JP2003283229A - Method of controlling array antenna - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To change the directional characteristics of an array antenna without referring to learning sequence signals. <P>SOLUTION: In a method of controlling the array antenna, three steps are repeated. In the first step, signals received by means of the antenna elements 1-1 to 1-N of the array antenna 100 are multiplied by prescribed weighting factors and an output signal z obtained by summing the multiplied results is outputted. In the second step, in a cumulant of degree 2m having m (m: an integer of ≥2) first variables, (m-1) second variables, and one third variable, a cumulant vector d which includes m identical output signal z as the first variables, (m-1) identical signal z* (complex conjugate of the output signal z) as the second variables, and the complex conjugate vector x* of a received signal vector having each received signal as the third variable, is calculated. In the third step, a weighting factor vector c containing weighting factors as components is calculated based on the autocorrelation matrices R of the received signal vectors x and the cumulant vector d. <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an array antenna control method capable of changing the directional characteristics of an array antenna device including a plurality of antenna elements.

[0002]

2. Description of the Related Art In order to adaptively filter a desired wave signal from a plurality of transmitted interference wave signals at a receiving side terminal device, an array antenna including a plurality of antenna elements is adaptively controlled at the receiving side. There is a technique of directing a main beam in the direction of a desired wave and forming a null in the direction of an interference wave (see, for example, Japanese Patent Application No. 2000-55655). As a method of adaptively controlling this array antenna on the receiving side, a learning sequence signal is included in advance at the beginning of each wireless packet data on the transmitting side, and the same signal as the learning sequence signal is generated on the receiving side.
On the receiving side, the directivity characteristic of the variable reactance element is changed by changing the reactance value of the variable reactance element with reference to the maximum cross-correlation between the received learning sequence signal and the generated learning sequence signal. By this, the directivity of the array antenna is adaptively controlled so as to have an optimum pattern, that is, a pattern in which the main beam is directed in the direction of the desired wave and a null is formed in the direction of the interference wave.

[0003]

However, in this conventional example, it is necessary to have a reference signal such as a learning sequence signal, and it is necessary to match this reference signal in advance on both the transmitting side and the receiving side. However, this causes a problem that the circuit for adaptive control becomes complicated.
In practice, for example, in a mobile communication system where the time of the pilot signal is limited, or in an application system such as a communication reverse detection system, sonar,
There are situations where the reference signal of the desired signal source has a short duration or the reference signal is not available at all. In this case, there is a problem that the above-mentioned adaptive control method cannot be used.

The object of the present invention is to solve the above problems, to simplify the control circuit without the need for a reference signal, to direct the main beam of the array antenna in the desired wave direction and in the interference wave direction. An object of the present invention is to provide a control method of an array antenna that can be adaptively controlled so as to direct a null.

[0005]

An array antenna control method according to an aspect of the present invention is an array antenna control method comprising a plurality of N antenna elements that are closely arranged in a predetermined arrangement shape. A first step of calculating an autocorrelation matrix R of a received signal vector x having a plurality of N received signals respectively received by the antenna elements, and for the received N received signals,
The second step of multiplying each of a plurality of N predetermined weighting factors and then adding the respective signals of the multiplication results, and outputting the output signal z, and m being an integer of 2 or more, In a 2mth order cumulant having a variable, (m-1) second variables, and one third variable, including m identical output signals z as a first variable, Compute a cumulant vector d that contains (m-1) complex conjugate signals z ^* of the same output signal as the second variable and the complex conjugate vector x ^* of the received signal vector x as the third variable. Based on the third step, the autocorrelation matrix R of the received signal vector x calculated above, and the cumulant vector d calculated above,

[Equation 2] By repeating the fourth step of calculating and setting the weight coefficient vector c having each weight coefficient as a component and the second to fourth steps, the main beam of the array antenna is converted into a desired wave. And a fifth step of adaptively controlling the null so that the null is directed to the interference wave and to the direction of the interference wave.

