A Spectrum Sensing Method for SαS Noise Based on Parameter Estimation and Logarithmic Moment Preprocessing

Abstract

This invention relates to a spectrum sensing method for SαS noise based on parameter estimation and logarithmic moment preprocessing. The method comprises three stages: SαS distributed noise parameter estimation, received signal logarithmic moment preprocessing, and detection decision. In the SαS distributed noise parameter estimation stage, the cognitive user estimates the mean and variance in absolute logarithmic form based on offline SαS distributed noise data received from multiple antennas. In the logarithmic moment preprocessing stage, the cognitive user first performs logarithmic operations on the received signal data and then further normalizes it. In the detection decision stage, the difference between the largest eigenvalue and the mean of the reciprocals of all eigenvalues ​​of the preprocessed sample covariance matrix is ​​used as the sensing decision quantity. Simultaneously, asymptotic processing and the probability distribution of extreme eigenvalues ​​are combined to calculate the theoretical decision threshold. This invention does not require prior statistical information about the SαS distributed noise, exhibits blind detection characteristics, has a wide range of applications, and is highly practical for detecting primary user signals in SαS distributed noise.

Description

Technical Field

[0001] This invention relates to a spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing, belonging to the field of cognitive radio in wireless communication technology. (Note: SαS is an abbreviation for SymmetricAlpha Stable Distribution, where Alpha represents the Greek letter α.) Background Technology

[0002] Spectrum sensing refers to the detection and determination of the presence of signals in the wireless spectrum, and is a key technology in cognitive radio. Traditional spectrum sensing methods are often based on Gaussian white noise algorithms. However, in real-world environments, spectrum noise sources are widespread and not simply ideal Gaussian white noise, often exhibiting non-Gaussian properties. For example, Alpha stable distribution noise is used to describe the widespread impulse noise, with the SαS distribution being the most commonly used model of the Alpha stable distribution. The statistical characteristics of this type of noise are more complex than Gaussian noise, posing a significant challenge to spectrum sensing.

[0003] The eigenvalue index α determines the strength of the Gaussianity of the Alpha stable distribution; the larger α is, the stronger the Gaussianity of the noise. The Alpha stable distribution model can cover special cases such as Gaussian, Cauchy, and Lévy distributions. This characteristic makes the Alpha stable distribution quite flexible, making it an ideal choice for modeling non-Gaussian noise. Currently, some scholars have studied the spectrum sensing problem in cognitive radio SαS noise backgrounds. Considering that SαS noise lacks second-order and higher-order statistics, this poses a significant challenge to spectrum sensing methods based on the eigenvalues ​​of the covariance matrix. Currently, this adverse effect is mainly eliminated through preprocessing of the received signal. Existing research is based on fractional low-order moment preprocessing to reduce its impulse characteristics. A typical example is the DMGM method based on the difference of eigenvalues, which uses fractional low-order preprocessing combined with the geometric mean of eigenvalues ​​to construct the sensing decision quantity. However, this method has two main problems: first, cognitive users need to know the SαS distributed noise parameters in advance, such as the noise's eigenvalue index and scale parameters; second, fractional-order parameters need to be set during the detection process. The setting of this parameter directly affects the performance of the sensing algorithm, but current methods do not provide a way to select this parameter. These two issues make fractional low-order moment preprocessing methods quite limited in handling spectral sensing problems under SαS distributed noise. Summary of the Invention

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

[0005] Technical Solution: To address the aforementioned problems, this invention proposes a spectrum sensing method for SαS noise based on parameter estimation and logarithmic moment preprocessing. This method processes offline SαS distributed noise samples and estimates the relevant statistical parameters of the noise, thus eliminating the need for prior statistical information about the noise. Simultaneously, by introducing logarithmic moments and normalization preprocessing, the non-Gaussianity of the SαS distributed noise is effectively reduced. Compared to fractional low-order sensing methods, the preprocessing proposed in this invention does not require setting other parameters that affect sensing performance. This method exhibits blind detection characteristics and is highly applicable to spectrum sensing problems in SαS distributed noise backgrounds.

