APSK demodulation method based on K-Means clustering

Abstract

The invention relates to an APSK (Amplitude Phase Shift Keying) demodulation method based on K-Means clustering, and the method comprises the steps that a transmitting end transmits an APSK modulation signal, and a constellation diagram corresponding to the signal is known; a receiving end receives the signal, estimates and eliminates a static direct current component of the received signal, and obtains a processed signal; calculating each constellation point of the processed signal according to a constellation diagram corresponding to the sent APSK modulation signal and the processed signal; according to the constellation points obtained through calculation, clustering is carried out through a K-Means clustering algorithm, and residual direct current components of the processed signals are eliminated; and taking the clustering convergence center after clustering as a constellation point theoretical value of an MAP algorithm, performing soft demodulation by adopting the MAP algorithm, and solving to obtain accurate log-likelihood ratio information. According to the invention, the direct current component in the received signal can be eliminated, and the bit error rate of the APSK demodulation signal at the receiving end is obviously reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite wireless communications, and in particular relates to an APSK demodulation method based on K-Means clustering. Background Art

[0002] In order to overcome the problem of blind spots in traditional ground mobile communication systems, the sixth generation of mobile communication technology will be combined with satellite communication technology to build a three-dimensional network structure based on ground-based networks and extended by space-based networks and air-based networks, so as to achieve global seamless coverage of space-ground integration. Amplitude Phase Shift Keying (APSK) modulation technology is more suitable for nonlinear satellite wireless channels due to its unique constellation structure and less amplitude changes, so it has attracted extensive attention from academia and industry.

[0003] Due to the existence of static and residual DC components in satellite communication systems, the received constellation points are distorted or aliased. In the time division multiple access system, the static DC component is manifested as the mean of the received signal amplitude. Because they are continuous, unlimited, and do not change over time. Affected by nonlinear interference factors such as Gaussian noise and multipath Doppler in the satellite wireless channel, there is still a significant residual DC component at the receiving end after the static DC component is eliminated. Therefore, how to estimate and eliminate the DC component at the receiving end is crucial for APSK demodulation.

[0004] K-Means clustering is the most famous clustering algorithm in unsupervised learning. It has the characteristics of simple algorithm, lightweight, and high convergence efficiency, which makes it widely used. Given a data set and the number of clusters K specified by the user, the K-Means clustering algorithm divides the data points into K clusters according to the Euclidean distance. Using an iterative method, K converged center points are finally obtained.

[0005] The MAP (Maximum A Posteriori) algorithm, or the maximum a posteriori probability estimation algorithm, is a statistical method used to estimate the optimal value of model parameters under given observation data. It belongs to the category of Bayesian inference, but unlike the maximum likelihood estimation (MLE), MAP takes into account the prior distribution information of the parameters.

[0006] Maximum Likelihood Estimation (MLE) is a method for estimating model parameters in statistics. Its basic idea is: given the observed data, select the model parameter value that maximizes the "likelihood" of the observed data as the estimated value of the parameter. The "likelihood" here is quantified by the likelihood function.

[0007] How to efficiently apply the K-Means clustering algorithm to the estimation and elimination process of the DC component of satellite wireless communication systems, thereby improving the APSK demodulation bit error rate performance, is a scientific issue that requires in-depth research. Summary of the invention

[0008] In order to solve the above technical problems, the present invention proposes an APSK demodulation method based on K-Means clustering, which includes:

[0009] S1: The transmitter sends an APSK modulated signal, and the constellation diagram corresponding to the signal is known;

[0010] S2: The receiving end receives the signal, estimates and eliminates the static DC component of the received signal, and obtains the processed signal;

[0011] S3: Calculate the constellation points C of the processed signal according to the constellation diagram corresponding to the transmitted APSK modulated signal and the processed signal k ;

[0012] S4: According to the calculated constellation points C k , clustering is performed using the K-Means clustering algorithm;

[0013] S5: The cluster centers after clustering As the theoretical value of the constellation point of the MAP algorithm, the MAP algorithm is used for soft demodulation to obtain accurate log-likelihood ratio information.

