Method for discriminating over-the-horizon communication mode based on logistic regression model

Abstract

The present disclosure is a kind of over-the-horizon communication mode discrimination method based on logistic regression model, comprising: obtaining measured data of wave propagation path loss;Group the data and calculate the average and standard deviation of path loss in each group, the average change rate of path loss of adjacent groups;Least square method is used to obtain the switching point set of average and standard deviation, define potential switching point indicator variable;Construct the measured data feature matrix, calculate the over-the-horizon communication mode switching point indicator variable;Using logistic regression model and path loss measured data feature matrix, calculate the prediction probability of communication mode switching under the optimal solution, candidate threshold and over-the-horizon communication mode switching probability optimal threshold;Discriminate over-the-horizon communication mode.The present application can accurately discriminate over-the-horizon communication mode, be used to guide the adjustment of over-the-horizon communication system and key parameters such as working bandwidth, and improve the adaptability and reliability of over-the-horizon communication system.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for identifying maritime beyond-line-of-sight communication modes based on a logistic regression model. Background Technology

[0002] Besides satellite communication, the two main methods for achieving over-the-horizon communication at sea are evaporative waveguides and tropospheric scattering.

[0003] The formation mechanism of evaporation waveguides is as follows: With the continuous evaporation and diffusion of water vapor at the sea surface, the air humidity near the sea surface decreases rapidly with increasing altitude. This, in turn, causes the atmospheric refractive index to decrease rapidly with increasing altitude, ultimately exhibiting a negative gradient. This results in radio waves of a certain frequency being refracted and propagating towards the sea surface. When the downward refraction curvature is greater than the Earth's curvature, the radio waves are trapped within the evaporation waveguide layer, significantly reducing their propagation path loss and enabling over-the-horizon communication at sea.

[0004] The formation mechanism of tropospheric scattering is as follows: In the troposphere above the sea surface in mid- and low-latitude regions (mid-latitude: 10km-12km above the sea surface, low-latitude: 17km-18km above the sea surface), there are a large number of scatterers, such as various turbulent vortices (such as vortex air masses), clouds (such as cloud droplets, ice crystals and other water condensates), warm fronts and cold fronts, and horizontal stratification with uneven refractive index. These scatterers refract and re-radiate microwaves and millimeter waves, thereby enabling over-the-horizon communication at sea.

[0005] Although evaporative waveguides and tropospheric scattering have different formation mechanisms, they are closely related. Influenced by the complex meteorological environment at sea, the height of evaporative waveguides exhibits significant time-varying characteristics, causing the over-the-horizon (OTH) communication mode at sea to switch between evaporative waveguide and tropospheric scattering: when the evaporative waveguide height is high and the communication distance is short, the OTH communication mode is dominated by evaporative waveguides; when the evaporative waveguide height is low or the communication distance is long, the OTH communication mode is dominated by tropospheric scattering. Therefore, accurately identifying the communication modes of evaporative waveguides and tropospheric scattering, as well as the switching state between them, and optimizing key parameters such as transmit power, operating frequency, antenna height, modulation method, and operating bandwidth of the OTH communication system based on the identification results, can enable the OTH communication system to fully utilize evaporative waveguides and improve performance.

[0006] However, current methods for distinguishing between evaporation waveguide and tropospheric scattering communication modes are mainly based on tropospheric scattering propagation attenuation prediction models, evaporation waveguide height prediction models (such as the NPS model), or engineering experience. Due to model errors and a lack of extensive experimental data, existing methods are ill-suited to the complex and variable meteorological conditions at sea, significantly reducing the accuracy of over-the-horizon communication mode identification. Furthermore, current research has not yet addressed the switching state between evaporation waveguide and tropospheric scattering.

[0007] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0008] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0009] The purpose of this invention is to provide a method for identifying maritime beyond-line-of-sight communication patterns based on a logistic regression model, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0010] This invention provides a method for identifying maritime over-the-horizon communication patterns based on a logistic regression model, comprising:

[0011] S1. Obtain measured data of radio wave propagation path loss in the X-band of the maritime over-the-horizon communication link, and smooth the measured path loss data.

[0012] S2, divide the smoothed path loss measured data into multiple groups according to a preset time span, calculate the average path loss and standard deviation of each group, and calculate the rate of change of the average path loss between each two adjacent groups based on the average path loss of all groups.

[0013] S3, the path loss average sequence and standard deviation sequence are segmented using the least squares sum of squared errors criterion to minimize the sum of squared residuals between the data in each segment and the mean of the corresponding segment, thus obtaining a set of switching points; then the corresponding indicator variables are used to mark the switching points in the two types of sequences; combining the two types of indicator variables, the potential switching point indicator variable for maritime over-the-horizon communication mode is defined.

[0014] S4. Based on the absolute value of the average change rate of path loss and the potential switching point indicator variable, construct the feature matrix of the measured path loss data, calculate the 80th percentile and 30th percentile of the absolute value of the average change rate of path loss, and calculate the switching point indicator variable of the maritime over-the-horizon communication mode based on the percentile and the potential switching point indicator variable.

[0015] S5. Using the logistic regression model and the feature matrix of the measured path loss data, the predicted probability, candidate threshold, and optimal threshold for the switching probability of maritime over-the-horizon communication mode are calculated under the optimal solution.

[0016] S6. Based on the predicted probability of switching over-the-horizon communication modes at sea under the optimal solution, the optimal threshold for the probability of switching communication modes, and the average change rate of path loss, the over-the-horizon communication mode at sea is determined.

[0017] In this invention, in step S1, the SG filtering algorithm is used to smooth the measured path loss data.

[0018] In this invention, step S3 includes the following steps:

[0019] S301 uses the least squares error sum of squares criterion to divide the path loss average sequence composed of all path loss averages into multiple segments, so that the sum of the squared residuals between the path loss average in each segment and the corresponding segment mean is minimized, thereby obtaining the set of switching points of the path loss average.

