A score field waveform parameter selection method based on goodness-of-fit test

Abstract

The application discloses a score field waveform parameter selection method based on goodness-of-fit test, and belongs to the technical field of wireless communication.The application solves the problem that the probability of the transmitted information being detected is still high in the prior art.The application takes Gaussian white noise as a background noise model, calculates the distance between the distribution function of the received sample signal and the Gaussian white noise distribution function, compares the distance with a threshold, and then judges the existence of the detected signal, and finally selects the waveform parameters according to the detection probability corresponding to each group of waveform parameters.The application fully utilizes the diversity advantage of the waveform after the extended weighted fractional Fourier transform, optimizes the transform parameters with the advantage of low detection probability, makes the optimized waveform have the statistical characteristics of Gaussian distribution, increases the detection difficulty of the eavesdropper, and reduces the probability of the transmitted information being detected.The application can be applied to the technical field of wireless communication.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and specifically relates to a method for selecting fractional domain waveform parameters based on goodness-of-fit test. Background Technology

[0002] The weighted fractional Fourier transform (FFT) alters the original time-frequency characteristics of a signal, transforming it into a hybrid carrier form containing both single-carrier and multi-carrier components. Under certain parameters, the constellation diagram in the complex plane exhibits characteristics similar to Gaussian white noise. This white noise transformation of communication behavior increases the difficulty for eavesdroppers to detect and identify, ensuring secure information transmission. The extended weighted fractional Fourier transform (EFT) expands the single-parameter transformation to a four-parameter transformation based on the classic EFT, allowing for more flexible signal transformation. However, not all signals transformed by the extended weighted fractional Fourier transform possess Gaussian-like statistical properties. Therefore, leveraging waveform diversity to construct Gaussian-like signals and proposing a new parameter optimization scheme to reduce the probability of transmitted information being detected is a worthwhile research topic. Summary of the Invention

[0003] The purpose of this invention is to reduce the probability of transmitted information being detected, and a fractional domain waveform parameter selection method based on goodness-of-fit test is proposed.

[0004] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a method for selecting fractional domain waveform parameters based on goodness-of-fit test, the method specifically including the following steps:

[0005] Step 1: Randomly generate M signal sequences of length 2N points, and denote the d-th signal sequence as s. d s d =[s d,1 ,s d,2 ,...,s d,2N ], s d,1 ,s d,2 ,...,s d,2N Represents the signal sequence s d The 1st, 2nd, ..., 2Nth element in the sequence;

[0006] Step 2: Process the signal sequence s d Perform QPSK mapping to obtain the mapped N-point baseband signal sequence x. d x d =[x d,1 ,x d,2 ,...,x d,N ], x d,1 ,x d,2 ,…,x d,NRepresents the baseband signal sequence x d The 1st, 2nd, ..., Nth element in the list;

[0007] Step 3: Establish a waveform parameter database for extended weighted fractional Fourier transform. Use the M baseband signal sequences obtained in Step 2 to select waveform parameters.

[0008] Further, any set of waveform parameters in the waveform parameter database of the extended weighted fractional Fourier transform is denoted as... The waveform parameters satisfy: and

[0009] Furthermore, the waveform parameters are selected using the M baseband signal sequences obtained in step two; the specific process is as follows:

[0010] Step 3: 1. Initialize the number of waveform parameter groups a = 1;

[0011] Step 3.2: Initialize the baseband signal sequence number d = 1;

[0012] Step 3: Obtain the weighting coefficients of the extended weighted fractional Fourier transform based on the waveform parameters of group a. Then, using the weighting coefficients, perform an extended weighted fractional Fourier transform on the d-th baseband signal sequence to obtain the transformed signal.

[0013] Steps three and four: Transform the signal The elements X1, X2, ... X in the data N After taking the square of the modulus of each result, sort the N results in ascending order, and then obtain the theoretical distribution function based on the sorting results.

[0014] Step 35: Construct the test statistic AD(Z) based on the theoretical distribution function, and then determine the threshold value λ of the test statistic;

[0015] Step 36: Compare the test statistic AD(Z) with the threshold λ to obtain the decision result; specifically:

[0016] If the test statistic is greater than or equal to the threshold value, then

[0017] If the test statistic is less than the threshold value, then

[0018] Step 37: Determine whether d = M is satisfied, where M represents the total number of baseband signal sequences;

[0019] If d = M is satisfied, then proceed to step three eight;

[0020] If d = M is not satisfied, then let d = d + 1 and return to step 3.