[0014] Further, the processed signal C is calculated k The calculation process of each constellation point includes:

[0015] Calculate the corresponding average amplitude value according to all post-processed signals;

[0016] According to the average amplitude value of all processed signals and the ratio of the radii of each constellation ring in the constellation diagram corresponding to the known APSK modulated signal to be transmitted, and calculating the radii of each constellation ring in the constellation diagram corresponding to the processed signal;

[0017] The constellation points are calculated according to the calculated radii of each constellation ring in the constellation diagram corresponding to the processed signal.

[0018] Further, according to the calculated constellation points C k , clustering is performed using the K-Means clustering algorithm, and the specific clustering process includes:

[0019] C k As the initial cluster center of the K-Means clustering algorithm;

[0020] Iteratively calculate each processed signal y′ n The Euclidean distance to each cluster center C is used to assign the processed signal to the cluster with the closest cluster center, and the cluster convergence center after clustering is obtained.

[0021] Beneficial effects of the present invention: After receiving the APSK modulated signal, the present invention preliminarily estimates and eliminates the static DC component of the received signal to obtain a processed signal; calculates each constellation point C of the processed signal k , clustering is performed using the K-Means clustering algorithm to eliminate the residual DC component of the processed signal. The present invention can estimate and eliminate the static DC component and the residual DC component, significantly reducing the bit error rate at the receiving end. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0024] Figure 1 is a flow chart of the steps of the present invention;

[0025] Figure 2 It is a schematic diagram of comparison between the constellation points of the 32APSK modulation signal at the transmitting end and the clustering centers before and after the 32APSK clustering at the receiving end in an embodiment of the present invention;

[0026] Figure 3 A Gray decimal schematic diagram of constellation points for sending a 32APSK modulated signal in an embodiment of the present invention;

[0027] Figure 4 This is a constellation point distribution diagram for sending a 32APSK modulated signal in an embodiment of the present invention;

[0028] Figure 5 is a schematic diagram of an actual received signal and its DC component in an embodiment of the present invention;

[0029] Figure 6 It is the initial cluster center diagram of the signal after 32APSK processing in the embodiment of the present invention;

[0030] Figure 7 It is a convergence cluster center diagram of the signal after 32APSK processing in an embodiment of the present invention;

[0031] Figure 8 This is a comparison chart of the bit error rate performance between the method of the present invention and the traditional MAP algorithm. DETAILED DESCRIPTION

[0032] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the scheme of the present invention will be further described below. In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention can also be implemented in other ways different from those described herein; it is obvious that the embodiments in the specification are only part of the embodiments of the present invention, not all of them.

[0033] The embodiment of the present invention provides an APSK demodulation method based on K-Means clustering, referring to Figure 1 As shown, the method includes:

[0034] S1: The transmitter sends an APSK modulated signal, and the constellation diagram corresponding to the signal is known;

[0035] S2: The receiving end receives the signal, estimates and eliminates the static DC component of the received signal, and obtains the processed signal;

[0036] S3: Calculate the constellation points C of the processed signal according to the constellation diagram corresponding to the transmitted APSK modulated signal and the processed signal k ;

[0037] S4: According to the calculated constellation points C k , clustering is performed using the K-Means clustering algorithm;

[0038] S5: Converging the clusters into a cluster center As the theoretical value of the constellation point of the MAP algorithm, the MAP algorithm is used for soft demodulation to obtain accurate log-likelihood ratio information.

[0039] After being affected by the DC component of the channel, the APSK modulated signal received by the receiving end includes a static DC component and a residual DC component. In step S2, the static DC component of the received signal is estimated and eliminated. Since the transmitting end sends an APSK modulated signal, the corresponding constellation diagram is known, so the constellation diagram of the received signal can be obtained; through specific experiments, it can be known that the center points of the two constellations are offset and the outer ring receiving signals of the two constellations are offset, so the offset of the center point represents the offset static DC component, and the offset of the outer ring receiving signal represents the offset residual DC component.

[0040] In some embodiments, the processed signal is represented by:

[0041]

[0042]

[0043] Where y' represents the processed signal after eliminating the static DC component, y n represents the nth received signal, represents the mean of all received signals, N represents the length of the received signal, re(·) represents the real part operation, im(·) represents the imaginary part operation, and i represents the imaginary unit.

[0044] The mean value of all received signals Indicates: The static DC component estimated by the mean value in the constellation diagram corresponding to the received signal.

