A method for blind separation of PCMA signals

Abstract

This invention discloses a method for blind separation of PCMA signals, mainly addressing the problems of high computational complexity and difficulty in separating two QPSK signals with similar amplitudes in existing technologies. The implementation scheme is as follows: receiving a single PCMA signal and estimating its parameters; demodulating the PCMA signal using the estimated parameters to obtain cosine and sine demodulated signals; using the K-means algorithm to cluster the demodulated sequence; calculating the total variance using cluster centroids to determine sampling invariant points; tabulating the signal state after PCMA demodulation using sampling invariant points; replacing each point in its cluster with the cluster centroids, and performing symbol decision based on the signal state table to obtain the symbol sequences of the two uplink signals, thus completing the blind separation of the PCMA signal. This invention offers high flexibility, low computational complexity, high separation accuracy, and significant engineering application value, and can be used in PCMA satellite communication systems composed of two QPSK signals with different amplitudes and initial phases.

Description

Technical Field

[0001] This invention belongs to the field of communication technology and relates to paired carrier multiple access (PCMA) signal processing, which can be used in PCMA satellite communication systems. Background Technology

[0002] Paired Carrier Multiple Access (PCMA) is an emerging communication technology used to improve the bandwidth utilization of satellite channels. In PCMA satellite communication systems, because two different ground stations share the uplink and downlink, the uplink signals transmitted by the two satellite terminals occupy the same frequency band, and these two uplink signals overlap in the time domain. In certain special situations, it is necessary to extract the information sequence transmitted by both communicating parties from the PCMA signal. For example, in some special situations, it is necessary to intercept intelligence as a third party. In such cases, traditional PCMA technology cannot be used in non-cooperative communications.

[0003] From the perspective of signal separation, acquiring PCMA signals involves separating the two uplink signals from a single sensor's received PCMA signal; this is a single-channel blind separation problem. Since the two uplink signals constituting a PCMA signal have identical frequencies, time slots, and symbol rates, and their power is comparable, traditional single-channel blind separation algorithms based on different power, symbol rates, and rollover coefficients cannot solve this problem. Existing technologies commonly use particle filtering algorithms and the successive Path Per Spectrum (PSP) method to address the single-channel blind separation problem in communication signals.

[0004] Patent application CN11526103A discloses a patent application for a "single-channel blind separation method for PCMA signals." This method first performs initial estimations of the signal and channel parameters, then establishes multiple state distributions based on a particle filter framework, introduces a genetic evolution mechanism for particle resampling, and finally incorporates a binary search method to optimize the channel parameters, retaining the optimal particle. While this method improves the robustness of modulation channel parameter estimation errors through improvements to the weight update step, its complexity remains relatively high.

[0005] In their paper "Blind Separation Algorithm for PCMA Signals with Different Symbol Rates Based on DG-PSP," Guo Yiming et al. proposed a dual-grid, surviving-path-by-survival separation algorithm, DG-PSP. The algorithm first constructs a mixed-signal model for PCMA signals with different symbol rates, treating the channel state and input of the two signal components as two sets of dynamic grids. By iteratively updating the states of the two sets of grids, the mixed signal is reconstructed, thus achieving blind separation of PCMA signals. This algorithm effectively solves the problem of blind separation of PCMA signals with different symbol rates, but its performance is significantly affected by the amplitude ratio of the two signal components. When the amplitude ratios of the two signals are close, the bit error rate is high, and the demodulation performance is unstable. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the prior art by proposing a PCMA signal blind separation method, which reduces the computational complexity of the PCMA signal blind separation algorithm, achieves effective separation when the amplitudes of two QPSK signals are close, and improves the stability of demodulation performance.

[0007] The technical approach to achieve the objective of this invention is as follows: by using a group separation method, the variance of the demodulated signal is calculated to determine the sampling invariant point, avoiding particle sampling and weight updates at each time step, thereby reducing computational complexity. By introducing the K-means clustering algorithm to cluster the signal and making a decision on the demodulated PCMA signal type, effective separation is achieved when the amplitudes of the two QPSK signals are similar.

[0008] Based on the above ideas, the implementation steps of this invention are as follows:

[0009] (1) Receive the PCMA signal y(t) and estimate its parameters;

[0010] (2) The PCMA signal is demodulated using the estimated parameters. Each sampling point in the demodulated signal is used as the starting point to obtain different signal sequences, including one cosine demodulated signal sequence s. LI (t m ) and a sinusoidal demodulated signal sequence s LQ (t m );

[0011] (3) The sequence s LI (t m ) and s LQ (t m The signal is converted into a two-dimensional scatter image to obtain a constellation diagram corresponding to the two signal sequences. The constellation diagram is then clustered using the K-means clustering algorithm to obtain N clusters and their center points. The value of N is determined according to the signal type.

