Method for modulation recognition of mp-wfrft signals based on fourth-order cumulants

Abstract

The application discloses a modulation recognition method of MP-WFRFT signal based on fourth-order cumulant, and belongs to the field of signal processing.The application comprises the following steps: initializing receiving parameters, performing inverse transformation on a receiving signal, which is opposite to the transformation of a sending end, and calculating the fourth-order cumulant of the inverse transformation result; a gradient descent search algorithm is adopted to find the minimum value of the fourth-order cumulant; two quantitative relationships between sending parameter components are obtained through the minimum value of the fourth-order cumulant, the inverse transformation is performed on the receiving signal by using the two quantitative relationships respectively, and two signal sequences are obtained; and any one of the two signal sequences is selected, and modulation pattern recognition is performed on the signal sequence. The application can realize modulation recognition of non-cooperative signals, and fills the blank in the field of non-cooperative MP-WFRFT signal modulation recognition.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, specifically relating to an MP-WFRFT signal modulation recognition method based on fourth-order cumulants. Background Technology

[0002] Since Shih proposed the theory of the classical weighted-type fractional Fourier transform (WFRFT), WFRFT has been extensively and deeply studied in the field of communications. Single-parameter WFRFT (SP-WFRFT) has only one transform parameter α. Non-cooperative parties can estimate α through parameter scanning, thereby performing modulation identification and demodulation of the received signal.

[0003] To further improve the encryption performance of communication systems, multi-parameter WFRFT (MP-WFRFT) was proposed. Compared with traditional SP-WFRFT, MP-WFRFT is not only highly compatible with SP-WFRFT in terms of constellation distribution, but also possesses more complex constellation mapping criteria, enabling the spread, rotation, and splitting of the communication signal constellation, disguising the original signal as other higher-order modulations. Furthermore, because MP-WFRFT has multiple parameters, each affecting the signal's modulation characteristics, MP-WFRFT-based communication systems exhibit stronger resistance to parameter scanning than SP-WFRFT-based systems, significantly increasing the difficulty for non-cooperative parties to correctly interpret the signal. Therefore, MP-WFRFT offers higher security than SP-WFRFT and has been widely applied in the field of encryption.

[0004] However, there is currently no research on the problem of MP-WRFT signal parameter estimation, especially on the modulation identification of non-cooperative signals. Summary of the Invention

[0005] The purpose of this invention is to provide a modulation recognition method for MP-WFRFT signals based on fourth-order cumulants, which solves the current problem of being unable to achieve modulation recognition for non-cooperative MP-WFRFT signals.

[0006] The technical solution adopted in this invention is as follows:

[0007] A modulation identification method for MP-WFRFT signals based on fourth-order cumulants is used at the receiver to identify the modulation of MP-WFRFT signals sent from the transmitter. The method includes the following steps:

[0008] Step 1, Initialize the receive parameter Z r =[0,zr0 ,z r1 ,z r2 Perform an inverse transform on the received signal, which is the opposite of the transform at the transmitting end, and calculate the fourth-order cumulant C from the result of the inverse transform. 42 ;

[0009] Step 2: Use an approximate gradient descent search algorithm to find C. 42 Minimum value;

[0010] Step 3, via C 42 The minimum value yields two quantitative relationships between the transmitted parameter components. These two quantitative relationships are then used to perform the inverse transformation on the received signal to obtain two signal sequences.

[0011] Step 4: Select any one of the two signal sequences and identify its modulation pattern.

[0012] Furthermore, the specific method of step 1 is as follows:

[0013] Step 101, the inverse transform, which is the opposite of the transmitter transform, is:

[0014]

[0015] Where ξ = [ξ0, ξ1, ξ2, ξ3], g(x) is an arbitrary complex sequence, G(x), g(-x), and G(-x) are the 1st, 2nd, and 3rd discrete Fourier transforms of g(x), respectively, and the weighting coefficients χ l (ξ), defined as

[0016]

[0017] Where i is the imaginary unit, ξ k Let k be any real number, k = 0, 1, 2, 3;

[0018] Step 102, the MP-WFRFT signal received by the receiver is represented as follows:

[0019]

[0020] Among them, the weighting coefficient w l (α t V t ), defined as

[0021]

[0022] Where X0 is the transmitted data, X1, X2, and X3 are the 1st, 2nd, and 3rd Discrete Fourier Transforms of X0, respectively, and α t V t The parameter set for the sender, α tV is the transformation order. t =[MV t NV t ] is the scale vector, MV t =[m t0 ,m t1 ,m t2 ,m t3 ], NV t =[n t0 ,n t1 ,n t2 ,n t3 ], MV t and NV t All are integer vectors;