In the above array antenna control method,
Preferably, in a 2m-th order cumulant having m first variables and m second variables each time the output signal z is output, m identical same variables are used as the first variables. Compute the cumulant of the output signal z containing the output signal z and containing, as the second variable, m identical complex conjugate signals z ^* of the output signal, calculate the power of the output signal z, and Calculating the value of the ratio of the cumulant of the output signal z to the power of the output signal z as the value of the objective function, and the value of the calculated objective function,
Further comprising the step of stopping the processing of the fifth step when the difference from the value of the objective function calculated based on the output signal z output last time is smaller than a predetermined threshold value. And

[0007]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of an array antenna apparatus according to an embodiment of the present invention. The array antenna control method according to the present embodiment does not particularly require a receiving terminal to generate and refer to a learning sequence signal having the same data sequence as the learning sequence signal generated at the transmitting station, and to obtain a desired wave. The feature is that the beam is directed to the arrival direction of the signal and the null is directed to the interference wave signal.

As shown in FIG. 1, a schematic configuration of an array antenna control apparatus according to this embodiment has a plurality of N antenna elements 1-1 to 1- 1 which are juxtaposed in parallel on a straight line.
A multiplier 5 that outputs a signal of each multiplication result after multiplying a plurality of N reception signals received by the linear array antenna 100 of N using a predetermined weighting coefficient.
1 to 5-N and the output signal of each multiplication result are added to output an output signal z (t) of the array antenna apparatus, and an adder 6 based on a high-order statistic of the received signal. An adaptive control type controller 10 for calculating a weighting coefficient by outputting the weighting coefficient to the multipliers 5-1 to 5-N and setting the weighting coefficient. Here, in the calculation of the weighting factor, as a high-order statistic, a received signal vector x having the received signal as a component is received.
Based on (t) and the output signal z (t), a weight coefficient vector c having each weight coefficient as a component is calculated using a 2m-th order cumulant having 2m variables in which m is an integer of 2 or more. calculate.

The received signals received by the antenna elements 1-1 to 1-N are low noise amplifiers 2-1 to 2-, respectively.
After being amplified by N, the down converters 3-1 to 3-
N is input to the down converters 3-1 to 3-N.
Respectively, low-pass-converts the input received signal into a signal of a predetermined intermediate frequency (hereinafter referred to as IF signal), and
Output to the D converters 4-1 to 4-N. Furthermore, A
The / D converters 4-1 to 4-N respectively receive the received signals x ₁ (t), x ₂ (t), ..., X, which are digitized by analog-to-digital conversion of the input IF signal.
_N (t) and output to the multipliers 5-1 to 5-N, and each received signal is received signal vector x
(T) = [x ₁ (t), x ₂ (t), ..., x _N (t)]
Is output to the adaptive control type controller 10.

The adaptive control type controller 10 outputs k
ー Antenna adaptive control processing step number (corresponding to the time
As the received signal vector x (t) and the array
Output signal z of the adder 6 of the tenor device^(K-1)To (t)
Based on the weighting coefficient vector c ^(K)To calculate multiplier 5
-1 to 5-N, and the multipliers 5-1 to 5-N output
Received signal x₁(T), ..., x_NWeighting factor for (t)
Vector c^(K)N weighting factors that are each component of
Multiply and weight, then the weighted received signal is
It is added by the adder 6. The adder 6 outputs the output signal of the addition result.
No. z^(K)(T) is output to the demodulator 7, and
It outputs to the adaptive control type controller 10 as well. one
On the other hand, the demodulator 7 outputs the input output signal z^(K)To (t)
The specified demodulation processing is performed on the
No. is output.

