KR100877225B1 - Detector clipping squared signals - Google Patents

Abstract

A detector for limiting the amplitude of squared signals is provided to estimate noise variance by using the squared component of a received signal in case the amplitude of the received signal is smaller than a threshold level, or by using the squared component of the threshold level so as to suppress an increase in the amplitude of the received signal in case the amplitude is larger than the threshold level. A detector comprises a noise variance estimator(110) which estimates the noise variance of noise signals under the assumption that the noise signals have the Gaussian distribution. The noise variance estimator estimates the noise variance by using the squared value of received signals, when the amplitude of the received signals is smaller than a preset limited value, or using the squared value of the limited value instead of the received signals by replacing the received signals with the squared value of the limited value so that an increase in the amplitude of received signals, when the amplitude of the received signals is bigger than the limited value. The noise variance estimator estimates the noise variance by using the result obtained by comparing the absolute value of the receives signal with the limited value through a limit function.

Description

Detector to limit square signal size {Detector clipping squared signals}

The present invention relates to a detector for limiting a square signal size, and more particularly, when noise reception is larger than a limit value which is an arbitrary limit value when estimating noise variance, the increase of the received signal is suppressed by using the limit value. It relates to a detector for limiting the square signal size, which can improve the detection probability according to the estimation.

Detection theory has been used since the World War II radar field, and its applications range from Sonar, Radar, Radio Astronomy, and Security.

This method is used to select one of two hypotheses, 'signal and noise' or 'noise', and it is a theory of how to set a threshold. Here, 'signal' is set to Deterministic and 'noise' is set to Random Process.

Conventionally, a method of detecting a received signal using a linear detector is disclosed as shown in FIG. 1, and the detection process using the linear detector 10 will be described in detail as follows.

First, as shown in Equation A below, hypothesis ₀ includes only a 'noise signal' in a received signal, and hypothesis ₁ indicates that both a 'transmission signal' and a 'noise signal' exist in the received signal. If it is.

Equation A

H _j : x [i] = S _j + w [i], (i = 1, ..., n), j = 0,1

-> H ₀ : x [i] = S ₀ + w [i], (i = 1, ..., n), j = 0

-> H ₁ : x [i] = S ₁ + w [i], (i = 1, ..., n), j = 1

Where x [i] is the i-th received signal, S _j is the transmit signal, w [i] is the i-th noise signal, n is the number of samples of the received signal received within a predetermined period, i is i of the 1st to nth samples It means the received signal sample corresponding to the first. That is, x [i] is the i-th received signal sample, and w [i] is the noise signal included in the i-th received signal sample, which means the i-th noise signal.

On the other hand, the distribution of w (n) can be expressed as f ₀ (x) and f ₁ (x), respectively, and it is assumed that this follows the Gaussian distribution of iid (Independent Identical Distribution). Same as That is, looking at Equation B, it can be seen that the distribution of the sum result for each sample means the distribution of the noise signal. Here, the reason for sum of the samples is that when a plurality of samples are input, the samples are cut at regular intervals, and the samples during the period are summed.

Equation B

Here, since the signal is deterministic, S ₀ is 0, S ₁ is a constant whose value is already known, and the variance of noise (σ ² ) is unknown, so in the linear detector 10 as shown in FIG. It is assumed that this is calculated. Here, of course, j = 0 and j = 1 mean the assumption of H ₀ , H ₁ in Equation A, respectively.

L (x ₁ , ..., x _n ), which is the Likelihood Ratio of the linear detector 10, is calculated as in Equation C.

Equation C

Here, T represents a threshold that is a detection reference of the received signal on the linear detector 10.

For example, when the likelihood ratio L of Equation C with respect to the received signal is greater than the threshold value T, it may be detected as 1, and when it is smaller than the threshold value T, it may be detected as 0. Of course, when the calculated likelihood ratio L is equal to the threshold value T, it can be detected as 1 or 0, which can be selectively changed according to circumstances.

On the other hand, Equation C can be arranged as Equation D below using Equation B.

[Equation D]

Meanwhile, as described above, since S ₀ is 0 and the variance of noise σ ² is a constant, Equation D can be simply summarized as Equation E.

