performance of the cyclic correlation matched filter is significantly better than that of the traditional matched filter, especially at low signal-to-noise ratios, the monitoring success rate is much higher than that of the traditional matched filter, when the signal- to-noise ratio is -15dB, the success rate of the cyclic correlation matched filter is 88%, and the success rate of the traditional matched filter is 73% lower than that of the cyclic correlation matched filter. The fact that the cyclic correlation matched filter can still detect the desired signal mixed in the signal even when the signal-to-noise ratio of the received signal is small shows the effectiveness of the signal separation algorithm proposed in this paper.

Table 1.

Comparison of two filters

Signal-to-noise ratio(dB)	Cyclic matching filtering/%	Matched filter/%
-20	33	3.8
-15	88	15
-10	98	45
-5	100	82
0	100	92
5	100	100
10	100	100
15	100	100
20	100	100

4.3

Validation of the self-extraction method

In order to verify the effectiveness of the cyclic frequency feature self-extraction method of electronic communication signals in this paper, SVM method and BP method are used to carry out relevant comparison experiments with the algorithm of this paper. The experimental results of the feature extraction integrity of the methods are shown in Fig. 9. The average integrity of the feature extraction results of the SVM method and the BP method is low, and the average values of the feature extraction results of the SVM method and the BP method are 77% and 73%, respectively, and the average value of the integrity of the feature extraction results of the method of this paper reaches 95% compared to the low feasibility of the self-extraction method of the cyclic frequency features of the electronic communication signals in this paper. The method proposed in this paper enables the separation of signal components and effectively improves the integrity of the signal extraction results.

The experimental results of the feature extraction accuracy of the method are shown in Figure 10, from which it can be seen that the accuracy of the self-extraction method of the cyclic frequency features of the electronic communication signals can basically be maintained above 91%, while the accuracy of the feature extraction results of the SVM method and BP method fluctuates continuously with the increase in the number of experiments and is low, floating around 78% up and down. The main reason for this result is that: based on the overlapping signal separation, the cyclic frequency features in the communication channel are introduced to extract the signals such as BPSK, QPSK, OQPSK and MSK, which effectively enhance the accuracy of the signal feature extraction results. According to the above experiments, the superior performance of the proposed method has been proven.

5

Conclusion

The main objective of this project is to develop a Markov model-based method for recognizing features in digital communications, and the following three main aspects have been completed.

The signal detail network of the extracted features with wavelet packet decomposition is clear and achieves excellent noise reduction effects. At a signal to noise ratio of -15dB, there is a maximum value of the signal at the value of 0 and the electronic communication signal is detected. When the signal-to-noise ratio is -50dB, the output waveform does not have a maximum value at 0 value, indicating that the loop-matched filter fails to detect in this case.

When the signal-to-noise ratio is lower than -15dB, the signal monitoring success rate of the cyclic correlation matched filter is 73% higher than that of the traditional matched filter, which indicates that the signal detection performance of the cyclic correlation matched filter is significantly better than that of the traditional matched filter, and it can effectively separate the spectrally overlapping signals.

The average value of the completeness of the feature extraction results of the SVM method and the BP method is 77% and 73%, respectively, and the average value of the completeness of the feature extraction results of this paper’s method reaches 95%, and the accuracy of the self-extraction method stays above 91%, whereas the accuracy of the feature extraction results of the SVM method and the BP method fluctuates up and down around 78%, which indicates that the method proposed in this paper effectively improves the completeness of the signal extraction results and the accuracy.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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Markov model based circular frequency feature extraction method for electronic communication signal anti-jamming

Lei Yang

Published Online: Mar 19, 2025

Received: Oct 23, 2024

Accepted: Feb 14, 2025

DOI: https://doi.org/10.2478/amns-2025-0445

KeywordsWavelet packet thresholding noise reduction, Spectral overlap signal separation, Hidden Markov Model, Feature extraction algorithm

© 2025 Lei Yang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Wavelet packet thresholding noise reduction, Spectral overlap signal separation, Hidden Markov Model, Feature extraction algorithm

Signal-to-noise ratio(dB)	Cyclic matching filtering/%	Matched filter/%
-20	33	3.8
-15	88	15
-10	98	45
-5	100	82
0	100	92
5	100	100
10	100	100
15	100	100
20	100	100