Total blind multi-master user spectrum sensing method based on extreme value characteristic value

Abstract

The invention relates to a full-blind multi-master-user spectrum sensing method based on extreme value characteristic values, which is characterized in that a sensing judgment quantity is constructed by using a difference value of the extreme value characteristic values and harmonic average: firstly, a multi-antenna sensing node calculates a sampling covariance matrix # imgabs0 # by using a received signal vector so as to calculate a maximum characteristic value and a minimum characteristic value of the sampling covariance matrix # imgabs0 #; thirdly, constructing a perception decision amount # imgabs1 # by using the ratio of the difference value of the extreme value characteristic values to the harmonic average value, and calculating a decision threshold t based on the analysis result of the extreme value characteristic values; and finally, carrying out perception judgment: when # imgabs2 is greater than t, judging that a multi-master user signal exists; otherwise, determining that the multi-master user signal does not exist. The method provided by the invention has reliable false alarm performance, and the detection probability higher than that of classical maximum and minimum characteristic value ratio and covariance absolute value detection can be obtained under the condition of low signal-to-noise ratio; and the method can realize total blind detection, the judgment threshold can be directly calculated based on closed expression, and the method has the advantages of simplicity and convenience in calculation and low complexity.

Description

Technical Field

[0001] The invention relates to a multi-master user spectrum sensing method suitable for cognitive radio, and belongs to the technical field of cognitive radio in wireless communications. Background Art

[0002] With the development of wireless communication technologies such as the Internet of Things, Industrial Internet, and ultra-dense networks, multiple primary user signals will often share the same frequency band in future cognitive radio networks. Therefore, designing an effective multi-primary user signal detection method has become an important research direction.

[0003] With the development of high-dimensional random matrix theory, spectrum sensing methods based on the extreme eigenvalues ​​of random matrices have attracted widespread attention. Among them, the most representative methods are spectrum sensing methods based on the ratio of the maximum and minimum eigenvalues, and the difference between the maximum and minimum eigenvalues ​​and their improvements. The spectrum sensing method based on the ratio of the maximum and minimum eigenvalues ​​uses the ratio of the extreme eigenvalues ​​of the sampled covariance matrix as the perception decision quantifier. Since this decision quantifier can effectively reflect the energy brought by the primary user signal and the changes in the related characteristics of the received signal, this method can well detect whether the primary user signal appears in the authorized frequency band. In theory, this method is not only applicable to the single primary user signal detection scenario, but also to the multi-primary user signal detection scenario. The spectrum sensing method based on the difference between the maximum and minimum eigenvalues ​​and its improvements estimates the noise variance and can be effectively applied to the spectrum sensing scenario with unknown noise variance. Existing research results show that this type of method has better perception performance than the classic energy detection method when the noise is uncertain. Unfortunately, in the use of the spectrum sensing method based on the difference between the maximum and minimum eigenvalues ​​and its improvements, the accurate estimation of the noise variance depends on the assumption that the covariance matrix of the primary user signal is a rank 1 matrix. The actual situation is that this matrix is ​​usually a full-rank matrix in the multi-user spectrum sensing scenario. Obviously, this type of algorithm no longer has the best detection performance. Therefore, how to design a fully blind multi-user spectrum sensing method based on the difference of extreme eigenvalues ​​has important practical application value. Summary of the invention

[0004] Technical problem: The present invention is based on the maximum and minimum eigenvalues ​​of the received signal sampling covariance matrix, and uses the difference between the maximum and minimum eigenvalues ​​and the ratio of their harmonic means to construct a perception decision quantity, and proposes a fully blind multi-user spectrum sensing method based on extreme eigenvalues ​​with reliable perception performance.

[0005] Technical solution: The method proposed in the present invention uses the difference of the extreme eigenvalues ​​of the sampled covariance matrix and the harmonic mean to construct a statistical perception decision amount: first, the multi-antenna signal of the perception node is continuously sampled to obtain a set of received signal data vectors; then, the received signal data vector is used to calculate the sampling covariance matrix of the received signal, and its maximum eigenvalue and minimum eigenvalue are calculated; then, the perception decision amount is constructed using the ratio of the extreme eigenvalue difference and the harmonic mean, and the perception decision threshold is calculated based on the analysis results of the extreme eigenvalues ​​of the random matrix; finally, a perception decision is made: when the perception decision amount is greater than the set threshold value, it is determined that a multi-master user signal exists, otherwise it is determined that a multi-master user signal does not exist. The specific steps of this method are:

[0006] (1) At the nth sampling time, the multi-primary user received signals on the M antennas of the sensing node are sampled to obtain an M×1 dimensional received signal data vector x(n)=[x1(n),x2(n),…,x M (n)] T , where the superscript T represents the matrix transposition operation. On this basis, the sensing node samples the received signal N times continuously to obtain the received signal data vectors x(1), x(2), …, x(N);

[0007] (2) The sensing node calculates the corresponding sampling covariance matrix:

[0008] (3) Perception Node Computation The maximum eigenvalue of and the minimum eigenvalue

[0009] (4) The sensing node calculates the difference of the extreme eigenvalues

[0010] (5) The sensing node calculates the harmonic mean of the extreme eigenvalues

[0011] (6) The sensing node calculates the sensing decision quantity Γ = λ DV / λ HM ;

[0012] (7) The sensing node calculates the false alarm probability value P of the target according to the pre-given value. f Calculate the perception decision threshold Where c = M / N, F1 -1 (·) represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution;

[0013] (8) The sensing node performs a sensing decision: When the sensing decision amount t obtained by step (6) is greater than the sensing decision threshold t obtained by step (7), the sensing node determines that a multi-active user signal exists; otherwise, the sensing node determines that a multi-active user signal does not exist.

[0014] Notes on the symbols involved

[0015]

[0016] Beneficial effects: The beneficial effects of the present invention are mainly reflected in the following three aspects:

[0017] 1) Different from the classic spectrum sensing method based on the difference of extreme eigenvalues, the method proposed in the present invention does not need to estimate the noise variance, and can obtain more reliable false alarm performance in the multi-primary user signal scenario, so that secondary users can get more opportunities to use idle spectrum;

[0018] 2) The method proposed in the present invention uses the difference of the extreme eigenvalues ​​of the sampled covariance matrix and the harmonic mean to construct a statistical perception decision metric, which can fully characterize the difference between the presence and absence of multi-primary user signals and obtain a higher detection probability under low signal-to-noise ratio conditions;

[0019] 3) The method proposed in the present invention can realize full-blind detection in the absence of multi-user signals and channel information, and its perception decision threshold can be directly calculated based on closed-form expression, which has the advantages of simple calculation and low complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 The invention is a flow chart for realizing a fully blind multi-master user spectrum sensing method based on extreme eigenvalues.

[0021] Figure 2 The number of received signal data vectors is N = 50, the number of primary user signals and the number of antennas are both set to 30, and the target false alarm probability is P f =0.1, the actual false alarm probability comparison curve of the method based on the ratio of the extreme eigenvalue difference to the harmonic mean proposed in the present invention, the classical method based on the difference between the maximum and minimum eigenvalues ​​and the improved method thereof.

[0022] Figure 3 The number of received signal data vectors is N = 50, the number of primary user signals and the number of antennas are both set to 30, and the target false alarm probability is P f =0.1, the actual detection probability and false alarm probability comparison curves of the three methods proposed in the present invention, namely, the ratio of the extreme eigenvalue difference to the harmonic mean, the ratio of the classic maximum and minimum eigenvalues, and the covariance absolute value detection. DETAILED DESCRIPTION

[0023] The present invention provides a fully blind multi-user spectrum sensing method based on extreme eigenvalues, which uses the difference and harmonic mean of the extreme eigenvalues ​​of the sampled covariance matrix to construct a statistical sensing decision quantity, and derives a closed-form solution of the sensing decision threshold based on high-dimensional random matrix theory. The following is a detailed description of the multi-user spectrum sensing model, sensing method and specific implementation steps.

[0024] 1. Multi-user spectrum sensing model

[0025] At the nth sampling time, the multi-user received signals on the M antennas of the sensing node are sampled to obtain an M×1 dimensional received signal data vector x(n)=[x1(n),x2(n),…,x M (n)] T , where the superscript T represents the matrix transposition operation. On this basis, the sensing node samples the received signal N times continuously to obtain the received signal data vector x(1), x(2), ..., x(N). Note that the received signal x(n) = Hs(n) + w(n) is the superposition of the multi-user signal and the noise, where H represents the wireless channel gain matrix between the M×L dimensional multi-user signal and the multi-antenna received signal, and w(n) represents the noise variance σ 2 The Gaussian noise vector s(n) corresponds to the transmitted signal vector of L multi-primary users. The multi-primary user spectrum sensing problem can be mathematically expressed as the following binary hypothesis testing model:

[0026]

[0027] Wherein, H0 indicates that the multi-master user signal does not appear, that is, the authorized frequency band is not occupied; H1 indicates that the multi-master user signal appears, that is, the authorized frequency band is occupied.

