JP2009251361A - Device and method for estimating incident wave number - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an incident wave number estimating device capable of estimating the number of incident waves, based on the magnitude of each column vector of a mixed matrix estimated value. <P>SOLUTION: The device includes an independent component analysis processing part 41 to output the mixed matrix estimated value from received signals obtained by the interference of mutually independent incident waves, and a column vector magnitude computing part 42 for computing the magnitude of each column vector of the mixed matrix estimated value based on the norm of each column vector of the mixed matrix estimated value and the number of received signals. The device estimates the number of incident waves using the magnitude of the column vector of the mixed matrix estimated value. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  In the present invention, in the signal separation processing by independent component analysis (ICA), it is necessary to set the incident wave number setting parameter in advance. The incident wave number is calculated based on the size of the column vector of the mixing matrix estimation value. The present invention relates to an incident wave number estimation apparatus and an incident wave number estimation method to be estimated.

  Independent component analysis ICA is a method of separating each incident wave from the received signal using only the property that each incident wave is statistically independent from the received signal obtained by interference of a plurality of incident waves. . This method is applied in various fields such as interference separation of voices of a plurality of speakers, separation of interference radio waves in communication, and the like. Since the separation is performed using only the statistical independence of signals, there is an advantage that prior information on each incident wave is unnecessary.

  Various methods have been proposed for independent component analysis ICA, but a typical method is shown in Non-Patent Document 1. Although details of the method are given in Non-Patent Document 1, what is important here is that the independent component analysis needs to set the incident wave number as a setting parameter in advance. If the number of incident waves is incorrect, all incident waves cannot be separated correctly.

  For this reason, when estimating the incident wave number of a mixed incident wave, the incident wave number is generally estimated from information on the eigenvalues of the covariance matrix of the received signal. Among them, a representative method is a method called MDL (Minimum Description Length) (see Non-Patent Document 2). Although details of the method are given in Non-Patent Document 2, this method determines the incident wave number using eigenvalues obtained by eigenvalue decomposition of the covariance matrix of the received signal.

  Here, the outline of the independent component analysis ICA will be described with a focus on the essential points in the description of the embodiments described later. Details are left to Non-Patent Document 1. Non-Patent Document 1 is a complex ICA that separates complex signals, but the same applies to an ICA that separates real signals.

  FIG. 5 is a diagram showing an outline of the independent component analysis processing. FIG. 6 is a diagram showing an example of a separated signal when the incident wave number parameter is set to a value different from the true value.

  As described above, the independent component analysis ICA is a method of separating each incident wave from a reception signal obtained by interference of a plurality of incident waves using only the property that the incident waves are statistically independent from each other. ICA is an algorithm that separates each incident wave from a received signal obtained by interference of mutually independent incident waves in the following interference model.

Here, s = [s ₁ ,..., S _J ] ^T is an incident wave vector in which each incident wave s _j (j = 1,..., J) is stored as a vector, A is a mixing matrix representing interference, and n = [N ₁ ,..., N _I ] ^T is a receiver noise vector in which receiver noise received by the receivers of the respective receiving antennas #i (i = 1,..., I) is stored in a vector form, x = [x ₁ ,..., X _I ] ^T is a received signal vector in which received signals x _i received by the respective receiving antennas #i are stored in vector form. The number of incident waves is J, and the number of received signals is I. Each element of the mixing matrix is a coefficient indicating interference, and is a value determined from various conditions such as the direction in which the signal enters, the frequency of the signal, the arrangement of the antenna 1, and the gain.

For example, the received signals _{x 1} receive antenna ♯1 _{is, x 1 = A 11 s 1} +, ..., + A 1J s J + n becomes shaped like a _1, the received signal _{x 1} is _s 1, ..., _{s J} is mixed It can be seen that interference occurs in the form of linear addition after multiplication by matrix coefficient A _ij , and each incoming wave s _j cannot be obtained with the received signal as it is.