[0023] Step 103, let z tk =(4m tk +1)α t (4n tk +k), k=0,1,2,3, transform equation (3) into

[0024]

[0025] Among them, Z t =[z t0 ,z t1 ,z t2 ,z t3 [] represents the parameters to be sent; initialize Z. r =[0,z r0 ,z r1 ,z r2 The recipient has the right to... Perform the inverse transform, since It has additivity, therefore we get

[0026]

[0027] Step 104, find Fourth-order cumulative For a random sequence X, its fourth-order cumulant is expressed as:

[0028] C 42 (X)=E[(XX * ) 2 ]-|E(X 2 )| 2 -2[E(XX * )] 2 (7)

[0029] Among them, E(·), |·|, (·) * and(·) 2 Let represent the mean, modulus, conjugate, and square of the random sequence, respectively.

[0030] Furthermore, the specific method for step 2 is as follows:

[0031] In Z r =[0,z r0 ,z r1 ,z r2 Based on the initial value, for Z r There are six possibilities: adding or subtracting a step size from one of the three unknown parameters. Using the new parameters obtained under each possibility, [the following is applied to...]. Perform the inverse transformation to calculate the values ​​of each new set of parameters. Then select The set of parameters that decreases the fastest, update Z. r and

[0032] Based on the new parameters, adjust the step size again, and repeat the above process until... To obtain the minimum value;

[0033] There are two types of step size: large step size and small step size. Initially, a large step size is used. In a certain iteration, six new sets of parameters are obtained... All are updated compared to the previous iteration. When the step size is large, replace the large step size with a small step size and restart the current cycle.

[0034] Furthermore, step 3 is performed as follows:

[0035] X l Given four uncorrelated random sequences, l = 0, 1, 2, 3, calculate... The fourth-order cumulant is obtained.

[0036]

[0037] X1 and X3 approximately follow a Gaussian distribution, since the C of a Gaussian signal... 42 Approaching 0, therefore C 42 (X1) and C 42 (X3) approaches 0; C 42 (X0) is denoted as S, and since X0 and X2 have the same distribution, then C 42 (X0)=C 42 (X2) = S, thus expressing equation (8) as

[0038]

[0039] Substituting equation (2) into equation (9) and simplifying, we get

[0040]

[0041] According to equation (10), |χ0(ΔZ)| 4 +|χ2(ΔZ)| 4 There exists a maximum value of 1, and since the fourth-order cumulant of a conventional digital modulation signal is a negative number, that is, S in equation (10) is a negative number, therefore, through The minimum value determines Δz k The quantitative relationships between them, k = 0, 1, 2, 3, are used to determine the transmission parameter Z. t =[z t0 ,z t1 ,z t2 ,z t3 The quantitative relationship between the components in ] is [0, -z r0 ,-z r1 ,-z r2 [] or [0, -z] r0 +2,-z r1 ,-z r2 +2];

[0042] Assume the sending parameter is Z t =[a,az r0 ,az r1 ,az r2 ], where a∈[0,4) and the value is uncertain; using these two quantitative relationships, the inverse transform of the received signal is performed, that is, Z r =-[0,-z r0 ,-z r1 ,-z r2 ]、Z r =-[0,-z r0 +2,-z r1 ,-z r2 +2] respectively and Z t Substituting into equation (6), we get

[0043]

[0044]

[0045] Among them, ΔZ=[a,a,a,a], ΔZ'=[a,a-2,a,a-2];

[0046] When ΔZ = [a,a,a,a], |χ0(ΔZ)| = 1, at which point the transmitted data X0 rotates counterclockwise. The sequence; when ΔZ'=[a,a-2,a,a-2], |χ2(ΔZ')|=1, at this time we get the transmitted data X0 reversed and rotated counterclockwise. The sequence, where a∈[0,4) and the specific value is uncertain.

[0047] Furthermore, step 4 is specifically implemented as follows: select feature parameters, set a discrimination threshold, and use a classification decision tree method to perform modulation pattern recognition.

[0048] The beneficial effects of this invention are:

[0049] 1. This invention proposes a parameter estimation theory for MP-WFRFT signals based on fourth-order cumulants through theoretical derivation, thereby realizing the modulation recognition of non-cooperative signals and filling the current gap in the field of non-cooperative MP-WFRFT signal modulation recognition.

