Anomalous signal recognition algorithm for electronic communication equipment based on improved gradient projection method

The anti-jamming communication channel model is shown in Fig. 1, and the channel coefficients of the three links from the jamming source to the transmitter (JT), the transmitter to the receiver (TR), and the jamming source to the receiver (JR) are h₁,h₂ as well as h₃. The channel is assumed to be a flat-block fading channel model, i.e., all the channel coefficients are kept constant at one channel coherence time, while they are varied at different coherence times. In real communication counter scenarios, the CSIs of the jamming channels JT and JR links as well as the type of jamming model are difficult to obtain, and therefore, it is assumed that this information is unknown at both the transmitter and the receiver. In this thesis, without loss of generality, the transmitter operates in the FD mode, i.e., signal transmission and signal reception occur simultaneously in the same frequency band.

Figure 1.

Anti-interference communication channel model

The specific process of signal transmission is as follows:

1) Signal transmission: after the interference source discovers the transmitter and receiver of our communication node, it starts to broadcast an interference signal to attack the communication channel between the transmitter and receiver. Therefore the expression of the received signal Y_T(t) at the transmitter is: (1) YT(t)=hlXJ(t)\[{{Y}_{T}}(t)={{h}_{l}}{{X}_{J}}(t)\] where X_J(t) denotes the unknown interference signal. For computational purposes, both the PGA noise at the transmitter and the self-interference introduced by the FD mode are combined into the noise at the receiver.

In this case, the communication between the transmitter and the receiver employs an interference modulation technique, which maps the information to be transmitted to different PGA amplification coefficients, amplifies the interference signal to different degrees, and forwards it to the receiver. Therefore, the expression for the transmitter’s emitted signal X_T(t) is given by: (2) XT(t)=A(t)YT(t)=A(t)h1XJ(t)\[{{X}_{T}}(t)=A(t){{Y}_{T}}(t)=A(t){{h}_{1}}{{X}_{J}}(t)\] where A(t) ∈ {a_k : k = 1,2,…,K} denotes the PGA amplification factor mapped by the information to be transmitted by the transmitter and satisfying distribution p(A(t) = a_k) = p_k∑k=1Kpk=1$\sum\limits_{k=1}^{K}{{{p}_{k}}}=1$.

Based on Eq. (4), the expression for SINR can be further written as: (5) SINR=E[ |h1h2XJ[n−nτ]ak|2 ]E[ |h3XJ[n]+ZR[n]|2 ]&=|h1|2|h2|2|ak|2PJ|h3|2PJ+σR2\[SINR=\frac{\text{E}\left[ |{{h}_{1}}{{h}_{2}}{{X}_{J}}[n-{{n}_{\tau }}]{{a}_{k}}{{|}^{2}} \right]}{\text{E}\left[ |{{h}_{3}}{{X}_{J}}[n]+{{Z}_{R}}[n]{{|}^{2}} \right]}\And =\frac{|{{h}_{1}}{{|}^{2}}|{{h}_{2}}{{|}^{2}}|{{a}_{k}}{{|}^{2}}{{P}_{J}}}{|{{h}_{3}}{{|}^{2}}{{P}_{J}}+\sigma _{R}^{2}}\] where P_J is the average power of the interfering signal.

From Eq. (5), it can be seen that the adaptive transmission scheme can be considered for the strength of the interfering signal, and the selection of the amplification factor A(t) is determined by the strength of the interfering signal X_J(t), while the energy level of the received signal is mainly determined by the amplification factor A(t).

In summary, the signal demodulation can be summarized in the following three steps:

Step1: Calculate the average power of the pilot signal in the received signal.

It is worth noting that the energy detection criterion, as a non-coherent demodulation method, uses only the average power of the received signal, i.e., Q=1N∑n=1N| yR[ n ] |2\[Q=\frac{1}{N}\sum\limits_{n=1}^{N}{{{\left| {{y}_{R}}\left[ n \right] \right|}^{2}}}\], to decode the useful information.