[0028] 2. Proposed Perception Method

[0029] The sampling covariance matrix of the multi-primary user received signal can be expressed as:

[0030]

[0031] On this basis, the perception node is decomposed by eigenvalue The maximum eigenvalue of and the minimum eigenvalue And calculate the difference λ of the extreme eigenvalues ​​respectively DV and the harmonic mean λ HM :

[0032]

[0033]

[0034] Note that in the H0 state, the law of large numbers shows that The difference λ of the extreme eigenvalues DV tends to 0, while the harmonic mean λ of the extreme eigenvalues HM → 2 , then there is λ DV / λ HM →0; in the H1 state, due to the effect of multiple primary user signals and wireless channels, The difference λ of the extreme eigenvalues DV will no longer approach 0, and at this time λ HM It is no longer tending to σ 2 In view of this, the present invention proposes the following perceptual decision metric:

[0035]

[0036] Obviously, unlike the classic spectrum sensing method based on the difference between the maximum and minimum eigenvalues ​​and its improvement, which only uses the difference between the maximum and minimum eigenvalues ​​when designing the sensing decision amount, the present invention simultaneously considers the use of extreme eigenvalue harmonic mean information when designing the sensing decision amount, thereby avoiding the estimation of the noise variance and generalizing the extreme eigenvalue difference method to the multi-user spectrum sensing scenario. At the same time, different from the classic spectrum sensing method based on the ratio of the maximum and minimum eigenvalues, the present invention is more conducive to characterizing the difference in whether the multi-user signals appear by comprehensively utilizing the difference and harmonic mean of the eigenvalues, thereby helping to improve the detection performance under low signal-to-noise ratio conditions.

[0037] In order to obtain the perception decision threshold, it is necessary to first determine the perception decision amount Γ = λ DV / λ HM Distribution in the H0 state. Using the approximate results about extreme eigenvalues ​​in high-dimensional random matrix theory, it can be proved that when the number of received signal data vectors N is sufficiently large, we have:

[0038]

[0039] and

[0040]

[0041] In the formula, c = M / N. Therefore, when N is sufficiently large, we have:

[0042]

[0043] At the same time, from the high-dimensional random matrix theory, we know that The obedience parameters are The first-order Tracy-Widom distribution. It can be proved that when the false alarm probability of a given target is Pf When , the perception decision threshold can be expressed as:

[0044]

[0045] Where F1 -1 (·) represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution. Once the sensing decision threshold is determined, the presence of multi-primary user signals can be determined by comparing the sensing decision amount with the sensing decision threshold.

[0046] (III) Specific implementation steps

[0047] Combined with the above analysis process and process Figure 1 , the implementation steps of a fully blind multi-master user spectrum sensing method based on extreme eigenvalues ​​involved in the present invention are further described:

[0048] (a) At the nth sampling time, the multi-user received signals on the M antennas of the sensing node are sampled to obtain an M×1-dimensional received signal data vector x(n)=[x1(n),x2(n),…,x M (n)] T , where the superscript T represents the matrix transposition operation. On this basis, the sensing node samples the received signal N times continuously to obtain the received signal data vectors x(1), x(2), …, x(N);

[0049] (b) The sensing node calculates the corresponding sampling covariance matrix

[0050] (c) Perception Node Computation The maximum eigenvalue of and the minimum eigenvalue

[0051] (d) The sensing node calculates the difference of the extreme eigenvalues

[0052] (f) The sensing node calculates the harmonic mean of the extreme eigenvalues

[0053] (f) The sensing node calculates the sensing decision quantity Γ = λ DV / λ HM ;

[0054] (g) The sensing node calculates the sensing decision threshold Where c = M / N, P f is the pre-given target false alarm probability, F1 -1 (·) represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution;

[0055] (h) The sensing node performs a sensing decision: when the sensing decision quantity Γ calculated by step (f) is greater than the sensing decision threshold t obtained by step (g), the sensing node determines that a multi-active user signal exists; otherwise, the sensing node determines that a multi-active user signal does not exist.

