CN112260779A - Signal detection method for small mobile master user - Google Patents

Signal detection method for small mobile master user Download PDF

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CN112260779A
CN112260779A CN202011025125.1A CN202011025125A CN112260779A CN 112260779 A CN112260779 A CN 112260779A CN 202011025125 A CN202011025125 A CN 202011025125A CN 112260779 A CN112260779 A CN 112260779A
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signal
matrix
user
sampling
false alarm
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钟玮超
蒋尚华
陈雅芳
林超雄
闻建中
吴金海
罗益荣
高琳
蒋秀
李永锐
区楚虹
甘慧芳
杨学文
高垣
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Jiangmen Power Supply Bureau of Guangdong Power Grid Co Ltd
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Abstract

The invention relates to the technical field of signal detection, in particular to a signal detection method of a small mobile master user, which is used for a system consisting of the small master user and a plurality of secondary users and comprises the following steps: s1: the secondary user receives data of a small mobile primary user signal; s2: forming the data into a sampling signal matrix X; s3: determining a sampling covariance matrix R (N) of a sampled signal matrix Xs) (ii) a S4: solving a sampling covariance matrix R (N)s) The maximum characteristic value and the minimum characteristic value are obtained, and the detection quantity T is calculated according to the maximum characteristic value and the minimum characteristic value; s5: setting false alarm probability, and determining a decision threshold gamma of the detection quantity T according to the false alarm probability; s6: and judging whether a main user signal exists or not according to the relation between the detection quantity T and the judgment threshold gamma. In the invention, the decision threshold gamma is directly determined by the false alarm probability, so that the error of a noise signal is not brought in, and the value of the decision threshold is different according to the difference of the false alarm probability, thereby the detection precision can be higher.

Description

Signal detection method for small mobile master user
Technical Field
The invention relates to the technical field of signal detection, in particular to a signal detection method of a small mobile main user.
Background
A very big challenge exists in the spectrum sensing technology, namely how to detect the signal of a small mobile main user; by small mobile primary user (SSPU), it is meant a primary user whose signal strength is very small and which is extremely weak with respect to surrounding noise and which is essentially submerged in the ambient noise. Due to the characteristic of weak signal intensity of the small mobile master user, the signal transmission distance of the small mobile master user is generally 100-150 m; meanwhile, the switch time-space characteristics of the small mobile primary user are greatly changed, for example, the wireless microphone device can be changed into a switch state at any time or place in the moving process, and the secondary user is not informed in advance; in addition, the small-sized mobile main user is in a mobile state frequently, and the stay time of each place is short, so that the difficulty in sensing the small-sized mobile main user is very high.
Chinese patent CN106169945A discloses a cooperative spectrum sensing method based on the difference between the maximum and minimum eigenvalues, which includes: a cognitive user receiving end carries out random sampling on a received signal and calculates a received signal matrix; calculating a sample covariance matrix through a received signal matrix, and decomposing the eigenvalue of the sample covariance matrix; selecting the difference between the maximum eigenvalue and the minimum eigenvalue as a detection statistic; calculating a threshold value when an authorized user exists; comparing the detection statistic with a threshold value, and judging whether a master user exists or not; and if the statistic is larger than or equal to the threshold value, indicating that the master user exists, otherwise, indicating that the master user does not exist, so that the cognitive user can access the frequency band. The calculation of the threshold value is related to noise, therefore, the detection precision is greatly influenced by the noise value, the noise value is an estimated value, an error exists, the larger the noise is, the larger the error of the threshold value is, the larger the threshold value setting is, erroneous judgment easily occurs, the strength of the small-sized mobile main user signal is too low, the small-sized mobile main user signal is basically in a state of being submerged in the noise, and the threshold value of the algorithm is very sensitive in an environment with a low signal-to-noise ratio, so that the threshold value setting cannot meet the detection precision requirement of the small-sized mobile main user with low signal strength.
Disclosure of Invention
The invention provides a signal detection method of a small-sized master user, which avoids noise influence and has high detection precision, for overcoming the defects in the prior art.
In the technical scheme, a signal detection method of a small mobile master user is provided and is used for a system consisting of the small master user and a plurality of secondary users; the method comprises the following steps:
s1: the secondary user receives data of a small mobile primary user signal;
s2: forming the data into a sampling signal matrix X;
s3: solving a sampling covariance matrix R (Ns) of the sampling signal matrix X;
s4: solving the maximum eigenvalue and the minimum eigenvalue of the sampling covariance matrix R (Ns), and solving the detection quantity T according to the maximum eigenvalue and the minimum eigenvalue;
s5: setting false alarm probability, and determining a decision threshold gamma of the detection quantity T according to the false alarm probability;
s6: and judging whether a main user signal exists or not according to the relation between the detection quantity T and the judgment threshold gamma.