[0021] Step 38: Calculate the detection probability of the waveform parameters in group a.

[0022] Compare detection probabilities The size of the threshold t0, if If it is less than t0, then the waveform parameters of group a are retained; if If t0 is greater than or equal to t0, then discard the waveform parameters of group a;

[0023] Next, determine whether a = K is satisfied, where K represents the total number of waveform parameter groups in the waveform parameter database;

[0024] If a = K is satisfied, then proceed to step 39;

[0025] If a = K is not satisfied, then let a = a + 1 and return to step 3.2.

[0026] Step 39: Obtain the set of all retained group waveform parameters.

[0027] Furthermore, the step of obtaining the weighting coefficients of the extended weighted fractional Fourier transform based on the waveform parameters of the a-th group specifically involves:

[0028]

[0029] in, represents the weighting coefficients of the extended weighted fractional Fourier transform, and i represents the imaginary unit.

[0030] Furthermore, the specific process of steps three and four is as follows:

[0031] Step 3-4: Let X1, X2, ..., X N All are complex Gaussian distributed variables, X n =b n +ic n n = 1, 2, ..., N, real part b n and the imaginary part c n It is an independent and identically distributed real Gaussian random variable with real part b. n and the imaginary part c n Follows a Gaussian distribution N(0,σ) 2 ), σ 2 It is the variance of a Gaussian distribution, for the variable X. n The square of the modulus:

[0032]

[0033] Step 3-42, regarding |X n |2 Perform ascending sorting, and denote the elements in the sorted result as X1′, X2′, ..., X′. N Then, calculate the variable U based on each element in the sorting results. n :

[0034]

[0035] Step 3-43, Variable U n If n = 1, 2, ..., N follows a chi-square distribution with 2 degrees of freedom, then the variable U n The theoretical distribution function is:

[0036]

[0037] Where F(·) represents the theoretical distribution function, e represents the base of the natural logarithm, and Z n U n The corresponding theoretical distribution function value.

[0038] Furthermore, in step three-five, the specific process of constructing the test statistic AD(Z) based on the theoretical distribution function is as follows:

[0039]

[0040] Where AD(Z) represents the test statistic, Z = [Z1, Z2, ..., Zn] N ].

[0041] Furthermore, in step three of the above, the specific process for determining the threshold value of the test statistic is as follows:

[0042]

[0043] Where P(AD(Z)≤λ) represents the probability that AD(Z)≤λ, r j =(-1) j Γ(j+0.5) / (Γ(0.5)j!), where Γ is the Gamma function and w represents the integration variable;

[0044] The significance level α = P(AD(Z)>λ) = 1-P(AD(Z)≤λ) is used to calculate the threshold value λ corresponding to the significance level α.

[0045] Furthermore, the specific process of step three eight is as follows:

[0046]

[0047] in, This represents the detection probability of the waveform parameters in group a.

[0048] Furthermore, the method also includes a fourth step, which is to transmit the signal to be transmitted using the retained waveform parameters.

[0049] Furthermore, the specific process of step four is as follows:

[0050] Step 41: Perform QPSK mapping on the signal sequence to be transmitted at the transmitting end to obtain the mapped baseband signal sequence;

[0051] Step 42: Select any group of waveform parameters from all the retained groups of waveform parameters, use the selected waveform parameters to generate weighting coefficients for the extended weighted fractional Fourier transform, and then use the generated weighting coefficients to perform an extended weighted fractional Fourier transform on the mapped baseband signal sequence.

[0052] Step 43: Modulate the signal after extended weighted fractional Fourier transform onto the carrier frequency to obtain modulated data, and then transmit the modulated data through the antenna.