[Equation E]

를 의미할 수 있다. 그리고, S₁은 상수이므로 수학식 E의

는 상수가 된다. 따라서, 가능도비(L_L)가

보다 큰 경우 1로 검파되고,

보다 작은 경우 0으로 검파될 수 있고, 상기 가능도비(L_L)가

와 동일한 경우는 1 또는 0으로 검파될 수 있다. That is, the likelihood ratio of the linear detector 10 of FIG. 1 may be redefined to L _L as shown in Equation E, and T shown in FIG.

It may mean. Since S ₁ is a constant, E ₁

Becomes a constant. Therefore, the likelihood ratio L _L

Is greater than 1,

If less, it can be detected as 0, and the likelihood ratio L _L is

If the same as can be detected as 1 or 0.

On the other hand, unlike the linear detector 10, the following 'improved detector' is proposed to estimate the variance assuming that the variance of noise (σ ² ) is not a constant.

In the case of the 'improved detector', the distribution of w (n), which is a noise signal, can be expressed as f ₀ (x) and f ₁ (x) below, as in the linear detector 10, and w ( Assuming that n) follows the Gaussian distribution of iid, the distribution of the sum of the samples can be expressed as Equation F.

Equation F

로 두며, 이러한 잡음 분산은 분산추정기를 통해 추정될 수 있다. 그리고, 수학식 F에서 S₀는 0이며 S₁는 이미 값을 아는 상수이다.For this 'improved detector', the variance of noise (σ ² ) is not assumed to be 1

This noise variance can be estimated through the variance estimator. In Equation F, S ₀ is 0 and S ₁ is a constant that already knows a value.

에 대해 미분한 값이다.For variance estimation, the following equation G must also be satisfied, which is f _{i in} equation F. Function (distribution function for sum of samples)

Differentiate for.

[Equation G]

)은 수학식 H와 같이

로 재정의 가 능하다.Noise variance described in Equation G (

) Is the same as

Can be redefined.

[Equation H]

Here, since n, x, and S _j have been described above in the example of the linear detector 10, a detailed description thereof will be omitted.

Meanwhile, the likelihood ratio of the above-described 'improved detector' may be expressed by Equation I.

[Equation I]

Here, T may refer to T on Equation D calculated in the case of the linear detector 10.

On the other hand, equation (I) can be expressed simply as shown in equation (J).

[Equation J]

In addition, Equation J can be redefined by Equation K below.

[Equation K]

로 재정의되어

를 기준으로 한 검파가 수행될 수 있으며

는 상수가 된다. 따라서, 가능도비(L_R)가

보다 큰 경우 1로 검파되고,

보다 작은 경우 0으로 검파될 수 있고,

와 동일한 경우는 1 또는 0으로 검파될 수 있다.Likelihood ratio of the 'improved detector' is referred to as L _R as shown in Figure 2, the threshold (Threshold) using the T value as shown in Equation K

Overridden by

Can be performed based on

Becomes a constant. Therefore, the likelihood ratio (L _R ) is

Is greater than 1,

Less than 0 can be detected,

If the same as can be detected as 1 or 0.

These 'improved detectors' are described in Fundamentals of Statistics Signal Processing Volume II, page 338 of the Detection Theory, Example 9.1, and the contents of the book) are the limits contained within the noise dispersion estimator 110 of FIG. The same is true except for the clipping function using (k).

On the other hand, after detection using Equation K, it is possible to perform a simulation on the detection probability of the received signal.

과

값을 계산한다.First, in E and E, False Alarm Probability (P _f ) is {10 ^-2 , 10 ^-3 , 10 ^-4 } and E _b / N _o (Signal to Noise Rate) is -3.02. Each threshold under dB (S ₁ = 1, σ ² = 1)

and

Calculate the value.

By using the calculated threshold value, E _b / N _o is changed (in this case, the transmission signal S ₁ is changed while the noise variance σ ² is fixed to 1), respectively, as shown in Equations L and M below. Detect Probability (P _d ) can be calculated and compared.

[Equation L]

Equation M

를 사용하여 검출확률을 구하는 식이고, 수학식 M은 도 2와 같은 '개선된 검파기'에서

를 사용하여 검출확률을 구하는 식이다. That is, equation (L) in the linear detector 10 of FIG.

Equation M is used to calculate the detection probability using Equation (M).

The probability of detection is found by using.

