JP5328210B2 - Incident wave number estimation device and incident wave number estimation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain a device for estimating an incident wave number which can estimate the incident wave number on the basis of a time shift correlation coefficient value of each splitting signal. <P>SOLUTION: The device includes an independent component analysis processing part 41 which outputs the splitting signal from received signals obtained from interference of incident waves independent of one another, a time shifting part 42 which obtains a time-shifted splitting signal by shifting the time of the splitting signal by a time shifting amount parameter, and a correlation coefficient calculating part 43 which calculates the time shift correlation coefficient values of each splitting signal and the time-shifted splitting signal, and the incident wave number is estimated by using the time shift correlation coefficient value of each splitting signal. <P>COPYRIGHT: (C)2010,JPO&amp;INPIT

Description

  The present invention solves the problem that an incident wave number setting parameter needs to be set in advance in signal separation processing by independent component analysis (ICA), and incident wave number estimation for estimating the incident wave number based on the time shift correlation coefficient value. The present invention relates to an apparatus and an incident wave number estimation method.

  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. Details of the method are given in Non-Patent Document 1, but what is important here is that the independent component analysis needs to set the incident wave number in advance as a setting parameter. 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). Details of the method are given in Non-Patent Document 2, but in this method, the incident wave number is determined using the eigenvalue 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 calculation of negentropy, but since these 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 object is to estimate the incident wave number based on a new method not based on eigenvalues, that is, based on the time-shift correlation coefficient value of each separated signal. An incident wave number estimating apparatus and an incident wave number estimating method capable of performing the above are obtained.

An incident wave number estimation device according to the present invention includes an independent component analysis processing unit that outputs a separated signal from a received signal obtained by interference of mutually independent incident waves, and shifts the time of the separated signal by a time shift amount parameter. Provides a time shift unit that obtains a time-shifted separated signal and a correlation coefficient calculation unit that calculates a time-shifted correlation coefficient value of each separated signal and the time-shifted separated signal. The correlation coefficient calculation unit calculates a time shift correlation coefficient of noise by changing the time shift amount parameter when only noise is present. The time shift amount parameter is set so that the calculated time shift correlation coefficient is smaller than a preset allowable correlation coefficient value .

  The incident wave number estimating apparatus according to the present invention has an effect that the incident wave number can be estimated based on a new method not based on the eigenvalue, that is, based on the time shift correlation coefficient value of each separated signal.

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 time shift unit 42, a correlation coefficient calculation unit 43, and a threshold determination unit 44.

  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 example of a time shift correlation coefficient value of the incident wave number estimation apparatus based on Embodiment 1 of this invention.

  Here, an incident wave number estimation device based on the time shift correlation coefficient value of each separated signal will be described.

This incident wave number estimation apparatus is based on the following concept.
1) In general, noise has a strong randomness. Therefore, when the correlation coefficient value is calculated while shifting the time, the value is ideally zero.
2) In general, since an incident wave is a signal to which a certain carrier frequency and some modulation method are added, its randomness is weaker than noise. For this reason, even if the time is shifted, the correlation coefficient value does not become zero.
3) When the incident wave number is set to a large true value, noise is output in addition to the incident wave.

  Utilizing these properties, the incident wave number is set to a large value, and after ICA processing, the obtained separated signals and the correlation coefficient values of those obtained by time-shifting them are calculated. If determined, the number of incident waves can be estimated from the total number determined as incident waves.

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 time shift unit 42 (step 102) obtains the hat s ₁ (k-sh),..., The hat s _JP (k-sh) by shifting the time of the separated signal by sh.

Next, the correlation coefficient calculation unit 43 (step 103) calculates a correlation coefficient between each separated signal and the time-shifted signal. The time shift correlation coefficient value C _j is calculated by the following equation.

Here, sh is a time shift amount parameter. In ICA, since the dispersion value of the separation signal hat s _j is normalized to 1, the denominator of the equation (16) is 1, and in the actual calculation, only the numerator needs to be calculated.

  Finally, the threshold wave determination unit 44 (step 104) estimates the incident wave number by performing threshold determination on the value calculated by the equation (16). The total number of objects exceeding the threshold is the incident wave number estimation result.

Here, C _th is a threshold value and takes a value of 0 ≦ C _th ≦ 1.

  FIG. 3 shows an example of time shift correlation coefficient values. In FIG. 3, when the number of correct answers is 3, the time shift correlation coefficient value of each separated signal obtained after ICA is executed with the set number being 6 waves is shown. To make it easier to understand, they are arranged in descending order. 10 trials of Monte Carlo are shown. As described above, the three time shift correlation coefficient values 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.

For setting the threshold value of the threshold value determination unit 44, the operator can manually determine the value while looking at the time shift correlation coefficient value. However, for example, the following method can be considered.
1) After the ICA process is performed on the received signal when no incident wave exists and only noise exists, the time shift correlation coefficient value of each obtained separated signal 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 is present, after the ICA process is performed on the received signal, the time shift correlation coefficient value of each obtained separated signal 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 exists, after the ICA process is performed on the received signal, a time shift correlation coefficient value of each obtained separated signal is calculated, and an 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 configuration of the incident wave number estimation apparatus according to the third embodiment of the present invention is the same as that of the first embodiment.

  That is, the incident wave number estimation apparatus 4 according to Embodiment 3 of the present invention includes an independent component analysis (ICA) processing unit 41, a time shift unit 42, a correlation coefficient calculation unit 43, and a threshold determination unit 44. It has been. The correlation coefficient calculation unit 43 sets the time shift amount parameter sh based on the filter length N.