In the invention, after the detection quantity is obtained through the maximum and minimum characteristic values, the judgment threshold gamma is compared with the judgment threshold to judge whether the main signal exists, and the judgment threshold gamma is directly determined through the set false alarm probability and is not influenced by the noise signal, so that in the detection of the small-sized mobile main user, even if the noise signal is far greater than the main signal, the set judgment threshold can not bring too much noise signal to cause overlarge error and cause the condition of misjudgment, and the signal detection precision can be improved.
Preferably, in the above step S1, the received main user signal data is represented as a matrix x (n), where x (n) is [ × ]1(n),x2(n),L,xP(n)]T；
Wherein N is 1,2, L, N; p is the number of secondary users; t represents [ x ]1(n),x2(n),L,xP(n)]The transposed matrix of (2).
Preferably, the step S2 includes the following steps:
s21: setting xi(n) is signal data received by the ith secondary user at the time k, the set noise signal is pure Gaussian white noise, and the set noise signal is not related to the input signal;
s22: forming a sampling signal matrix X:
Figure BDA0002701910780000021
wherein, N is the limited signal sampling number, and P is the number of the secondary users.
Preferably, the step S3 includes the following steps:
s31: setting the sampling covariance matrix to R (N)S)：
Figure BDA0002701910780000031
Figure BDA0002701910780000032
H＝PL×(N+PL)，
Figure BDA0002701910780000033
Wherein R issAn autocorrelation matrix that is an input signal; h is a gain matrix; hHHermitian transpose matrix representing the gain matrix H; i isNAn identity matrix of P × L;
Figure BDA0002701910780000034
variance of stable white Gaussian noise; n is a radical ofsRepresents an infinite number of samples; p is the number of users; l is the number of signals continuously output by the secondary user; n is a radical ofjRank which is the maximum channel gain;
s32: solving a sampling covariance matrix R (N)s) Is estimated value of
Figure BDA0002701910780000035
Figure BDA0002701910780000036
Wherein N isSRepresenting an infinite number of samples, x (n) representing signal data received by a secondary user, xH(n) a transposed matrix representing the matrix x (n);
s33: obtaining a sampling covariance matrix from the sampled signal matrix
Figure BDA0002701910780000037
Wherein XHIs a Hermite transpose matrix of a sampling signal matrix X; n is a radical ofsIs an infinite number of samples.
Preferably, the step S4 includes the following steps:
S41: solving a sampling covariance matrix R (N)S) Characteristic value λ of1，λ2，…，λPWherein P is the number of secondary users;
s42: screening for maximum eigenvalue lambdamaxAnd minimum eigenvalue λmin：
λmin＝min[λ1,λ2,LλP]，
λmin＝min[λ1,λ2,LλP]，
S43: calculating limit values of the maximum eigenvalue and the minimum eigenvalue:
Figure BDA0002701910780000038
Figure BDA0002701910780000041
wherein the content of the first and second substances,
Figure BDA0002701910780000042
variance of stable white Gaussian noise; n is a radical ofsRepresents an infinite number of samples; p is the number of the secondary users, and L is the number of signals continuously output by the secondary users;
s44: calculating a detection quantity T:
Figure BDA0002701910780000043
preferably, the step S5 specifically includes the following steps:
s51: defining a maximum eigenvalue lambdamaxIs Tracy-Widom distribution (telios-Widom distribution);
s52: let F1The cumulative distribution function for the Tracy-Widom (teliesivumdom) 1 st distribution:
Figure BDA0002701910780000044
q″(u)＝uq(u)+2q3(u)，
wherein q (u) is a solution of a second order nonlinear differential equation q ″ (μ), t is a variable of an accumulative distribution function, and u represents a variable of the q (u) equation;
s53: calculating false alarm probability Pf：
Figure BDA0002701910780000045
Wherein gamma is a decision threshold; ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function;
s54: the result of step S53 is simplified:
Figure BDA0002701910780000046
wherein gamma is a decision threshold; ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function;
Figure BDA0002701910780000047
is F1The inverse function of (c); pf is false alarm probability;
s55: let the signal be real noise, have
Figure BDA0002701910780000048
And
Figure BDA0002701910780000049
wherein Ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function;
s56: calculating a decision threshold gamma according to the steps S54 and S55:
Figure BDA0002701910780000051
wherein, PfAs false alarm probability, F1 -1Is F1The inverse function of (c); p is the number of secondary users, NSIs an infinite number of samples.