[0020] S302, use the average switching point indicator variable to mark whether the time period corresponding to each path loss average in the path loss average sequence is a switching point of the path loss average;

[0021] S303 uses the least squares sum of squared errors criterion to divide the path loss standard deviation sequence composed of all path loss standard deviations into multiple segments, so that the sum of the squared residuals between the path loss standard deviation in each segment and the mean of the corresponding segment is minimized, thereby obtaining the set of switching points of path loss standard deviation.

[0022] S304, using the standard deviation switching point indicator variable to mark whether the time period corresponding to each path loss standard deviation in the path loss standard deviation sequence is a switching point of the path loss standard deviation;

[0023] S305 defines potential switching point indicator variables for maritime over-the-horizon communication modes based on the average switching point indicator variable and the standard deviation switching point indicator variable.

[0024] In this invention, S4 represents the feature matrix of measured path loss data. as follows:

[0025]

[0026] in, The rate of change of the average path loss between two adjacent groups. G Number of groups for measured path loss data; As an indicator variable for potential switching points; in the feature matrix, .

[0027] In this invention, the maritime over-the-horizon communication mode switching point indicator variable The expression is as follows:

[0028]

[0029] in, , .

[0030] In this invention, step S5 includes the following steps:

[0031] S501 transforms the polynomial function of the linear regression model into a logistic regression function to represent the predicted probability of switching modes in maritime over-the-horizon communication.

[0032] S502, construct the log-likelihood loss function with L2 norm regularization term;

[0033] S503 uses the gradient descent method to find the optimal solution of the feature weights and the optimal solution of the bias term that minimizes the log-likelihood loss function, and iteratively updates them to obtain the trained logistic regression model.

[0034] S504. Input the feature matrix of the measured path loss data into the trained logistic regression model to calculate the predicted probability of switching of the maritime beyond-line-of-sight communication mode under the optimal solution.

[0035] S505, the predicted probabilities of switching modes in maritime over-the-horizon communication are sorted in ascending order and used as candidate thresholds;

[0036] S506, calculate the TP, FP, TN and FN indices of the confusion matrix based on candidate thresholds;

[0037] S507, calculate the true positive rate based on TP, FP, TN, and FN indicators. and false positive rate ;

[0038] S508, according to and Find the optimal threshold for the mode switching probability of maritime beyond-line-of-sight communication.

[0039] In this invention, step S6 includes the following steps:

[0040] S601. Compare the predicted probability of switching over-the-horizon communication mode at sea under the optimal solution with the optimal threshold of the communication mode switching probability to determine whether the over-the-horizon communication mode at sea has switched: if the former is greater than or equal to the latter, it means that a switch has occurred; otherwise, it means that a switch has not occurred.

[0041] S602, the specific switching mode is determined based on the average path loss change rate: if the average path loss change rate is less than 0, it indicates that the time period corresponding to the switching point is switched from tropospheric scattering mode to evaporation waveguide mode; if the average path loss change rate is greater than 0, it indicates that the time period corresponding to the switching point is switched from evaporation waveguide mode to tropospheric scattering mode.

[0042] S603 determines whether the time periods of the left and right neighbors of the current switching point are switching points and the switching mode.

[0043] The technical solution provided by this invention may include the following beneficial effects:

[0044] This invention discloses a method for identifying maritime over-the-horizon communication modes based on a logistic regression model. By utilizing the logistic regression model and measured path loss data, the method can accurately identify maritime over-the-horizon communication modes. This method can be used to guide the adjustment of key parameters such as transmit power, operating frequency, antenna height, modulation method, and operating bandwidth of maritime over-the-horizon communication systems, thereby improving the adaptability and reliability of maritime over-the-horizon communication systems. Attached Figure Description

[0045] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0046] Figure 1 A flowchart is shown for the maritime over-the-horizon communication mode discrimination method based on a logistic regression model in this invention.

[0047] Figure 2 The diagram illustrates the application effect of this invention in the measured path loss data of a 150km cross-sea beyond-line-of-sight communication link in the 7.82GHz band on June 19, 2024.

[0048] Figure 3 The diagram illustrates the application effect of this invention in the measured path loss data of a 150km cross-sea beyond-line-of-sight communication link in the 7.82GHz band on June 28, 2024.

[0049] Figure 4 The diagram illustrates the application effect of this invention in the measured path loss data of a 188km cross-sea beyond-line-of-sight communication link at the 7.96GHz frequency band on June 18, 2024.

[0050] Figure 5 The diagram illustrates the application effect of this invention in the measured path loss data of a 188km cross-sea beyond-line-of-sight communication link in the 7.96GHz band on June 22, 2024.

[0051] Figure 6 The diagram illustrates the application effect of this invention in the measured path loss data of the 8.46GHz band on a 248km cross-sea beyond-line-of-sight communication link on July 10, 2024.

[0052] Figure 7 The diagram shows the application effect of the present invention in the measured path loss data of the 8.46GHz band on a 248km cross-sea beyond-line-of-sight communication link on July 13, 2024. Detailed Implementation

[0053] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0054] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0055] This example implementation provides a method for identifying maritime over-the-horizon communication patterns based on a logistic regression model. Please refer to [link / reference]. Figure 1 The method includes: S1-S6, as follows:

[0056] S1. Obtain measured data of radio wave propagation path loss in the X-band of the maritime over-the-horizon communication link, and smooth the measured path loss data.

[0057] S2, divide the smoothed path loss measured data into multiple groups according to a preset time span, calculate the average path loss and standard deviation of each group, and calculate the rate of change of the average path loss between each two adjacent groups based on the average path loss of all groups.

[0058] S3, the path loss average sequence and standard deviation sequence are segmented using the least squares sum of squared errors criterion to minimize the sum of squared residuals between the data in each segment and the mean of the corresponding segment, thus obtaining a set of switching points; then the corresponding indicator variables are used to mark the switching points in the two types of sequences; combining the two types of indicator variables, the potential switching point indicator variable for maritime over-the-horizon communication mode is defined.