The signal data of the electronic communication equipment is stored in the server disk in text format, and it is necessary to screen and count these data, delete the null value in the signal data, remove the erroneous signal data and irrelevant signal data due to human operation, organize and classify the signal data and standardize the storage and management, and adjust the format of the signal data and then re-save it. According to different signal data types for classification and storage, the same type of signal data in the same folder for differentiation, using data compression methods to standardize the signal data constraints. The normalization of signal data is intended to ensure that the recognition results can accurately and truthfully reflect the recognition of signals by electronic communication equipment. The formula for normalizing the data is: (16) x=x−xminxmax−xmin\[x=\frac{x-{{x}_{\text{min}}}}{{{x}_{\text{max}}}-{{x}_{\min }}}\]

Where x is the data that can be used as a sample after normalization, x_max is the maximum value in the data without normalization, and x_min is the minimum value in the data without normalization.

In the process of signal identification of electronic communication equipment, some frequency points are not working at some moments, when the signal data of that frequency point is abnormal signal data. If this data is removed, it will cause loss of signal when that frequency point is working. Abnormal signals are generated by misidentification during the recognition process. Although the abnormal signals themselves do not have any significance, the study of how the abnormal signals are recognized by the electronic communication equipment can make the safety of the electronic communication equipment secure. Standardized processing of data can improve the true validity of data, and the standardized processing formula is: (17) x′=x′−ns\[{{x}^{\prime }}=\frac{{{x}^{\prime }}-n}{s}\] where x'${{x}^{'}}$ is the data that can be used as a sample after standardization is performed. n is the mean of the data without normalization and is the standard deviation of the data without normalization. Finally do not select signal data that are unique and repetitive, select signal data that can be correlated with each other and can be coded with the attributes of the data source to correct the data for omission filling and uniformity, selected so that the data can be given attribute names and values of attributes to facilitate the later research can be carried out smoothly.

The features of the signals of electronic communication devices are extracted using deep learning methods. By using the coding network of the autoencoder and the coding network in the decoding network, the processed data is further compressed and processed to reduce the amount of signal data processed at the coding end as the input data, and since the input data of the implicit layer may be reduced, the signal data set is passed through the signal dataset, the root node data is selected, and then traversed to select the leaf nodes and construct a feature tree, which facilitates the training of the DNN cascade. Reduce unnecessary waste of resources. Using the deep learning autoencoder for DNN cascade training, the DNN can obtain the required feature information of abnormal signals from the sample signal data provided by electronic communication devices [28].

Using the BP algorithm of deep learning, the abnormal signal data of electronic communication equipment obtained by DNN is then adjusted so that the feature information of the abnormal signal of electronic communication equipment obtained by DNN is more complete and accurate. The deep learning adjustment process is shown in Fig. 2.

Figure 2.

Deep learning adjustment process

To analyze the feature data of the abnormal signal of electronic communication equipment obtained through DNN, let the scale of the signal be x and the time delay be y. The feature parameters of the abnormal signal data of the electronic communication equipment are calculated by the formula: (18) Z′(y)=(x′−x)×y′Z(y)\[{{Z}^{\prime }}(y)=\frac{({{x}^{\prime }}-x)\times {{y}^{\prime }}}{Z(y)}\] where Z(y) is the characteristic parameter of the anomalous signal data to be obtained.

Separating the spectral offset characteristics of the anomalous signals of electronic communication equipment, the parameters associated with frequency and time can be obtained, which are expressed in the form: (19) { m1(y)=−2Zcosϕ(y)m2(y)=Z2(y)\[\left\{ \begin{array}{*{35}{l}} {{m}_{1}}(y)=-2{{Z}^{\cos \phi }}(y) \\ {{m}_{2}}(y)={{Z}^{2}}(y) \\ \end{array} \right.\]

Where ϕ is the dynamic phase angle of the anomaly signal output, and m₁(y) and m₂(y) indicate that the two parameters are correlated with each other.