[0006] This invention presents a spectrum sensing method for SαS noise based on parameter estimation and logarithmic moment preprocessing, comprising three stages: SαS distributed noise parameter estimation, received signal logarithmic moment preprocessing, and detection decision. In the SαS distributed noise parameter estimation stage, the cognitive user estimates the logarithmic mean and variance of the SαS distributed noise based on offline SαS distributed noise data received from multiple antennas. In the logarithmic moment preprocessing stage, the cognitive user first performs logarithmic operations on the received signal data, and then further performs normalization processing to reduce the impulse characteristics of the SαS distributed noise. In the detection decision stage, the difference between the largest eigenvalue and the mean of the reciprocals of all eigenvalues ​​of the sample covariance matrix after received signal preprocessing is used as the sensing decision quantity. Simultaneously, a theoretical decision threshold is calculated by combining asymptotic processing and the probability distribution of extreme eigenvalues, and the sensing decision is then implemented based on this threshold.

[0007] The specific steps of this method are as follows:

[0008] Step 1. SαS distribution noise parameter estimation: Let the offline SαS distribution noise vector obtained by the cognitive user be 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 matrix transpose operator; accordingly, the cognitive user takes the absolute value of the received SαS distributed noise data, performs logarithmic operation on this basis, and obtains the mean estimate and unbiased estimate variance of the processed SαS distributed noise data.

[0009] Step 2. The cognitive user samples the signal from the M receiving antennas at time n. Let the resulting M×1 dimensional primary user received signal components be x(n)=[x1(n),x2(n),...,xM (n)] T N consecutive samplings yield N received primary user signal vectors x(1), x(2), ..., x(N); the received signal with SαS distributed noise is identified 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 then performs normalization preprocessing to obtain... Therefore, the sample covariance matrix of the preprocessed received signal is calculated.

[0010] Step 3. Process the preprocessed sample covariance matrix Perform eigenvalue decomposition to obtain all its eigenvalues, and then construct the perceptual decision factor from them: in, express The largest eigenvalue, and They represent The i-th and j-th eigenvalues;

[0011] Step 4. Using the unbiased estimate variance of the offline SαS distribution noise data obtained in Step 1, the theoretical sensing decision threshold η is approximately calculated.

[0012] Step 5. Perform a perception decision: If the perception decision quantity Φ is greater than the perception decision threshold η, the primary user signal is determined to exist; otherwise, the primary user signal is determined not to exist.

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

[0014] in,

[0015] Step 1.1. For the offline SαS distribution noise data components w with unknown parameters m (q) Take the absolute value and perform logarithmic operations to obtain

[0016] Step 1.2. Utilize Calculate the mean estimate of the SαS distribution noise Unbiased estimation of variance

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

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

[0019] Step 2.2. Understanding User Perception Normalization process is performed to obtain Therefore, we obtain Where m = 1, 2, ..., N, n = 1, 2, ..., N, and the preprocessed sample covariance matrix is ​​calculated accordingly.

[0020] In step 4, the theoretical perception decision threshold η is calculated as follows:

[0021]

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

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

[0024] 1. This invention utilizes an estimation method to estimate the statistical parameters of SαS distributed noise, effectively overcoming the drawback of the classic fractional low-order spectrum sensing method under the background of SαS distributed noise, which requires prior knowledge of the noise statistical parameters;

[0025] 2. This invention effectively reduces the impulse 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 require the introduction of preprocessing parameters, and the algorithm is more robust.

[0026] 3. This invention provides a spectrum sensing method based on the inverse average of eigenvalues, which utilizes all eigenvalue information and the decision quantity is more sensitive to changes in smaller eigenvalues, thus being more beneficial for sensing decisions under low signal-to-noise ratio.

[0027] 4. Compared with the classic fractional low-order spectrum sensing method under SαS distributed noise, the method proposed in this invention does not require SαS distributed noise, main user signal and channel information, and belongs to a completely blind detection method with a wider range of applications. Attached Figure Description

[0028] Figure 1 This is a flowchart of a spectrum sensing method for SαS noise based on parameter estimation and logarithmic moment preprocessing.

[0029] Figure 2 For M=5, N=300, Pf The graph shows a comparison of the detection probability of the proposed method and the DMGM method with the generalized signal-to-noise ratio when α = 0.1 and α = 1.8.