[0012] (4) Using the cluster center point, calculate the variance of the constellation points in each cluster of each constellation diagram; select the sampling points that meet the sampling invariant point condition from all the sampling points corresponding to the total variance as the sampling invariant points;

[0013] (5) Using the sampling invariant points, tabulate the signal state after PCMA demodulation so that different baseband symbols correspond to different clusters in the constellation diagram;

[0014] (6) Use the cluster center point to replace each point in its own cluster, make symbol decisions according to the signal state table, obtain the symbol sequence of the two uplink signals, and complete the blind separation of the PCMA signal.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] First, this invention directly demodulates the PCMA signal y(t) using the estimated parameters, and uses the K-means clustering algorithm to process a cosine demodulated signal sequence s. LI (t n ) and a sinusoidal demodulated signal sequence s LQ (t n The clustering partitioning method calculates the total variance to determine the sampling invariant points, and then converts the sampling sequence into a two-dimensional scatter plot and uses a state table to make symbol decisions. This method overcomes the shortcomings of existing technologies based on particle filter algorithms, such as complex models, large computational load, and limited application scope. As a result, this invention has the advantages of high flexibility and low computational complexity.

[0017] Second, this invention uses demodulation formulas to create tables, uses the center point of each cluster to replace other points in the cluster, and uses the average value between each pair of cluster center points as a decision condition, thereby achieving a one-to-one correspondence between cluster center points and state tables, making this invention more adaptable and of higher engineering application value. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0019] Figure 2 This is a schematic diagram of the PCMA communication link in this invention;

[0020] Figure 3 This is a two-dimensional scatter plot in this invention;

[0021] Figure 4 This is a graph showing the bit error rate of the two QPSK signals in this invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0023] It should be noted that the step numbers in the specification and claims of this invention are only for the purpose of clearly describing the embodiments of this invention and facilitating understanding, and their order is not limited.

[0024] like Figure 2As shown, the implementation scenario of this example includes two communication stations, 1 and 2, which transmit uplink signals using the same frequency, time slot, and spreading code. and These two uplink signals, after passing through a transparent satellite transponder, correspond to the downlink signals respectively. and Therefore, ignoring noise, the downlink signals received by communication station 1 and communication station 2 are both

[0025] Uplink signal and The complex baseband form of the constructed PCMA mixed signal is expressed as follows:

[0026]

[0027] In the formula: y1(t) and y2(t) are uplink signals transmitted by two different satellite stations, h1 and h2 are the instantaneous amplitudes corresponding to y1(t) and y2(t) respectively, Δω1 and Δω2 are the residual carrier frequencies corresponding to y1(t) and y2(t) respectively, θ1 and θ2 are the initial phases corresponding to y1(t) and y2(t) respectively, and v(t) is a frequency with variance σ 2 The additive white Gaussian noise, x1(t) and x2(t) are two baseband signals, and their expressions are as follows:

[0028]

[0029] In the formula a i,n For the nth symbol sent via the i-th path; g i (t) is the equivalent channel filter, T is the symbol period; τ i Let τ be the channel transmission delay of the i-th uplink signal, satisfying 0 ≤ τ i ≤T.

[0030] In this embodiment of the invention, both baseband signals x1(t) and x2(t) are shaped using raised cosine roll forming. Therefore, the impulse response function g of the shaping filter used for these two baseband signals is... i The expression for (t) is as follows:

[0031]

[0032] Where α i The coefficient of the raised cosine roll.

[0033] Reference Figure 1 In the above scenario, the implementation steps of this embodiment are as follows:

[0034] Step 1: A single sensor receives the PCMA signal y(t) and performs parameter estimation on it.

[0035] 1.1) Squaring y(t) yields y. 2 The amplitude-frequency response of (t) is used to obtain the symbol rate f of the two quadrature phase shift keying (QPSK) signals. d1 f d2 ;

[0036] 1.2) Perform a fourth power operation on y(t) to find y. 4 The amplitude-frequency response of (t) is used to obtain the carrier frequency f of the two QPSK signals. c1 f c2 ;

[0037] 1.3) Introduce an auxiliary signal to y(t) to obtain the initial phase θ. i :

[0038] 1.3.1) Multiply y(t) by Obtain auxiliary signal Regarding the auxiliary signal z i (t) is raised to the fourth power and the expected value is calculated.