[0059] S4. Based on the absolute value of the average change rate of path loss and the potential switching point indicator variable, construct the feature matrix of the measured path loss data, calculate the 80th percentile and 30th percentile of the absolute value of the average change rate of path loss, and calculate the switching point indicator variable of the maritime over-the-horizon communication mode based on the percentile and the potential switching point indicator variable.

[0060] S5. Using the logistic regression model and the feature matrix of the measured path loss data, the predicted probability, candidate threshold, and optimal threshold for the switching probability of maritime over-the-horizon communication mode are calculated under the optimal solution.

[0061] S6. Based on the predicted probability of switching over-the-horizon communication modes at sea under the optimal solution, the optimal threshold for the probability of switching communication modes, and the average change rate of path loss, the over-the-horizon communication mode at sea is determined.

[0062] In this embodiment, the maritime over-the-horizon communication mode can be accurately identified using a logistic regression model and measured path loss data. This can be used to guide the adjustment of key parameters such as transmit power, operating frequency, antenna height, modulation method, and operating bandwidth of the maritime over-the-horizon communication system, thereby improving the adaptability and reliability of the maritime over-the-horizon communication system.

[0063] The specific process of each step in the above embodiments will be described below.

[0064] S1. First, a cross-sea over-the-horizon communication link is established in a designated sea area using a maritime over-the-horizon communication system to obtain measured data of the radio wave propagation path loss in the X-band. Based on the transmit power, transmit and receive antenna gain, receive signal strength, and system loss of the maritime over-the-horizon communication system, the measured path loss value on the cross-sea over-the-horizon communication link is obtained using formula (1). :

[0065] (1)

[0066] in, The unit is dB; This indicates the transmit power of a maritime over-the-horizon communication system, expressed in dBm. and The values ​​represent the transmit and receive antenna gains of the maritime over-the-horizon communication system, respectively, in dBi; RSSI represents the received signal strength, in dBm. This indicates the loss of the maritime over-the-horizon communication system, expressed in dB.

[0067] Secondly, the Savitzky-Golay (SG) filtering algorithm is used to smooth the aforementioned path loss measurement data and remove outliers that deviate significantly from the normal trend curve, thus preserving the variation trend in the original measurement data. It should be noted that Savitzky-Golay is existing technology in this field and is generally not translated into Chinese.

[0068] The SG filtering process is as follows:

[0069] (1) Select the measured path loss data before fitting. left and right M Each sample point, With the center point as the center, construct a window with a width of . an array, i.e. .For example, M It can take the value 25.

[0070] (2) Adopt p ( A polynomial of order 1 is used to fit the measured path loss data points within the window to obtain the polynomial fitting value. :

[0071] (2)

[0072] in, n For the relative position index within the window, satisfying ; k The power index of the polynomial fitting term. For the first k ( The fitting coefficients of order 1 are obtained by solving the least squares method. Among them, p It can take the value 3, etc.

[0073] (3) Calculate the polynomial fitting value Compared with the measured value of the original path loss Sum of squared residuals between The formula is as follows:

[0074] (3)

[0075] (4) The first polynomial fit l order coefficient ( Taking the partial derivative and setting it to 0, we obtain the following equation:

[0076] (4)

[0077] Note: From formula (3), we can see that the polynomial fitting value Compared with the measured value of the original path loss Sum of squared residuals between It is a vector of fitting coefficients. A quadratic nonnegative function, therefore The best fit is achieved when the minimum value is obtained.

[0078] (5) Express equation (4) in matrix form:

[0079] (5)

[0080] Among them, matrix This is the Vandermonde matrix, where the number of rows is the size of the filtering window. W Each row corresponds to a data point within the window, and the number of columns is... p The order of the fitted polynomial is increased by 1, and each column corresponds to a power of the polynomial. The specific form of this matrix is: ; This represents a column vector of measured path loss data before fitting.

[0081] (6) Multiply both sides of equation (5) by the left inverse of matrix A. The fitted path loss measurement data were obtained. That is, the first element of the fitting coefficient vector a:

[0082] (6)

[0083] Note: Due to the Vandermonde matrix It is not necessarily a square matrix, and its inverse matrix may not exist. Therefore, both sides of equation (5) need to be multiplied by the left inverse matrix of matrix A. .

[0084] (7) Move the window to the next measured path loss value and repeat steps (1)-(6) above until all measured path loss data to be fitted have been traversed to obtain the fitted measured path loss dataset. .

[0085] S2, the fitted path loss measured dataset Divided into G Group The time span of the path loss data in each group is (For example (It can be 0.5 hours), and then calculate the first time separately. j ( ) groups Average path loss within and standard deviation The formula is as follows:

[0086] (7)

[0087] (8)

[0088] in, Indicates the first j The first group i Path loss data, satisfying ; For the first j The sample size of the measured path loss data within each group.

[0089] Among them, when h time, G The range of values ​​is , This represents the ideal situation where path loss measurement data is collected continuously for 24 hours a day.

[0090] Based on the average path loss within each group of S2, calculate the rate of change of the average path loss between adjacent groups. The formula is as follows:

[0091] (9)

[0092] in The unit is dB / h.

[0093] S3 is the process of sequentially detecting the switching point by calculating the average path loss and the standard deviation of path loss from the measured path loss data. S3 specifically includes the following steps:

[0094] S301 uses the least squares error sum of squares criterion to divide the path loss average sequence composed of all path loss averages into multiple segments, so that the sum of the squared residuals between the path loss average in each segment and the corresponding segment mean is minimized, thereby obtaining the set of switching points of the path loss average.

[0095] Specifically, the optimization problem (10) is solved using the least squares sum of squared errors criterion to determine the set of path loss average switching points that minimize the sum of squared residuals between the average path loss in each segment and the mean of the corresponding segment. , where H represents the number of switching points for the average path loss.