  These vectors are obtained in time series (k = 1,..., K) at the timing sampled by the A / D converter 3, that is, x = {x (1),..., X (K). }, S = {s (1),..., S (K)}, n = {n (1),..., N (K)}. FIG. 5 shows an example (J = 3) in which the number of incident waves is three.

The independent component analysis ICA needs to set the number of incident waves as a parameter in advance. Hereinafter, assuming that the incident wave number parameter _JP is correctly set ( _JP = J), an outline of the ICA process will be described. In ICA, the received signal x is whitened by PCA (Principal Component Analysis) as preprocessing. Whitening means that the signals are uncorrelated with each other and have the same power. The covariance matrix hat R of the received signal x is calculated by the following equation (2).

  Here, E {·} means an expected value, and H means a complex conjugate transpose. Arrange the eigenvalues and eigenvectors obtained by eigenvalue decomposition of the above matrix so that the eigenvalues are in descending order,

And From the J _P eigenvalues and the corresponding eigenvectors, the whitening matrix M∈C J ^{× I,}

It is defined as _{Here, diag {1 / √λ 1,} ..., 1 / √λ J} is, ₁ / √λ 1, ..., is a square matrix with 1 / √λ _J on the diagonal. Multiply the received signal by M.

  in this case,

It becomes. I _{J × J} is a unit matrix of J × J. The off-diagonal term of the identity matrix is zero. That is, this means that the received signal vector x has been converted to a J-order vector tilde x that is uncorrelated with each other. Since non-correlation is a necessary condition for being independent, it can be said that substantially half of the ICA processing is finished. After that, it is only necessary to find the most independent signal from the signal tilde x uncorrelated with each other.

Next, ICA maximizes an index value called negentropy in order to find the most independent signal from tilde x. This negentropy is a scale defined to be 0 for Gaussian variables. Actually, the probability density function of each incident wave is necessary for the calculation of negentropy, but since they are generally unknown, some evaluation function G is introduced to maximize the sum of the negentropy approximations of each separated signal. To reduce the problem. Specifically, this is a process of finding an orthogonal transformation matrix W that maximizes the sum of the negentropy values E _j of the separated signals in the following equation.

_{Here, y gauss} is separated signal hat _s ^j _{= W} j ^H tilde x and Gaussian signal having the same variance, G is (differentiable) some smooth function, E {·} is the expectation value, The sample average value is used to calculate the expected value. As the function G (y), for example,

  A is a setting parameter. Since the solution of the optimization problem of Equation (8) is not important here, it will be omitted.

  Finally, the separated signal hat s is extracted by multiplying the tilde x by the complex conjugate transpose of the orthogonal transformation matrix W obtained by the optimization problem of Expression (8).

  The generalized inverse matrix of the finally obtained mixed matrix estimate hat A is

  It is. At this time,

It is. It is assumed that the mixing matrix can be estimated without error, that is, hat A = A. At this time, since the hat A ^† A is a unit matrix, the separated signal hat s is expressed by the following equation.

In the equation (14), although the noise term A ^† n remains, there is no interference coefficient in the s term, so that s can be obtained correctly. The above is the processing when the incident wave number parameter _JP is correctly set ( _JP = J).

However, when larger than the true value J incident wave number parameter J _P (J _{P> J),} separating the signal hat s is E obtained by the following equation.

Here, B is a certain matrix. Compared with equation (14), in addition to the incident wave component s + A ^† n, a linear sum signal Bn of noise n is output. That, J wave incident wave component of the separated signal, the remaining J _P -J wave linear sum signal Bn of the noise n can be obtained. Since the linear sum of Gaussian signals is Gaussian, when n is Gaussian noise, Bn is also Gaussian noise. The expression (15) represents the upper J wave in the vector as an incident wave component and the lower J _P -J as a noise component. However, in actual ICA, there is a property of order uncertainty. The order of the separated signals is unknown.