Preferably, the specific formula determined in step S6 is as follows:
Figure BDA0002701910780000052
wherein H0Is no signal, H1A small mobile master user signal is present; t is a detection amount; gamma is a decision threshold.
Preferably, F in the above step S531The value of (t) is related to the second order nonlinear differential equation q' (mu) by looking up a known q (u) data look-up table.
Preferably, the noise variance estimation value in the above step S31 is
Figure BDA0002701910780000053
The uncertainty of the noise is B ═ max {10lg β } (dB), where β is the uncertainty factor, subject to [ -B, B [ ]]Is uniformly distributed.
Preferably, the false alarm probability P in the step S53 isf≤0.1。
Compared with the prior art, the beneficial effects are:
in the invention, after the detection quantity is obtained through the maximum and minimum characteristic values, the main signal is compared with the judgment threshold to judge whether the main signal exists, the judgment threshold gamma is only determined through the false alarm probability and is not influenced by the noise signal or other factors, therefore, in the detection of the small-sized mobile main user, even if the noise signal is far greater than the main signal, the setting of the judgment threshold can not bring too much noise signal to cause overlarge error and cause misjudgment, therefore, the judgment threshold determined by the false alarm probability can not introduce the error of the noise, the signal detection precision can be improved, and the method is more suitable for the detection of the small-sized mobile main user with low signal-to-noise ratio.
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FIG. 1 is a schematic flow chart of a signal detection method for a small mobile primary user according to the present invention;
fig. 2 is a schematic diagram of a cognitive network composition of the signal detection method for a small mobile primary user according to the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "long", "short", etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the drawings, it is only for convenience of description and simplicity of description, but does not indicate or imply that the device or element referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationships in the drawings are only used for illustrative purposes and are not to be construed as limitations of the present patent, and specific meanings of the terms may be understood by those skilled in the art according to specific situations.
The technical scheme of the invention is further described in detail by the following specific embodiments in combination with the attached drawings:
examples
Fig. 1 shows an embodiment of a signal detection method for a small mobile primary user, which is used in a system formed by a small mobile primary user (WM) and a plurality of Secondary Users (SUs), wherein the small mobile primary user may be a wireless microphone, an intercom, etc., and the secondary users may be devices, such as sensors, for receiving signals of the primary user, and the method includes the following steps:
s1: the secondary user receives data of a small mobile primary user signal;
s2: forming the data into a sampling signal matrix X;
s3: determining a sampling covariance matrix R (N) of a sampled signal matrix Xs)；
S4: solving a sampling covariance matrix R (N)s) The maximum characteristic value and the minimum characteristic value are obtained, and the detection quantity T is calculated according to the maximum characteristic value and the minimum characteristic value;
s5: setting false alarm probability, and determining a decision threshold gamma of the detection quantity T according to the false alarm probability;
s6: and judging whether a main user signal exists or not according to the relation between the detection quantity T and the judgment threshold gamma.
In step S1 in this embodiment, the received primary user signal data is represented as a matrix x (n), where x (n) ═ x1(n),x2(n),L,xP(n)]T；
Wherein N is 1,2, L, N; p is the number of secondary users; t represents [ x ]1(n),x2(n),L,xP(n)]The transposed matrix of (2).
Step S2 in this embodiment specifically includes the following steps:
s21: setting xi(n) is signal data received by the ith secondary user at the time k, the set noise signal is pure Gaussian white noise, and the set noise signal is not related to the input signal;
s22: forming a sampling signal matrix X:
Figure BDA0002701910780000071
wherein, N is the limited signal sampling number, and P is the number of the secondary users.
Step S3 in this embodiment specifically includes the following steps:
s31: setting the sampling covariance matrix to R (N)S)：
Figure BDA0002701910780000072
Figure BDA0002701910780000073
H＝PL×(N+PL)，
Figure BDA0002701910780000074
Wherein R issAn autocorrelation matrix that is an input signal; h is a gain matrix; hHHermitian transpose matrix representing the gain matrix H; i isNAn identity matrix of P × L;
Figure BDA0002701910780000075
variance of stable white Gaussian noise; n is a radical ofsRepresents an infinite number of samples; p is the number of users; l is the number of signals continuously output by the secondary user; n is a radical ofjRank which is the maximum channel gain;
s32: solving a sampling covariance matrix R (N)s) Is estimated value of
Figure BDA0002701910780000076
Figure BDA0002701910780000077
Wherein N isSRepresenting an infinite number of samples, x (n) representing signal data received by a secondary user, xH(n) denotes a transposed matrix of the matrix x (n).