[0039]

[0040] Among them, a i,n τ is the complex symbol in the i-th signal. i Let g be the time delay of the i-th signal. i (t) is the equivalent filter for the i-th signal, and T is the symbol period;

[0041] 1.3.2) Based on the expected value Find the initial phase θ i :

[0042] Based on the independent nature of the two signals in the mixed signal, ignoring the cross term in the fourth power (i.e., the second term), and according to the constant mode property of digital modulation, we know that:

[0043]

[0044] From this equation, we obtain The following simplified form:

[0045]

[0046] right By performing a complex number to determine the phase, we obtain the following equation:

[0047]

[0048] From the above formula, we get

[0049]

[0050] Where arg(·) represents the phase of a complex number.

[0051] The final estimated parameters obtained in this step are the symbol rates f of the two QPSK signals. d1 f d2 Carrier frequency f c1 f c2 , initial phases θ1, θ2.

[0052] Step 2: Demodulate the PCMA signal using the estimated parameters.

[0053] 2.1) Assume uplink signal and The modulation method is QPSK modulation, let s1(t) represent s2(t) represents Its representation is as follows:

[0054]

[0055] In the formula, a 1,n It is the I-channel symbol of the first signal at time n, b 1,n It is the Q-channel symbol of the first signal at time n, a 2,n It is the I-channel symbol of the second signal at time n, b 2,n A1 is the Q-channel symbol of the second signal at time n; A2 is the amplitude of the first signal; g(t) is the normalized symbol shaping function; f c1 f represents the carrier frequency of the first QPSK signal. c2 θ1 is the carrier frequency of the second QPSK signal; θ2 is the initial phase of the first QPSK signal; τ1 is the delay of the first QPSK signal; τ2 is the delay of the second QPSK signal.

[0056] 2.2) From the uplink signal and The PCMA signal s(t) is represented as follows:

[0057] s(t) = s1(t) + s2(t) + v(t)

[0058] Where v(t) is a variable with variance σ 2 Additive white Gaussian noise;

[0059] 2.3) Using the estimated carrier frequency and the first meeting Construct a cosine carrier wave of a signal and sinusoidal carrier in

[0060] 2.4) Ignoring v(t), multiply the cosine carrier and sine carrier of one signal by the mixed-modulation signal s(t), and then pass it through a low-pass filter to obtain a cosine demodulated signal s. LI (t) and a sinusoidal demodulated signal s LQ (t):

[0061]

[0062] in, θ1 is the initial phase estimate of the first QPSK signal, and θ2 is the initial phase estimate of the second QPSK signal. It is the carrier frequency estimate of the first QPSK signal, ω c2 It is the carrier frequency of the second QPSK signal.

[0063] Step 3: Obtain different signal sequences based on the demodulated signal.

[0064] 3.1) Demodulate one cosine signal s LI Each sampling point in (t) serves as the starting point, resulting in a different cosine demodulated signal sequence s. LI (t m ):

[0065]

[0066] Among them, s LI (t m ) is a cosine-demodulated signal sequence, t m It is the starting point of the sampling point.

[0067] 3.2) Demodulate one sinusoidal signal s LQ Each sampling point in (t) serves as the starting point, resulting in a different sinusoidal demodulated signal sequence s. LQ (t m ):

[0068]

[0069] Among them, s LQ (t m ) is a sinusoidal demodulated signal sequence, t m It is the starting point of the sampling point.

[0070] Step 4, using the cosine demodulated signal sequence s LI (t m ) and a sinusoidal demodulated signal sequence s LQ (t m A constellation diagram is constructed and then clustered.

[0071] 4.1) Demodulate one cosine signal sequence sLI (t m Using s as the horizontal axis, a sinusoidal demodulated signal sequence s is plotted. LQ (t m Using the vertical axis as the y-axis, a two-dimensional scatter plot is formed, i.e., a constellation plot;

[0072] 4.2) Clustering the constellation diagram:

[0073] Existing clustering algorithms include K-means, hierarchical clustering, and fuzzy C-means. This embodiment uses, but is not limited to, the K-means clustering algorithm to cluster the constellation diagram. The specific implementation is as follows:

[0074] 4.2.1) For a QPSK hybrid PCMA signal, let the number of cluster points N = 16. Randomly select 16 data points in the graph as the initial cluster centers and divide the graph into 16 different clusters.

