Frequency spectrum sensing method under S alpha S noise based on parameter estimation and logarithmic moment preprocessing

Abstract

The invention relates to a spectrum sensing method under S [alpha] S noise based on parameter estimation and logarithmic moment preprocessing. The method comprises three stages of S [alpha] S distribution noise parameter estimation, received signal logarithmic moment preprocessing and detection judgment. In an S alpha S distribution noise parameter estimation stage, a cognitive user estimates a mean value and a variance of an absolute value logarithm form based on offline S alpha S distribution noise data received by multiple antennas; in the logarithmic moment preprocessing stage, a cognitive user firstly carries out logarithmic operation processing on received signal data and then further carries out normalization processing; in the detection and judgment stage, the difference between the maximum characteristic value of a preprocessed sample covariance matrix and the mean value of reciprocals of all characteristic values is used as a perception judgment quantity, meanwhile, a theoretical judgment threshold value is calculated in combination with asymptotic processing and extreme value characteristic value probability distribution, prior statistical information of S alpha S distribution noise is not needed, the blind detection characteristic is achieved, and the detection accuracy is improved. The method is wide in application range, and has good practicability for the main user signal detection problem in the S alpha S distribution noise.

Description

Technical Field

[0001] The present invention relates to a spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing, which belongs to the field of cognitive radio in wireless communication technology. (Note: SαS is the abbreviation of Symmetric Alpha Stable Distribution, where Alpha represents the Greek letter α) Background Art

[0002] Spectrum sensing refers to the process of determining whether there is a signal in the wireless spectrum through detection, and is a key technology of cognitive radio. Traditional spectrum sensing methods are often based on Gaussian white noise for algorithm design. However, in real environments, since spectrum noise comes from a wide range of sources, rather than simply ideal Gaussian white noise, it often exhibits non-Gaussian characteristics. For example, Alpha stable distribution noise is used to describe the widespread impulse noise, among which SαS distribution is the most commonly used model of Alpha stable distribution. The statistical characteristics of this type of noise are more complex than Gaussian noise, which poses a great challenge to spectrum sensing.

[0003] The characteristic index α determines the strength of the Gaussianity of the Alpha stable distribution. When α is larger, the Gaussianity of the noise is stronger. The Alpha stable distribution model can cover special cases such as Gaussian distribution, Cauchy distribution and Levy distribution. It is this feature that makes the Alpha stable distribution quite flexible and an ideal choice for modeling non-Gaussian noise. At present, some scholars have studied the spectrum sensing problem in the SαS noise background of cognitive radio. Considering that SαS noise does not have second-order statistics and high-order statistics, this poses a severe challenge to the spectrum sensing method based on the eigenvalue of the covariance matrix. At present, this adverse effect is mainly eliminated by preprocessing the received signal. Existing research is based on fractional low-order moment preprocessing to reduce its pulse characteristics. Typical methods include the DMGM method based on the difference of eigenvalues. This method uses fractional low-order preprocessing and combines the geometric mean of eigenvalues ​​to construct the perception decision quantifier. However, this method has two main problems. First, cognitive users need to know the SαS distribution noise parameters in advance, such as the characteristic index and scale parameters of the noise; second, the fractional order parameters need to be set during the detection process. The setting of this parameter has a direct impact on the performance of the perception algorithm, and the current methods do not provide a method for selecting this parameter. These two problems make the fractional low-order moment preprocessing method have great limitations in dealing with spectrum perception problems under SαS distribution noise. Summary of the invention

[0004] Technical problem: The present invention proposes a spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing. The method does not require prior statistical information of SαS distributed noise, has blind detection characteristics, and has good practical application value for the detection of primary user signals in SαS distributed noise.

[0005] Technical solution: To solve the above problems, the present invention proposes a spectrum perception method under SαS noise based on parameter estimation and logarithmic moment preprocessing. This method processes offline SαS distribution noise samples and estimates the relevant statistical parameters of the noise, so no statistical prior information of the noise is required; at the same time, the non-Gaussianity of the SαS distribution noise is effectively reduced by introducing the logarithmic moment and normalization preprocessing process. Compared with the fractional low-order perception method, the preprocessing process proposed in the present invention does not need to set other parameters that affect the perception performance. This method has blind detection characteristics and is very applicable to spectrum perception problems in the SαS distribution noise background.