S33: obtaining a sampling covariance matrix from the sampled signal matrix
Figure BDA0002701910780000078
Wherein XHIs a Hermite transpose matrix of a sampling signal matrix X; n is a radical ofsIs an infinite number of samples.
Step S4 in the present embodiment includes the following steps:
s41: solving a sampling covariance matrix R (N)S) Characteristic value λ of1，λ2，…，λPWherein P is the number of secondary users;
s42: screening for maximum eigenvalue lambdamaxAnd minimum eigenvalue λmin：
λmin＝min[λ1,λ2,LλP]，
λmin＝min[λ1,λ2,LλP]，
Wherein, P is the number of secondary users;
s43: calculating limit values of the maximum eigenvalue and the minimum eigenvalue:
Figure BDA0002701910780000081
Figure BDA0002701910780000082
wherein the content of the first and second substances,
Figure BDA0002701910780000083
variance of stable white Gaussian noise; n is a radical ofsRepresents an infinite number of samples; p is the number of users, and L is the number of signals continuously output by the secondary user;
s44: calculating a detection quantity T:
Figure BDA0002701910780000084
step S5 in this embodiment specifically includes the following steps:
s51: setting the maximum eigenvalue λmaxIs Tracy-Widom distribution (telios-Widom distribution);
s52: setting F1The cumulative distribution function for the Tracy-Widom (teliesivumdom) 1 st distribution:
Figure BDA0002701910780000085
q″(μ)＝μq(u)+2q3(μ)，
wherein q (u) is a solution of a second order nonlinear differential equation q ″ (μ), t is a variable of the cumulative distribution function, and u is a variable of the q (u) equation;
s53: calculating false alarm probability Pf：
Figure BDA0002701910780000086
Wherein gamma is a decision threshold; ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function;
s54: the result of step S53 is simplified:
Figure BDA0002701910780000091
wherein gamma is a decision threshold; ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function; f1 -1Is F1The inverse function of (c); pf is false alarm probability;
s55: let the signal be real noise, have
Figure BDA0002701910780000092
And
Figure BDA0002701910780000093
wherein Ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function;
s56: calculating a decision threshold gamma according to the steps S54 and S55:
Figure BDA0002701910780000094
wherein, PfAs false alarm probability, F1 -1Is F1The inverse function of (c); p is the number of secondary users, NSIs an infinite samplingThe number of times.
The determination manner in step S6 in this embodiment is specifically as follows:
Figure BDA0002701910780000095
wherein H0Is no signal, H1A small mobile master user signal is present; t is a detection amount; gamma is a decision threshold.
In step S53 in the present embodiment, F1The value of (t) is related to the second order nonlinear differential equation q "(mu) by looking up a known q (u) data look-up table, which has been experimentally determined and is known, as follows:
Figure BDA0002701910780000096
in the present embodiment, the noise variance estimation value in step S31 is
Figure BDA0002701910780000097
The uncertainty of the noise is B ═ max {10lg β } (dB), where β is the uncertainty factor, subject to [ -B, B [ ]]Is uniformly distributed.
False alarm probability P in step S53 in this embodimentf≤0.1。
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. A signal detection method of a small mobile master user is used for a system consisting of the small master user and a plurality of secondary users; the method is characterized by comprising the following steps:
s1: the secondary user receives data of a small mobile primary user signal;
s2: forming the data into a sampling signal matrix X;
s3: determining a sampling covariance matrix R (N) of a sampled signal matrix Xs)；
S4: solving a sampling covariance matrix R (N)s) The maximum characteristic value and the minimum characteristic value are obtained, and the detection quantity T is calculated according to the maximum characteristic value and the minimum characteristic value;
s5: setting false alarm probability, and determining a decision threshold gamma of the detection quantity T according to the false alarm probability;
s6: and judging whether a main user signal exists or not according to the relation between the detection quantity T and the judgment threshold gamma.
2. The signal detection method of a small-sized mobile primary user according to claim 1, wherein said step S1 represents the received primary user signal data as a matrix x (n), x (n) ═ x (n)1(n),x2(n),L,xP(n)]T；
Wherein N is 1,2, L, N; p is the number of sub-users, [ x ]1(n),x2(n),L,xP(n)]TIs represented by [ x ]1(n),x2(n),L,xP(n)]The transposed matrix of (2).
3. The method as claimed in claim 2, wherein the step S2 specifically includes the following steps:
s21: setting xi(n) is signal data received by the ith secondary user at the time k, the set noise signal is pure Gaussian white noise, and the set noise signal is not related to the input signal;
s22: forming a sampling signal matrix X:
Figure FDA0002701910770000011
wherein, N is the limited signal sampling number, and P is the number of the secondary users.