[0045] S301: Calculate the corresponding average amplitude value according to all processed signals;

[0046] S302: Based on the average amplitude value of all processed signals and the ratio of the radii of each constellation ring in the constellation diagram corresponding to the known APSK modulated signal to be transmitted, and calculating the radii of each constellation ring in the constellation diagram corresponding to the processed signal;

[0047] S303: Calculate the constellation points according to the calculated radius of each constellation ring in the constellation diagram corresponding to the processed signal, which is specifically expressed as:

[0048] C k =r v exp(2πθ v,k i)

[0049] In the formula, C k represents the kth constellation point in the constellation diagram corresponding to the processed signal, r v represents the radius of the vth constellation ring in the constellation diagram corresponding to the processed signal, θ v,k represents the angle of the kth constellation point on the vth constellation ring in the constellation diagram corresponding to the processed signal, and i represents an imaginary unit.

[0050] In some embodiments, in S301, the average amplitude value of all processed signals is estimated, which is specifically expressed as:

[0051]

[0052] In the formula, represents the average amplitude value of all processed signals, N represents the length of the processed signal, the length of the processed signal is equal to that of the transmitted signal, y′ n represents the nth processed signal after eliminating the static DC component, re(·) represents the real part operation, and im(·) represents the imaginary part operation;

[0053] In some embodiments, in S302, according to the average amplitude value of all processed signals The radius of each constellation ring in the constellation corresponding to the processed signal is calculated based on the ratio of the radius of each constellation in the constellation corresponding to the known APSK modulated signal. The calculation formula is as follows:

[0054]

[0055] In the formula, r 1 represents the radius of the first constellation ring in the constellation diagram corresponding to the processed signal, M represents the order of the transmitted APSK modulated signal, represents the average amplitude value of all processed signals, τ 1 Indicates the number of constellation points on the first constellation ring in the constellation diagram corresponding to the APSK modulated signal sent, p 2 Indicates the ratio of the radius of the second constellation ring to the radius of the first constellation ring in the constellation diagram corresponding to the APSK modulated signal, p v Indicates the ratio of the radius of the vth constellation ring to the radius of the first constellation ring in the constellation diagram corresponding to the APSK modulated signal, p V Indicates the ratio of the radius of the Vth constellation ring to the radius of the 1st constellation ring in the constellation diagram corresponding to the APSK modulated signal, p v ∈{p 1 ,p 2 ,…,p v ,…,p V},1<v<V, V represents the number of constellation rings in the constellation diagram corresponding to the APSK modulation signal, r 2 represents the radius of the second constellation ring in the constellation diagram corresponding to the processed signal, p 3 Indicates the ratio of the radius of the third constellation ring to the radius of the first constellation ring in the constellation diagram corresponding to the APSK modulated signal, r 3 represents the radius of the third constellation ring in the constellation diagram corresponding to the processed signal, r v represents the radius of the vth constellation ring in the constellation diagram corresponding to the processed signal, r v ∈{r 1 ,r 2 ,…,r v ,…,r V},1<v<V.

[0056] In some embodiments, in S4, according to the calculated constellation points C k , clustering is performed using the K-Means clustering algorithm, and the specific clustering process includes:

[0057] S401: Initialize each constellation point and use it as the initial cluster center C k .

[0058] The kth initial cluster center C k ∈{C 1 ,C 2 ,…,C k …,C K},1<k<K,{C 1 ,C 2 ,…,C k …,C K} represents the initial cluster center set divided by calculation, K represents the number of initial cluster centers, which is also the number of clusters during clustering; K = M, that is, the number of clusters of constellation point clustering is equal to the order of APSK modulated signal.

[0059] S402: Iteratively calculate each processed signal y′ n The Euclidean distance to each cluster center C is used to assign the processed signal to the cluster with the closest cluster center, and the convergent cluster center after clustering is obtained.

[0060] Furthermore, the Euclidean distance from each received signal to each cluster center is iteratively calculated, and the calculation formula is:

[0061]

[0062] Where dis(y′n,C) represents the Euclidean distance from the nth processed signal to each cluster center C, y′ n represents the nth processed signal, C represents the cluster centers in the clustering process, and N represents the length of the processed signal.