[0050] 2. This invention employs an approximate gradient descent search algorithm, which greatly reduces computational complexity. Attached Figure Description

[0051] Figure 1 This is a classification decision tree diagram in an embodiment of the present invention;

[0052] Figure 2 This is a graph showing the modulation recognition accuracy of BPSK signals as a function of signal-to-noise ratio in an embodiment of the present invention.

[0053] Figure 3 This is a graph showing the modulation recognition accuracy of QPSK signals as a function of signal-to-noise ratio in an embodiment of the present invention.

[0054] Figure 4 This is a graph showing the modulation recognition accuracy of the PSK signal as a function of the signal-to-noise ratio in Embodiment 8 of the present invention.

[0055] Figure 5 This is a graph showing the modulation recognition accuracy of the QAM signal as a function of the signal-to-noise ratio in Embodiment 16 of the present invention.

[0056] Figure 6 This is a graph showing the modulation recognition accuracy of the QAM signal as a function of the signal-to-noise ratio in Embodiment 32 of the present invention.

[0057] Figure 7 The graph shows the average number of searches for five signals—BPSK, QPSK, 8PSK, 16QAM, and 32QAM—as a function of signal-to-noise ratio in an embodiment of the present invention.

[0058] Figure 8 This is a graph showing the bit error rate of the QAM signal as a function of the signal-to-noise ratio in an embodiment of the present invention.

[0059] Figure 9 This is a graph showing the average number of search attempts for the QAM signal as a function of the signal-to-noise ratio in an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and beneficial effects of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0061] A modulation identification method for MP-WFRFT signals based on fourth-order cumulants is proposed. First, a new transform is defined, and its additivity is proven through theoretical derivation. Then, the MP-WFRFT definition is converted to the definition of the new transform, and it is proven through theoretical derivation that minimizing the fourth-order cumulant of the received signal under the new transform definition yields a sequence of transmitted data rotated by a certain angle and a sequence of transmitted data rotated by a certain angle after being reversed. Next, an approximate gradient descent search algorithm is proposed to find the minimum value. Finally, the traditional decision tree classification method is used to identify the modulation pattern of the obtained sequences.

[0062] The specific steps of this method are as follows:

[0063] Includes the following steps:

[0064] Step 1, Initialize the receive parameter Z r =[0,z r0 ,z r1 ,z r2 Perform an inverse transform on the received signal, which is the opposite of the transform at the transmitting end, and calculate the fourth-order cumulant C from the result of the inverse transform. 42 ;

[0065] Step 2: Use an approximate gradient descent search algorithm to find C. 42 Minimum value;

[0066] Step 3, via C 42 The minimum value yields two quantitative relationships between the transmitted parameter components. These two quantitative relationships are then used to perform the inverse transformation on the received signal to obtain two signal sequences.

[0067] Step 4: Select any one of the two signal sequences and identify its modulation pattern.

[0068] The specific method for step 1 is as follows:

[0069] Step 101, the inverse transform, which is the opposite of the transmitter transform, is:

[0070]

[0071] Where ξ = [ξ0, ξ1, ξ2, ξ3], g(x) is an arbitrary complex sequence, G(x), g(-x), and G(-x) are the 1st, 2nd, and 3rd discrete Fourier transforms of g(x), respectively, and the weighting coefficients χ l(ξ), defined as

[0072]

[0073] Where i is the imaginary unit, ξ k Let k be any real number, k = 0, 1, 2, 3;

[0074] Step 102, the MP-WFRFT signal received by the receiver is represented as follows:

[0075]

[0076] Among them, the weighting coefficient w l (α t V t ), defined as

[0077]

[0078] Where X0 is the transmitted data, X1, X2, and X3 are the 1st, 2nd, and 3rd Discrete Fourier Transforms of X0, respectively, and α t V t The parameter set for the sender, α t V is the transformation order. t =[MV t NV t ] is the scale vector, MV t =[m t0 ,m t1 ,m t2 ,m t3 ], NV t =[n t0 ,n t1 ,n t2 ,n t3 ], MV t and NV t All are integer vectors;

[0079] Step 103, let z tk =(4m tk +1)α t (4n tk +k), k=0,1,2,3, transform equation (3) into

[0080]

[0081] Among them, Z t =[z t0 ,z t1 ,z t2 ,z t3 [] represents the parameters to be sent; initialize Z. r =[0,z r0,z r1 ,z r2 The recipient has the right to... Perform the inverse transform, since It has additivity, therefore we get

[0082]

[0083] Step 104, find Fourth-order cumulative For a random sequence X, its fourth-order cumulant is expressed as:

[0084] C 42 (X)=E[(XX * ) 2 ]-|E(X 2 )| 2 -2[E(XX * )] 2 (7)

[0085] Among them, E(·), |·|, (·) * and(·) 2 Let represent the mean, modulus, conjugate, and square of the random sequence, respectively.