[0075] 4.2.2) Calculate the distance between each data point and the 16 cluster centers, and assign each data point to the cluster to which its nearest cluster center belongs;

[0076] 4.2.3) Recalculate the centroid for each cluster, i.e., take the average of all data points within the cluster as the new centroid;

[0077] 4.2.4) Repeat steps (4.2.2) and (4.2.3) until the cluster center points no longer change significantly and the total distance between each data point and its cluster center point is minimized, finally obtaining 16 clusters after clustering.

[0078] Step 5: Using the cluster center point, calculate the variance of the constellation points in each cluster of the constellation diagram to obtain the sampling invariant points.

[0079] 5.1) Represent the 16 cluster centers as a center point set.

[0080]

[0081] in, This represents the center point of the i-th cluster, where 1 ≤ i ≤ 16;

[0082] 5.2) For each cluster of data points, calculate the sum of squared differences between the data points and the cluster center, then divide by the total number of data points in that cluster to obtain the variance D of that cluster. i :

[0083]

[0084] In the formula, K represents a two-dimensional data point in the i-th cluster. iThis represents the total number of data points in the i-th cluster;

[0085] 5.3) Calculate the sum of the variances of the 16 clusters to obtain the total variance D:

[0086]

[0087] 5.4) Set the sampling invariant point condition, that is, take the sampling starting point where the total variance D reaches the minimum value as the sampling invariant point.

[0088] Step 6: Using the sampling invariant points, tabulate the signal state after PCMA demodulation.

[0089] 6.1) Under the condition of sampling invariance, ignoring time delay, the cosine demodulation sequence s LI (t m1 The expression is divided into the following three items:

[0090] First item:

[0091] Second item:

[0092] Third item:

[0093] 6.2) Based on a cosine demodulated signal sequence s LI (t m1 The three separated parts are listed in the signal status table, as shown in Table 1:

[0094] Table 1s LI (t m1 ) signal status table

[0095]

[0096] In Table 1: the first 3 columns are a 1,n a 2,n b 2,n The values ​​of these three code elements are {0, 1}.

[0097] Column 4 is s LI (t m1 ) in a 1,n a 2,n b 2,n The expression for taking different symbols, where G is the value sampled by the filter at the sampling invariant point.

[0098] Column 5 is s LI (t m1 The relative values ​​of ) are represented by the corresponding numbers {-4,-3,-2,-1,+1,+2,+3,+4}, and the correspondence is only related to the parameter settings of the two QPSK signals;

[0099] 6.3) Under the condition of sampling invariance, ignoring time delay, the sinusoidal demodulation sequence s LQ (t m1 The expression is divided into the following three items:

[0100] First item:

[0101] Second item:

[0102] Third item:

[0103] 6.4) Based on a sinusoidal demodulated signal sequence s LQ (t m1 The three separated parts are listed in the signal status table, as shown in Table 2:

[0104] Table 2s LQ (t m1 ) signal status table

[0105]

[0106] In Table 2: the first three columns are b 1,n a 2,n b 2,n The values ​​of these three code elements are {0, 1}.

[0107] Column 4 is s LQ (t m1 ) in b 1,n a 2,n b 2,n The expression for taking different symbols, where G is the value sampled by the filter at the sampling invariant point.

[0108] Column 5 is s LQ (t m1 The relative values ​​of ) are represented by the corresponding numbers {-4,-3,-2,-1,+1,+2,+3,+4}, and the correspondence is only related to the parameter settings of the two QPSK signals.

[0109] Step 7: Replace each point in its own cluster with the cluster center point, make symbol decisions according to the signal state table, obtain the symbol sequence of the two uplink signals, and complete the blind separation of the PCMA signal.

[0110] 7.1) Calculate the mean (MeanI, MeanQ) of every two neighboring cluster centers:

[0111]

[0112] Where, meanI(j) is sLI (t m1 The mean of the j-th center and the (j+1)-th center, meanQ(j) is s. LQ (t m1 The mean of the j-th center and the (j+1)-th center of the two QPSK signals is N = 16, 1 ≤ j ≤ 7.