[0063] Furthermore, the clustering convergence center after clustering is specifically expressed as:

[0064]

[0065] In the formula, represents the kth cluster convergence center after clustering, y′ n represents the nth processed signal, y′ n ∈S k It means that the nth processed signal is clustered into the kth cluster, {S 1 ,S 2 ,…,S k …,S K} represents the K cluster sets after clustering, where S K represents the Kth cluster after clustering, |S k| represents the number of all processed signals in the kth cluster after clustering.

[0066] Figure 2 Schematic diagram of comparison between the constellation points of sending a 32APSK modulated signal and the constellation points before and after receiving the 32APSK clustering algorithm in an embodiment of the present invention.

[0067] Initial cluster center C k It is determined by the transmitter constellation diagram and the processed signal. Figure 2 As shown in the figure, the residual DC component will completely change the initial position of the signal and is limited by the ratio of the transmitter radius, so that the calculated initial cluster center is biased towards the center of the circle and cannot reach the optimal constellation point position. By calculating the Euclidean distance between the processed signal and the cluster center, the processed signal is clustered into the cluster center cluster with the minimum Euclidean distance. After all processed signals are iterated in this way, the processed signals in the cluster have high similarity and the cluster center is the mean of the processed signals in the cluster. Finally, this cluster center is the optimal constellation point. The optimal constellation point is the cluster convergence center. In summary, the cluster center can dynamically change with the processed signal affected by the residual DC component through the clustering algorithm, thereby eliminating the residual DC component.

[0068] After clustering in step S4, the residual DC component of the processed signal is eliminated, thereby improving the demodulation effectiveness.

[0069] Figure 3 Schematic diagram of Gray decimal system for sending constellation points of 32APSK modulation signals in an embodiment of the present invention.

[0070] Specifically, in S5, the cluster convergence center after clustering is As the theoretical value of the constellation point of the MAP algorithm, the MAP algorithm is used for soft demodulation, and the specific process includes:

[0071] The processed signal and constellation points in the signal space have their binary form. The binary form of each 32APSK processed signal and constellation point in the signal space is b 5 b 4 b 3 b 2 b 1 , generally speaking, the right side of the binary is the lowest bit b 1 . Constellation point bit b i ,0<i<6 is 1 and will be divided into the set The set whose i-th bit is "1" and the set whose i-th bit is 0 will be divided into the set The i-th bit is a set of "0". The binary signal after processing is unknown, so it is necessary to judge the possibility of each bit being decoded as "1" and "0" in turn. This possibility is the log-likelihood ratio information.1 Start calculating each processed signal to and The square of the Euclidean distance of the constellation points in the set is calculated, and each calculation result is compared with the noise power to take the negative exponential, and finally the processed signal is The sum is higher than Take the logarithm of and find the log-likelihood ratio information. i When the LLR is less than 0, it is decoded as "0", otherwise it is decoded as "1".

[0072] Furthermore, the log-likelihood ratio information is specifically expressed as:

[0073]

[0074] In the formula, LLR(b i ) represents bit b i The log-likelihood ratio information, and Represents bit b i The constellation point set with hard decision of "1" and "0" for different bit positions b i , whose constellation point set and The included constellation points are different, σ 2 is the variance of the additive white Gaussian noise, re(y′) represents the real part of the processed signal y′, im(y′) represents the imaginary part of the processed signal y′, Indicates constellation points The real part of Represents constellation points The imaginary part of .

[0075] Figure 4 This is a constellation point distribution diagram for sending a 32APSK modulated signal in an embodiment of the present invention.

[0076] For more specific description, the transmitting end of the embodiment of the present invention selects 32APSK modulation signal. Figure 4 As shown in the figure, assume that the radius of each ring of 32APSK is selected as [0.0491, 0.1280, 0.2227], then the average power of APSK signal is 0.0313. The FEC coding scheme is selected as Turbo code with 1 / 3 code rate and code length of 3840, and the wireless channel is selected as additive white Gaussian noise channel. Figure 4 In the figure, the constellation point coordinate set corresponding to the 32APSK modulation signal is represented as SET1, which is specifically:

[0077] SET1={0.0347+0.0347i,-0.0347+0.0347i,0.0347-0.0347i,-0.0347-0. 0347i,0.1236+0.0331i,-0.1236+0.0331i,0.1236-0.0331i,-0.1236-0.0 331i,0.0331+0.1236i,-0.0331+0.1236i,0.0331-0.1236i,-0.0331-0.12 36i,0.0905+0.0905i,-0.0905+0.0905i,0.0905-0.0905i,-0.0905-0.090 5i,0.0434+0.2184i,-0.0434+0.2184i,0.0434-0.2184i,-0.0434-0.2184 i,0.1237+0.1851i,-0.1237+0.1851i,0.1237-0.1851i,-0.1237-0.1851i ,0.2184+0.0434i,-0.2184+0.0434i,0.2184-0.0434i,-0.2184-0.0434i, 0.1851+0.1237i,-0.1851+0.1237i,0.1851-0.1237i,-0.1851-0.1237i}.

[0078] Demodulation is performed by following the steps below:

[0079] Step a: Estimate and eliminate the static DC component, specifically:

[0080] First, the real and imaginary parts of all received signals are added and averaged to estimate the static DC component value, that is, the mean value of all received signals. This represents the actual center position of each circle of the 32APSK constellation diagram after being affected by the channel DC component. The center point position is offset compared to the center point position of the known 32APSK constellation diagram at the transmitter.

[0081] Figure 5 Schematic diagram of an actual received signal and its DC component in an embodiment of the present invention.

[0082] Use formula (2) to add the real and imaginary parts of all received signals and average them to estimate the actual center point The received signal and the actual center point are Figure 5 shown.

[0083] Eliminating the static DC component, it can be expressed as:

[0084]

[0085] Step b: Initialize the K-Means cluster centers.

[0086] Specifically: for the processed signal y' after eliminating the static DC component, the relative positions of the constellation points in the constellation diagram corresponding to the processed signal y' are calculated based on the known ratio of the radii of each constellation ring in the constellation diagram corresponding to the transmission of 32APSK, and used as the initial clustering center of each cluster in the K-Means algorithm {C 1 ,C 2 ,…,C k ,C K},1<k<K.

[0087] Step b 1: Calculate the average amplitude value of the processed signal y'.

[0088] Specifically: Based on the processed signal y' after eliminating the static DC component, the average amplitude value of the processed signal y' is estimated using formula (3):

[0089] Step b2: Calculate the radius of each constellation ring in the constellation diagram corresponding to the processed signal y'.

[0090] Specific: Based on the above average amplitude value Based on the known relationship between the ratio of the radii of each constellation ring in the constellation diagram corresponding to the transmission of 32APSK, the radius of each constellation ring in the constellation diagram corresponding to the processed signal y' is calculated. In the case of the present invention, the transmitter knows that the APSK modulation order is 4+12+16, the total number of constellation rings is 3, and the ratio of the constellation ring radius is [1, 2.6069, 4.5356]. The new radius is calculated by formula (4) as [0.0628, 0.1638, 0.2850].

[0091] Step b3: Calculate each constellation point in the constellation diagram corresponding to the processed signal y'.

[0092] Specifically: The new radius value obtained in step b2 is used to calculate the new constellation point using formula (5), and is used as the initial clustering center of each cluster in the K-Means algorithm {C 1 ,C 2 ,…,C k ,C K},1<k<K.

[0093] Step c: Iteratively calculate the K-Means cluster center.

[0094] Specifically: According to the APSK modulation order, the processed signal y' is divided into K clusters, and based on the initial cluster center obtained in step b2, the convergence center of K-Means clustering is calculated by formula (6) or using the MATLAB library function kmeans It can be expressed as SET2.

[0095] Figure 6 This is the initial cluster center diagram of the signal after 32APSK processing in the embodiment of the present invention.

[0096] Since the modulation order of the APSK system selected in the embodiment of the present invention is 32, the received signal is divided into 32 clusters, and the coordinate set obtained in step b is set as the initial cluster center of the K-Means algorithm. Figure 6 shown.

[0097] Figure 7 It is a convergence cluster center diagram of the signal after 32APSK processing in an embodiment of the present invention.