  An example of operation when an incorrect incident wave number parameter is set larger than the true value in the independent component analysis ICA will be described. Fig. 6 (a) shows an example of a separated signal when the incident wave number is set to be smaller than the true value (corrected 3 waves are set as 2 waves ⇒ wrong output), and Fig. 6 (b) shows a separated signal when the incident wave number is set correctly. Signal example (all 3 waves are output correctly), Fig. 6 (c) shows an example of a separated signal when the incident wave number is set larger than the true value (set 5 correct waves to 5 waves → output noise other than 3 waves) Show. Here, three sine waves with slightly different frequencies are used as incident waves, and Gaussian noise is added to the observation noise.

  FIG. 6 shows that in FIG. 6B, all the incident waves can be correctly separated because the wave number is set correctly, but when the incident wave number parameter is set smaller than the true value, the signal cannot be correctly separated and extracted. . On the other hand, when the incident wave number is set larger than the true value, all signals are correctly separated and extracted, and a noise signal is output as the remaining signal components.

Next, when the incident wave number parameter is set to be smaller than the true value ( _JP <J), the projection onto a space narrower than the signal space is performed in Expression (4), and therefore all incident waves cannot be correctly separated.

Bingham E. and Hyvarinen A., “A fast fixed-point algorithm for independent component analysis of complex valued signals,” International Journal of Neural Systems, Vol. 10, No.1, pp.1-8, Feb. 2000. Mati Wax and Thomas Kailath, "Detection of Signals by Information Theoretic Criteria", IEEE Trans. On Acoustics, Speech and Signal Processing, Vol. ASSP-33, No. 2, Apr. 1985.

  In the independent component analysis ICA, it is necessary to set an incident wave number parameter in advance. However, in actuality, when separating a plurality of unknown interference waves, it is difficult to know the incident wave number in advance. Further, when the incident wave number parameter is different from the true value, there is a problem that only all incident waves cannot be correctly separated and extracted. In addition, the method based on the eigenvalues of the covariance matrix of the received signal such as MDL has a problem in that the incident wave number is erroneous in the actual environment due to noise coloration or the like.

  The present invention has been made to solve the above-described problems, and its purpose is to estimate the incident wave number based on a new method that is not based on eigenvalues, that is, the size of the column vector of the mixing matrix estimation value. An incident wave number estimation device and an incident wave number estimation method that can be obtained are obtained.

  An incident wave number estimation apparatus according to the present invention includes an independent component analysis processing unit that outputs a mixing matrix estimation value from a received signal obtained by interference of mutually independent incident waves, and a norm of each column vector of the mixing matrix estimation value And a column vector size calculation unit for calculating the size of each column vector of the mixing matrix estimation value based on the number of received signals, and the number of incident waves using the size of the column vector of the mixing matrix estimation value Is estimated.

  The incident wave number estimation apparatus according to the present invention has an effect that the incident wave number can be estimated based on a new method that is not based on the eigenvalue, that is, the size of the column vector of the mixing matrix estimation value.

Embodiment 1 FIG.
An incident wave number estimation apparatus according to Embodiment 1 of the present invention will be described with reference to FIGS. 1 is a diagram showing a configuration of a receiver including an incident wave number estimation apparatus according to Embodiment 1 of the present invention. In addition, in each figure, the same code | symbol shows the same or equivalent part.

  In FIG. 1, the receiver is provided with a plurality (I) of receiving antennas 1, an adder 2, an A / D converter 3, and an incident wave number estimating device 4.

  In addition, the incident wave number estimation apparatus 4 includes an independent component analysis (ICA) processing unit 41, a column vector magnitude calculation unit 42, and a threshold determination unit 43.

  Next, the operation of the incident wave number estimation apparatus according to the first embodiment will be described with reference to the drawings. FIG. 2 is a flowchart showing the operation of the incident wave number estimation apparatus according to Embodiment 1 of the present invention. Moreover, FIG. 3 is a figure which shows the magnitude value example of the column vector of the incident wave number estimation apparatus based on Embodiment 1 of this invention.