Measuring the linear spectrum of the anomalous signal of the electronic communication equipment, the measurement calculation formula is: (20) n(i)=a(i)δ(i)+ηmin−β\[n(i)=\frac{a(i)}{\delta (i)+{{\eta }_{min}}}-\beta \]

Where, β is the parameter factor, δ(i) is the loss function, η_min is the minimum value in the convergence error, a(i) is the dynamic phase of the output, and n(i) is the anomalous signal spectrum.

Analyze the signal characteristics of the electronic communication device through the measurement results. Decompose the left and right wave eigenvalues of the anomalous signals of the electronic communication equipment, use the characteristic aggregation of the signals, get the characteristic spectrum of the anomalous signals, and extract the characteristics of the anomalous signals of the electronic communication equipment. Calculate the extraction using equation (21): (21) Wz=hmax[n(i)cos(2ϕ−θ)]\[{{W}_{z}}={{h}_{max}}[n(i)\cos (2\phi -\theta )]\]

Where w_x is the abnormal signal characteristic of the electronic communication equipment, h_max is the effective characteristic quantity of the abnormal signal, and θ is the phase angle of the abnormal signal characteristic value of the electronic communication equipment. Through the above series of operations, the extraction of the abnormal signal characteristics of the electronic communication equipment is completed.

The problem of identifying anomalous signals of electronic communication devices can be transformed into a sparse signal reconstruction problem. For sparse signal x, if it has S nonzero elements, its sparsity level is S. Thus the set of supports of sparse signal x can be defined as: (22) Γ={k:k∈{1,2,⋯,K},xk≠0}\[\Gamma =\{k:k\in \{1,2,\cdots ,K\},{{x}_{k}}\ne 0\}\]

Using the idea of convex optimization algorithm [29], the signal model is transformed into an unconstrained convex optimization problem, viz: (23) minx12||y−Hx||22+τ||x||1\[{{\min }_{x}}\frac{1}{2}||y-Hx||_{2}^{2}+\tau ||x|{{|}_{1}}\]

In Eq. (23), ||x||1=∑i=12K|xi|$||x|{{|}_{1}}=\sum\limits_{i=1}^{2K}{|{{x}_{i}}|}$ denotes the l₁-parameter of x. τ is a non-negative parameter to balance sparsity and residuals.

In order to solve for x in Eq. (23) based on the l₁-paradigm, x is divided into 2 parts, positive and negative, viz: (24) x=u−v\[x=u-v\]

In Eq. (24), the elements in vectors u and v satisfy u_t = (x_t)₊,v_t = (–x_t)₊,t = 1,2,⋯,2K, where (·)₊ denotes the taking of the positive part, defined as (x)₊ = max{0,x}. Thus, ||x||1=12KTu+12KTv$||x|{{|}_{1}}=1_{2K}^{T}u+1_{2K}^{T}v$, where 1_2K = [1,1,⋯,1]^T. This transforms the unconstrained convex optimization problem of Eq. (23) into a bounded quadratic programming (BCQP) problem, denoted as: (25) minu,v12||y−H(u−v)||22+τ12KTu+τ12KTvs.t.u≥0,v≥0\[\begin{align} & \underset{u,v}{\mathop{\min }}\,\frac{1}{2}||y-H(u-v)||_{2}^{2}+\tau 1_{2K}^{T}u+\tau 1_{2K}^{T}v \\ & \begin{matrix} s.t. & u\ge 0,v\ge 0 \\ \end{matrix} \\ \end{align}\]

Further Eq. (25) is rewritten as a rigorous BCQP problem, i.e: (26) minqF(q)=12qTWq+cTqs.t.q≥0\[\begin{align} & {{\min }_{q}}F(q)=\frac{1}{2}{{q}^{T}}Wq+{{c}^{T}}q \\ & \begin{matrix} s.t. & q\ge 0 \\ \end{matrix} \\ \end{align}\]