[0098] The K-Means algorithm is used to estimate the 32 cluster convergence centers corresponding to the 32 clusters. Figure 7 As shown, after clustering, the convergent cluster center coordinate set of each cluster is obtained as SET2 = {0.0392+0.0292i, -0.0322+0.0308i, -0.0332-0.0402i, 0.0368-0.0392i, 0.1272+0.0276i, -0.1205+0.0274i, 0.1267-0 .0383i,-0.1215-0.0381i,0.0336+0.1189i,-0.0313+0.1187i,0.0363-0.126 7i,-0.0298-0.1273i,0.0934+0.0870i,-0.0881+0.0870i,0.0938-0.0962i,- 0.0891-0.0945i,0.0648+0.3016i,-0.0564+0.3029i,0.0650-0.3110i,-0.05 94-0.3082i,0.1756+0.2543i,-0.1695+0.2558i,0.1765-0.2615i,-0.1708-0 .2623i,0.3078+0.0580i,-0.3010+0.0536i,0.3083-0.0659i,-0.3033-0.063 1i,0.2629+0.1668i,-0.2571+0.1700i,0.2623-0.1790i,-0.2553-0.1790i}.

[0099] Step d: 32APSK soft demodulation.

[0100] Specifically: The cluster convergence center of each cluster obtained in step c As the theoretical value of the constellation point in the MAP algorithm, the received signal is soft-demodulated by the MAP algorithm, and the accurate log likelihood ratio (LLR) information is calculated using formula (8). Based on the log likelihood ratio information, each bit of the processed signal is judged, and finally a 32APSK demodulated signal is obtained.

[0101] Simulation verification:

[0102] By building a simulation link through MATLAB, under the additive white Gaussian noise (AWGN) channel, after the received signal passes through the Gaussian channel, a static DC component with a real part and an imaginary part of 0.0246 is generated, and a random disturbance of 0.1 times is added on this basis. Although the residual DC component has many forms of expression, the present invention takes the Euclidean distance between the received signal y and the center point of the receiving end constellation diagram as greater than or equal to (r 2 +r 3 ) / 2 received signal is multiplied by an offset factor of 1.48 to simulate the residual DC component.

[0103] Simulation results: Comparison of the bit error rate performance of the traditional MAP demodulation algorithm and the K-Means clustering-MAP demodulation algorithm. The forward error correction coding (FEC) scheme selects Turbo coding with a code length of 3840 and a code rate of 1 / 3. The signal to noise ratio (SNR) range is 6-7.6dB, the interval is 0.2dB, and the simulation is 10 -5 Second-rate.

[0104] Figure 8 This is a comparison chart of the bit error rate performance of the method proposed in the present invention and the MAP method. Figure 8 It can be seen that when the bit error rate performance reaches 10 -3 When , the proposed demodulation method has a performance improvement of about 0.25dB in bit error rate performance compared with the MAP method.

[0105] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An APSK demodulation method based on K-Means clustering, characterized in that: The method includes: The transmitter sends an APSK modulated signal, and the constellation diagram corresponding to the signal is known; The receiving end receives the signal, estimates and eliminates the static DC component of the received signal, and obtains a processed signal; According to the constellation diagram corresponding to the APSK modulated signal and the processed signal, the constellation points C of the processed signal are calculated. k ; According to the calculated constellation points C k , clustering is performed using the K-Means clustering algorithm; The cluster convergence center after clustering As the theoretical value of the constellation point of the MAP algorithm, the MAP algorithm is used for soft demodulation to obtain the log-likelihood ratio information.

2. The APSK demodulation method based on K-Means clustering according to claim 1, characterized in that: The processed signal is expressed as: Where y' represents the processed signal after eliminating the static DC component, y n represents the nth received signal, represents the mean of all received signals, N represents the length of the received signal, re(·) represents the real part operation, im(·) represents the imaginary part operation, and i represents the imaginary unit.

3. The APSK demodulation method based on K-Means clustering according to claim 1, characterized in that: Calculate the constellation points C of the processed signal k , the calculation process includes: Calculate the corresponding average amplitude value based on all processed signals; According to the average amplitude value of all processed signals and the ratio of the radii of each constellation ring in the constellation diagram corresponding to the known APSK modulated signal to be transmitted, and calculating the radii of each constellation ring in the constellation diagram corresponding to the processed signal; According to the calculated radius of each constellation ring in the constellation diagram corresponding to the processed signal, the constellation point is calculated, which is specifically expressed as: C k =r v exp(2πθ v,k ·i) In the formula, C k represents the kth constellation point in the constellation diagram corresponding to the processed signal, r v represents the radius of the vth constellation ring in the constellation diagram corresponding to the processed signal, θ v,k represents the angle of the kth constellation point on the vth constellation ring in the constellation diagram corresponding to the processed signal, and i represents an imaginary unit.