[0096] (10)

[0097] in, This is the sample index (integer) of the segment boundary in the path loss average sequence. h ( The index set of the average path loss samples is: The sample size is Therefore, the first The mean of the path loss of the segment is expressed as .when hour, The sample index indicating the starting boundary of the observation period is only used to define the starting point of the first segment and is not a switching point; The sample index that indicates the end boundary of the observation. This represents the sum of squared residuals of the difference between the average path loss sample and the mean of the corresponding segment within each segment.

[0098] Note: Due to the complex and variable marine weather environment, the over-the-horizon communication mode at sea switches between evaporation waveguide and tropospheric scattering multiple times within a day. Therefore, there are multiple switching points in the average path loss within a day, and these multiple switching points constitute the set of switching points of the average path loss. .

[0099] S302, using the average switching point indicator variable, marks whether the time period corresponding to each path loss average in the path loss average sequence is a switching point for the path loss average. Average switching point indicator variable. The definition is as follows:

[0100] (11)

[0101] in, To determine the average path loss Whether the corresponding time period is an indicator variable for the switching point: when At that time, the average path loss The corresponding time period is the switching point, that is The corresponding time period is the switching period for beyond-line-of-sight communication mode; when At that time, the average path loss The corresponding time period is not the switching point.

[0102] S303 uses the least squares sum of squared errors criterion to divide the path loss standard deviation sequence composed of all path loss standard deviations into multiple segments, so that the sum of the squared residuals of the path loss standard deviation and the corresponding segment mean in each segment is minimized, thereby obtaining the set of switching points of path loss standard deviation.

[0103] Specifically, the optimization problem (12) is solved using the least squares sum of squared errors criterion to determine the set of path loss standard deviation switching points that minimize the sum of the squared residuals between the standard deviation of path loss in each segment and the mean of the standard deviation of path loss in the corresponding segment. ,in This represents the number of switching points representing the standard deviation of path loss.

[0104] (12)

[0105] in, This is the sample index (integer) of the segment boundary in the path loss standard deviation sequence. ( The index set of the standard deviation samples of path loss is: The sample size is Therefore, the first The mean of the standard deviation of the path loss of a segment is expressed as: .when hour, The sample index indicating the starting boundary of the observation period is only used to define the starting point of the first segment and is not a switching point; The sample index that indicates the end boundary of the observation. This represents the sum of squared residuals of the difference between the standard deviation of path loss samples within each segment and the mean of their corresponding segment.

[0106] S304 uses the standard deviation switching point indicator variable to mark whether the time period corresponding to each path loss standard deviation in the path loss standard deviation sequence is a switching point of the path loss standard deviation. Standard deviation switching point indicator variable The definition is as follows:

[0107] (13)

[0108] in, Indicates the standard deviation of the discrimination path loss. Whether the corresponding time period is an indicator variable for the switching point: when hour, The corresponding time period is the switching point, that is The corresponding time period is the switching period for over-the-horizon communication modes at sea; when hour, The corresponding time period is not the switching point.

[0109] S305 defines potential handover point indicator variables for maritime over-the-horizon communication modes based on the average handover point indicator variable and the standard deviation handover point indicator variable. As shown below:

[0110] (14)

[0111] S4 is the process of constructing the feature matrix of measured path loss data and defining the indicator variable for the switching point of maritime over-the-horizon communication mode. The specific process of S4 is as follows:

[0112] (1) Take the absolute value of the average change rate of the calculated path loss.

[0113] (2) Construct the feature matrix of the measured path loss data :

[0114] (15)

[0115] Wherein, the first and second columns of the feature matrix X are respectively The absolute value of the average rate of change of path loss for each path There are several potential switching point indicator variables, and each row of the feature matrix X represents a feature input for a time interval.

[0116] Note: The number of potential switching point indicator variable values ​​is... G However, only The absolute value of the average rate of change of path loss. To ensure consistency in the number of feature inputs, the last potential switching point indicator variable is discarded. That is, the final feature input is .

[0117] (3) Calculate the absolute value of the rate of change of the average path loss. 80th percentile and the 30th percentile The formula is as follows:

[0118] (16)

[0119] (17)

[0120] in, and These represent the absolute values ​​of the rate of change of the average path loss. After arranging the values ​​in ascending order, the values ​​at the 80th and 30th percentiles are taken. If the 80th and 30th percentile positions are not integers, the percentiles are determined using linear interpolation. Taking the 80th percentile as an example, the position is first calculated... ,in The data volume represents the absolute value of the rate of change of the average path loss; if Q If it is a non-integer, take its integer part. With the decimal part d By sorting the first With the Linear interpolation is performed on the data to obtain the 80th percentile.

[0121] (4) Based on the percentile of the absolute value of the average rate of change of path loss and the potential switching point indicator variable in S305, calculate the switching point indicator variable for maritime over-the-horizon communication mode. :

[0122] (18)

[0123] in, The average rate of change of path loss, average path loss, and standard deviation of path loss were taken into account. =1 indicates that the maritime over-the-horizon communication mode is in j The time period has changed; =0 indicates that the maritime over-the-horizon communication mode is in... The time period did not switch, meaning the channel was stable.

[0124] S5 includes the following steps:

[0125] S501 transforms the polynomial function of the linear regression model into a logistic regression function to represent the predicted probability of switching modes in maritime over-the-horizon communication.

[0126] Specifically, the polynomial function of the linear regression model yThis is converted to the corresponding Sigmoid function, i.e., the logistic regression function:

[0127] (19)

[0128] in, This represents the predicted probability of switching modes in maritime over-the-horizon communication. y The polynomial function representing the linear regression model is defined as follows:

[0129] (20)

[0130] in, and As characteristic variables, and For feature weights, b This is a bias term.

[0131] S502, construct the log-likelihood loss function with L2 norm regularization.