[0086] The specific method for step 2 is as follows:

[0087] In Z r =[0,z r0 ,z r1 ,z r2 Based on the initial value, for Z r There are six possibilities: adding or subtracting a step size from one of the three unknown parameters. Using the new parameters obtained under each possibility, [the following is applied to...]. Perform the inverse transformation to calculate the values ​​of each new set of parameters. Then select The set of parameters that decreases the fastest, update Z. r and

[0088] Based on the new parameters, adjust the step size again, and repeat the above process until... To obtain the minimum value;

[0089] There are two types of step size: large step size and small step size. Initially, a large step size is used. In a certain iteration, six new sets of parameters are obtained... All are updated compared to the previous iteration. When the step size is large, replace the large step size with a small step size and restart the current cycle.

[0090] The specific method for step 3 is as follows:

[0091] Xl Given four uncorrelated random sequences, l = 0, 1, 2, 3, calculate... The fourth-order cumulant is obtained.

[0092]

[0093] X1 and X3 approximately follow a Gaussian distribution, since the C of a Gaussian signal... 42 Approaching 0, therefore C 42 (X1) and C 42 (X3) approaches 0; C 42 (X0) is denoted as S, and since X0 and X2 have the same distribution, then C 42 (X0)=C 42 (X2) = S, thus expressing equation (8) as

[0094]

[0095] Substituting equation (2) into equation (9) and simplifying, we get

[0096]

[0097] According to equation (10), |χ0(ΔZ)| 4 +|χ2(ΔZ)| 4 There exists a maximum value of 1, and since the fourth-order cumulant of a conventional digital modulation signal is a negative number, that is, S in equation (10) is a negative number, therefore, through The minimum value determines Δz k The quantitative relationships between them, k = 0, 1, 2, 3, are used to determine the transmission parameter Z. t =[z t0 ,z t1 ,z t2 ,z t3 The quantitative relationship between the components in ] is [0, -z r0 ,-z r1 ,-z r2 [] or [0, -z] r0 +2,-z r1 ,-z r2 +2];

[0098] Assume the sending parameter is Z t =[a,az r0 ,az r1 ,az r2 ], where a∈[0,4) and the value is uncertain; using these two quantitative relationships, the inverse transform of the received signal is performed, that is, Z r =-[0,-z r0 ,-z r1,-z r2 ]、Z r =-[0,-z r0 +2,-z r1 ,-z r2 +2] respectively and Z t Substituting into equation (6), we get

[0099]

[0100]

[0101] Among them, ΔZ=[a,a,a,a], ΔZ'=[a,a-2,a,a-2];

[0102] When ΔZ = [a,a,a,a], |χ0(ΔZ)| = 1, at which point the transmitted data X0 rotates counterclockwise. The sequence; when ΔZ'=[a,a-2,a,a-2], |χ2(ΔZ')|=1, at this time we get the transmitted data X0 reversed and rotated counterclockwise. The sequence, where a∈[0,4) and the specific value is uncertain.

[0103] Step 4 involves selecting feature parameters, setting a discrimination threshold, and using a classification decision tree method for modulation pattern recognition.

[0104] The principle of this method is as follows:

[0105] (1) Introduce the basic principles of MP-WFRFT.

[0106] 4-WFRFT is a widely studied MP-WFRFT method, and this method will be based on 4-WFRFT expansion. If X0 is a random complex sequence, and X1, X2, and X3 are the 1st to 3rd discrete Fourier transforms of X0, then MP-WFRFT is defined as follows:

[0107]

[0108] Among them, the weighting coefficient w l (α,V), (l=0,1,2,3) are defined as

[0109]

[0110] Where α is the transform order, V = [MV, NV] is the scaling vector, MV = [m0, m1, m2, m3], NV = [n0, n1, n2, n3], and MV and NV are both integer vectors. The period of α is 4, and the other 8 parameters have no obvious periodicity. When V = 0, MP-WFRFT becomes single-parameter WFRFT.

[0111] Based on the rotational additivity of MP-WFRFT, we can obtain

[0112]

[0113] From equations (1) and (2), it can be seen that, Therefore, in order to complete an accurate inverse MP-WFRFT, it is necessary to accurately obtain a total of 9 parameters, including α, MV, and NV.

