CN117892072B - Signal detection method based on Gaussian rank correlation coefficient - Google Patents
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Abstract
The invention provides a signal detection method based on Gaussian rank correlation coefficients, which comprises the following steps: acquiring echo signals received by two paths of receivers; calculating rank statistics of the echo signals, and performing Gaussian rank conversion on the echo signals; constructing statistics based on the Gaussian rank transformed echo signals; calculating a corresponding threshold value according to the given false alarm probability; and comparing the statistic with the threshold value to finish the detection process. The method has the advantages of simple structure, easy engineering realization and strong robustness, and can be used as a powerful tool for signal detection under the background noise containing pulse components.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a signal detection method based on a Gaussian rank correlation coefficient.
Background
The signal detection is an important signal analysis technology and is widely applied to the fields of phased array radars, underwater sonars, mobile communication and the like. The purpose is to determine whether and when a useful signal is present, and facilitate the subsequent extraction of more useful high quality signals by the system through techniques such as parameter estimation, code recognition, modulation analysis, and the like.
Currently, matched filters are classic signal detection algorithms in the literature. It is popular because of its simple form, complete theory, easy implementation. The matched filter is a linear correlator that maximizes the signal-to-noise ratio of the signal output with optimal performance in an additive white gaussian noise background. However, due to factors such as atmospheric radiation and channel interference, noise sources in actual scenes may also generate some noise following non-gaussian distribution in addition to additive gaussian noise. These non-gaussian distributed noise features a short duration but a large amplitude, commonly referred to as impulse noise. The signal-to-noise ratio of the received echo signal is rapidly reduced over a period of time due to the presence of impulse noise, resulting in rapid deterioration or even failure of the matched filter.
Disclosure of Invention
Aiming at the problems, the invention uses Gaussian rank transformation of signals to realize suppression of large abnormal values in impulse noise, and then calculates correlation functions of the transformed signals to design statistics, thereby realizing high-precision signal detection in impulse noise environment.
The technical scheme of the invention is as follows:
A signal detection method based on Gaussian rank correlation coefficient comprises the following steps:
acquiring echo signals received by two paths of receivers;
Respectively calculating rank statistics of the two paths of echo signals, and carrying out Gaussian rank conversion on the two paths of echo signals;
constructing statistics based on the two paths of echo signals after Gaussian rank conversion;
Calculating a corresponding threshold value according to the given false alarm probability;
Comparing the statistic with the threshold value to determine the detection result of the source signal.
Further, the two echo signals specifically are:
x(i)＝θ1s(i)+z1(i)
y(i)＝θ2s(i)+z2(i)
i＝1,2…,n
Wherein { x (i), y (i) } is an echo signal received by two paths of receivers at a sampling time i, s (i) is a source signal, θ l is less than or equal to 1, z l (i) is background noise, l=1, 2 is a first path of receiver, and n is a signal length.
Further, the formula for calculating the rank statistics of the two echo signals respectively is as follows:
i＝1,2…,n
Wherein R i represents the rank statistic of the first echo signal x (i), and Q i represents the rank statistic of the second echo signal y (i);
wherein H (·) represents heaviside step functions.
Further, the gaussian rank conversion for the two echo signals is specifically:
i＝1,2…,n
Wherein Φ -1 (·) represents the inverse of the standard normal distribution cumulative distribution function Φ.
Further, the construction statistics based on the two paths of echo signals after Gaussian rank transformation is specifically as follows:
Wherein the coefficient is
Wherein the coefficient isRepresenting the variance value of the signal after gaussian rank transformation, Φ -1 (·) represents the inverse of the standard normal distribution cumulative distribution function Φ.
Further, the calculating the corresponding threshold according to the given false alarm probability specifically includes:
λ＝σΦ-1(1-Pf)
Where Φ -1 (·) represents the inverse of the standard normal distribution cumulative distribution function Φ, σ represents the variance of the statistics, and P f is the given false alarm probability.
Further, the comparing statistics and the threshold value are specifically:
Comparing the statistic with the threshold value, and if the statistic is larger than the threshold value, the source signal exists; and if the statistic is smaller than or equal to the threshold value, the source signal is considered to be absent.
The invention has the technical effects that:
The invention fully suppresses the negative influence of a large abnormal value in impulse noise by carrying out Gaussian rank conversion on the signals, and shows excellent robustness in the impulse noise environment. Therefore, under the environment noise containing pulse components, the Gaussian rank correlation coefficient is an effective tool for signal detection, and the performance is quite good.