4. The APSK demodulation method based on K-Means clustering according to claim 3, characterized in that: Estimate the average amplitude of all processed signals. The calculation formula is as follows: In the formula, represents the average amplitude value of all processed signals, N represents the length of the processed signal, y′ n represents the nth processed signal after eliminating the static DC component, re(·) represents the real part operation, and im(·) represents the imaginary part operation.

5. The APSK demodulation method based on K-Means clustering according to claim 3, characterized in that: The radius of each constellation ring in the constellation diagram corresponding to the processed signal is calculated, and the calculation formula is specifically as follows: r2＝r1p2 r3＝r1p3 r v ＝r1p v Wherein, r1 represents the radius of the first constellation ring in the constellation diagram corresponding to the processed signal, M represents the order of the transmitted APSK modulated signal, represents the average amplitude value of all processed signals, τ1 represents the number of constellation points on the first constellation ring in the constellation diagram corresponding to the APSK modulated signal, p2 represents the ratio of the radius of the second constellation ring to the radius of the first constellation ring in the constellation diagram corresponding to the APSK modulated signal, and p v Indicates the ratio of the radius of the vth constellation ring to the radius of the first constellation ring in the constellation diagram corresponding to the APSK modulated signal, p V Indicates the ratio of the radius of the Vth constellation ring to the radius of the 1st constellation ring in the constellation diagram corresponding to the APSK modulated signal, p v ∈{p1,p2,…,p v ,…,p V },1<v<V, V represents the number of constellation rings in the constellation diagram corresponding to the APSK modulated signal, r2 represents the radius of the second constellation ring in the constellation diagram corresponding to the processed signal, p3 represents the ratio of the radius of the third constellation ring in the constellation diagram corresponding to the APSK modulated signal to the radius of the first constellation ring, r3 represents the radius of the third constellation ring in the constellation diagram corresponding to the processed signal, r v represents the radius of the vth constellation ring in the constellation diagram corresponding to the processed signal, r v ∈{r1,r2,…,r v ,…,r V },1<v<V.

6. The APSK demodulation method based on K-Means clustering according to claim 1, characterized in that: According to the calculated constellation points C k , clustering is performed using the K-Means clustering algorithm, and the specific clustering process includes: Initialize the constellation points and use them as the initial cluster center C k ; Iteratively calculate each processed signal y′ n The Euclidean distance to each cluster center C is used to assign the processed signal to the cluster with the closest cluster center, and the cluster convergence center after clustering is obtained.

7. The APSK demodulation method based on K-Means clustering according to claim 6, characterized in that: Iteratively calculate each processed signal y′ n The Euclidean distance to each cluster center C is calculated as: Where dis(y′n,C) represents the Euclidean distance from the nth processed signal to each cluster center, y′ n represents the nth processed signal, C represents the cluster centers in the clustering process, and N represents the length of the processed signal.

8. The APSK demodulation method based on K-Means clustering according to claim 6, characterized in that: The clustering convergence center after clustering is specifically expressed as: Sk∈{S1,S2,…,S k …,S K } In the formula, represents the kth cluster convergence center after clustering, y′ n represents the nth processed signal, y′ n ∈S k represents the nth processed signal in the kth cluster, {S1,S2,…,S k …,S K } represents the K cluster sets after clustering, where S K represents the Kth cluster after clustering, |S k | represents the number of all processed signals in the kth cluster after clustering.

9. The APSK demodulation method based on K-Means clustering according to claim 1, characterized in that: The log-likelihood ratio information is specifically expressed as: In the formula, LLR(b i ) represents bit b i The log-likelihood ratio information, and Represents bit b i The constellation point set with hard decision "1" and "0" for different bit positions b i , whose constellation point set and The included constellation points are different, σ 2 is the variance of the additive white Gaussian noise, re(y′) represents the real part of the processed signal y′, im(y′) represents the imaginary part of the processed signal y′, Indicates constellation points The real part of Represents constellation points The imaginary part of .

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