The adaptive control type controller 10 executes the adaptive control processing shown in FIG. 2 as follows. First, the adaptive controller 10 calculates the autocorrelation matrix R of the received signal vector x (t) by using Expression 16 described later (step S1), and outputs the output signal z from the adder 6.
^(K-1) After measuring (t), m is an integer of 2 or more, m first variables, (m-1) second variables, and one third variable In a 2m th order cumulant having (and p = m and q = m−1 in Eq. 76), m identical output signals z ^(k−1) (t) are used as the first variables. As a second variable (m
-1) Complex conjugate signals z of the same output signal
^(K-1) * include (t), calculates the cumulant vector ^{d (k-1)} containing a complex conjugate vector ^x of the received signal vector x as a third variable * (t). The adaptive control controller 10 further uses Equation 75 described below based on the calculated autocorrelation matrix R of the received signal vector x (t) and the calculated cumulant vector d ^(k-1). , A weighting coefficient vector c ^(k) having each of the weighting factors as a component is calculated, and multipliers 5-1 to 5-N
Is set (step S5). The adaptive controller 10 measures the output signal z ^(k-1) (t), calculates the cumulant vector d ^(k-1), and calculates and sets the weighting coefficient vector c ^(k). By repeating the process (steps S4 to S8),
It is characterized in that the main beam of the array antenna is adaptively controlled so as to direct the main beam toward the desired wave and the null toward the interference wave. Further, the adaptive control type controller 10 is
Each time the output signal z ^(k) (t) is output (that is, as shown in Expression 77, the received signal vector x
Each time (t) is multiplied by the weighting coefficient vector c ^(k) ), using m = n, the number 146
In the 2mth order cumulant having m variables and m second variables, the same m output signals z ^(k) (t) are included as the first variables, and the m second m variables are included as the second variables. Signal z ^{(k) *} (t) of the complex conjugate of the same output signal of
The cumulant of the output signal z including is calculated, the power of the output signal z is calculated, and the value of the ratio of the cumulant of the output signal z to the calculated power of the output signal z is calculated as the value of the objective function ( Steps S3 and S6),
The value of the objective function calculated above J (z ^(k) (t)) = J
(C ^{( k)} ) and the output signal z output last time
^(K-1) based on (t) (that is, the output signal z based on the previously calculated weighting coefficient vector c ^{(k-1))
(K-1) (t)} = (c (k-1)) T x on the basis of a (t)) computed objective function value J (z
^The adaptive control process is stopped when the difference between ^(k-1) (t)) = J (c ^(k-1) ) is smaller than a predetermined threshold value (step S7).

Next, the adaptive control type controller 1 of FIG.
The principle of the application control process executed by 0 will be described. In the adaptive control process of this embodiment, when changing the directional characteristics of the array antenna, it is necessary to generate the same learning sequence signal as the learning sequence signal generated in the transmitting station in the receiving terminal in which the array antenna device is located. The feature is that there is no "blind adaptive beam forming", and the adaptive control processing according to the present invention is hereinafter referred to as "blind beam forming" or "BB". This adaptive control process is further characterized by implementing a super-exponential algorithm that converges at a speed of exponentiation.

Before formulating blind adaptive beamforming, an adaptive filtering which is not limited to blind beamforming without loss of generality and an adaptive control type array antenna apparatus which executes the processing of the adaptive filtering are formulated. . To simplify the formulation, we consider an independent non-Gaussian spatial source signal without multipath propagation without loss of generality. If there is an array antenna composed of a plurality of N antenna elements and P (P ≦ N) signal sources that transmit non-Gaussian signals, the received signal vector x of the array antenna
(T) is expressed by the following equation.

[0015]

[Equation 3]

Where a (θ) and ω (t) = [ω
₁ (t), ..., ω _N (t)] ^T is an array steering vector and an array noise vector associated with the array antenna. For example, in the case of a linear array antenna with a half wavelength interval, if the phase reference point is set at the center of the linear array antenna, the steering vector a
(Θ) can be expressed by the following equation.

[0017]

[Equation 4]

The source signals coming from each transmission signal source and the array antenna used are assumed as follows.

<A1> Source signal b _p (t), p = 1,
…, P is an independent non-Gaussian signal and its power is
It is shown by the following formula.

[0020]

[Equation 5]

<A2> The noise vector ω (t) has a zero mean and is spatially white.