[0132] Specifically, construct a regularization term with L2 norm. log-likelihood loss function :

[0133] (twenty one)

[0134] in, Represents the regularization coefficient. N This is the number of training samples (if the number of samples specified in the model is less than 6, the model training will fail). This represents the sample number used in model training, i.e., the current sample participating in the training. One sample, Indicates the first The indicator variable for the switching point of the maritime beyond-line-of-sight communication mode corresponding to each training sample.

[0135] It should be noted that, generally, the log-likelihood loss function for logistic regression takes the form of: The beyond-line-of-sight communication mode switching point indicator variable in this invention Determined based on measured path loss data, issues such as sample imbalance exist. Directly minimizing... This could lead to overfitting, therefore equation (21) in The L2 norm regularization term is introduced. .

[0136] S503 uses gradient descent to find the optimal solution for the feature weights and the optimal solution for the bias term that minimizes the log-likelihood loss function, and iteratively updates them to obtain the trained logistic regression model.

[0137] Specifically, the gradient descent method is used to solve for... The optimal solution that achieves the minimum feature weights , and the optimal solution of the bias term The iterative update formula is as follows:

[0138] (twenty two)

[0139] (twenty three)

[0140] (twenty four)

[0141] in, This represents the learning rate, used to control the step size of each iteration. The iteration terminates when the difference between the loss functions of adjacent iterations is less than a given threshold or when the maximum number of iterations is reached.

[0142] Learning rate Taking a value that is too large can easily lead to parameter oscillations and failure to converge, while taking a value that is too small will result in a slow convergence speed and increase training costs. In this embodiment, we take a value that is too small. .

[0143] S504: Input the feature matrix of the measured path loss data into the trained logistic regression model to calculate the predicted probability of switching modes of maritime beyond-line-of-sight communication under the optimal solution.

[0144] Specifically, the feature matrix of the measured path loss data Input the trained logistic regression model and calculate the predicted probability of mode switching in maritime over-the-horizon communication under the optimal solution. :

[0145] (25)

[0146] S505 ranks the predicted probabilities of over-the-horizon communication mode switching in ascending order and uses them as candidate thresholds. :

[0147] (26)

[0148] in, Indicates the first s One candidate threshold, Indicates the first digit after ascending order. s Each predicted probability, This represents the number of all predicted probabilities.

[0149] S506, TP, FP, TN, and FN indices of the confusion matrix are calculated based on the candidate thresholds, as shown below:

[0150] (27)

[0151] in, This indicates a switch has occurred in the beyond-line-of-sight communication mode. And the model predicts probability ≥threshold The number of samples, i.e. the number of switching events correctly identified by the logistic regression model; This indicates that no handover has occurred. However, the model predicts the probability. ≥threshold The number of samples, i.e., the number of false alarms during switching events in the logistic regression model; This indicates that no handover has occurred. And the model predicts probability Less than the threshold The number of samples, i.e. the number of non-switching events correctly identified by the logistic regression model; This indicates that a real switch has occurred. However, the model predicts the probability. Less than the threshold The number of samples, i.e. the number of missed reports of model switching events. This is an indicator function that takes the value 1 when the condition is true and 0 otherwise.

[0152] S507, calculate the true positive rate based on TP, FP, TN, and FN indicators. and false positive rate The formula is as follows:

[0153] (28)

[0154] (29)

[0155] in, This indicates the proportion of samples where the logistic regression model correctly determined the actual occurrence of over-the-horizon communication mode switching at sea. This indicates the proportion of samples where the logistic regression model incorrectly identified actual over-the-horizon communication mode switching at sea.

[0156] S508, according to and Find the optimal threshold for the mode switching probability of maritime beyond-line-of-sight communication.

[0157] Calculated For the horizontal axis, Establish a two-dimensional coordinate system with the vertical axis as the ordinate, and obtain... Coordinates of points Then, arrange them in ascending order of their horizontal coordinates (FPR) to obtain a point sequence. , , ..., ,connect The receiver operating characteristic (ROC) curve is obtained from each point. The area under the curve, along with the horizontal and vertical axes, is calculated as follows:

[0158] (30)

[0159] in, This indicates the position of the point involved in the area calculation within the point sequence sorted by FPR from smallest to largest.

[0160] Solve for the Youden exponent To achieve the optimal threshold for the highest probability of switching modes in maritime over-the-horizon communication. :

[0161] (31)

[0162] in, .

[0163] Note: The ROC curve is used to evaluate the overall performance of a classification model, showing the relationship between the false positive rate and the true positive rate. AUC is the area under the ROC curve, representing the ability of the logistic regression model to distinguish between positive and negative examples. The value of AUC ranges from 0.5 to 1, and the closer it is to 1, the better the performance of the logistic regression model.

[0164] S6 includes the following steps:

[0165] S601. Compare the predicted probability of switching over-the-horizon communication mode at sea under the optimal solution with the optimal threshold of the communication mode switching probability to determine whether the over-the-horizon communication mode at sea has switched: if the former is greater than or equal to the latter, it means that a switch has occurred; otherwise, it means that a switch has not occurred.

[0166] Specifically, the predicted probability of switching over-the-horizon communication modes at sea under the optimal solution is: The optimal threshold for the probability of communication mode switching is ,like If the switching occurs, the over-the-horizon (OTH) maritime communication mode will switch during the time period corresponding to that switching point; otherwise, the OTH maritime communication mode will not switch.

[0167] S602, the specific switching mode is determined based on the average path loss change rate: if the average path loss change rate is less than 0, it indicates that the time period corresponding to the switching point is switched from tropospheric scattering mode to evaporation waveguide mode; if the average path loss change rate is greater than 0, it indicates that the time period corresponding to the switching point is switched from evaporation waveguide mode to tropospheric scattering mode.

[0168] If the average change rate of path loss Then the time period corresponding to this switching point switches from tropospheric scattering to evaporation waveguide; if Then, the time period corresponding to this switching point is switched from evaporation waveguide to tropospheric scattering.