Here, the operation of the incident wave number estimation apparatus based on the size of the column vector of the mixing matrix estimation value will be described. First, before that, it will be described that each column vector of the mixing matrix estimated value hat A obtained by the independent component analysis ICA is related to the power value of each incident wave. For the sake of simplicity, the noise term is ignored now. In the independent component analysis ICA, signal separation is performed on a received signal obtained by interference of an incident wave s _j having arbitrary power, but in practice, the separated signal is normalized so that the power value becomes 1. Is obtained. That is,

It is. In other words, there is a relationship between the separated signal hat s _j and the incident wave s _j via a certain coefficient α _j . That is,

  It means that. Now to reconstruct the received signal from this separated signal:

  It becomes. If the mixing matrix estimate is obtained without error, the reconstructed hat x and the actual x should be the same. For this purpose, each column vector of the mixed matrix estimation value needs to be multiplied by the amount obtained by dividing each separation signal by a certain coefficient in Expression (17). That is,

It is. Actually, the mixing matrix estimated value obtained by the independent component analysis ICA is in the form of Equation (19). Assuming that the power (dispersion value) of each incident wave s _j is σ _j ² , the power E {| hat s _j | ² } of the separated signal is expressed by Equation (16) and Equation (17) as follows:

  Therefore, from equation (20),

Where | α _j | ² represents the power σ _j ² (dispersion value) of the incident wave s _j . In addition, the size of each column vector hat A _j of the mixed matrix estimation value is given by Equation (19):

Assuming that | A _1j | ² = 1, from Equation (22),

It is. As described above, the magnitude of the coefficient α _j , that is, the power of each incident wave is obtained by dividing the magnitude of each column vector hat A _j by √I in Expression (23). The above is the relationship between each column vector of the mixing matrix estimation value and each separated signal power.

This incident wave number estimation apparatus is based on the following concept.
1) Each column vector of the mixing matrix estimate is related to the power of each separated signal.
2) If the S / N is sufficiently high, the noise power should be sufficiently lower than that of the incident wave, so the value shown in equation (23) should also be small.
3) When the incident wave number parameter of ICA is set large, a noise signal can be obtained in addition to the incident wave.

From these properties, perform the ICA was set larger incident wave number parameter J _P of ICA _{(J P>} J), and calculates the size of each column vector of the mixed matrix estimate, the magnitude of the value Therefore, if it is determined whether it is an incident wave or noise, the number of incident waves can be estimated from the total number determined to be incident waves.

  Here, it demonstrates according to FIG. 1 which shows the structure of the incident wave number estimation apparatus which concerns on Embodiment 1, and FIG. 2 which shows the operation | movement.

First, an incident wave s = [s ₁ s ₂ s ₃ ] ^T (three waves as an example in FIG. 1) having an unknown incident wave number is mixed and received by I receiving antennas 1.

Then, the ICA process unit 41 (step 101), sets a larger incident wave number parameter value _{J P,} performs signal separation from the interference reception signal. At this time, the hat _{s 1,} ..., isolated signals in total _{J P-wave} of the hat _{s JP} is obtained.

Next, the column vector size calculator 42 (step 102) calculates the size of each column vector. The column vector size F _j is calculated by the following equation.

  Finally, the threshold value determination unit 43 (step 103) determines the incident wave and noise by the threshold value determination, and estimates the incident wave number. The total number of objects exceeding the threshold is the incident wave number estimation result.

Here, F _th is a threshold value and takes a value of 0 ≦ F _th .

  FIG. 3 shows an example of the magnitude value of the column vector. In FIG. 3, when the number of correct answers is 3, the magnitude value of each column vector of the obtained mixed matrix estimation value is shown after ICA is executed with the set number being 6 waves. To make it easier to understand, they are arranged in descending order. 10 trials of Monte Carlo are shown. As described above, the magnitude values of the three time series vectors exceed the threshold value, and are determined to be three waves by the threshold determination, and are correct.