It is assumed here that F ₀ and F ₁ follow a Gaussian distribution as described above.

However, in the case of the linear detector and the improved detector, which are conventionally proposed as described above, no limitation is given when estimating the noise variance, so that the limitation is impossible when the size of the received signal is large and the detection probability is not possible. There is a problem of this deterioration.

The present invention has been made to solve the above-described problems, and when estimating noise variance, when the magnitude of the received signal is smaller than a predetermined limit, the noise variance is estimated using a square component of the received signal. An object of the present invention is to provide a detector for limiting a square signal size, in which a signal detection probability can be improved by estimating noise variance using a square component of the limit value so that a magnitude of a received signal is suppressed.

The detector for limiting the square signal size of the present invention for achieving the above object, by using a noise dispersion estimator to estimate the noise dispersion of the noise signal on the received signal including the transmission signal and the noise signal, In the detector for detecting a received signal by comparing a Likelihood Rate using noise variance with a threshold, the noise variance of the noise signal is estimated on the assumption that the noise signal has a Gaussian distribution. When the magnitude of the received signal is smaller than a predetermined limit, the noise variance is estimated using a square of the received signal, and when the magnitude of the received signal is larger than the limit, the increase in magnitude of the received signal is suppressed. Replace the received signal with the square of the limit and use the square of the limit instead of the received signal. And a noise variance estimator for estimating the noise variance.

In addition, the noise dispersion estimator applies the result of comparing the absolute value of the received signal x with the limit value k using the limit function h _R (x) of Equation 1 to Equation 2 above. Noise variance can be estimated.

[Equation 1]

(Where h _R (x): limit function, x: received signal, k: limit value)

[Equation 2]

: 잡음신호의 분산, n: 일정주기 내에 수신되는 수신신호의 샘플수, x_i; 1 내지 n번째 샘플 중 i번째에 해당되는 수신신호 샘플, S_j: j 경우의 송신신호, j=0: 수신신호에 잡음신호만이 존재하는 경우, j=1: 수신신호에 송신신호와 잡음신호가 모두 존재하는 경우)(here,

: Variance of noise signal, n: number of samples of received signal received within a certain period, x _i ; Received signal sample corresponding to i th of 1 th to n th samples, S _j : transmission signal in case of j, j = 0: when only noise signal is present in the reception signal, j = 1: transmission signal and noise in the reception signal If all signals are present)

)을 이용하여 수학식 3 및 수학식 4를 통해 재정의된 가능도비를, 재정의된 문턱값(

)과 비교하는 것에 의해 상기 수신신호를 검파하는 검파부를 더 포함할 수 있다.On the other hand, the present invention, the noise dispersion estimated by the noise dispersion estimator (

), The likelihood ratio redefined by Equation 3 and Equation 4

The detector may further include a detector configured to detect the received signal.

[Equation 3]

[Equation 4]

: 재정의된 문턱값)(Where L (x ₁ , ..., x _n ): likelihood ratio before redefinition, T: threshold before redefinition, L _R (x ₁ , ..., x _n ): likelihood likelihood ,

: Overridden threshold)

According to the present invention, the input unit may further include an input unit for inputting the limit value used for the noise dispersion estimator or for changing the input limit value.

Herein, the input unit may input an operation signal for changing the sample number n.

The detector for limiting the square signal size according to the present invention provides the following effects.

First, when the magnitude of the received signal is smaller than the predetermined limit, the noise dispersion estimator estimates the noise variance using a square component of the received signal, but when the magnitude of the received signal is larger than the limit, the increase of the received signal is suppressed. By estimating the noise variance using the square component, the signal detection probability can be improved as compared with the conventional linear detector.

Second, when the limit value is used, the detection probability characteristic is excellent even when the noise having the Laplacian distribution is actually input.

Third, not only the input and change of the limit value k but also the change of the number of signal samples n added through the input part can be adjusted, and thus the detection probability can be adjusted.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, terms or words used in the present specification and claims should not be construed as being limited to the common or dictionary meanings, and the inventors should properly explain the concept of terms in order to best explain their own invention. Based on the principle that it can be defined, it should be interpreted as meaning and concept corresponding to the technical idea of the present invention.