[0169] Note: Under the condition that the communication distance, operating frequency, antenna gain, and antenna height remain consistent, the path loss in the evaporative waveguide communication mode is significantly lower than that in the tropospheric scattering mode. Therefore, when When this occurs, it indicates that during this period, the over-the-horizon communication mode at sea has switched from the tropospheric scattering communication mode with high path loss to the evaporative waveguide communication mode with low path loss; when The time indicates that during this period, the beyond-line-of-sight communication mode switched from evaporative waveguide with lower path loss to tropospheric scattering with higher path loss.

[0170] S603, determine whether the potential switching points to the left and right of the current switching point are switching points and the switching mode.

[0171] Specifically, when the switching mode at the current switching point is switched from tropospheric scattering mode to evaporation waveguide mode, the switching mode for each adjacent time period and the over-the-horizon communication mode at sea are determined according to Table 1.

[0172] Table 1. Distinguishing between switching modes and maritime over-the-horizon communication modes.

[0173]

[0174] If any switching point The various sub-cases for determining whether the adjacent time period is the switching point and the switching mode are similar to those in the table above when switching from evaporation waveguide to tropospheric scattering.

[0175] Repeat the above steps to determine the communication patterns of all switching points and the left and right neighboring time periods throughout the day.

[0176] The following specific experiments further illustrate the beneficial effects of the maritime over-the-horizon communication mode discrimination method based on logistic regression model proposed in this application.

[0177] The accuracy of the proposed maritime over-the-horizon communication mode discrimination method was verified by selecting path loss measurement data in the 7.82GHz band obtained on June 19 and June 28, 2024, on a 150km cross-sea over-the-horizon communication link from Jizhao Bay, Zhanjiang City, Guangdong Province to Jinshan Town, Wenchang City, Hainan Province. Figure 2 and Figure 3 The measured path loss data in the 7.82 GHz band during the periods of 0:00-21:00 on June 19, 2024 and 0:00-23:30 on June 28, 2024 were plotted, as well as the curves of the average path loss, standard deviation of path loss, and rate of change of path loss over time for every 30 minutes.

[0178] Figure 2 In the study, the actual path loss sample size was 178,888, and the number of path loss outliers detected using the SG filtering algorithm was 1,202. Therefore, the effective path loss data sample size for judging the mode switching of maritime over-the-horizon communication was 177,686. By detecting switching points using the average and standard deviation of path loss, and using a logistic regression model, the optimal solution for the feature weights and bias terms in the polynomial function of the linear regression model was calculated. and the optimal threshold By comparing the predicted probability of over-the-horizon (OTH) communication mode switching under the optimal solution with the optimal threshold, and determining the specific switching mode based on the sign of the average path loss change rate, a total of 10 OTH communication mode switching events were obtained. Among them, 5 were switching from tropospheric scattering to evaporation waveguide, and 5 were switching from evaporation waveguide to tropospheric scattering. Taking the time period of 13:30-14:00 corresponding to the switching point as an example, the OTH communication mode during this time period was determined to be switching from tropospheric scattering to evaporation waveguide using the method of this invention. Since the time periods to the left and right of the switching point are not switching points, the OTH communication mode to the left of the switching point, i.e., the time period of 13:00-13:30, was determined to be tropospheric scattering, and the OTH communication mode to the right of the switching point, i.e., the time period of 14:00-14:30, was determined to be evaporation waveguide.

[0179] Figure 3 In the study, the actual path loss sample size was 211,404, and the number of path loss outliers detected using the SG filtering algorithm was 2,145. Therefore, the effective path loss data sample size for beyond-line-of-sight communication mode switching discrimination was 209,259. Switching points were detected using the average and standard deviation of path loss, and the optimal solution for the feature weights and bias terms in the polynomial function of the linear regression model was calculated using a logistic regression model. and the optimal threshold Furthermore, a total of 12 over-the-horizon communication mode switches at sea were obtained, of which 8 were switching from scattering to waveguide and 4 were switching from waveguide to scattering. Figure 3Taking the time period of 14:00-14:30 corresponding to the switching point as an example, the communication mode of this time period is determined to be scattering switching to waveguide. Since the time periods to the left and right of the switching point are both switching points and the switching direction is the same, the communication mode of the time period to the left of the switching point, i.e., 13:30-14:00, and the time period to the right of the switching point, i.e., 14:30-15:00, is scattering switching to waveguide.

[0180] The accuracy of the proposed maritime over-the-horizon communication mode discrimination method was verified by selecting path loss measurement data in the 7.96GHz band obtained on June 18 and June 22, 2024, on a 188km cross-sea over-the-horizon communication link between Yangxi City, Guangdong Province and Jinshan Town, Wenchang City, Hainan Province. Figure 4 and Figure 5 The measured path loss data in the 7.96 GHz band during the periods of 0:00-23:30 on June 18, 2024 and 0:00-23:00 on June 22, 2024 were plotted, as well as the curves of the average path loss, standard deviation of path loss, and rate of change of path loss over time for every 30 minutes.

[0181] Figure 4 In the study, the actual path loss sample size was 211,498, and the number of path loss outliers detected using the SG filtering algorithm was 1,821. Therefore, the effective path loss data sample size for beyond-line-of-sight communication mode switching discrimination was 209,677. Switching points were detected using the average and standard deviation of path loss, and the optimal solution for the feature weights and bias terms in the polynomial function of the linear regression model was calculated using a logistic regression model. and the optimal threshold Further analysis revealed a total of 11 over-the-horizon (OTH) communication mode switches at sea, including 6 switches from scattering to waveguide and 5 switches from waveguide to scattering. Taking the time period corresponding to the switch point, 5:00-5:30, as an example, the OTH communication mode during this time period was determined to be a switch from scattering to waveguide. Since the time period to the left of the switch point was not a switch point, and the time period to the right was a switch point with the opposite switching direction, the communication mode for the time period to the left of the switch point, i.e., 4:30-5:00, was determined to be scattering, and the communication mode for the time period to the right of the switch point, i.e., 5:30-6:00, was determined to be a switch from waveguide to scattering.