[0056] Finally, the beneficial effects of the present invention are verified by Monte-Carlo simulation. Figure 2 Given the number of received signal data vectors N = 50, the number of primary user signals and the number of antennas are both set to 30, and the target false alarm probability is P f =0.1, the actual false alarm probability comparison curve of the method based on the ratio of the extreme eigenvalue difference to the harmonic mean and the classical method based on the difference between the maximum and minimum eigenvalues ​​and its improved method proposed in the present invention. It can be seen from the simulation results that the actual false alarm probability of the classical method based on the difference between the maximum and minimum eigenvalues ​​and its improved method is much higher than the preset target false alarm probability value. Specifically, the actual average false alarm probabilities corresponding to the above two methods are close to 42% and 30%, respectively, that is, the actual false alarm probability reaches 420% and 300% of the target false alarm probability. This means that in the multi-master user signal perception scenario, the classical method based on the difference between the maximum and minimum eigenvalues ​​and its improved method cannot correctly set the appropriate decision threshold, so that the risk of misjudging the state of the non-existence of the multi-master user signal as the existence of the multi-master user signal increases sharply, thereby generating an extremely unreliable multi-master user perception decision result, thereby greatly wasting the opportunity of cognitive users to use idle authorized spectrum. In comparison, the actual false alarm probability generated by the method proposed in the present invention is very close to the target false alarm probability, which means that the new method can produce reliable perception results in the multi-master user perception scenario. This also shows that the new method proposed in the present invention uses the difference between extreme eigenvalues ​​and the harmonic mean information to characterize the changes in the characteristics of the received signal caused by the presence of multi-user signals, and no longer needs to estimate the noise variance, thereby expanding the scope of application of the classic method based on the difference between the maximum and minimum eigenvalues. Furthermore, Figure 3 The actual detection probability and false alarm probability comparison curves of the three methods proposed by the present invention, namely, the ratio of the extreme eigenvalue difference to the harmonic mean, the ratio of the classical maximum and minimum eigenvalues, and the covariance absolute value detection, are given under the same parameter settings. From the perspective of the false alarm probability index, the actual false alarm probabilities generated by the above three methods are all less than the target false alarm probability, but the actual false alarm probability of the method proposed by the present invention is closest to the target value of 0.1, so it has the best false alarm performance; from the perspective of the detection probability index, the detection probability of the method proposed by the present invention is significantly better than the classical methods based on the ratio of the maximum and minimum eigenvalues ​​and the covariance absolute value detection, and also has the best detection performance.

Claims

1. A fully blind multi-user spectrum sensing method based on extreme eigenvalues, characterized in that This method uses the difference and harmonic mean of the extreme eigenvalues ​​of the sampling covariance matrix to construct the perception decision quantity: first, the multi-antenna signal of the perception node is sampled N times continuously to obtain an M-dimensional received signal data vector x(n), n = 1, 2, ..., N; then, the received signal data vector is used to calculate the sampling covariance matrix of the received signal And calculate its maximum eigenvalue and minimum eigenvalue; then, use the ratio of the extreme eigenvalue difference and the harmonic mean to construct the perceptual decision quantifier And the perception decision threshold t is calculated based on the results of the extreme eigenvalue analysis of the random matrix; finally, the perception decision is made: when the perception decision amount When it is greater than the set perception threshold t, the perception node determines that the multi-active user signal exists; otherwise, it determines that the multi-active user signal does not exist.

2. According to the method for fully blind multi-master spectrum sensing based on extreme eigenvalues ​​according to claim 1, the specific steps are as follows: ① At the nth sampling time, the multi-user received signals on the M antennas of the sensing node are sampled to obtain an M×1 dimensional received signal data vector x(n)=[x1(n),x2(n),…,x M (n)] T ,in, The superscript T represents the matrix transposition operation. On this basis, the sensing node samples the received signal N times continuously to obtain the received signal data vectors x(1), x(2), …, x(N); ② The sensing node calculates the corresponding sampling covariance matrix ③Perception node computing The maximum eigenvalue of and the minimum eigenvalue ④The sensing node calculates the difference of the extreme eigenvalues ⑤ The sensing node calculates the harmonic mean of the extreme eigenvalues ⑥ The sensing node calculates the sensing decision ⑦ The sensing node calculates the threshold value Where c = M / N, P f is the pre-given target false alarm probability, F1 -1 (·) represents the inverse cumulative distribution function of the first-order Tracy-Widom distribution; ⑧ The sensing node performs sensing judgment: when the sensing judgment amount t obtained in step ⑥ is greater than the sensing judgment threshold t obtained in step ⑦, the sensing node determines that the multi-active user signal exists; otherwise, the sensing node determines that the multi-active user signal does not exist.

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