[0030] Figure 3 For M=5, N=300, P f Comparison of detection probability curves with generalized signal-to-noise ratio under different feature indices α when α=0.1. Detailed Implementation

[0031] All symbol annotations

[0032]

[0033]

[0034] This invention proposes a spectrum sensing method for SαS noise based on parameter estimation and logarithmic moment preprocessing. The method comprises three stages: distributed noise parameter estimation, received signal logarithmic moment preprocessing, and detection decision. In the SαS distributed noise parameter estimation stage, the cognitive user estimates the logarithmic mean and variance of the SαS distributed noise based on offline SαS distributed noise data received from multiple antennas. In the logarithmic moment preprocessing stage, the cognitive user first performs logarithmic operations on the received signal data, and then further normalizes it to reduce the impulse characteristics of the SαS distributed noise. In the detection decision stage, the difference between the largest eigenvalue and the mean of the reciprocals of all eigenvalues ​​of the sample covariance matrix after received signal preprocessing is used as the sensing decision quantity. Simultaneously, a theoretical decision threshold is calculated by combining asymptotic processing and the probability distribution of extreme eigenvalues, and a sensing decision is then implemented based on this. In the calculation of the sensing decision threshold, since the distribution characteristics of the reciprocal mean are relatively complex, the smallest eigenvalue is substituted to simplify the calculation process, thereby obtaining an approximate threshold value. The following section elaborates on the design of the blind spectrum sensing method under SαS distributed noise, which combines parameter estimation and logarithmic moment preprocessing, as proposed in this invention.

[0035] (I) Mathematical Model

[0036] Assume that the M×1 dimensional primary user received signal components obtained by the cognitive user sampling the signals on the M receiving antennas at time n are x(n)=[x1(n),x2(n),…,x M (n)] T N consecutive samplings yield N received primary user signal vectors x(1), x(2), ..., x(N). The received signal with SαS distributed noise is identified as z(n) = x(n) + w(n), where w(n) = [w1(n), w2(n), ..., w...]. M (n)] TLet z(n) be an M×1 dimensional SαS distributed noise vector, where z(n) = [z1(n), z2(n), ..., z M (n)] T Let H0 represent the received signal vector obtained by the secondary user, and H1 represent the state where the primary user signal is absent. Then, the spectrum sensing problem in SαS distributed noise can be mathematically represented by the following binary hypothesis testing model:

[0037]

[0038] (II) Theoretical Analysis of Implementation Methods

[0039] Most existing research on spectrum sensing algorithms based on SαS distributed noise is conducted under conditions where parameters are known. However, in real-world scenarios, these parameters are unknown, making these algorithms impractical. The parameter estimation method of this invention effectively solves this problem. By performing logarithmic moment and normalization preprocessing on the received signal, the impulse characteristics of SαS distributed noise can be effectively reduced, while avoiding the parameter setting issues required by other preprocessing methods, such as the fractional order parameters in fractional low-order moment preprocessing. Regarding threshold calculation, since the distribution of the inverse mean of eigenvalues ​​is complex, it is calculated using the smallest eigenvalue, thus obtaining a simple theoretical closed-form threshold.

[0040] First, the offline SαS distribution noise data component w with unknown parameters... m (q) is obtained by taking the absolute value and performing a logarithmic operation:

[0041]

[0042] Based on this, utilize Calculate the mean estimate and unbiased variance estimate of the SαS distributed noise:

[0043]

[0044] The cognitive user obtains the result by taking the absolute value of the received signal from multiple antennas and performing logarithmic operations. Based on this, Normalization process is performed to obtain Therefore, we obtain Where m = 1, 2, ..., M, n = 1, 2, ..., N, and the preprocessed sample covariance matrix is ​​calculated accordingly. The preprocessed sample covariance matrix Perform eigenvalue decomposition and construct a perceptual decision metric based on all the obtained eigenvalues:

[0045]