[0053] The beneficial effects of this invention are:

[0054] This invention uses Gaussian white noise as the background noise model. It calculates the distance between the distribution function of the received sample signal and the distribution function of the Gaussian white noise, compares this distance with a threshold to determine the presence of the detection signal, and then selects waveform parameters based on the detection probabilities corresponding to each set of waveform parameters. This invention fully leverages the diversity of waveforms after extended weighted fractional Fourier transform, achieving optimal transformation parameters with a low detection probability. The optimized waveform possesses Gaussian-like statistical characteristics, increasing the difficulty of detection for the eavesdropper, reducing the probability of detection, and significantly improving the security of communication activities. Attached Figure Description

[0055] Figure 1 This is a flowchart of a fractional-domain waveform parameter selection method based on goodness-of-fit test according to the present invention;

[0056] Where: GWFRFT represents Extended Weighted Fractional Fourier Transform;

[0057] Figure 2 This is a flowchart of signal transmission based on the selected parameters. Detailed Implementation

[0058] Specific implementation method one: Combining Figure 1 This embodiment describes a method for selecting fractional-domain waveform parameters based on goodness-of-fit testing. The method specifically includes the following steps:

[0059] Step 1: Randomly generate M signal sequences of length 2N points, and denote the d-th signal sequence as s.d s d =[s d,1 ,s d,2 ,...,s d,2N ], s d,1 ,s d,2 ,...,s d,2N Represents the signal sequence s d The 1st, 2nd, ..., 2Nth element in the sequence;

[0060] Step 2: Process the signal sequence s d Perform QPSK mapping to obtain the mapped N-point baseband signal sequence x. d x d =[x d,1 ,x d,2 ,...,x d,N ], x d,1 ,x d,2 ,...,x d,N Represents the baseband signal sequence x d The 1st, 2nd, ..., Nth element in the list;

[0061] This invention is compatible with various modulation methods; QPSK modulation is used as an example here.

[0062] Step 3: Establish a waveform parameter database for extended weighted fractional Fourier transform. Use the M baseband signal sequences obtained in Step 2 to select waveform parameters.

[0063] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that any set of waveform parameters in the waveform parameter database of the extended weighted fractional Fourier transform is denoted as... The waveform parameters satisfy: and

[0064] The other steps and parameters are the same as in Specific Implementation Method 1.

[0065] In this invention, a set of waveform parameters It forms an arithmetic sequence, and by adjusting The value of and and By varying the intervals between them, multiple sets of waveform parameters can be obtained, and these multiple sets of waveform parameters can be used to form a waveform parameter database.

[0066] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that it utilizes the M baseband signal sequences obtained in step two to select waveform parameters, thereby obtaining the selected waveform parameters. The specific process is as follows:

[0067] Step 3: 1. Initialize the number of waveform parameter groups a = 1;

[0068] Step 3.2: Initialize the baseband signal sequence number d = 1;

[0069] Step 3: Obtain the weighting coefficients of the extended weighted fractional Fourier transform based on the waveform parameters of group a. Then, using the weighting coefficients, perform an extended weighted fractional Fourier transform on the d-th baseband signal sequence to obtain the transformed signal.

[0070]

[0071] In the formula, Let f(t) = x be the waveform parameters of the a-th group. d The frequency domain component F(t) and the time domain component f(t) are a Fourier transform pair, that is, F(t) is the Fourier transform result of f(t), f(-t) is the inverse function of f(t) centered at the origin, and F(-t) is the inverse function of F(t) centered at the origin.

[0072] Steps three and four: Transform the signal The elements X1, X2, ... X in the data N After taking the square of the modulus of each result, sort the N results in ascending order, and then obtain the theoretical distribution function based on the sorting results.

[0073] Step 35: Construct the test statistic AD(Z) based on the theoretical distribution function, and then determine the threshold value λ of the test statistic;

[0074] Step 36: Compare the test statistic AD(Z) with the threshold λ to obtain the decision result; specifically:

[0075] If the test statistic is greater than or equal to the threshold value, then the decision is H1, i.e.

[0076] If the test statistic is less than the threshold value, then the result is H0, i.e.

[0077] Step 37: Determine whether d = M is satisfied, where M represents the total number of baseband signal sequences;

[0078] If d = M is satisfied, then proceed to step three eight;

[0079] If d = M is not satisfied, then let d = d + 1 and return to step 3.

[0080] Step 38: Calculate the probability that the waveform parameters of group a accept the alternative hypothesis H1, that is, calculate the detection probability of the waveform parameters of group a.