In the formula: (27) q=[ uTνT ]T;W=[ HTH−HTH−HTHHTH ];c=τ14K+[ −y¯Ty¯T ]T\[q={{\left[ \begin{matrix} {{u}^{T}} & {{\nu }^{T}} \\ \end{matrix} \right]}^{T}};W=\left[ \begin{matrix} {{H}^{T}}H & -{{H}^{T}}H \\ -{{H}^{T}}H & {{H}^{T}}H \\ \end{matrix} \right];c=\tau {{1}_{4K}}+{{\left[ \begin{matrix} -{{{\bar{y}}}^{T}} & {{{\bar{y}}}^{T}} \\ \end{matrix} \right]}^{T}}\] where y¯=HTy$\bar{y}={{H}^{T}}y$, W are semipositive definite matrices.

However, it is very difficult to solve Eq. (27) directly, and in this paper, we propose an algorithm based on the Improved Gradient Projection (IGP) method to solve Eq. (27) iteratively [30]. In the algorithmic process, the superscript (i) of each variable indicates the ith iteration process.

First calculate the gradient of function F(q⁽ⁱ⁾) at q⁽ⁱ⁾ in Eq. (27), i.e., ∇F(q⁽ⁱ⁾) = Wq⁽ⁱ⁾+c. Choose the step factor α⁽ⁱ⁾ > 0 and calculate the gradient factor δ⁽ⁱ⁾ as: (28) δ(i)=(q(i)−α(i)∇F(q(i)))+−q(i)\[{{\delta }^{(i)}}={{({{q}^{(i)}}-{{\alpha }^{(i)}}\nabla F({{q}^{(i)}}))}_{+}}-{{q}^{(i)}}\]

Next, scale factor λ⁽ⁱ⁾ ∈ [0,1] is chosen and q⁽ⁱ⁺¹⁾ is computed by iteration as: (29) q(i+1)=q(i)+λ(i)δ(i)\[{{q}^{(i+1)}}={{q}^{(i)}}+{{\lambda }^{(i)}}{{\delta }^{(i)}}\]

The objective of minimizing F(q⁽ⁱ⁺¹⁾) is achieved through Eq. (29).

In order to accurately detect the active users and their data information, the estimation of the target signal, i.e., q(i+1)→x^c(i+1)${{q}^{(i+1)}}\to \hat{x}_{c}^{(i+1)}$, is derived first after each selection of generations.Unlike the traditional gradient projection (GP) method, in this paper, we are going to preprocess x^c(i+1)$\hat{x}_{c}^{(i+1)}$ first, i.e., obtain the estimation vector of the target signal by maximizing the l₂-parameter of x^c(i+1)$\hat{x}_{c}^{(i+1)}$. Here, x˜(i+1)${{\tilde{x}}^{(i+1)}}$ is used to denote the estimation vector of the target signal obtained after preprocessing x^c(i+1)$\hat{x}_{c}^{(i+1)}$, denoted as: (30) x˜(i+1)=max||x^c(i+1)||2\[{{\tilde{x}}^{(i+1)}}=\max ||\hat{x}_{c}^{(i+1)}|{{|}_{2}}\]

The process of maximizing x^c(i+1)$\hat{x}_{c}^{(i+1)}$ based on the l₂-paradigm can be described as follows: first sort the elements in x^c(i+1)$\hat{x}_{c}^{(i+1)}$, keep the first S larger elements in x^c(i+1)$\hat{x}_{c}^{(i+1)}$, and set the other elements in x^c(i+1)$\hat{x}_{c}^{(i+1)}$ to 0, and then update the set of detected signal supports Γ⁽ⁱ⁺¹⁾ accordingly as: (31) Γ(i+1)=supp(x˜(i+1))\[{{\Gamma }^{(i+1)}}=\sup p\text{(}{{\tilde{x}}^{(i+1)}}\text{)}\]

In Eq. (31), supp(x˜(i+1))\[\sup p\text{(}{{\tilde{x}}^{(i+1)}}\text{)}\] denotes the position index of the nonzero element in x^(i+1)${{\hat{x}}^{(i+1)}}$. The preprocessed detection symbol x˜c(i+1)$\tilde{x}_{c}^{(i+1)}$ is transformed into a real number q⁽ⁱ⁺¹⁾, i.e., x˜c(i+1)→q(i+1)$\tilde{x}_{c}^{(i+1)}\to {{q}^{(i+1)}}$, to prepare for the next iteration.