[0046] in, express The largest eigenvalue, and They represent The i-th and j-th eigenvalues ​​are used. Since the distribution characteristics of the average p / q of the reciprocals of all eigenvalues ​​are complex, to simplify the calculation process, it is replaced by the smallest eigenvalue, thus obtaining an approximate threshold value. Based on this, if the perceived decision value is greater than the decision threshold, the primary user signal is determined to exist; otherwise, the primary user signal is determined not to exist. From the definition of false alarm probability:

[0047]

[0048] Replacing the inverse average of the eigenvalues ​​with the smallest eigenvalue yields:

[0049]

[0050] definition Then we have:

[0051]

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

[0053]

[0054] in, Therefore there is

[0055]

[0056] According to the theory of random matrices, if Then, in state H0, the following conclusion holds:

[0057]

[0058] Therefore, we can conclude that:

[0059]

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

[0061] (III) Specific Implementation Steps

[0062] Based on the above analysis and flowchart, the implementation steps of the blind spectral sensing method for SαS distributed noise based on a combination of parameter estimation and logarithmic moment preprocessing involved in this invention will be further explained:

[0063] (a) Let the offline SαS noise vector obtained by the cognitive user be 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" indicates the matrix transpose operator. Based on this, the cognitive user takes the absolute value of the received SαS distributed noise data and performs logarithmic processing on it, thereby obtaining an estimate of the mean and an unbiased estimate of the variance of the processed SαS distributed noise data.

[0064] (b) The cognitive user samples the signals on the M receiving antennas at time n. Let the resulting M×1 dimensional primary user received signal components be x(n) = [x1(n), x2(n), ..., x...]. M (n)] T N consecutive samplings yield N received primary user signal vectors x(1), x(2), ..., x(N). The received signal with SαS distributed noise is identified as z(n) = x(n) + w(n), where z(n) = [z1(n), z2(n), ..., z...]. M (n)] T The cognitive user performs logarithmic moment operations on it and then performs normalization preprocessing to obtain... Therefore, the sample covariance matrix of the preprocessed received signal is calculated.

[0065] (c) The preprocessed sample covariance matrix Perform eigenvalue decomposition to obtain all its eigenvalues, and then construct the perceptual decision factor from them: in, express The largest eigenvalue, and They represent The i-th and j-th eigenvalues.

[0066] (d) Combining the unbiased estimate variance of the offline SαS distributed noise data obtained in step (a), the theoretical sensing decision threshold η is approximately calculated.

[0067] (e) Perform perception decision: If the perception decision quantity Φ is greater than the perception decision threshold η, determine that the main user signal exists; otherwise, determine that the main user signal does not exist.

[0068] in,

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

[0070] Step ① For the offline SαS distribution noise data components w with unknown parameters m (q) Take the absolute value and perform logarithmic operations to obtain

[0071] Step ② utilize Calculate the mean estimate of the SαS distribution noise Unbiased estimation of variance

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

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

[0074] Step 2: Understanding User Perception Normalization process is performed to obtain Therefore, we obtain Where m = 1, 2, ..., N, n = 1, 2, ..., N, and the preprocessed sample covariance matrix is ​​calculated accordingly.

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

[0076]

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

[0078] Figure 2 For N=5, N=300, P fThe graph shows the difference in eigenvalues ​​between the proposed method and the DMGM method under different fractional low-order moment preprocessing orders t when α = 0.1 and α = 1.8, and is a curve illustrating the variation of detection probability with generalized signal-to-noise ratio (GSNR). The detection performance of the proposed method improves with increasing GSNR. Simulation results show that the detection performance of the classic DMGM algorithm based on fractional low-order moment preprocessing changes with the order t of the preprocessing; however, this algorithm does not provide any method for selecting a suitable order t for the preprocessing. In contrast, the proposed method uses logarithmic moment preprocessing, requires no preprocessing parameter settings, and exhibits excellent detection performance and robustness, making it more widely applicable.

[0079] Figure 3 For M=5, N=300, P f The graph shows the detection probability of the proposed method as a function of the generalized signal-to-noise ratio (GSNR) under different feature exponents α when α = 0.1. Simulation results show that, given α, the detection performance of the proposed method also improves with the increase of the GSNR. It is also noted that when the feature exponent α is not equal to 2, the SαS distribution noise exhibits impulse noise characteristics. The simulation results show that even when the noise exhibits very strong non-Gaussian characteristics (α = 0.8), the proposed method still demonstrates excellent detection performance. Therefore, the logarithmic moment preprocessing method proposed in this invention can effectively suppress the non-Gaussian characteristics of noise, thereby effectively ensuring that the cognitive user makes the correct decision during the perception process.