[0081] Based on the system's security requirements, the detection probabilities are compared. The size of the threshold t0, if If it is less than t0, then the waveform parameters of group a are retained; if If the value is greater than or equal to t0, then the waveform parameters of group a are discarded; the threshold t0 can be set according to the actual security requirements in the communication process.

[0082] Next, determine whether a = K is satisfied, where K represents the total number of waveform parameter groups in the waveform parameter database;

[0083] If a = K is satisfied, then proceed to step 39;

[0084] If a = K is not satisfied, then let a = a + 1 and return to step 3.2.

[0085] Step 39: Obtain the set of all retained group waveform parameters.

[0086] Other steps and parameters are the same as in specific implementation method one or two.

[0087] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the weighting coefficients of the extended weighted fractional Fourier transform obtained based on the waveform parameters of the a-th group are specifically as follows:

[0088]

[0089] in, represents the weighting coefficients of the extended weighted fractional Fourier transform, and i represents the imaginary unit.

[0090] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0091] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the specific process of steps three and four is as follows:

[0092] Step 3-4: Let X1, X2, ..., X N All are complex Gaussian distributed variables, X n =b n +ic n n = 1, 2, ..., N, real part b n and the imaginary part c n It is an independent and identically distributed real Gaussian random variable with real part b. n and the imaginary part c n Follows a Gaussian distribution N(0,σ) 2 ), σ 2 It is the variance of a Gaussian distribution, for the variable X. n The square of the modulus:

[0093]

[0094] Step 3-42, regarding |X n | 2 Perform ascending sorting, and denote the elements in the sorted result as X1′, X2′, ..., X′. N Then, calculate the variable U based on each element in the sorting results. n :

[0095]

[0096] Step 3-43, Variable U n If n = 1, 2, ..., N follows a chi-square distribution with 2 degrees of freedom, then the variable U n The theoretical distribution function is:

[0097]

[0098] Where F(·) represents the theoretical distribution function, e represents the base of the natural logarithm, and Z n U n The corresponding theoretical distribution function value.

[0099] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0100] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that the specific process of constructing the test statistic AD(Z) based on the theoretical distribution function in steps three and five is as follows:

[0101]

[0102] Where AD(Z) represents the test statistic, Z = [Z1, Z2, ..., Zn] N ].

[0103] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0104] The distribution of AD(Z) is independent of the distribution of the null hypothesis H0, and the distribution function of AD(Z) converges when N≥5.

[0105] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the specific process for determining the threshold value of the test statistic in step three to five is as follows:

[0106]

[0107] Where P(AD(Z)≤λ) represents the probability that AD(Z)≤λ, r j =(-1) jΓ(j+0.5) / (Γ(0.5)j!), where Γ is the Gamma function and w represents the integration variable;

[0108] The significance level α = P(AD(Z)>λ) = 1-P(AD(Z)≤λ). The threshold value λ corresponding to the significance level α is calculated. α is set according to the actual needs in the communication process. In this invention, it is set to 0.05.

[0109] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0110] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the specific process of step three is as follows:

[0111]

[0112] in, This represents the detection probability of the waveform parameters in group a.

[0113] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0114] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that it further includes Step Four, which is: transmitting the signal to be transmitted using the retained waveform parameters.

[0115] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0116] Specific Implementation Method Ten: Combining Figure 2 This embodiment is described below. The difference between this embodiment and any one of specific embodiments one through nine is that the specific process of step four is as follows:

[0117] Step 41: Perform QPSK mapping on the signal sequence to be transmitted at the transmitting end to obtain the mapped baseband signal sequence;

[0118] Step 42: Select any group of waveform parameters from all the retained groups of waveform parameters, use the selected waveform parameters to generate weighting coefficients for the extended weighted fractional Fourier transform, and then use the generated weighting coefficients to perform an extended weighted fractional Fourier transform on the mapped baseband signal sequence.

[0119] Step 43: Modulate the signal after extended weighted fractional Fourier transform onto the carrier frequency to obtain modulated data, and then transmit the modulated data through the antenna.

[0120] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0121] The above examples of this invention are merely illustrative of the computational model and process of this invention, and are not intended to limit the implementation of this invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of this invention are still within the scope of protection of this invention.