Drawings
The accompanying drawings illustrate various embodiments by way of example in general and not by way of limitation, and together with the description and claims serve to explain the inventive embodiments. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. Such embodiments are illustrative and not intended to be exhaustive or exclusive of the present apparatus or method.
FIG. 1 is a schematic flow chart of a signal detection method of the present invention;
FIG. 2 shows a schematic diagram of the detection structure of the detection method of the present invention;
fig. 3 shows a comparison graph of detection probabilities of signal detection in a pulse noise environment for a matched filter and a gaussian rank correlation detector.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The application will be described in detail below with reference to the drawings in connection with embodiments.
The embodiment provides a signal detection method based on a gaussian rank correlation coefficient, as shown in fig. 1, comprising the following steps:
step S10: collecting echo signals received by two paths of receivers;
Step S20: calculating rank statistics of two paths of received signals, and acquiring corresponding nonlinear Gaussian rank conversion;
step S30: calculating correlation functions of the two paths of transformed received signals, and constructing test statistics T;
step S40: calculating a corresponding threshold lambda according to the given false alarm probability P f;
Step S50: comparing the statistic with the threshold value, and if the statistic T is larger than the threshold value lambda, the source signal exists. Otherwise, the source signal is considered to be absent, thereby completing the detection process.
As a preferred implementation manner of this embodiment, the echo signals received by the two-way receiver at the ith sampling time have the following form:
x(i)＝θ1s(i)+z1(i)
y(i)＝θ2s(i)+z2(i)，i＝1,2…,n
where { x (i), y (i) } is an echo signal received by two paths of receivers, s (i) is a source signal, θ l +.1 (l=1, 2) represents a signal attenuation factor, z l (i) (l=1, 2) represents background noise, and n is a signal length. Our goal is to determine whether a signal s is present by measuring the degree of correlation of two received signals.
As a preferred implementation manner of this embodiment, calculating rank statistics of two paths of received signals may be implemented by the following formula:
wherein H (·) represents heaviside step functions.
As a preferred implementation manner of this embodiment, the gaussian rank transform of the two-path received signal is:
As a preferred implementation of this example, the test statistic is constructed by:
Wherein the coefficient is
As a preferred implementation manner of this embodiment, the formula for calculating the threshold value by the false alarm probability is:
λ＝σΦ-1(1-Pf)
Where Φ -1 (·) represents the inverse of the standard normal distribution cumulative distribution function Φ, σ represents the variance of the statistic, which is defined as:
as a preferred implementation of this embodiment, the signal detection process is implemented by the following decision:
Theoretical basis for calculating threshold value.
According to the statistic expression and in combination with the definition of the rank statistic, the average value of the statistic can be obtained as follows:
when n is an even number, it is possible to obtain
And when n is an odd number
To sum up, the mean value of the statistics isAccording to the relation between the variance and the mean, the statistic variance has the following calculation formula:
It has been demonstrated in the literature that for independent co-distributed binary samples { { x (1), y (1) },.+ -. X (n), y (n) }, the corresponding rank statistic is { (R 1,Q1),...,(Rn,Qn) }, assuming J, K, L, M are real valued functions
The expression of the statistic variance σ 2 can be found by combining the above equations.
When the sample length n is sufficiently large, the false alarm probability P f is expressed by:
at this time, a calculation formula of the threshold value can be obtained by inversion.
Example 1
In order to analyze the performance of the Gaussian rank correlation detector and the matched filter in signal detection under pulse noise, the invention is verified by a Monte Carlo experiment. Fig. 2 is a schematic diagram of a detection structure of a gaussian rank correlation detector, where x (1), x (2) …, x (n) and y (1), y (2) …, y (n) are echo signals received by two receivers, R 1,R2…,Rn and Q 1,Q2…,Qn are rank statistics of two received signals, x '(1), x' (2) …, x '(n) and y' (1), y '(2) …, y' (n) are signals obtained by performing gaussian rank conversion on two received signals, t is a statistic obtained by performing correlation operation on the two converted signals, and finally comparing the statistic t with a threshold lambda to obtain a binary hypothesis test result (i.e. 0: the source signal is absent or i 1: the source signal is present).
The experimental parameters were set as follows:
The source signal is randomly generated from a length n=200 of signal subject to a standard normal distribution.