Therefore, the embodiments described in the specification and the drawings shown in the drawings are only the most preferred embodiment of the present invention and do not represent all of the technical idea of the present invention, various modifications that can be replaced at the time of the present application It should be understood that there may be equivalents and variations.

2 is a block diagram of a detector for limiting a square signal size according to an exemplary embodiment of the present invention, and FIG. 3 is a graph showing a general Gaussian distribution and a Laplacian distribution.

According to the present invention, a noise variance estimator estimates a noise variance of the noise signal on a received signal including a transmission signal and a noise signal, and estimates a Likelihood Rate using the estimated noise variance as a reference value. It is a kind of detector that detects the received signal in comparison with the value.

Since the structure and principle of the linear detector and the improved detector, which are detectors using the likelihood ratio and threshold, have already been introduced above, a detailed description thereof will be omitted.

Here, the detector for limiting the square signal size according to the present invention employs the structure of the conventional 'improved detector' presented in the above-mentioned 'background art', but the threshold value is greater when the received signal is larger than an arbitrary threshold value when the noise is estimated. By suppressing the increase of the signal by further increasing, the detection probability can be excellent compared to the linear detector 10 of FIG. 1 even when a noise having a Gaussian distribution or a Laplacian distribution is actually input.

Hereinafter, the configuration of the present invention will be described in more detail.

As shown in FIG. 2, in the detector 100 for limiting a square signal size according to an embodiment of the present invention, the noise dispersion estimator 110 assumes that the noise signal has a Gaussian distribution. Estimate the noise variance of

Here, the noise dispersion estimator 110 estimates the noise dispersion using a square of the received signal when the magnitude of the received signal is smaller than a predetermined limit value.

Alternatively, the noise dispersion estimator 110 replaces the received signal with a squared value of the limit so that the increase in the received signal is suppressed when the magnitude of the received signal is greater than the limit. The noise variance is estimated using the square of the limit value.

More specifically, the noise dispersion estimator 110 calculates a result of comparing the absolute value of the received signal x with the limit value k using the limit function h _R (x) of Equation 1 The noise variance can be estimated by applying to Equation 2.

[Equation 1]

Where h _R (x) is a limit function, x is a received signal, and k is a limit value.

[Equation 2]

는 잡음신호의 분산, n은 일정주기 내에 수신되는 수신신호의 샘플수, x_i는 1 내지 n번째 샘플 중 i번째에 해당되는 수신신호 샘플, S_j는 j 경우의 송신신호이다. here,

Is the variance of the noise signal, n is the number of samples of the received signal within a certain period, x _i is the received signal sample corresponding to the i th among 1 to n th sample, S _j is the transmission signal in the case of j.

In addition, as in the principles of the conventional 'linear detector' and 'improved detector' described above in the background art, when j = 0, only a noise signal exists in a received signal, and j = 1 In this case, both the transmission signal and the noise signal are present in the received signal.

)을 추정한다. That is, the noise variance estimator 110 applies the limiting function h _R (x) when the absolute value size (| x |) of the received signal (x) is smaller than the predetermined limit value k as shown in Equation 1 below. The received signal x is replaced with a squared value x ² of the received signal. As this is applied to Equation 2, the noise variance (S) is obtained by using a value obtained by adding the transmission signal S to a square value x ² of the received signal.

Estimate).

)을 추정한다.In addition, the noise dispersion estimator 110 receives the received signal as shown in Equation 1 such that the magnitude increase of the received signal x is suppressed when the absolute value magnitude | x | of the received signal is greater than the limit value k. (x) one of adding the squared value (k ²⁾ to as alternative by applying the equation (2) the received signal (x) instead of the square value of the limit (s) the transmission signal (S) to (k ²⁾ of the limit value Using the noise variance (

Estimate).

)은 임의의 크기인 한계치(k)를 이용하여 추정되어 추후 신호의 검파에 이용될 수 있도록 한다.That is, the noise variance (for large signals)

) Is estimated using a threshold value k of arbitrary magnitude so that it can be used for later detection of the signal.

According to the present invention, the input unit 120 for inputting the limit value k or changing the input limit value k used in the noise dispersion estimator 110 may be further included. The input unit 120 may be a method of directly inputting from a user or automatically selected by a program through input means such as a keyboard, a button, a touch screen, a mouse, and the like.