[0182] Figure 5 In the study, the actual path loss sample size was 206,983, and the number of path loss outliers detected using the SG filtering algorithm was 827. Therefore, the effective path loss data sample size for beyond-line-of-sight communication mode switching discrimination was 206,156. Switching points were detected using the average and standard deviation of path loss, and the optimal solution for the feature weights and bias terms in the polynomial function of the linear regression model was calculated using a logistic regression model. and the optimal threshold Further analysis revealed a total of nine over-the-horizon (OTH) communication mode switches at sea, six of which were switches from scattering to waveguide and three were switches from waveguide to scattering. Taking the time period corresponding to the switch point, 17:00-17:30, as an example, the OTH communication mode during this period was determined to be a switch from waveguide to scattering. Since the time period to the left of the switch point was a switch point with the same switching direction, and the time period to the right was not a switch point, the communication mode for the time period to the left of the switch point, i.e., 16:30-17:00, was determined to be a switch from waveguide to scattering, and the communication mode for the time period to the right of the switch point, i.e., 17:30-18:00, was determined to be scattering.

[0183] The accuracy of the proposed maritime over-the-horizon communication mode discrimination method was verified by selecting path loss measurement data in the 8.46 GHz band obtained on July 10 and July 13, 2024, on a 248 km cross-sea over-the-horizon communication link between Yangjiang City, Guangdong Province and Jinshan Town, Wenchang City, Hainan Province. Figure 6 and Figure 7 The measured path loss data in the 8.46 GHz band during the periods of 0:00-23:30 on July 10, 2024 and 0:00-23:30 on July 13, 2024 were plotted, as well as the curves of the average path loss, standard deviation of path loss, and rate of change of path loss over time for every 30 minutes.

[0184] Figure 6 In the study, the actual path loss sample size was 211,082, and the number of path loss outliers detected using the SG filtering algorithm was 1,144. Therefore, the effective path loss data sample size for beyond-line-of-sight communication mode switching discrimination was 209,938. By detecting switching points using the average and standard deviation of path loss, the optimal solution for the feature weights and bias terms in the polynomial function of the linear regression model was calculated using a logistic regression model. and the optimal threshold Further analysis revealed a total of 10 over-the-horizon (OTH) communication mode switches at sea, including 5 switches from scattering to waveguide and 5 switches from waveguide to scattering. Taking the time period corresponding to the switch point, 14:30-15:00, as an example, the OTH communication mode during this period was determined to be a switch from scattering to waveguide. Since the left adjacent time period of this switch point was a switch point with the same switching direction, and the right adjacent time period was a switch point with the opposite switching direction, it was determined that the communication mode of the left adjacent time period, i.e., 14:00-14:30, was a switch from scattering to waveguide, and the communication mode of the right adjacent time period, i.e., 15:00-15:30, was a switch from scattering to waveguide to scattering.

[0185] Figure 7In the study, the actual path loss sample size was 211,490, and the number of path loss outliers detected using the SG filtering algorithm was 1,703. Therefore, the effective path loss data sample size for beyond-line-of-sight communication mode switching discrimination was 209,787. Switching points were detected using the average and standard deviation of path loss, and the optimal solution for the feature weights and bias terms in the polynomial function of the linear regression model was calculated using a logistic regression model. and the optimal threshold Further analysis revealed a total of 11 over-the-horizon (OTH) communication mode switches at sea, including 6 switches from scattering to waveguide and 5 switches from waveguide to scattering. Taking the time period corresponding to the switch point, 5:30-6:00, as an example, the OTH communication mode during this time period was determined to be a switch from waveguide to scattering. Since the left and right adjacent time periods of this switch point were also switch points and the switching directions were opposite to this switch point, it was determined that the communication mode of the left adjacent time period (5:00-5:30) and the right adjacent time period (6:00-6:30) was a switch from scattering to waveguide.

[0186] When the communication mode is identified as evaporating waveguide, the channel conditions are favorable, and the path loss in the beyond-line-of-sight communication link is low. In this case, the operating frequency can be adjusted to the X-band or a higher frequency band close to the X-band, while the height of the transmitting and receiving antennas can be appropriately lowered to a lower height of 4–6 m to enhance the trapping effect of radio waves within the evaporating waveguide layer. Simultaneously, a higher-order modulation scheme (such as 16-QAM) and a wider operating bandwidth (such as 20 MHz or 40 MHz) or lower transmit power can be used to fully utilize the favorable evaporating waveguide channel conditions and achieve high-speed or low-power reliable beyond-line-of-sight communication.

[0187] When the communication mode is determined to be tropospheric scattering, channel conditions are poor and path loss is increased. In this case, the operating frequency can be adjusted to the C-band or a lower frequency band close to the C-band, while the height of the transmitting and receiving antennas can be increased to a higher height of 8-12m to extend the line-of-sight communication distance and utilize tropospheric scattering for beyond-line-of-sight communication. Simultaneously, a lower-order modulation scheme (such as QPSK) and a narrower operating bandwidth (such as 2.5MHz or 5MHz) or a higher transmit power can be used to achieve reliable beyond-line-of-sight communication. Furthermore, when the communication mode is determined to be a switching state between evaporative waveguide and tropospheric scattering, such as when the communication mode is determined to be a waveguide switching to scattering, the operating bandwidth can be gradually decreased or the transmit power gradually increased to maintain reliable beyond-line-of-sight communication.

[0188] In summary, the maritime over-the-horizon (BTH) communication mode discrimination method proposed in this invention can guide maritime BTH communication systems to improve their performance by adjusting key parameters such as transmit power, operating frequency, antenna height, modulation method, and operating bandwidth, thereby enhancing the adaptability and reliability of the maritime BTH communication system. The method proposed in this invention can provide key technical support for the design of hardware modules such as antennas and power amplifiers, as well as waveforms, in maritime BTH communication systems, and can be used to guide the development and subsequent upgrades of maritime BTH communication systems.