[0114] (2) Define a new transformation and prove its additivity.

[0115] Define the new transformation as follows:

[0116]

[0117] Where ξ = [ξ0, ξ1, ξ2, ξ3], g(x) is a random complex sequence, G(x), g(-x), and G(-x) are the 1st to 3rd discrete Fourier transforms of g(x), and the weighting coefficients χ are respectively. l (ξ), (l=0,1,2,3) is defined as

[0118]

[0119] Let α = [α0, α1, α2, α3], β = [β0, β1, β2, β3], we can get

[0120]

[0121] Among them, α+β=[α0+β0, α1+β1, α2+β2, α3+β3]. From formula (5) we can see that ξ k The period of (k = 0, 1, 2, 3) is 4. We can also obtain...

[0122]

[0123] Substituting equation (5) into equations (6) and (7) respectively, we get

[0124]

[0125] therefore, It has additivity, that is

[0126] (3) It is proven that under the definition of the new transformation, minimizing the fourth-order cumulant of the received signal can yield two data sequences related to the original sequence.

[0127] For a random sequence X, its fourth-order cumulant C 42 It can be represented as

[0128] C42 (X)=E[(XX * ) 2 ]-|E(X 2 )| 2 -2[E(XX * )] 2 (9)

[0129] Among them, E(·), |·|, (·) * and(·) 2 Let represent the mean, modulus, conjugate, and square of the random sequence, respectively.

[0130] Assume the sender performs an MP-WFRFT on data X0, with the transform parameter being α. t V t =[MV t NV t ], among which, MV t =[m t0 ,m t1 ,m t2 ,m t3 ], NV t =[n t0 ,n t1 ,n t2 ,n t3 According to equation (1), the transmitted data can be represented as follows:

[0131]

[0132] Let z tk =(4m tk +1)α t (4n tk +k), (k=0,1,2,3), then equation (10) becomes

[0133]

[0134] Among them, Z t =[z t0 ,z t1 ,z t2 ,z t3 The recipient's response to the received data. The parameter is Z r =[z r0 ,z r1 ,z r2 ,z r3 The inverse MP-WFRFT of ], due to It has additivity, so it can be obtained.

[0135]

[0136] According to equation (5), when ΔZ = [0,0,0,0], Therefore, in order to complete an accurate inverse MP-WFRFT, four parameters need to be accurately obtained.

[0137] When the length of sequence X0 is large enough, X l (l=0,1,2,3) can be viewed as four uncorrelated random sequences. Calculate... C 42 ,get

[0138]

[0139] When the length of sequence X0 is sufficiently large, X1 and X3 approximately follow a Gaussian distribution, due to the C-order distribution of the Gaussian signal. 42 Approaching 0, therefore C 42 (X1) and C 42 (X3) approaches 0. Let C... 42 (X0) is denoted as S, and since X0 and X2 have the same distribution, then C 42 (X0)=C 42 (X2) = S, equation (13) can be expressed as

[0140]

[0141] Substituting equation (5) into equation (14) and simplifying, we get

[0142]

[0143] The following will discuss |χ0(ΔZ)| 4 +|χ2(ΔZ)| 4 We will discuss the case where the maximum value is obtained:

[0144] Because of the newly defined transformation The period of all four parameters is 4, so the received parameter Z... r =[z r0 ,z r1 ,z r2 ,z r3 The scan range of each parameter is [-4, 0), then Δz k ∈[-4,4),(k=0,1,2,3). According to equation (15), when Δz k When the relationships between (k = 0, 1, 2, 3) simultaneously satisfy |Δz0 - Δz2| = 0 or 4, |Δz1 - Δz3| = 0 or 4, and |Δz0 - Δz1| = 0 or 2 or 4 or 6, |χ0(ΔZ)| 4 +|χ2(ΔZ)| 4 The maximum value is obtained. Therefore, through |χ0(ΔZ)|4 +|χ2(ΔZ)| 4 The maximum value can determine Δz k The quantitative relationship between (k = 0, 1, 2, 3) is used to determine the transmission parameter Z. t =[z t0 ,z t1 ,z t2 ,z t3 The quantitative relationship between [0, z] is given by [0, z]. r0 -z r1 ,z r0 -z r2 ,z r0 -z r3 [0, z] or [0, z] r0 -z r1 +2,z r0 -z r2 ,z r0 -z r3 +2].