)을 이용하여 수학식 3 및 수학식 4를 통해 재정의된 가능도비(L_R)를, 재정의된 문턱값(

)과 비교하는 것에 의해 수신신호(x)를 검파한다.On the other hand, in the present invention, the detector 130, the noise dispersion estimated by the noise dispersion estimator (110)

), The likelihood ratio (L _R ), which is redefined using Equations 3 and 4, is defined as

), The received signal x is detected.

[Equation 3]

[Equation 4]

는 재정의된 문턱값을 나타낸다.Where L (x ₁ , ..., x _n ) is the likelihood ratio before redefinition, T is the threshold before redefinition, L _R (x ₁ , ..., x _n ) is the likelihood probability overridden,

Represents an overridden threshold.

에 상기 수학식 2를 대입한 후 수학식 I의 가능도비(L) 식에 적용함으로써 유도될 수 있다.Equation 3 is represented by Equation F described above in the Background Art.

It can be derived by substituting Equation 2 into and applying it to the likelihood ratio (L) of Equation I.

)과 비교하는 것에 의해 신호의 검파를 수행한다.Meanwhile, the derived Equation 3 may be redefined as Equation 4 as in Equation K described above. Accordingly, the detector 130 may define the redefined probability ratio L _R as a threshold (

Detection of the signal by comparison with

보다 큰 경우 1로 검파되고,

보다 작은 경우 0으로 검파될 수 있고,

와 동일한 경우는 1 또는 0으로 검파될 수 있다.That is, the likelihood ratio (L _R ) is

Is greater than 1,

Less than 0 can be detected,

If the same as can be detected as 1 or 0.

In addition, the detection probability of the signal detected by the detector 130 may be calculated by Equation M described above.

4 to 6 are graphs showing P _d when the noise is Gaussian distribution for each of P _f = 10 ⁻² , 10 ⁻³ , and 10 ⁻⁴ , and FIGS. 7 to 9 show P _f = 10 ⁻² In the case of, 10 ^-3 and 10 ^-4 , P _d is a graph when the noise is a Laplacian distribution.

Estimation of noise variance on the detector 100 of the present invention is performed by assuming that the noise is a Gaussian distribution, but in practice, the noise signal may be a signal having a Laplacian distribution rather than a signal having an ideal Gaussian distribution as shown in FIG. 3.

Therefore, the detection probability verification of the detector 100 according to the present invention is not only the case of FIGS. 4 to 6 when the noise signal is Gaussian distribution, but also the case where the noise signal has the Laplacian distribution. All nine cases were considered.

When the noise signal is in the form of an impulse, an ultra low frequency communication signal, or in the case of atmospheric noise, it may have the above-described Laplacian distribution. The Laplacian distribution, unlike the Gaussian distribution as shown in FIG. 3, is referred to as heavy-tail distribution because the distribution of the tip portion is larger than that of the Gaussian distribution.

According to the present invention, when a noise signal having a most common Gaussian distribution or a Laplacian distribution is mixed with a transmission signal as an input signal and input to the noise dispersion estimator 110, the threshold value k in the noise dispersion estimator 110 as in the present invention. It can be seen that the use of the signal limiting function using a) shows a higher detection probability compared to the case of using a conventional linear detector (Linear part in FIG. 4 to FIG. 9).

That is, referring to all the data of FIGS. 4 to 9, it can be seen that the detection probability is improved when the detector 100 (+ symbol or ○ symbol) of the present invention is used in comparison with the case where the linear detector (□ symbol) is used. .

In addition, as the sum of the samples of the signals representing the Gaussian distribution of FIGS. 4 to 6 or the Laplacian distribution of FIGS. 7 to 9 increases, that is, as the number n of samples summed on FIGS. 4 to 9 increases, The detection probability of the detector 100 (+ symbol or o symbol) of the present invention is higher than that of the linear detector (□ symbol).

Herein, the input unit 120 of the present invention may further input an operation signal for changing the number of samples n. Accordingly, the detection probability may be appropriately adjusted by changing the sum of the number of sampled signals n. There is an advantage to that.

In the detector 100 of the present invention, an appropriate detection probability can be obtained by variously changing the limit value k through the input unit 120. If the limit value k is too small, for example, the Laplacian distribution can be obtained. In Figs. 7 to 9, when k = 1 (○ symbol), the signal is distorted and the detection probability is lowered. When k = 10 (+ symbol), an appropriate detection probability is shown.