According to the above analysis, the flow of the IGP-based abnormal signal recognition algorithm for electronic communication devices is shown in Fig. 3, and the corresponding operation steps are summarized as follows:

Step1: Input system parameters y_c,H_c,S,Iter,α_min,α_max. lter denotes the total number of iterations of the algorithm, α_min and α_max denote the minimum and maximum values of the scale factor required in the algorithm, respectively.

Figure 3.

Flow chart of IGP abnormal signal recognition algorithm

Before the start of the experiment, it is first necessary to prepare a compatible device, as well as electronic communication equipment, to connect and complete the conduction of various types of signals. This paper selects the electronic communication equipment for 2445IEC48RVV model communication equipment, its rated voltage is 220V, the implementation of the standard GB/T448.26-2020, the transmission rate of the signal is 1320bps, the sampling frequency is 54kHz, the carrier size of 32kHz. 120 different signals are randomly produced by the use of software settings, of which 60 are normal signals and 60 are abnormal signals.

The 120 signals conducted in the signaling process of 2445IEC48RVV model communication equipment are identified using the identification method proposed in this paper and the traditional identification method, respectively, and the same strong interference effects are applied to both identification methods during the identification process. In order to ensure that the experimental results have a higher degree of objectivity and fairness, in addition to the different recognition methods used, in the exact same case to complete the comparison experiment, the comparison of the experimental results under different recognition of the partition is shown in Table 3.

As shown in Table 3, the number of correctly recognized signals in this paper is exactly the same as the actual abnormal signals in different recognition partitions, while the number of correctly recognized signals in the traditional method is smaller than the number of actual abnormal signals. Therefore, it is further proved through comparative experiments that the anomalous signal recognition method for electronic communication equipment based on improved gradient projection method proposed in this paper can effectively improve the recognition accuracy of anomalous signals in practical applications. Introducing this identification method into practical applications can effectively provide protection for the normal transmission of communication signals, and at the same time, it can also provide a basis for the subsequent enhancement of the anti-interference ability of electronic communication equipment in the identification process, which is of higher value.

Experiments using 1200 groups of electronic communication equipment signals for experiments, of which, the abnormal signal has 500 groups, using the method of this paper and the traditional method of abnormal signal recognition experiments, then different experiments when the number of times the abnormal signal recognition as shown in Table 4.

The recognition performance of the proposed method is validated by calculating the recognition correctness rate, which is calculated as: (37) p=qQ×100%\[p=\frac{q}{Q}\times 100%\]

Where: p denotes the rate of correct recognition. Q denotes the total number of anomalous signals. q denotes the number of abnormal signals recognized using the recognition method.

Calculated by the above formula, the comparison of recognition correct rate is obtained as shown in Fig. 6.

Figure 6.

Comparison of recognition accuracy rates

As can be seen from Fig. 6, the recognition correct rate of the proposed method in this paper is significantly higher than that of the traditional method. In particular, the maximum and average recognition correct rate of the proposed method are 98.40% and 89.40%, respectively, while the maximum and average recognition correct rate of the traditional method are 85.80% and 57.16%, respectively, so the average recognition correct rate of the proposed method is 32.24% higher than that of the traditional method, which fully demonstrates that the proposed anomalous signal recognition method based on the improved gradient projection method of the electronic communication equipment has better recognition performance. This fully demonstrates that the proposed recognition method based on the improved gradient projection method for abnormal signals of electronic communication equipment has better recognition performance and higher recognition stability.