[0189] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for identifying maritime beyond-line-of-sight communication patterns based on a logistic regression model, characterized in that, include: S1. Obtain measured data of radio wave propagation path loss in the X-band of the maritime over-the-horizon communication link, and smooth the measured path loss data. S2, divide the smoothed path loss measured data into multiple groups according to a preset time span, calculate the average path loss and standard deviation of each group, and calculate the rate of change of the average path loss between each two adjacent groups based on the average path loss of all groups. S3, the path loss average sequence and standard deviation sequence are segmented using the least squares sum of squared errors criterion to minimize the sum of squared residuals between the data in each segment and the mean of the corresponding segment, thus obtaining a set of switching points; then the corresponding indicator variables are used to mark the switching points in the two types of sequences; combining the two types of indicator variables, the potential switching point indicator variable for maritime over-the-horizon communication mode is defined. S4. Based on the absolute value of the average change rate of path loss and the potential switching point indicator variable, construct the feature matrix of the measured path loss data, calculate the 80th percentile and 30th percentile of the absolute value of the average change rate of path loss, and calculate the switching point indicator variable of the maritime over-the-horizon communication mode based on the percentile and the potential switching point indicator variable. S5. Using the logistic regression model and the feature matrix of the measured path loss data, the predicted probability, candidate threshold, and optimal threshold for the switching probability of maritime over-the-horizon communication mode are calculated under the optimal solution. S6. Based on the predicted probability of switching over-the-horizon communication modes at sea under the optimal solution, the optimal threshold for the probability of switching communication modes, and the average change rate of path loss, the over-the-horizon communication mode at sea is determined. S3 includes the following steps: S301 uses the least squares sum of squared errors criterion to divide the path loss average sequence composed of all path loss averages into multiple segments, so that the sum of squared residuals between the path loss average in each segment and the corresponding segment mean is minimized, thereby obtaining the set of switching points of path loss averages. S302, use the average switching point indicator variable to mark whether the time period corresponding to each path loss average in the path loss average sequence is a switching point of the path loss average; S303 uses the least squares sum of squared errors criterion to divide the path loss standard deviation sequence composed of all path loss standard deviations into multiple segments, so that the sum of the squared residuals between the path loss standard deviation in each segment and the mean of the corresponding segment is minimized, thereby obtaining the set of switching points of path loss standard deviation. S304, using the standard deviation switching point indicator variable to mark whether the time period corresponding to each path loss standard deviation in the path loss standard deviation sequence is a switching point of the path loss standard deviation; S305 defines potential handover point indicator variables for maritime over-the-horizon communication modes based on the average handover point indicator variable and the standard deviation handover point indicator variable. As shown below: In the formula, The average switching point indicator variable, This is the standard deviation switching point indicator variable; S5 includes the following steps: S501 transforms the polynomial function of the linear regression model into a logistic regression function to represent the predicted probability of switching modes in maritime over-the-horizon communication. S502, construct the log-likelihood loss function with L2 norm regularization term; S503 uses the gradient descent method to find the optimal solution of the feature weights and the optimal solution of the bias term that minimizes the log-likelihood loss function, and iteratively updates them to obtain the trained logistic regression model. S504. Input the feature matrix of the measured path loss data into the trained logistic regression model to calculate the predicted probability of switching of the maritime beyond-line-of-sight communication mode under the optimal solution. S505, the predicted probabilities of switching modes in maritime over-the-horizon communication are sorted in ascending order and used as candidate thresholds; S506, calculate the TP, FP, TN and FN indices of the confusion matrix based on candidate thresholds; This indicates that the beyond-line-of-sight communication mode has switched and the model predicts the probability. ≥threshold The number of samples; This indicates that no switching occurred but the model predicted the probability. ≥threshold The number of samples; This indicates that no switching occurred and the model predicts the probability. Less than the threshold The number of samples; This indicates that a switch actually occurs, but the model predicts the probability. Less than the threshold The number of samples; S507, calculate the true positive rate based on TP, FP, TN, and FN indicators. and false positive rate ; S508, according to and Find the optimal threshold for the mode switching probability of maritime beyond-line-of-sight communication.

2. The maritime beyond-line-of-sight communication mode discrimination method based on logistic regression model according to claim 1, characterized in that, In S1, the SG filtering algorithm is used to smooth the measured path loss data.

3. The maritime beyond-line-of-sight communication mode discrimination method based on logistic regression model according to claim 1, characterized in that, In S4, the feature matrix of the measured path loss data as follows: in, The rate of change of the average path loss between two adjacent groups. G Number of groups for measured path loss data; As an indicator variable for potential switching points; in the feature matrix, .

4. The maritime beyond-line-of-sight communication mode discrimination method based on logistic regression model according to claim 3, characterized in that, Maritime over-the-horizon communication mode switching point indicator variable The expression is as follows: in, , .

5. The maritime beyond-line-of-sight communication mode discrimination method based on logistic regression model according to claim 1, characterized in that, S6 includes the following steps: S601. Compare the predicted probability of switching over-the-horizon communication mode at sea under the optimal solution with the optimal threshold of the communication mode switching probability to determine whether the over-the-horizon communication mode at sea has switched: if the former is greater than or equal to the latter, it means that a switch has occurred; otherwise, it means that a switch has not occurred. S602, the specific switching mode is determined based on the average path loss change rate: if the average path loss change rate is less than 0, it indicates that the time period corresponding to the switching point is switched from tropospheric scattering mode to evaporation waveguide mode; if the average path loss change rate is greater than 0, it indicates that the time period corresponding to the switching point is switched from evaporation waveguide mode to tropospheric scattering mode. S603 determines whether the time periods of the left and right neighbors of the current switching point are switching points and the switching mode.

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