4. The method as claimed in claim 3, wherein the step S3 specifically includes the following steps:
s31: setting the sampling covariance matrix to R (N)s)：
Figure FDA0002701910770000021
Figure FDA0002701910770000022
H＝PL×(N+PL)，
Figure FDA0002701910770000023
Wherein R issAn autocorrelation matrix that is an input signal; h is a gain matrix; hHHermitian transpose matrix representing the gain matrix H; i isNAn identity matrix of P × L;
Figure FDA0002701910770000024
variance of stable white Gaussian noise; n is a radical ofsRepresents an infinite number of samples; p is the number of users; l is the number of signals continuously output by the secondary user; n is a radical ofjRank which is the maximum channel gain;
s32: solving a sampling covariance matrix R (N)s) Is estimated value of
Figure FDA0002701910770000025
Figure FDA0002701910770000026
Wherein，NsRepresenting an infinite number of samples, x (n) representing signal data received by a secondary user, xH(n) a transposed matrix representing the matrix x (n);
s33: obtaining a sampling covariance matrix from the sampled signal matrix
Figure FDA0002701910770000027
Wherein XHIs a Hermite transpose matrix of a sampling signal matrix X; n is a radical ofsIs an infinite number of samples.
5. The signal detection method for the small mobile primary user according to claim 4, wherein said step S4 includes the following steps:
s41: solving a sampling covariance matrix R (N)s) Characteristic value λ of1，λ2，…，λPWherein P is the number of secondary users;
s42: screening for maximum eigenvalue lambdamaxAnd minimum eigenvalue λmin：
λmin＝min[λ1,λ2,LλP]，
λmin＝min[λ1,λ2,LλP]，
Wherein, P is the number of secondary users;
s43: calculating limit values of the maximum eigenvalue and the minimum eigenvalue:
Figure FDA0002701910770000028
Figure FDA0002701910770000031
wherein the content of the first and second substances,
Figure FDA0002701910770000032
variance of stable white Gaussian noise; n is a radical ofsRepresents an infinite number of samples;p is the number of the secondary users, and L is the number of signals continuously output by the secondary users;
s44: calculating a detection quantity T:
Figure FDA0002701910770000033
6. the signal detection method for the small mobile primary user according to claim 5, wherein said step S5 specifically comprises the following steps:
s51: setting the maximum eigenvalue λmaxIs a Tracy-Widom distribution;
s52: setting F1Cumulative distribution function for Tracy-Widom distribution 1:
Figure FDA0002701910770000034
q″(u)＝μq(u)+2q3(u)，
where q (u) is the solution of a second order nonlinear differential equation q' (mu), t is a variable of the cumulative distribution function,
u is a variable of the equation q (u);
s53: calculating false alarm probability Pf：
Figure FDA0002701910770000035
Wherein gamma is a decision threshold; ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function;
s54: the result of step S53 is simplified:
Figure FDA0002701910770000036
wherein gamma is a decision threshold; ns is infiniteThe number of samples; p is the number of secondary users; u is a variable of the equation q (u); v is a variable of the cumulative distribution function; f1 -1Is F1The inverse function of (c); pfIs the false alarm probability;
s55: let the signal be real noise, have
Figure FDA0002701910770000038
And
Figure FDA0002701910770000041
wherein Ns is an infinite number of samples; p is the number of secondary users; u is a variable of the equation q (u);
v is a variable of the cumulative distribution function;
s56: calculating a decision threshold gamma according to the steps S54 and S55:
Figure FDA0002701910770000042
wherein, PfAs false alarm probability, F1 -1Is F1The inverse function of (c); p is the number of secondary users, NSIs an infinite number of samples.
7. The method as claimed in claim 6, wherein the specific formula determined in step S6 is as follows:
Figure FDA0002701910770000043
wherein H0Is no signal, H1A small mobile master user signal is present; t is a detection amount; gamma is a decision threshold.
8. The method as claimed in claim 6, wherein F in step S531Value of (t) and second order nonlinearityThe differential equation q "(mu) relationship is obtained by looking up a known q (u) data look-up table.
9. The method as claimed in claim 7, wherein the noise variance estimation value in step S31 is
Figure FDA0002701910770000044
The uncertainty of the noise is B ═ max {10lg β } (dB), where β is the uncertainty factor, subject to [ -B, B [ ]]Is uniformly distributed.
10. The method as claimed in claim 7, wherein the false alarm probability P in step S53 is determined by the detection methodf≤0.1。
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