[0006] The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing of the present invention comprises three stages: SαS distribution noise parameter estimation, received signal logarithmic moment preprocessing, and detection and judgment. In the SαS distribution noise parameter estimation stage, a cognitive user estimates the mean and variance of offline SαS distribution noise data received by multiple antennas in logarithmic form. In the logarithmic moment preprocessing stage, the cognitive user first performs logarithmic operation on the received signal data, and further performs normalization processing on this basis to reduce the pulse characteristics of the SαS distribution noise. In the detection and judgment stage, the difference between the maximum eigenvalue of the sample covariance matrix after the received signal preprocessing and the mean of the inverses of all eigenvalues ​​is used as the perception judgment amount, and the theoretical judgment threshold is calculated in combination with asymptotic processing and extreme eigenvalue probability distribution, and the perception judgment is implemented on this basis.

[0007] The specific steps of this method are:

[0008] Step 1. SαS distribution noise parameter estimation: Assume that the offline SαS distribution noise vector obtained by the cognitive user is w(q) = [w1(q),w2(q),…,w M (q)] T , where q = 1, 2, ..., Q, M represents the number of receiving antennas, Q represents the number of noise vectors, and the superscript "T" represents the transposition operator of the matrix; accordingly, the cognitive user takes the absolute value of the received SαS distribution noise data, and performs logarithmic operation on this basis, thereby obtaining the mean estimate and unbiased estimated variance of the processed SαS distribution noise data;

[0009] Step 2: The cognitive user samples the signals on the M receiving antennas at time n, and the obtained M×1-dimensional primary user received signal component is assumed to be x(n)=[x1(n),x2(n),...,xM (n)] T , continuously sample N times to obtain N received main user signal vectors x(1), x(2), ..., x(N); identify the received signal with SαS distribution noise as z(n) = x(n) + w(n), where z(n) = [z1(n), z2(n), ..., z M (n)] T ; The cognitive user performs logarithmic moment preprocessing on it and performs normalization preprocessing to obtain The sample covariance matrix of the preprocessed received signal is calculated as

[0010] Step 3. Preprocess the sample covariance matrix Perform eigenvalue decomposition to obtain all its eigenvalues, and construct the perception decision amount based on them: in, express The maximum eigenvalue of and Respectively The i-th and j-th eigenvalues ​​of ;

[0011] Step 4. Combined with the unbiased estimated variance of the offline SαS distribution noise data obtained in step 1, the theoretical perception decision threshold η is approximately calculated;

[0012] Step 5. Perform a sensing decision: If the sensing decision value Φ is greater than the sensing decision threshold η, it is determined that the primary user signal exists; otherwise, it is determined that the primary user signal does not exist.

[0013] The specific steps of obtaining the mean estimate and unbiased estimate variance of the processed SαS distribution noise data by the cognitive user in step 1 of the present invention are as follows:

[0014] in,

[0015] Step 1.1. Offline SαS distribution of the noise data component w for unknown parameters m (q) Take the absolute value and perform logarithmic operation to obtain

[0016] Step 1.2. Exploitation Calculate the noise mean estimate of the SαS distribution and variance unbiased estimator

[0017] The logarithmic moment preprocessing operation in step 2 is:

[0018] Step 2.1. Cognitive user's response to multi-antenna received signal z m(n) Take the absolute value and perform logarithmic operation to obtain the processed data and mark it as

[0019] Step 2.2. Recognize the user After normalization, we get From this we get Where m = 1, 2, ..., N, n = 1, 2, ..., N, and the sample covariance matrix after preprocessing is calculated based on this

[0020] The theoretical perception decision threshold η in step 4 is calculated as:

[0021]

[0022] in, Calculated from step 1.2, P f is the target false alarm probability, F1 -1 (·) represents the inverse function of the first-order Tracy-Widom cumulative distribution function.

[0023] Beneficial effects: The beneficial effects of the present invention are mainly reflected in the following four aspects:

[0024] 1. The present invention estimates the statistical parameters of SαS distribution noise using an estimation method, which effectively overcomes the disadvantage that the classic fractional low-order spectrum sensing method under the SαS distribution noise background requires the prior knowledge of the noise statistical parameters;

[0025] 2. The present invention effectively reduces the pulse characteristics of SαS distribution noise through logarithmic moment preprocessing. Compared with the classic fractional low-order moment spectrum sensing algorithm, the proposed preprocessing method does not need to introduce preprocessing parameters, and the algorithm is more robust;

[0026] 3. The present invention provides a spectrum sensing method based on the reciprocal average of eigenvalues, which utilizes all eigenvalue information, and the decision amount is more sensitive to changes in smaller eigenvalues, thereby being more conducive to perception decisions under low signal-to-noise ratios;

[0027] 4. Compared with the classic fractional low-order spectrum sensing method under SαS distributed noise, the method proposed in the present invention does not require SαS distributed noise, primary user signal and channel information. It is a fully blind detection method with a wider range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 The flowchart of a spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing is shown in Figure 2.