[0022]

[6] ^{E {ω (t) ω T} (t)} = 0

## EQU7 ## E {ω (t) ω ^H (t)} = σ _ω ² I _{N × N}

Here, (•) ^T and (•) ^H represent transposition and conjugate transposition, respectively, σ _ω ² represents noise power, and I _{N × N} is an Nth-order unit matrix. Noise vector ω
(T) is uncorrelated with the source signal.

<A3> The steering vectors a (θ _p ) of all the source signals b _p (t) are linearly independent. Also, correlated source signals, such as, for example, multipath signals, can be converted to decorrelated source signals by decorrelation or orthogonal decomposition.

Next, the source signal b _p (t) is expressed by the following equation using the component relating to the power (see the equation 5) and the signal component (component changing with time) ba _p (t). Represent

[0026]

[Equation 8] p = 1, ..., P

The noise vector component ω _l (t) is
The component σ _ω related to the power and the component ωa ₁ (t) that changes with time are expressed by the following equation.

[0028]

Ω _l (t) = σ _ω ωa _l (t) l = 1, ..., N,

Further, the unit matrix I _{N × N} of order _N is expressed as follows.

[0030]

[Equation 10] I _{N × N} = [e _{N × 1} ^(l) , ..., E _{N × 1} ^(N) ]

The received signal matrix A (Θ), which is an N × P-order matrix whose component is the product of the component of the power of the source signal (see equation 5) and the steering vector a (θ), is expressed by the following equation. .

[0032]

[Equation 11]

According to the above notation, the channel response matrix H and the normalized received signal vector α (t) are defined as follows.

[0034]

[Equation 12]

Α (t) = [α ₁ (t), ..., α _{P + N} (t)] ^T = [ba ₁ (t), ..., ba _P (t), ωa ₁ (t), ..., ωa _N (t)] ^T

Therefore,

[Equation 14] E [α (t) α ^H (t)] = I _{(P + N) × (P + N)} , and the received signal vector x (t) of Equation 3 can be expressed as the following equation.

[0036]

[Equation 15]

Further, the following equation follows the assumptions A1 and A2,
It is an autocorrelation matrix of the received signal vector x (t) of the equation 3.

[0038]

[Number 16] ^{R = E [x (t)} x H (t)] = H T E [α (t) α H (t)] H * = H T H * = A (Θ) A H (Θ) + Σ _ω ² I _{N × N}

From equation 12, it can be seen that the channel response matrix H always has a rank equal to the number of columns. The output of the adaptive control type array antenna is formulated as follows.

[0040]

Z (t) = c ^T x (t) = c ^T H ^T α (t)

Here, c = [c ₁ , c ₂ , ..., C _N ] ^T
Represents the complex weighting coefficient vector of the adaptive array antenna.

Gain vector

S = [s ₁ , ..., s _{P + N} ] ^T = H
_{If (P + N) × N} c _{N × 1} is set, the output of the adaptive control type array antenna can be expressed as follows.

[0043]

[Formula 19]

Here, s _n represents the complex gain of the component α _n (t) of the normalized received signal vector.

Source reference signal given by fixing the signal source to the n ₀ th

[Equation 20] 1 ≦ n ₀ ≦ P exists, and under the assumptions A1 and A2, the source reference signal

[Equation 21] The mean square error MSE between the output signal z (t) of the adaptive control array antenna and the output signal z (t) can be expressed as follows.

[0046]

[Equation 22]

In order to minimize the MSE with respect to the weighting coefficient vector c, there is the following Wiener-Hop equation.

[0048]

[Equation 23]

Here, the vector d satisfies the following equation.

[Equation 24]

C _opt is the optimum weighting coefficient vector, or is called the optimum adaptive beamformer. In order to obtain the optimum weighting coefficient vector c _opt , the steering vector of the desired wave signal source, or more generally the spatial signature waveform signal (spatial response of the array antenna), is required The signature waveform signal is usually estimated by the cross-correlation between the known reference signal (learning sequence signal) of the desired signal source and the received signal of the array antenna.