[0113] 7.2) Demodulate the cosine signal sequence s LI (t m1 The mean I(j) between the pairwise center points of the signal is used as a threshold and compared with the sequence to determine the code elements of the two signals:

[0114] If s LI (t m1 If ) < meanI(1), then the I-way code element a of the first signal is... 1n =0, the I-code element a of the second signal 2n =0, Q-code element b of the second signal 2n =1;

[0115] If s LI (t m1 )≥meanI(1), and s LI (t m1 If ) < meanI(2), then the I-way code element a of the first signal is... 1n =0, the I-code element a of the second signal 2n =0, Q-channel code element b of the second signal 2n =0;

[0116] If s LI (t m1 )≥meanI(2), and s LI (t m1 If ) < meanI(3), then the I-way code element a of the first signal is... 1n =0, the I-code element a of the second signal 2n =1, Q-channel code element b of the second signal 2n =1;

[0117] If s LI (t m1 )≥meanI(3), and s LI (t m1 If ) < meanI(4), then the I-way code element a of the first signal is... 1n =1, the symbol a of the I-path of the second signal. 2n =0, Q-channel code element b of the second signal 2n =1;

[0118] If sLI (t m1 )≥meanI(4), and s LI (t m1 If ) < meanI(5), then the I-way code element a of the first signal is... 1n =0, the I-code element a of the second signal 2n =1, Q-channel code element b of the second signal 2n =0;

[0119] If s LI (t m1 )≥meanI(5), and s LI (t m1 If ) < meanI(6), then the I-way code element a of the first signal is... 1n =1, the I-channel symbol a of the second signal 2n =0, Q-channel code element b of the second signal 2n =0;

[0120] If s LI (t m1 )≥meanI(6), and s LI (t m1 If ) < meanI(7), then the I-way code element a of the first signal is... 1n =1, the I-channel symbol a of the second signal 2n =1, Q-channel code element b of the second signal 2n =1;

[0121] If s LI (t m1 If )≥meanI(7), then the I-way code element a of the first signal is... 1n =1, the I-channel symbol a of the second signal 2n =1, Q-channel code element b of the second signal 2n =0;

[0122] 7.3) Demodulate the sinusoidal signal sequence s LQ (t m1 The mean Q(j) between the pairwise center points of the signal is used as a threshold and compared with the sequence to determine the code elements of the two signals:

[0123] If s LQ (t m1 If ) < meanQ(1), then the Q-code elements b of the first signal are... 1n =0, the I-code element a of the second signal 2n =0, Q-channel code element b of the second signal 2n =0;

[0124] If s LQ (tm1 )≥meanQ(1), and s LQ (t m1 If ) < meanQ(2), then the Q-code element b of the first signal is... 1n =0, the I-code element a of the second signal 2n =1, Q-channel code element b of the second signal 2n =0;

[0125] If s LQ (t m1 )≥meanQ(2), and s LQ (t m1 If ) < meanQ(3), then the Q-code element b of the first signal is... 1n =0, the I-code element a of the second signal 2n =0, Q-channel code element b of the second signal 2n =1;

[0126] If s LQ (t m1 )≥meanQ(3), and s LQ (t m1 If ) < meanQ(4), then the Q-code element b of the first signal is... 1n =1, the I-channel symbol a of the second signal 2n =0, Q-channel code element b of the second signal 2n =0;

[0127] If s LQ (t m1 )≥meanQ(4), and s LQ (t m1 If ) < meanQ(5), then the Q-code element b of the first signal is... 1n =0, the I-code element a of the second signal 2n =1, Q-channel code element b of the second signal 2n =1;

[0128] If s LQ (t m1 )≥meanQ(5), and s LQ (t m1 If ) < meanQ(6), then the Q-code element b of the first signal is... 1n =1, the I-channel symbol a of the second signal 2n =1, Q-channel code element b of the second signal 2n =0;

[0129] If s LQ (t m1 )≥meanQ(6), and s LQ (tm1 If ) < meanQ(7), then the Q-code element b of the first signal is... 1n =1, the I-channel symbol a of the second signal 2n =0, Q-channel code element b of the second signal 2n =1;

[0130] If s LQ (t m1 If )≥meanQ(7), then the Q-code element b of the first signal is... 1n =1, the I-channel symbol a of the second signal 2n =1, Q-channel code element b of the second signal 2n =1;

[0131] 7.5) Calculate a at time n above. 1n b 1n a 2n b 2n The symbol states are combined in pairs, where:

[0132] a 1n With b 1n The combination yields the baseband symbol sequence of the first QPSK channel: B1 = {a 11 ,b 11 ,a 12 ,b 12 ,a 13 ,b 13 ,…};

[0133] a 2n With b 2n The combination yields the baseband symbol sequence of the second QPSK: B2 = {a 21 ,b 21 ,a 22 ,b 22 ,a 23 ,b 23 ,…};

[0134] Finally, the baseband symbol sequences B1 and B2 of the two uplink signals are obtained, completing the blind separation of the signals.