Embodiment 2. FIG.
An incident wave number estimation apparatus according to Embodiment 2 of the present invention will be described with reference to FIG. FIG. 4 is a diagram showing a threshold value setting method of the incident wave number estimation apparatus according to Embodiment 2 of the present invention. The configuration of the incident wave number estimation apparatus according to the second embodiment of the present invention is the same as that of the first embodiment.

Although the operator can manually determine the threshold value of the threshold value determination unit 43 while looking at the size of the column vector, for example, the following method can be considered for automation.
1) After the ICA process is performed on the received signal when no incident wave exists and only noise exists, the magnitude of the obtained column vector is calculated and set to a value somewhat larger than that value. When the incident wave actually enters, the threshold value is used. In this way, the threshold value is set too low, and noise is not erroneously determined as a signal.
2) In a situation where an incident wave exists, the received signal is subjected to ICA processing, and the magnitude of the obtained column vector is calculated and set to a value that is somewhat smaller than the maximum value. In this way, the threshold value is not set too high and the signal is not erroneously determined as noise.
3) In a situation where an incident wave is present, the received signal is subjected to ICA processing, the magnitude of the obtained column vector is calculated, and the average value thereof is set as a threshold value. In this way, trade-off values of 1) and 2) can be set.

4 (a), (b), and (c) show the concept of each of the methods 1) to 3). In FIG. 4, the incident wave 3 wave, shows an example of setting the J _P and six waves.

Embodiment 3 FIG.
An incident wave number estimation apparatus according to Embodiment 3 of the present invention will be described. The incident wave number estimation apparatus according to the third embodiment of the present invention includes an independent component analysis processing unit that outputs a mixing matrix estimation value from a reception signal obtained by interference of mutually independent incident waves, and the mixing matrix estimation. Based on each column vector of values and the antenna pattern in the incident direction of the incident wave of the antenna element, an incident wave power calculation unit that calculates the power of the incident wave, and the power of the incident wave calculated by the incident wave power calculation unit is A threshold determination unit is provided that estimates the total number of objects exceeding a predetermined threshold as the number of incident waves.

  As described in the first and second embodiments, the power of the incident wave itself may be calculated instead of the size of the column vector of the mixing matrix estimation value. Hereinafter, a method for calculating the power will be described.

For example, it is assumed that each element A _{i, j} of the mixing matrix A can be expressed by a model of the following equation when a time difference in which an incident wave reaches each receiving antenna 1 can be expressed by a phase difference in a narrowband signal.

Here, g _ij is an antenna pattern in the incident direction of the incident wave #j of the antenna element #i, a position vector of the q _i antenna element #i, p _j is an incident direction unit vector of the incident wave #j, and λ _j is an incident wave. This is the wavelength of #j. Now, suppose that ICA can be separated without separation error. That is, the hat A _j = α _j A _j and the hat s _j = s _j / α _j . In order to cancel the unknown scalar coefficient α _j , the following equation is calculated using an arbitrary element hat A _{i, j} .

If various information included in g _ij ^D at the right end of Equation (28) is known, the following equation is calculated using this value. Note that D = jP _j ^T q _i .

Equation (29) is a true signal with no uncertainty due to α _j . When this power is calculated, the power of the hat s _j is 1 because of the nature of the separated signal of ICA.

  It becomes. Equation (30) is the power of each signal (incident wave). If this value is calculated for all signals and it is determined whether the incident wave or noise is based on the magnitude of the value, the number of incident waves can be estimated from the total number determined to be incident waves.

It is a figure which shows the structure of the receiver containing the incident wave number estimation apparatus which concerns on Embodiment 1 of this invention. It is a flowchart which shows operation | movement of the incident wave number estimation apparatus which concerns on Embodiment 1 of this invention. It is a figure which shows the magnitude value example of the column vector of the incident wave number estimation apparatus which concerns on Embodiment 1 of this invention. It is a figure which shows the setting method of the threshold value of the incident wave number estimation apparatus which concerns on Embodiment 2 of this invention. It is a figure which shows the outline | summary of an independent component analysis process. It is a figure which shows the example of a separated signal when an incident wave number parameter is set to the value different from a true value.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 Reception antenna, 2 Adder, 3 A / D converter, 4 Incident wave number estimation apparatus, 41 Independent component analysis process part, 42 Column vector magnitude | size calculation part, 43 Threshold determination part.