[0029] Figure 2 M = 5, N = 300, Pf =0.1, α=1.8, the difference in eigenvalues ​​between the method proposed in the present invention and the DMGM method under different fractional low-order moment preprocessing orders t, and the comparison of the detection probability curves with the generalized signal-to-noise ratio.

[0030] Figure 3 M = 5, N = 300, P f =0.1, a comparison of the detection probability of the method proposed in the present invention with the generalized signal-to-noise ratio under different characteristic exponents α. DETAILED DESCRIPTION

[0031] All symbol annotations

[0032]

[0033]

[0034] The present invention proposes a spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing, which includes three stages: distributed noise parameter estimation, received signal logarithmic moment preprocessing, and detection and judgment. In the SαS distributed noise parameter estimation stage, the cognitive user estimates the mean and variance of the logarithmic form based on the offline SαS distributed noise data received by multiple antennas; in the logarithmic moment preprocessing stage, the cognitive user first performs logarithmic operation on the received signal data, and further performs normalization processing on this basis to reduce the pulse characteristics of the SαS distributed noise; in the detection and judgment stage, the difference between the maximum eigenvalue of the sample covariance matrix after the received signal preprocessing and the mean of the inverse of all eigenvalues ​​is used as the perception judgment amount, and the theoretical judgment threshold value is calculated by combining asymptotic processing and extreme eigenvalue probability distribution, and the perception judgment is implemented on this basis. In the calculation of the perception judgment threshold, since the distribution characteristics of the inverse mean are relatively complex, in order to simplify the calculation process, the minimum eigenvalue is replaced to obtain an approximate threshold value. The design of the blind spectrum sensing method under SαS distribution noise combining parameter estimation and logarithmic moment preprocessing proposed in the present invention is described in detail below.

[0035] 1. Mathematical model

[0036] Assume that the cognitive user samples the signals on M receiving antennas at time n and obtains the M×1-dimensional primary user received signal component x(n)=[x1(n),x2(n),…,x M (n)] T , continuous sampling N times to obtain N received main user signal vectors x(1), x(2), ..., x(N). The received signal with SαS distribution noise is identified as z(n) = x(n) + w(n), where w(n) = [w1(n), w2(n), ..., w M (n)] Tis an M×1-dimensional SαS distributed noise vector, z(n)=[z1(n),z2(n),...,z M (n)] T is the received signal vector obtained by the secondary user. H0 represents the state where the primary user signal does not exist, and H1 represents the state where the primary user signal exists. The spectrum sensing problem in SαS distribution noise can be mathematically expressed as the following binary hypothesis test model:

[0037]

[0038] 2. Theoretical analysis of implementation methods

[0039] Most of the existing studies on spectrum sensing algorithms based on SαS distributed noise are conducted under the condition that the parameters are known. However, in real scenarios, these parameters are unknown, which makes these algorithms lack practicality in real scenarios. The parameter estimation of the present invention can effectively solve this problem. By performing logarithmic moment and normalization preprocessing on the received signal, the pulse characteristics of the SαS distributed noise can be effectively reduced, while avoiding the need for other preprocessing methods to set parameters, such as the fractional order parameters in the fractional low-order moment preprocessing. In terms of threshold calculation, since the distribution of the inverse mean of the eigenvalue is relatively complex, it is replaced by the minimum eigenvalue to obtain a simple theoretical threshold closed form.

[0040] First, the noise data component w is distributed offline SαS with unknown parameters m (q) Take the absolute value and perform logarithmic operation to obtain:

[0041]

[0042] On this basis, using Calculate the unbiased estimate of the noise mean and variance of the SαS distribution:

[0043]

[0044] The cognitive user takes the absolute value of the multi-antenna received signal and performs logarithmic operation to obtain On this basis After normalization, we get From this we get Where m = 1, 2, ..., M, n = 1, 2, ..., N, and the sample covariance matrix after preprocessing is calculated based on this The sample covariance matrix after preprocessing Perform eigenvalue decomposition and construct the perception decision quantity based on all the obtained eigenvalues:

[0045]

[0046] in, express The maximum eigenvalue of and Respectively The i-th and j-th eigenvalues ​​of . Since the distribution characteristics of the average p / q of the inverse of all eigenvalues ​​are relatively complex, in order to simplify the calculation process, it is replaced by the minimum eigenvalue to obtain an approximate threshold value. On this basis, if the perceived decision amount is greater than the decision threshold, it is determined that the primary user signal exists, otherwise it is determined that the primary user signal does not exist. The false alarm probability is defined as:

[0047]

[0048] Replacing the reciprocal mean of the eigenvalues ​​with the minimum eigenvalue yields:

[0049]

[0050] definition Then we have:

[0051]

[0052] Note that if Then (θ MAX (B(N))-u) / v converges to the first-order Tracy-Widom distribution with probability 1. Therefore:

[0053]

[0054] in, Therefore

[0055]

[0056] From random matrix theory, we know that if Then in the H0 state, the following conclusions hold:

[0057]

[0058] From this we can get:

[0059]

[0060] Among them, F1 -1 (·) represents the inverse function of the first-order Tracy-Widom cumulative distribution function.