Of course, various modifications of the limit value k using the input unit 120 are applicable to the Gaussian distribution and the Laplacian distribution shown in FIGS. 4 to 9, and both characteristics are good when k = 10. Can be represented.

When the noise having a Laplacian distribution is mixed with the Gaussian distribution noise under the same condition (k = 10), that is, the signal input to the noise dispersion estimator 110 is limited through the limiting value k. In the case where the noise distribution is a heavy-tail distribution, the detection probability is higher than that in the Gaussian distribution, which is a comparison between FIGS. 4 and 7, 5 and 8, and 6 and 9. This can be seen through.

This phenomenon is more pronounced when the number of samples to be added (n) is smaller. In other words, when the number of samples to be added (n) is larger, the detection probability of the Gaussian distribution and the Laplacian distribution is similar to each other. Central Limit Theorem.

Meanwhile, since the Laplacian distribution noise is input but the Gaussian distribution noise is input, the equation is used as in the case of Gaussian distribution.

The detector 100 of the present invention can be extremely useful when the noise having the Laplacian distribution is actually input. Therefore, the present invention has a great advantage of increasing the detection probability even when the signal having the Laplacian distribution is input.

As described above, although the present invention has been described by way of limited embodiments and drawings, the present invention is not limited thereto and is intended by those skilled in the art to which the present invention pertains. Of course, various modifications and variations are possible within the scope of equivalents of the claims to be described.

1 is a block diagram of a conventional linear detector,

2 is a block diagram of a detector for limiting a square signal size according to an embodiment of the present invention;

3 is a graph showing a Gaussian distribution and a Laplacian distribution;

4 to 6 are graphs showing P _d when the noise is a Gaussian distribution for P _f = 10 ^-2 , 10 ^-3 , and 10 ^-4 , respectively.

7 to 9 are graphs showing P _d when noise is a Laplacian distribution for each of P _f = 10 ⁻² , 10 ⁻³ , and 10 ⁻⁴ .

<Explanation of symbols for the main parts of the drawings>

10 ... linear detector 11 ... detector

100 ... detector limits the square signal size

110 ... Noise Dispersion Estimator 120 ... Input

130 ... detector

Claims (5)

The noise variance estimator estimates the noise variance of the noise signal on the received signal, including the transmission signal and the noise signal, and compares the Likelihood Rate using the estimated noise variance with a threshold which is a reference value. In the detector for detecting the received signal by Under the assumption that the noise signal has a Gaussian distribution, the noise variance of the noise signal is estimated. When the magnitude of the received signal is smaller than a predetermined limit, the noise variance is estimated using the square of the received signal. Noise that estimates the noise variance by using a square of the limit instead of the received signal by replacing the received signal with a squared value so that the increase in the received signal is suppressed when the magnitude of the received signal is greater than the limit. A detector for limiting a square signal size, including a variance estimator. The noise dispersion estimator of claim 1, wherein The noise variance is estimated by applying the result of comparing the absolute value of the received signal x with the limit value k using the limit function h _R (x) of Equation 1 to Equation 2. A detector that limits the square signal size.

(Where h _R (x): limit function, x: received signal, k: limit value)

(here,

: Variance of noise signal, n: number of samples of received signal received within a certain period, x _i ; Received signal sample corresponding to i th of 1 th to n th samples, S _j : transmission signal in case of j, j = 0: when only noise signal is present in the reception signal, j = 1: transmission signal and noise in the reception signal If all signals are present) The method of claim 2, The noise variance estimated by the noise variance estimator (

), The likelihood ratio redefined by Equation 3 and Equation 4

And a detector configured to detect the received signal by comparing with a).

(Where L (x ₁ , ..., x _n ): likelihood ratio before redefinition, T: threshold before redefinition, L _R (x ₁ , ..., x _n ): likelihood likelihood ,

: Overridden threshold) The method of claim 2, And an input unit for inputting the limit value or changing an input limit value used for the noise dispersion estimator. The method of claim 4, wherein the input unit, And a detector for limiting the square signal size, wherein an operation signal for changing the number of samples (n) is further input.

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