[0135] The technical effects of the present invention will be further explained below with reference to simulation experiments.

[0136] 1. Simulation experimental conditions:

[0137] The simulation experiment hardware platform of this invention is: Intel(R) Core(TM) i5-8250U CPU with a main frequency of 1.60GHz and 8GB of memory.

[0138] The simulation experiment software platform of this invention is: Windows 10 operating system and MATLAB R2018b software.

[0139] Experimental parameter settings: A single sensor receives two QPSK hybrid modulated PCMA signals. In the simulation, the channel noise is Gaussian white noise, and the carrier-to-noise ratio (CNR) is used as the measure of noise magnitude.

[0140] The parameters for the two signals s1(t) and s2(t) are set as follows: symbol period T = 10. -6 The residual frequency offset Δω1 = 0 rad / s, amplitude A1 = 10, initial phase θ1 = 0, and timing deviation τ1 = 0 for the first uplink signal s1(t); the residual frequency offset Δω2 = 0 rad / s, amplitude A2 = 9.5, initial phase θ2 = π / 8, and timing deviation τ2 = 0 for the second uplink signal s2(t). The rolling coefficient of the shaping waveform generator in the experiment is 0.35.

[0141] 2. Simulation content and result analysis:

[0142] Simulation 1: Under the above conditions, this invention is used to separate QPSK-mixed PCMA signals at a carrier-to-noise ratio (CNR) of 14 dB. First, the K-means algorithm is used to cluster the two-dimensional scatter plot formed by the demodulated sequences. The total variance is calculated using the cluster centers to determine the sample-invariant points. Based on these sample-invariant points, a two-dimensional scatter plot composed of the cosine and sine demodulated sequences is obtained. The results are as follows: Figure 3 Where the horizontal axis represents the cosine demodulation sequence s. LI (t m1 The vertical axis represents the sinusoidal demodulation sequence s. LQ (t m1 ).

[0143] from Figure 3 As can be seen, there are 16 clusters in the scatter plot, and the cluster centers are separate, indicating that the present invention can successfully determine the sampling invariant points by using the K-means algorithm.

[0144] Simulation 2: Under the above conditions, this invention is used to separate QPSK-mixed PCMA signals at different carrier-to-noise ratios. First, the K-means algorithm is used to cluster the two-dimensional scatter plot of the demodulated sequences. The total variance is calculated using the cluster centers to determine the sampling invariant points. Then, a state table is created for the cosine and sine demodulated signals. Symbol discrimination is performed based on the state distribution in the table, ultimately achieving the separation of the PCMA signals. The results are as follows: Figure 4 The horizontal axis represents the carrier-to-noise ratio, and the vertical axis represents the bit error rate. In the figure, QPSK-1 represents the first uplink signal, and QPSK-2 represents the second uplink signal.

[0145] from Figure 4 As can be seen, when the carrier-to-noise ratio (CNR) is between 8dB and 18dB, the bit error rates of the two QPSK signals are similar, meaning their separation accuracy is comparable.

[0146] At a carrier-to-noise ratio (CNR) of 8 dB, the separation accuracy reaches 90%.

[0147] At a carrier-to-noise ratio of 13dB, the separation accuracy reaches 99%.

[0148] The separation accuracy reaches 99.9% at a carrier-to-noise ratio of 16dB.

[0149] At a carrier-to-noise ratio of 18dB, the separation accuracy reached 99.99%.

[0150] Simulation results show that the present invention can maintain a high separation accuracy even under low carrier-to-noise ratio conditions.