[0061] (III) Specific implementation steps

[0062] Combined with the above analysis process and flow chart, the implementation steps of the blind spectrum sensing method under SαS distribution noise based on parameter estimation and logarithmic moment preprocessing involved in the present invention are further explained:

[0063] (a) Assume that the offline SαS noise vector obtained by the cognitive user is w(q) = [w1(q),w2(q),...,w M (q)] T , where q = 1, 2, ..., Q, M represents the number of receiving antennas, Q represents the number of noise vectors, and the superscript "T" represents the transposition operator of the matrix. Based on this, the cognitive user takes the absolute value of the received SαS distribution noise data, and performs logarithmic operations on this basis, thereby obtaining the mean estimate of the processed SαS distribution noise data and the unbiased estimate of the variance.

[0064] (b) The cognitive user samples the signal on the M receiving antennas at time n, and the obtained M×1-dimensional primary user received signal component is assumed to be x(n)=[x1(n),x2(n),...,x M (n)] T , continuous sampling N times to obtain N received main user signal vectors x(1), x(2), ..., x(N). The received signal with SαS distribution noise is represented by z(n) = x(n) + w(n), where z(n) = [z1(n), z2(n), ..., z M (n)] T The cognitive user performs logarithmic moment operation on it and performs normalization preprocessing to obtain The sample covariance matrix of the preprocessed received signal is calculated as

[0065] (c) The covariance matrix of the preprocessed samples Perform eigenvalue decomposition to obtain all its eigenvalues, and construct the perception decision amount based on them: in, express The maximum eigenvalue of and Respectively The i-th and j-th eigenvalues ​​of .

[0066] (d) combining the unbiased estimated variance of the offline SαS distribution noise data obtained in step (a), and approximately calculating the theoretical perception decision threshold η;

[0067] (e) Performing a perception decision: If the perception decision value Φ is greater than the perception decision threshold η, it is determined that the primary user signal exists; otherwise, it is determined that the primary user signal does not exist.

[0068] in,

[0069] The specific steps of calculating the mean and variance of the SαS distribution noise parameters by the cognitive user using the offline SαS distribution noise data in step (a) are as follows:

[0070] Step ① Offline SαS distribution of noise data component w of unknown parameters m (q) Take the absolute value and perform logarithmic operation to obtain

[0071] Step 2: Use Calculate the noise mean estimate of the SαS distribution and variance unbiased estimator

[0072] The logarithmic moment preprocessing process described in step (b) is:

[0073] Step ① The cognitive user takes the absolute value of the multi-antenna received signal and performs logarithmic operation to obtain

[0074] Step ② Recognize the user After normalization, we get From this we get Where m = 1, 2, ..., N, n = 1, 2, ..., N, and the sample covariance matrix after preprocessing is calculated based on this

[0075] The specific calculation method of the theoretical perception decision threshold η in step (d) is:

[0076]

[0077] in, Calculated from step 1.2, P f is the target false alarm probability, F1 -1 (·) represents the inverse function of the first-order Tracy-Widom cumulative distribution function.

[0078] Figure 2 For N=5, N=300, P f=0.1, α=1.8. The difference in eigenvalues ​​between the method proposed in the present invention and the DMGM method under different fractional low-order moment preprocessing orders t. The curve diagram of the detection probability of the DMGM method changes with the generalized signal-to-noise ratio. The detection performance of the method proposed in the present invention improves with the increase of the generalized signal-to-noise ratio GSNR. From the simulation results, it can be seen that the detection performance of the classic DMGM algorithm based on fractional low-order moment preprocessing changes with the change of the order t of the fractional low-order moment preprocessing. However, for this algorithm, how to select the appropriate order t of the fractional low-order moment preprocessing is not provided. In contrast, the method proposed in the present invention adopts logarithmic moment preprocessing, does not require any preprocessing parameter setting, and exhibits excellent detection performance and has good robustness characteristics, and has a wider range of applications.