Claims

1. A spectrum sensing method for SαS noise based on parameter estimation and logarithmic moment preprocessing, comprising three stages: SαS distributed noise parameter estimation, received signal logarithmic moment preprocessing, and detection decision; in the SαS distributed noise parameter estimation stage, the cognitive user estimates the mean and variance in logarithmic form based on offline SαS distributed noise data received from multiple antennas; in the logarithmic moment preprocessing stage, the cognitive user first performs logarithmic operation on the received signal data, and then further performs normalization processing to reduce the impulse characteristics of SαS distributed noise; In the detection and decision stage, the difference between the largest eigenvalue and the mean of the reciprocals of all eigenvalues ​​of the sample covariance matrix after the received signal preprocessing is used as the sensing decision quantity. At the same time, the theoretical decision threshold is calculated by combining asymptotic processing and extreme value eigenvalue probability distribution, and the sensing decision is implemented on this basis. The specific steps of this method are as follows: Step 1. SαS distribution noise parameter estimation: Let the offline SαS distribution noise vector obtained by the cognitive user be w(q)=[w1(q),w2(q),...,w M (q)] T ,in, q = 1, 2, ..., Q, M represents the number of receiving antennas, Q represents the number of noise vectors, and the superscript "T" represents the matrix transpose operator; accordingly, the cognitive user takes the absolute value of the received SαS distributed noise data, performs logarithmic operation on this basis, and obtains the mean estimate and unbiased estimate variance of the processed SαS distributed noise data. Step 2. The cognitive user samples the signal from the M receiving antennas at time n. Let the resulting M×1 dimensional primary user received signal components be x(n)=[x1(n),x2(n),...,x M (n)] T N consecutive samplings yield N received primary user signal vectors x(1), x(2), ..., x(N); the received signal with SαS distributed noise is identified 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 then performs normalization preprocessing to obtain... Therefore, the sample covariance matrix of the preprocessed received signal is calculated. Step 3. Process the preprocessed sample covariance matrix Perform eigenvalue decomposition to obtain all its eigenvalues, and then construct the perceptual decision metric from them: in, express The largest eigenvalue, and They represent The i-th and j-th eigenvalues; Step 4. Using the unbiased estimate variance of the offline SαS distribution noise data obtained in Step 1, the theoretical sensing decision threshold η is approximately calculated. Step 5. Perform a perception decision: If the perception decision quantity Φ is greater than the perception decision threshold η, the primary user signal is determined to exist; otherwise, the primary user signal is determined not to exist.

2. The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing according to claim 1, characterized in that... The specific steps for obtaining the mean estimate and unbiased variance estimate of the processed SαS distributed noise data by the cognitive user in step 1 are as follows: Step 1.

1. For the offline SαS distribution noise data components w with unknown parameters m (q) Take the absolute value and perform logarithmic operations to obtain m=1,2,...,M, q=1,2,...,Q; Step 1.

2. Utilize Calculate the mean estimate of the SαS distribution noise Unbiased estimation of variance 3. The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing according to claim 2, characterized in that... The logarithmic moment preprocessing operation in step 2 is as follows: Step 2.

1. Understanding the user's perception of the multi-antenna received signal z m (n) Take the absolute value and perform logarithmic operation to obtain the processed data, and label it as... Step 2.

2. Understanding User Perception Normalization process is performed to obtain Therefore, we obtain Where m = 1, 2, ..., M, n = 1, 2, ..., N, and the preprocessed sample covariance matrix is ​​calculated accordingly.

4. The spectrum sensing method under SαS noise based on parameter estimation and logarithmic moment preprocessing according to claim 3, characterized in that... In step 4, the theoretical perception decision threshold η is calculated as follows: in, P is calculated from step 1.

2. f The probability of a false alarm for the target. It represents the inverse function of the first-order Tracy-Widom cumulative distribution function.

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