Under the signal environment formulated as described above, the iterative principle that converges "hyperexponentially", that is, converges at the speed of exponentiation and further exponentiation is further formulated. Prior Art Document 1 "O. Shalvi et al.," Super
-exponential methods for blind deconvolution ", IEE
E Transaction on Information Theory, Vol. 39, No.
2, pp.504-519, March 1993 ”, the following iterative procedure of the complex vector s is considered without considering the weighting coefficient vector c.

[0052]

S _n '= s _n ^p (s _n ^* ) ^q , n = 1, ..., P + N

[Equation 26]

Here, the following two notations are used.

[Number 27] _{s' = [s 1 ',} ..., s P + N'] T

[Equation 28]

For n = 1, ..., P + N,

S _n = s _n ^(k-1)

If s _n ^(k) = s _n ", the following iterative equation is obtained.

[0055]

[Equation 31] n = 1, ..., P + N

[0056]

[Equation 32] When n = 1, ..., P + N (where 0 ≦ φ _n <2
π and ζ _n are predetermined coefficients), and the following equation is obtained for k ≧ 1.

[0057]

[Expression 33] n = 1, ..., P + N

When p + q ≧ 2 and p−q = 1,

[Equation 34] Then, the following equation is obtained with k → ∞.

[0059]

[Equation 35]

From Eq. 33, this iterative procedure shows that the desired response is such that the magnitude of the principal components of the gain vector s (gain) approaches 1 and all other components approach zero, to the power of power and then to power. It can be seen that the gain s _n converges (super exponentially) with speed. As a more general case, the desired wave signal is an envelope with a finite absolute value (finite modulus).
Considering a hyperexponential iterative procedure under a complex weighting sequence such as
Is as follows:

[0061]

S _n ′ = β _n s _n ^p (s _n ^* ) ^q , n = 1, ..., P + N

[Equation 37]

Here, the element of finite modulus is

[Equation 38] | Β _n | <∞, n = 1, ..., P + N. Here, 0 ≦ φ _n <2π. As in the case of Expression 31, the following iterative equation is obtained for k ≧ 1.

[0063]

[Formula 39] n = 1, ..., P + N

Similarly to the equation 33,

[Formula 40] If n = 1, ..., P + N, then for k ≧ 1, we have:

[0065]

[Formula 41] n = 1, ..., P + N

If p + q ≧ 2, the equation 41 is as follows.

[Equation 42] n = 1, ..., P + N

The convergence behavior of the iterative sequence described above is shown in the following theorem.

<Theorem 1> Element of finite modulus, that is,

[Equation 43] For any weighted sequence with | β _n | <∞, n = 1, ..., P + N, the iterative sequence of Eq. 42 when k approaches infinity results in:

[Equation 44] The conditions for hyperexponentially converging on p are p + q ≧ 2 and the following equation.

[0069]

[Equation 45] n = 1, ..., P + N, n ≠ n ₀

<Proof of Theorem 1> When p + q ≧ 2, Equation 4
2 can be expressed as follows.

[0071]

[Equation 46]

The denominator of the gain s _n ^(k) is always 1 or more, that is,

[Equation 47] And this is

[Equation 48] When | β _n | <0, n = 1, ..., P + N, under the condition of Expression 45, that is,

[Equation 49] Under the condition of n = 1, ..., P + N, n ≠ n ₀ ,

[Equation 50] , N = 1, ..., P + N, n ≠ n ₀ , the numerator of | s _n ^(k) | converges to zero exponentially ((p + q) ^k ) when k → ∞. That is, the following 2
Two expressions are established at the same time.

[0073]

[Equation 51]

[Equation 52]

Therefore, when k → ∞, the following equation is obtained.

[0075]

| S _n ^(k) | → 0, n = 1, ..., P + N, n ≠ n ₀

[Equation 54]

Thus, Theorem 1 is proved.