[0145] Assume the sending parameter is Z t =[a,a+z r0 -z r1 ,a+z r0 -z r2 ,a+z r0 -z r3 ], where a∈[0,4) and the specific value is uncertain. Let Z r =-[0,z r0 -z r1 ,z r0 -z r2 ,z r0 -z r3 ]、Z r '=-[0,z r0 -z r1 +2,z r0 -z r2 ,z r0 -z r3 +2] respectively and Z t Substituting into equation (12) yields

[0146]

[0147]

[0148] Where ΔZ = [a,a,a,a], ΔZ' = [a,a-2,a,a-2]. When ΔZ = [a,a,a,a], |χ0(ΔZ)| = 1, and the original data X0 is rotated counterclockwise. The sequence; when ΔZ'=[a,a-2,a,a-2], |χ2(ΔZ')|=1, at this time we get the original data X0 reversed and rotated counterclockwise. The sequence is given by a ∈ [0, 4) and its specific value is uncertain.

[0149] C of conventional digital modulation signals 42 It is a negative number, that is, S in equation (15) is a negative number. In summary, by minimizing Two quantitative relationships between the transmitted parameters can be obtained. Then, these two quantitative relationships are used to perform inverse MP-WFRFT on the received signal to obtain a sequence of the original data rotated by a certain angle and a sequence of the original data rotated by a certain angle after being reversed.

[0150] (4) An approximate gradient descent search algorithm is proposed for searching. Minimum value.

[0151] By minimizing We can obtain two quantitative relationships between the transmitted parameters. Let's assume the received parameter is Z. r =[0,z r0 ,z r1 ,z r2 During the entire search process, the scanning range of the three unknown received parameters is [-4, 0). If a full search algorithm is used, the number of searches is 40 when the search step size is 0.1. 3 This will result in enormous computational complexity.

[0152] For minimum optimization problems, gradient descent is a good choice, as it's a method that minimizes the objective function by finding its derivative. Because the objective function... It is extremely complex, and differentiating its parameters would lead to enormous computational complexity. Therefore, an approximate gradient descent search algorithm is proposed, drawing inspiration from the gradient descent algorithm. The idea behind this algorithm is to find the value of Z... r =[0,z r0 ,z r1 ,z r2 For each unknown parameter, add a step size and subtract a step size respectively, and calculate... Then select Repeat this process in the direction of fastest descent until... To find the minimum value, two step sizes will be set: a large step size avoids getting trapped in local optima, while a small step size is responsible for searching for the global minimum.

[0153] (5) Perform modulation identification.

[0154] After obtaining the inverse MP-WFRFT sequence, feature parameters are selected, a discrimination threshold is set, and a classification decision tree method is used for modulation pattern recognition.

[0155] Figure 1 This is a classification decision tree diagram in an embodiment of the present invention. For five signals—BPSK, QPSK, 8PSK, 16QAM, and 32QAM—details are extracted. And F3=|C 80 Using three features as feature parameters, a classification decision tree method is employed for pattern recognition, where C... 42 For fourth-order cumulants, C 63 For a sixth-order cumulant, C 80 It is an eighth-order cumulative quantity.

[0156] Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 This is an experiment demonstrating the accuracy of identification of different non-cooperative signal modulations in this invention. Detailed explanation follows:

[0157] 1. Generate five signals: BPSK, QPSK, 8PSK, 16QAM, and 32QAM, with a sampling number of 2048.

[0158] 2. Perform MP-WFRFT on the signal. Transform order α t ∈[0,3.999], with an interval of 0.001; scale vector MV t NV t ∈[0,1000], interval is 1, α t MV t and NV t It is generated randomly each time.

[0159] 3. The signal is transmitted in a Gaussian white channel after passing through MP-WFRFT, with a signal-to-noise ratio range of [0,12] and an interval of 0.5.

[0160] 4. Perform the new transformation defined in this invention on the received signal, and initialize the receiving parameters to Z. r = [0, -2, -2, -2], then find C. 42An approximate gradient descent search algorithm is used to find the minimum value, with a large search step size of 0.8 and a small step size of 0.2. After obtaining two quantitative relationships between the transmitted parameters through the minimum value, the received signal is inversely transformed using these two quantitative relationships to obtain two sequences, one of which is selected. To demonstrate the effectiveness of the MP-WFRFT signal modulation recognition theory based on fourth-order cumulants proposed in this invention, an inverse transformation of the true parameters is also used to obtain the sequence. To demonstrate the effectiveness and efficiency of the approximate gradient descent search algorithm proposed in this invention, a full search algorithm with a step size of 0.4 is also used to obtain the sequence.