Claims

1. A method for selecting fractional-domain waveform parameters based on goodness-of-fit test, characterized in that, The method specifically includes the following steps: Step 1: Randomly generate M strings of length... The signal sequence of the point, and the first The signal sequence is denoted as , , Represents signal sequence The first, the second, ..., the first One element; Step 2: Process the signal sequence Perform QPSK mapping to obtain the mapped... Point baseband signal sequence , , Represents the baseband signal sequence The first, the second, ..., the first One element; Step 3: Establish a waveform parameter database for extended weighted fractional Fourier transform, and use the M baseband signal sequences obtained in Step 2 to select waveform parameters. Any set of waveform parameters in the waveform parameter database of the extended weighted fractional Fourier transform is denoted as... The waveform parameters satisfy: ,and , ; The waveform parameters are selected using the M baseband signal sequences obtained in step two; the specific process is as follows: Step 3. Initialize the number of waveform parameter groups. ; Step 3.2: Initialize the baseband signal sequence number ; Step 33, according to the... The weighting coefficients of the extended weighted fractional Fourier transform are obtained from the group waveform parameters. Then, using weighting coefficients to apply the first... Perform an extended weighted fractional Fourier transform on a baseband signal sequence to obtain the transformed signal. ; According to the first The weighting coefficients of the extended weighted fractional Fourier transform are obtained from the group waveform parameters, specifically: in, These represent the weighting coefficients of the extended weighted fractional Fourier transform. Represents the imaginary unit; Steps three and four: Transform the signal The elements in After taking the square of the modulus, then calculate the result. The results are sorted in ascending order, and the theoretical distribution function is obtained based on the sorting results. The specific process of steps three and four is as follows: Step 3-41, set All are complex Gaussian distributed variables. , , actual part and the virtual part It is an independent and identically distributed real Gaussian random variable with real part and the virtual part Follows a Gaussian distribution , It is the variance of the Gaussian distribution, for the variable The square of the modulus: Step 3-42, to Perform ascending sorting, and denote each element in the sorted result as follows: Then calculate the variables for each element in the sorting results. : Step 3-43, Variables If the variable follows a chi-square distribution with 2 degrees of freedom, then the variable... The theoretical distribution function is: in, Represents the theoretical distribution function. The base of the natural logarithm. express The corresponding theoretical distribution function value; Step 35: Construct the test statistic based on the theoretical distribution function. Then determine the threshold value of the test statistic. ; The test statistic is constructed based on the theoretical distribution function. The specific process is as follows: in, This represents the test statistic. ; The specific process for determining the threshold value of the test statistic is as follows: in, express The probability, , It is the Gamma function. Represents the integral variable; Significance level Calculate the significance level Corresponding threshold value ; Step 36: Calculate the test statistic. With threshold The comparison is used to arrive at a judgment result; specifically: If the test statistic is greater than or equal to the threshold value, then ; If the test statistic is less than the threshold value, then ; Step 37: Determine if the condition is met. , Indicates the total number of baseband signal sequences; If satisfied Then proceed to step three eight; If not satisfied Then let Return to step three; Step 38, Calculate the first Detection probability of group waveform parameters ; Comparison detection probability With threshold The size, if Less than Then the first Group waveform parameters are retained, if Greater than or equal to Then discard the first Group waveform parameters; Then determine whether it is satisfied. , This indicates the total number of waveform parameter groups in the waveform parameter database; If satisfied Then proceed to step 39; If not satisfied Then let Return to step three two; Step 39: Obtain the set of all retained group waveform parameters; Step 4: Transmit the signal to be transmitted using the preserved waveform parameters; The specific process of step four is as follows: Step 41: Perform QPSK mapping on the signal sequence to be transmitted at the transmitting end to obtain the mapped baseband signal sequence; Step 42: Select any group of waveform parameters from all the retained groups of waveform parameters, use the selected waveform parameters to generate weighting coefficients for the extended weighted fractional Fourier transform, and then use the generated weighting coefficients to perform an extended weighted fractional Fourier transform on the mapped baseband signal sequence. Step 43: Modulate the signal after extended weighted fractional Fourier transform onto the carrier frequency to obtain modulated data, and then transmit the modulated data through the antenna.

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