The time shift correlation coefficient value depends on the time shift amount parameter sh. When the noise is completely random, if sh is 1 or more, it is theoretically zero. However, for example, the receiver noise is colored due to a band limiting filter inserted between the A / D converter 3 of the receiver and the ICA processing unit 41, and the temporal correlation is increased. In this case, if sh is small, the time shift correlation coefficient value becomes large. In this case, the difference from the time shift correlation coefficient value of the incident wave becomes small, and in some cases, it is difficult to discriminate between the incident wave and noise. In such a case, a method of setting sh to a larger value is conceivable. For example, when the band limiting filter is FIR, if the filter length is N and the filter coefficients are h (0),..., H (N−1), the noise n _f after the filter is

  Time shift correlation is

Therefore, if sh is set to a value larger than the filter length N, Expression (19) is zero, that is, the time shift correlation coefficient of noise is zero. However, if it is increased unnecessarily, signal samples necessary for sufficiently taking the time width in which the hat s _j (k) and the hat s _j (k-sh) necessary for calculating the correlation coefficient overlap. Since the number increases, this should be set in consideration of this point.

  Even if the characteristics of the filter are not known, when only noise is present, sh is changed to calculate the time shift correlation coefficient of the noise, and sh is set such that the value is sufficiently low.

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 example of a time shift correlation coefficient value 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 Time shift part, 43 Correlation coefficient calculation part, 44 Threshold determination part.

Claims (12)

An independent component analysis processing unit that outputs a separated signal from a received signal obtained by interference of mutually independent incident waves, and
A time shift unit for obtaining a time-shifted separated signal by shifting the time of the separated signal by a time shift amount parameter;
A correlation coefficient calculation unit for calculating a time-shifted correlation coefficient value of each separated signal and the time-shifted separated signal;
An incident wave number estimating device that estimates an incident wave number using a time shift correlation coefficient value of each separated signal ,
The correlation coefficient calculation unit calculates a time shift correlation coefficient of noise by changing the time shift amount parameter when only noise is present, and the calculated time shift correlation coefficient is a preset allowable phase relationship. An incident wave number estimation apparatus, wherein a time shift amount parameter that is smaller than a numerical value is set . The incident wave number estimation device according to claim 1, further comprising a threshold value determination unit that estimates the total number of the time shift correlation coefficient values calculated by the correlation coefficient calculation unit exceeding a predetermined threshold value as the incident wave number. The correlation coefficient calculation unit calculates the time shift correlation coefficient value of each separated signal obtained 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 a value larger than all values is set as the predetermined threshold value . The correlation coefficient calculation unit calculates a time shift correlation coefficient value of each separated signal obtained after performing independent component analysis on the received signal in a situation where an incident wave is present, and is smaller than the maximum value of the calculated values. The incident wave number estimation apparatus according to claim 2 , wherein a value is set to the predetermined threshold value . The correlation coefficient calculation unit calculates a time shift correlation coefficient value of each separated signal obtained after performing independent component analysis on the received signal in a situation where an incident wave is present, and calculates an average value of the calculated values . The incident wave number estimation apparatus according to claim 2, wherein the incident wave number estimation apparatus is set to a predetermined threshold value . The correlation coefficient calculation unit calculates the time shift correlation coefficient of the noise by changing the time shift amount parameter when only noise is present when the characteristics of the filter are not known, and calculates the time shift phase relationship The time shift amount parameter that is smaller than the preset allowable correlation coefficient value is set, and when the characteristics of the filter are known, the time shift amount parameter is set based on the filter length. Or the incident wave number estimation apparatus of 2 description. An independent component analysis processing step for outputting a separated signal from a received signal obtained by interference of mutually independent incident waves;
A time shift step of obtaining a time-shifted separated signal by shifting the time of the separated signal by a time shift amount parameter;
A correlation coefficient calculating step for calculating a time-shifted correlation coefficient value of each separated signal and the time-shifted separated signal,
An incident wave number estimation method for estimating an incident wave number using a time shift correlation coefficient value of each separated signal ,
The correlation coefficient calculating step calculates a time shift correlation coefficient of noise by changing the time shift amount parameter when only noise is present, and the calculated time shift correlation coefficient is a preset allowable phase relationship. A method of estimating an incident wave number, wherein a time shift amount parameter that is smaller than a numerical value is set . The incident wave number estimation method according to claim 7, further comprising a threshold determination step of estimating a total number of the time shift correlation coefficient values calculated by the correlation coefficient calculation step exceeding a predetermined threshold as an incident wave number. The correlation coefficient calculating step calculates the time-shifted correlation coefficient value of each separated signal obtained 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 8 , wherein a value larger than all values is set as the predetermined threshold value . The correlation coefficient calculation step calculates the time-shift correlation coefficient value of each separated signal obtained after performing independent component analysis processing on the received signal in the presence of an incident wave, and is smaller than the maximum value of the calculated values. 9. The incident wave number estimation method according to claim 8 , wherein a value is set to the predetermined threshold value . The correlation coefficient calculating step calculates a time shift correlation coefficient value of each separated signal obtained after performing independent component analysis processing on the received signal in a situation where an incident wave is present, and calculates an average value of the calculated values . The incident wave number estimation method according to claim 8, wherein a predetermined threshold value is set. In the correlation coefficient calculation step, when the characteristics of the filter are not known, the time shift correlation coefficient of the noise is calculated by changing the time shift amount parameter when only noise is present, and the calculated time shift phase relationship 8. A time shift amount parameter whose number is smaller than a preset allowable correlation coefficient value is set, and when the characteristics of the filter are known, the time shift amount parameter is set based on a filter length. Or the incident wave number estimation method of 8 description.

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