[0161] 5. The obtained sequence is subjected to modulation pattern recognition using a classification decision tree method. 100 Monte Carlo simulations are performed, and the recognition accuracy and average number of searches are the average of the 100 experiments.

[0162] Figure 8 and Figure 9 This is an experiment demonstrating the demodulation performance of non-cooperative QAM signals in an embodiment of the present invention. Detailed explanation follows:

[0163] 1. Generate a QAM signal with 2048 sampling points.

[0164] 2. Perform MP-WFRFT on the signal. Transform order α t ∈[0,3.999], with an interval of 0.001; scale vector MV t NV t ∈[0,1000], interval is 1, α t MV t and NV t It is generated randomly each time.

[0165] 3. The signal is transmitted in a Gaussian white channel after passing through MP-WFRFT, with a signal-to-noise ratio range of [0,12] and an interval of 0.5.

[0166] 4. Perform the new transformation defined in this invention on the received signal, and initialize the receiving parameters to Z. r = [0, -2, -2, -2], then find C. 42 An approximate gradient descent search algorithm is used to find the minimum value. The large search step size is set to 0.8, and the small step sizes are set to 0.1 and 0.3 respectively. After obtaining the two quantitative relationships between the transmitted parameters through the minimum value, the received signal is inversely transformed using these two quantitative relationships to obtain two sequences.

[0167] 5. Rotate the two obtained sequences by 0°, 90°, 180°, and 270° respectively, resulting in a total of 8 sequences. Then, perform decoding and discrimination to obtain 8 bit sequences. One of these sequences is the true bit sequence, but it cannot be explicitly designated; here, the sequence with the lowest bit error rate is selected. To demonstrate the effectiveness of the MP-WFRFT signal modulation recognition theory based on fourth-order cumulants proposed in this invention, the inverse transformation of the true parameters will also be used to obtain the bit sequences. To demonstrate the effectiveness and efficiency of the approximate gradient descent search algorithm proposed in this invention, a full search algorithm with step sizes of 0.2 and 0.4 will also be used to obtain the bit sequences.

[0168] 6. Compare the obtained bit sequence with the original transmitted bit sequence to calculate the bit error rate. Perform 100 Monte Carlo simulations. The bit error rate and the average number of searches are the average of the 100 experiments.

[0169] In summary, this invention can obtain sequences of the original sequence rotated by a certain angle and sequences of the original data reversed and rotated by a certain angle, thereby enabling modulation pattern recognition of non-cooperative signals with modulation recognition accuracy close to the true parameters. Regarding the demodulation performance of this method, taking QAM signals as an example, eight bit sequences can be obtained, one of which is the true bit sequence. The bit error rate of this sequence is close to the true parameters, but cannot be explicitly specified. The approximate gradient descent search algorithm proposed in this invention, without affecting the accuracy of the results, has fewer search iterations than the full search algorithm, greatly reducing computational complexity. Therefore, the method proposed in this invention is effective and efficient.

Claims

1. A method for identifying MP-WFRFT signal modulation based on fourth-order cumulants, characterized in that, The method for modulation identification of MP-WFRFT signals sent from the transmitter at the receiver includes the following steps: Step 1, Initialize the receive parameter Z r =[0,z r0 ,z r1 ,z r2 Perform an inverse transform on the received signal, which is the opposite of the transform at the transmitting end, and calculate the fourth-order cumulant C from the result of the inverse transform. 42 ; Step 2: Use an approximate gradient descent search algorithm to find C. 42 Minimum value; Step 3, via C 42 The minimum value yields two quantitative relationships between the transmitted parameter components. These two quantitative relationships are then used to perform the inverse transformation on the received signal to obtain two signal sequences. Step 4: Select any one of the two signal sequences and identify its modulation pattern.