Claims

1. A method for blind separation of PCMA signals, characterized in that, Includes the following steps: (1) Receive the PCMA signal y(t) and estimate its parameters; (2) The PCMA signal is demodulated using the estimated parameters. Each sampling point in the demodulated signal is used as the starting point to obtain different signal sequences, including one cosine demodulated signal sequence s. LI (t m ) and a sinusoidal demodulated signal sequence s LQ (t m ); (3) The sequence s LI (t m ) and s LQ (t m The signal is converted into a two-dimensional scatter image to obtain a constellation diagram corresponding to the two signal sequences. The constellation diagram is then clustered using the K-means clustering algorithm to obtain N clusters and their center points. The value of N is determined according to the signal type. (4) Using the cluster center point, calculate the variance of the constellation points in each cluster of each constellation diagram; select the sampling points that meet the sampling invariant point condition from all the sampling points corresponding to the total variance as the sampling invariant points; (5) Using the sampling invariant points, tabulate the signal state after PCMA demodulation so that different baseband symbols correspond to different clusters in the constellation diagram; (6) Use the cluster center point to replace each point in its own cluster, make symbol decisions according to the signal state table, obtain the symbol sequence of the two uplink signals, and complete the blind separation of the PCMA signal.

2. The method according to claim 1, characterized in that, The PCMA signal in step (1) is represented as follows: In the formula: y1(t) and y2(t) are uplink signals transmitted by two different satellite stations, h1 and h2 are the instantaneous amplitudes corresponding to y1(t) and y2(t) respectively, Δω1 and Δω2 are the residual carrier frequencies corresponding to y1(t) and y2(t) respectively, θ1 and θ2 are the initial phases corresponding to y1(t) and y2(t) respectively, and v(t) is a frequency with variance σ 2 The additive white Gaussian noise, x1(t) and x2(t) are two baseband signals, and their expressions are as follows: In the formula a i,n For the nth symbol sent via the i-th path; g i (t) is the equivalent channel filter, T is the symbol period; τ i Let τ be the channel transmission delay of the i-th uplink signal, satisfying 0 ≤ τ i ≤T.

3. The method according to claim 1, characterized in that, In step (1), parameter estimation of the PCMA signal y(t) is performed as follows: (1a) Squaring y(t) yields y. 2 The amplitude-frequency response of (t) is used to obtain the symbol rate f of the two QPSK signals. d1 f d2 ; (1b) Perform a fourth power operation on y(t) to find y 4 The amplitude-frequency response of (t) is used to obtain the carrier frequency f of the two QPSK signals. c1 f c2 ; (1c) Introduce an auxiliary signal to y(t) to obtain the initial phase θ i : (1c1) Multiply y(t) by Obtain auxiliary signal Regarding the auxiliary signal z i (t) Perform fourth power calculation and calculate the expected value. Among them, a i,n τ is the complex symbol in the i-th signal. i Let g be the time delay of the i-th signal. i (t) is the equivalent filter for the i-th signal, and T is the symbol period; (1c2) Based on the independent characteristics of the two signals in the mixed signal, ignoring the cross term in the fourth power (i.e., the second term), and further from the constant mode property of digital modulation, we obtain... The following simplified form: (1c3) to By performing a complex phase calculation, we obtain the following formula: From the above formula, we get Where arg(·) represents the phase of a complex number.

4. The method according to claim 1, characterized in that, Step (2) is implemented as follows: (2a) Demodulate the PCMA signal using the estimated carrier frequency and initial relative frequency: (2a1) Let the modulation signal s i (t) is of type QPSK, and its representation is as follows: (2a2) Suppose that the PCMA signal s(t) is a QPSK hybrid modulated signal, which is represented as follows: (2a3) Using the estimated carrier frequency and the first meeting Construct a cosine carrier wave of a signal and sinusoidal carrier in (2a4) Multiply the cosine carrier and sine carrier of one signal by the mixed-modulation signal s(t), and then pass it through a low-pass filter to obtain the demodulated cosine demodulated signal s. LI (t) and a sinusoidal demodulated signal s LQ (t): In the formula, a 1,n It is the first signal I-channel symbol at time n, b 1,n It is the first signal Q-channel symbol at time n, a 2,n It is the second signal I-channel symbol at time n, b 2,n is the Q-channel symbol of the second signal at time n; g(t) is the normalized symbol shaping function, A1 is the amplitude of the first signal, and A2 is the amplitude of the second signal; θ2 represents the initial phase estimate of the first QPSK signal, and θ2 is the initial phase of the second QPSK signal. The carrier frequency estimate representing the first QPSK signal, ω c2 The carrier frequency representing the second QPSK signal; (2b) Taking each sampling point in the demodulated signal as the starting point, different signal sequences are obtained, as shown below: Among them, s LI (t m ) is a cosine-demodulated signal sequence, s LQ (t m ) is a sinusoidal demodulated signal sequence, t m It is the starting point of the sampling point.