[0079] Figure 3 M = 5, N = 300, P f =0.1, a curve diagram of the detection probability of the method proposed in the present invention changing with the generalized signal-to-noise ratio GSNR under different characteristic exponents α. The simulation results show that when α is given, the detection performance of the method proposed in the present invention also improves with the increase of the generalized signal-to-noise ratio GSNR. It is also noted that when the characteristic index α is not equal to 2, the SαS distribution noise exhibits the characteristics of impulse noise. It can be seen from the simulation results that even when the noise exhibits very strong non-Gaussian characteristics (α=0.8), the method proposed in the present invention also exhibits excellent detection performance. It can be seen that the method based on logarithmic moment preprocessing proposed in the present invention can well suppress the non-Gaussian characteristics of noise, thereby effectively ensuring that cognitive users make correct decisions in the perception judgment process.

Claims

1. A spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing, the method includes three stages: SαS distribution noise parameter estimation, received signal logarithmic moment preprocessing, and detection and judgment; in the SαS distribution noise parameter estimation stage, the cognitive user estimates the mean and variance of the logarithmic form based on the offline SαS distribution noise data received by multiple antennas; in the logarithmic moment preprocessing stage, the cognitive user first performs logarithmic operation on the received signal data, and further performs normalization processing on this basis to reduce the pulse characteristics of the SαS distribution noise; in the detection and judgment stage, the difference between the maximum eigenvalue of the sample covariance matrix after the received signal preprocessing and the mean of the inverse of all eigenvalues ​​is used as the perception judgment amount, and the theoretical judgment threshold is calculated by combining asymptotic processing and the probability distribution of extreme eigenvalues, and the perception judgment is implemented on this basis.

2. The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing according to claim 1 is characterized in that The specific steps of this method are: Step 1. SαS distribution noise parameter estimation: Assume that the offline SαS distribution noise vector obtained by the cognitive user is w(q) = [w1(q),w2(q),...,w M (q)] T , where q = 1, 2, ..., Q, M represents the number of receiving antennas, Q represents the number of noise vectors, and the superscript "T" represents the transposition operator of the matrix; accordingly, the cognitive user takes the absolute value of the received SαS distribution noise data, and performs logarithmic operation on this basis, thereby obtaining the mean estimate and unbiased estimated variance of the processed SαS distribution noise data; Step 2: The cognitive user samples the signal on the M receiving antennas at time n, and the obtained M×1-dimensional primary user received signal component is x(n)=[x1(n),x2(n),...,x M (n)] T , continuously sample N times to obtain N received main user signal vectors x(1), x(2), ..., x(N); identify the received signal with SαS distribution noise as z(n) = x(n) + w(n), where z(n) = [z1(n), z2(n), ..., z M (n)] T ; The cognitive user performs logarithmic moment preprocessing on it and performs normalization preprocessing to obtain The sample covariance matrix of the preprocessed received signal is calculated as Step 3. Preprocess the sample covariance matrix Perform eigenvalue decomposition to obtain all its eigenvalues, and construct the perception decision amount based on them: in, express The maximum eigenvalue of and Respectively The i-th and j-th eigenvalues ​​of ; Step 4. Combined with the unbiased estimated variance of the offline SαS distribution noise data obtained in step 1, the theoretical perception decision threshold η is approximately calculated; Step 5. Perform a sensing decision: If the sensing decision value Φ is greater than the sensing decision threshold η, it is determined that the primary user signal exists; otherwise, it is determined that the primary user signal does not exist.

3. The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing according to claim 2 is characterized in that Step 1: The cognitive user obtains the mean estimate and unbiased estimate variance of the processed SαS distribution noise data in the following specific steps: Step 1.

1. Offline SαS distribution of the noise data component w for unknown parameters m (q) Take the absolute value and perform logarithmic operation to obtain m=1, 2,...,M, q=1, 2,...,Q; Step 1.

2. Exploitation Calculate the noise mean estimate of the SαS distribution and variance unbiased estimator 4. The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing according to claim 2 is characterized in that The logarithmic moment preprocessing operation in step 2 is: Step 2.

1. Cognitive user's response to multi-antenna received signal z m (n) Take the absolute value and perform logarithmic operation to obtain the processed data and mark it as Step 2.

2. Recognize the user After normalization, we get From this we get Where m = 1, 2, ..., M, n = 1, 2, ..., N, and the sample covariance matrix after preprocessing is calculated based on this 5. The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing according to claim 2 or 3, characterized in that The theoretical perception decision threshold η in step 4 is calculated as: in, Calculated from step 1.2, P f is the target false alarm probability, Represents the inverse of the first-order Tracy-Widom cumulative distribution function.

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