2. The MP-WFRFT signal modulation recognition method based on fourth-order cumulants according to claim 1, characterized in that, The specific method for step 1 is as follows: Step 101, the inverse transform, which is the opposite of the transmitter transform, is: Where ξ = [x0, x1, x2, x3], g(x) is an arbitrary complex sequence, G(x), g(-x), and G(-x) are the 1st, 2nd, and 3rd discrete Fourier transforms of g(x), respectively, and the weighting coefficients c l (ξ) is defined as Where i is the imaginary unit, ξ k Let k be any real number, k = 0, 1, 2, 3; Step 102, the MP-WFRFT signal received by the receiver is represented as follows: Among them, the weighting coefficient w l (a t V t ), defined as Where X0 is the transmitted data, X1, X2, and X3 are the 1st, 2nd, and 3rd Discrete Fourier Transforms of X0, respectively, and α t V t The parameter set for the sender, α t V is the transformation order. t =[MV t NV t ] is the scale vector, MV t =[m t0 ,m t1 ,m t2 ,m t3 ], NV t =[n t0 ,n t1 ,n t2 ,n t3 ], MV t and NV t All are integer vectors; Step 103, let z tk =(4m tk +1)a t (4n tk +k), k=0,1,2,3, transform equation (3) into Among them, Z t =[z t0 ,z t1 ,z t2 ,z t3 [] represents the parameters to be sent; initialize Z. r =[0,z r0 ,z r1 ,z r2 The recipient has the right to... Perform the inverse transformation, since It has additivity, therefore we get Step 104, find Fourth-order cumulants For a random sequence X, its fourth-order cumulant is expressed as: C 42 (X)=E[(XX * ) 2 ]-|E(X 2 )| 2 -2[E(XX * )] 2 (7) Among them, E(·), |·|, (·)* and (·) 2 Let represent the mean, modulus, conjugate, and square of the random sequence, respectively.

3. The MP-WFRFT signal modulation recognition method based on fourth-order cumulants according to claim 2, characterized in that, The specific method for step 2 is as follows: In Z r =[0,z r0 ,z r1 ,z r2 Based on the initial value, for Z r There are six possibilities: adding or subtracting a step size from one of the three unknown parameters. Using the new parameters obtained under each possibility, [the following is applied to...]. Perform the inverse transformation to calculate the values ​​of each new set of parameters. Then select The set of parameters that decreases the fastest, update Z. r and Based on the new parameters, adjust the step size again, and repeat the above process until... To obtain the minimum value; There are two types of step size: large step size and small step size. Initially, a large step size is used. In a certain iteration, six new sets of parameters are obtained... All are updated compared to the previous iteration. When the step size is large, replace the large step size with a small step size and restart the current cycle.

4. The MP-WFRFT signal modulation recognition method based on fourth-order cumulants according to claim 3, characterized in that, The specific method for step 3 is as follows: X l Given four uncorrelated random sequences, l = 0, 1, 2, 3, calculate... The fourth-order cumulant is obtained. X1 and X3 approximately follow a Gaussian distribution, since the C of a Gaussian signal... 42 Approaching 0, therefore C 42 (X1) and C 42 (X3) approaches 0; C 42 (X0) is denoted as S, and since X0 and X2 have the same distribution, then C 42 (X0)=C 42 (X2) = S, thus expressing equation (8) as Substituting equation (2) into equation (9) and simplifying, we get According to equation (10), |c0(ΔZ)| 4 +|c2(ΔZ)| 4 There exists a maximum value of 1, and since the fourth-order cumulant of a conventional digital modulation signal is a negative number, that is, S in equation (10) is a negative number, therefore, through The minimum value determines Δz k The quantitative relationships between them, k = 0, 1, 2, 3, are used to determine the transmission parameter Z. t =[z t0 ,z t1 ,z t2 ,z t3 The quantitative relationship between the components in ] is [0, -z r0 ,-z r1 ,-z r2 [] or [0, -z] r0 +2,-z r1 ,-z r2 +2]; Assume the sending parameter is Z t =[a,az r0 ,az r1 ,az r2 ], where a∈[0,4) and the value is uncertain; using these two quantitative relationships, the inverse transform of the received signal is performed, that is, Z r =-[0,-z r0 ,-z r1 ,-z r2 ]、Z r =-[0,-z r0 +2,-z r1 ,-z r2 +2] respectively and Z t Substituting into equation (6), we get Among them, ΔZ=[a,a,a,a], ΔZ'=[a,a-2,a,a-2]; When ΔZ = [a,a,a,a], |c0(ΔZ)| = 1, at which point the transmitted data X0 rotates counterclockwise. The sequence; when ΔZ'=[a,a-2,a,a-2], |c2(ΔZ')|=1, at this time we get the transmitted data X0 reversed and rotated counterclockwise. The sequence, where a∈[0,4) and the specific value is uncertain.

5. The MP-WFRFT signal modulation recognition method based on fourth-order cumulants according to claim 4, characterized in that, Step 4 involves selecting feature parameters, setting a discrimination threshold, and using a classification decision tree method for modulation pattern recognition.

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