5. The method according to claim 1, characterized in that, In step (3), the K-means clustering algorithm is used to cluster the constellation diagram. The steps include the following: (3a) Use a cosine demodulation signal sequence s LI (t m ) and a sinusoidal demodulated signal sequence s LQ (t m A two-dimensional discrete sequence is constructed, and N data points are randomly selected as the initial cluster centers, and the entire sequence is divided into N different clusters. (3b) Calculate the distance between each data point and the N cluster centers, and assign each data point to the cluster to which the nearest cluster center belongs; (3c) Recalculate the center point for each cluster, that is, take the average value of all data points in the cluster as the new center point; (3d) Repeat steps (3b) and (3c) until the changes in the cluster centers are no longer significant and the total distance between each data point and its cluster center is minimized, finally obtaining N clusters after clustering.

6. The method according to claim 1, characterized in that, In step (4), the variance of constellation points in each cluster of each constellation diagram is calculated using the cluster center point. The steps include the following: (4a) Use a cosine demodulation signal sequence s LI (t m ) and a sinusoidal demodulated signal sequence s LQ (t m A two-dimensional discrete sequence is constructed, and the K-means algorithm is applied to cluster the two-dimensional discrete sequence to obtain N clusters and their corresponding cluster center points; (4b) For each cluster of data points, calculate the sum of squares of the differences between the data points and the cluster center, and then divide it by the total number of data points in the cluster to obtain the variance of the cluster. (4c) Calculate the sum of the variances of the N clusters to obtain the total variance.

7. The method according to claim 1, characterized in that, The sampling invariant point condition in step (4) is that the starting point of the sampling point is t. m With the sampling start point t m Different total variances are calculated based on the different values ​​of the total variance. The sampling starting point that minimizes the total variance is selected as the sampling invariant point.

8. The method according to claim 1, characterized in that, In step (6), the baseband symbols are determined based on the signal state table. The steps include the following: (6a) Under the condition of sampling invariance, based on one cosine demodulated signal sequence s LI (t m1 ) and a sinusoidal demodulated signal sequence s LQ (t m1 List the baseband symbol states and the signal status table. (6b) Using the K-means algorithm, a cosine demodulated signal sequence s is processed. LI (t m1 ) and a sinusoidal demodulated signal sequence s LQ (t m1 Clustering is performed on the two-dimensional discrete sequence composed of N clusters and their corresponding cluster centers. The value states of the baseband symbols are made to correspond to the cluster centers according to the signal state table. (6c) Calculate the mean (MeanI, MeanQ) of every two neighboring cluster centers, which is expressed as follows: (6d) Use the above mean as the decision threshold to make a decision on the symbol state at time n: (6d1) For a cosine demodulated signal sequence s LI (t m1 To render a judgment: If s LI (t m1 If ) < meanI(1), then the I-way code of the first signal is obtained according to the state table decision. The I-code element of the second signal The second channel signal Q code element Let the range of values ​​for variable j be... If s LI (t m1 )≥meanI(j), and s LI (t m1 If ) < meanI(j+1), then the I-way code of the first signal is obtained according to the state table decision. The I-code element of the second signal Q-code elements of the second signal if Then, the first signal I-channel code element is obtained based on the state table decision. Second signal channel I symbol The second channel signal Q code element (6d2) For a sinusoidal demodulated signal sequence s LQ (t m1 To render a judgment: If s LQ (t m1 If ) < meanQ(1), then the Q-code elements of the first signal are obtained according to the state table decision. The I-code element of the second signal Q-code elements of the second signal Let the range of values ​​for variable j be... If s LQ (t m1 )≥meanQ(j), and s LQ (t m1 If ) < meanQ(j+1), then the Q-code elements of the first signal are obtained according to the state table. The I-code element of the second signal Q-code elements of the second signal if Then, the Q-channel code element of the first signal is obtained according to the state table decision. The I-code element of the second signal Q-code elements of the second signal (6e) The above n-times a 1n b 1n a 2n b 2n The symbol states are combined in pairs, where: a 1n With b 1n The combination yields the baseband symbol sequence of the first QPSK, i.e., {a 11 ,b 11 ,a 12 ,b 12 ,a 13 ,b 13 ,…}; a 2n With b 2n The combination yields the baseband symbol sequence of the second QPSK, i.e., {a 21 ,b 21 ,a 22 ,b 22 ,a 23 ,b 23 ,…}; Finally, the baseband symbol sequences of the two uplink signals were obtained, completing the blind separation of the signals.

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