Impulse noise is modeled by a mixed gaussian distribution:
Where ε=0.01 denotes the probability that the pulse component occurs throughout the impulse noise environment and δ 2＝100＞＞δ1 denotes the standard deviation of the pulse component. The signal-to-noise ratio of the received signal at this time can be defined as:
Through Monte Carlo experiments, performance performances of the Gaussian rank correlation detector and the matched filter under different signal to noise ratios are compared and analyzed, and the Gaussian rank correlation detector can be verified to have robustness under the impulse noise environment. The number of experiments is 10 4, the false alarm probability is P f =0.1, and the signal attenuation factor is θ 1＝θ2 =0.5. The experimental results are shown in FIG. 3.
As shown in the experimental result of fig. 3, the detection probability curve of the matched filter is close to a horizontal line with P f =0.1 due to the existence of the pulse component, so that the detection effect is completely lost, and the gaussian rank correlation detector has higher detection probability and shows robustness to the impulse noise, so that the gaussian rank correlation coefficient can be used as a powerful tool for signal detection in the impulse noise environment.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical solution of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (6)
1. A signal detection method based on Gaussian rank correlation coefficients is characterized by comprising the following steps:
acquiring echo signals received by two paths of receivers;
Respectively calculating rank statistics of the two paths of echo signals, and carrying out Gaussian rank conversion on the two paths of echo signals;
constructing statistics based on the two paths of echo signals after Gaussian rank conversion;
Calculating a corresponding threshold value according to the given false alarm probability;
Comparing the statistic with the threshold value to determine the detection result of the source signal;
the construction statistics of the two paths of echo signals based on Gaussian rank transformation is specifically as follows:
Wherein the coefficient is
Wherein the coefficient isThe variance value of the signal after the gaussian rank conversion is represented, Φ -1 (·) represents an inverse function of a standard normal distribution cumulative distribution function Φ, n is a signal length, R i represents rank statistics of the first echo signal x (i), Q i represents rank statistics of the second echo signal y (i), x '(i) is a signal after the first echo signal x (i) is subjected to the gaussian rank conversion, and y' (i) is a signal after the second echo signal y (i) is subjected to the gaussian rank conversion.
2. The signal detection method based on a gaussian rank correlation coefficient according to claim 1, wherein the two echo signals are specifically:
x(i)＝θ1s(i)+z1(i)
y(i)＝θ2s(i)+z2(i)
i＝1,2…,n
Wherein { x (i), y (i) } is an echo signal received by two paths of receivers at a sampling time i, s (i) is a source signal, θ l is less than or equal to 1, z l (i) is background noise, l=1, 2 is a first path of receiver, and n is a signal length.
3. The signal detection method based on a gaussian rank correlation coefficient according to claim 1, wherein the formula for calculating rank statistics of two echo signals respectively is:
i＝1,2…,n
Wherein R i represents the rank statistic of the first echo signal x (i), and Q i represents the rank statistic of the second echo signal y (i);
wherein H (·) represents heaviside step functions.
4. The signal detection method based on a gaussian rank correlation coefficient according to claim 1, wherein performing a gaussian rank transform on two echo signals is specifically:
i＝1,2…,n
Wherein Φ -1 (·) represents the inverse of the standard normal distribution cumulative distribution function Φ.
5. The signal detection method based on a gaussian rank correlation coefficient according to claim 1, wherein said calculating a corresponding threshold value according to a given false alarm probability is specifically:
λ＝σΦ-1(1-Pf)
Where Φ -1 (·) represents the inverse of the standard normal distribution cumulative distribution function Φ, σ represents the variance of the statistics, and P f is the given false alarm probability.
6. The signal detection method based on a gaussian rank correlation coefficient according to claim 1, wherein the magnitude of the comparison statistic and the threshold value is specifically:
Comparing the statistic with the threshold value, and if the statistic is larger than the threshold value, the source signal exists; and if the statistic is smaller than or equal to the threshold value, the source signal is considered to be absent.
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| KR20120032232A (en) * | 2010-09-28 | 2012-04-05 | 동아대학교 산학협력단 | Signal detection device on generalized normal-laplace distributed noise environments |
| CN105761216A (en) * | 2016-01-25 | 2016-07-13 | 西北大学 | Image de-noising processing method and device |
| CN110568415A (en) * | 2019-07-22 | 2019-12-13 | 广东工业大学 | signal detection method based on Arctan function under Gaussian mixture model |
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| KR20120032232A (en) * | 2010-09-28 | 2012-04-05 | 동아대학교 산학협력단 | Signal detection device on generalized normal-laplace distributed noise environments |
| CN105761216A (en) * | 2016-01-25 | 2016-07-13 | 西北大学 | Image de-noising processing method and device |
| CN110568415A (en) * | 2019-07-22 | 2019-12-13 | 广东工业大学 | signal detection method based on Arctan function under Gaussian mixture model |
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