Claims (14)

An independent component analysis processing unit that outputs a mixing matrix estimation value from a received signal obtained by interference of mutually independent incident waves; and
A column vector size calculation unit that calculates the size of each column vector of the mixing matrix estimation value based on the norm of each column vector of the mixing matrix estimation value and the number of received signals;
An incident wave number estimation apparatus that estimates an incident wave number using a column vector magnitude of the mixing matrix estimation value. The incident wave number estimation according to claim 1, further comprising a threshold value determination unit that estimates a total number of the column vectors calculated by the column vector size calculation unit exceeding a predetermined threshold value as an incident wave number. apparatus. The predetermined threshold value is a value larger than all the calculated values after calculating the size of the obtained column vector after performing independent component analysis on the received signal when no incident wave exists and only noise exists. The incident wave number estimation apparatus according to claim 2, wherein The predetermined threshold value is set to a value smaller than the maximum value of the calculated value by calculating the magnitude of the obtained column vector after the independent component analysis processing of the received signal in the situation where the incident wave exists. The incident wave number estimation apparatus according to claim 2, wherein The predetermined threshold value is set to an average value of the calculated values after calculating the magnitude of the obtained column vector after performing independent component analysis processing on the received signal in a situation where an incident wave exists. The incident wave number estimation apparatus according to claim 2. An independent component analysis processing unit that outputs a mixing matrix estimation value from a received signal obtained by interference of mutually independent incident waves; and
An incident wave power calculation unit that calculates the power of the incident wave based on each column vector of the mixing matrix estimation value and the antenna pattern in the incident direction of the incident wave of the antenna element,
An incident wave number estimating apparatus that estimates an incident wave number using the electric power of the incident wave. The incident wave number estimation device according to claim 6, further comprising a threshold value determination unit that estimates the total number of incident wave powers calculated by the incident wave power calculation unit exceeding a predetermined threshold as the incident wave number. An independent component analysis processing step of outputting a mixing matrix estimation value from a received signal obtained by interference of mutually independent incident waves;
A column vector size calculating step of calculating the size of each column vector of the mixing matrix estimate based on the norm of each column vector of the mixing matrix estimate and the number of received signals;
An incident wave number is estimated by using the magnitude of a column vector of the mixing matrix estimation value. 9. The incident wave number estimation according to claim 8, further comprising a threshold determination step of estimating a total number of the column vectors whose magnitudes calculated by the column vector magnitude calculation step exceed a predetermined threshold as an incident wave number. Method. The predetermined threshold value is a value larger than all the calculated values after calculating the size of the obtained column vector after performing independent component analysis on the received signal when no incident wave exists and only noise exists. The incident wave number estimation method according to claim 9, wherein: The predetermined threshold value is set to a value smaller than the maximum value of the calculated value by calculating the magnitude of the obtained column vector after the independent component analysis processing of the received signal in the situation where the incident wave exists. 10. The incident wave number estimation method according to claim 9, wherein the incident wave number is estimated. The predetermined threshold value is set to an average value of the calculated values after calculating the magnitude of the obtained column vector after performing independent component analysis processing on the received signal in a situation where an incident wave exists. The incident wave number estimation method according to claim 9. An independent component analysis processing step of outputting a mixing matrix estimation value from a received signal obtained by interference of mutually independent incident waves;
An incident wave power calculation step of calculating the power of the incident wave based on each column vector of the mixing matrix estimation value and the antenna pattern of the incident direction of the incident wave of the antenna element,
Incident wave number is estimated using the power of the incident wave. The incident wave number estimation method according to claim 13, further comprising a threshold value determination step of estimating a total number of incident wave powers calculated by the incident wave power calculation step exceeding a predetermined threshold value as an incident wave number.

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