However, note that Theorem 1 relates only to the iterative complex vector s when the weighting coefficient vector c is not considered. Therefore, blind adaptive beamforming can be formulated by considering the behavior of the iterative complex vector s when controlling the weighting coefficient vector c.

Instead, we then formulate blind adaptive beamforming. For the given initial value complex weighting coefficient vector c ⁽⁰⁾ of the adaptive control type array antenna, the following gain vector is obtained according to Eq.

[0079]

S ⁽⁰⁾ = [s ₁ ⁽⁰⁾ , ..., s _{P + N}
⁽⁰⁾ ] ^T = Hc ⁽⁰⁾

S ^(k) = [s ₁ ^(k) , ..., s _{P + N}
^(K) ] ^T = Hc ^(k)

By adjusting the weighting coefficient vector c, it is expected that only one source signal will be present at the output of the adaptive array antenna, while the other superimposed source signals will be completely suppressed. . This means that one component of the gain vector s is equal to 1 and the other component is equal to zero, which is a so-called perfect process. However, since the channel response matrix H has a rank equal to the number of columns in the presence of noise, and the dimension of the channel response matrix H is higher than the dimension of the weight coefficient vector c, the weight coefficients It is impossible to find the vector c. Optimal adjustment or iteration of the weighting factor vector c is performed in the sense of the minimum mean square error (MMSE) between the output gain vector s ^(k) and the desired gain vector. From Theorem 1, the desired gain vector can be formulated according to the equations 36 and 37. Let the following equation be the desired gain vector in the k-1th iteration.

[0081]

G ^(k−1) = [β ₁ (s ₁ ^(k−1) ) ^p
(S ₁ ^{(k-1) *} ) ^q , ..., β _{P + N} (s _{P + N}
^(K-1) ) ^p (s _{P + N} ^{(k-1) *} ) ^q ] ^T

The associated normalized gain vector s ^(k)
The MMSE criterion of Eq. (59 ⁾ subject to is that the optimal iterative weighting coefficient vector c ^(k) follows.

That is,

[Mathematical formula-see original document] Assuming ‖s ^(k) ‖ = ‖Hc ^(k) ‖ = 1, the vector Hc ^(k) and the gain vector g
^The squared error of ^(k-1) is minimized with respect to the weighting coefficient vector c ^(k) .

[0084]

[Equation 59]

Using the Lagrange multiplier method, the iterative weighting coefficient vector c ^(k) is solved and given by:

[0086]

[Equation 60]

[0087]

When d ^(k-1) = H ^H g ^(k-1) , the formula 60 can be expressed as follows by the definition of the autocorrelation matrix R of the formula 16.

[0088]

[Equation 62]

Here, the autocorrelation matrix R can be evaluated for a plurality of samples (or received signal snapshots). The gain vector g ^(k-1) of Equation 57 is
Weight coefficient vector c without knowledge of channel response matrix H
^Since it cannot be obtained directly from ^(k-1) ,
Evaluating the vector d ^{(k-1) of} is the main subject of the present invention.

First, consider the following cumulants.

[0091]

[Equation 63]

In the cumulant of equation 63, p pieces thereof
The output signal z (t) of the adder 6 is included as the first variable of
The q second variables of the complex conjugate of the output signal
Signal z ^*(T) is included and is accepted as the one third variable.
Complex conjugate vector x of signal signal vector x^*Contains (t)
I'm out.

For the definition of this cumulant and the properties of the cumulant relevant to the present invention, refer to Prior Art 2
"JM Mendel," Tutorial on higher-order statisti
cs (spectra) in signal processings and system theo
ry: theoretical results andsome applications ", Pro
ceedings of the IEEE, Vol. 79, No. 3, pp.278-305,
March 1991 ”. According to it, a vector x = (x ₁ , x ₂ ,
..., x _n ) and a vector of the same dimension as v = (v ₁ ,
For v ₂ , ..., V _n ), the following equation is defined as a cumulant generation function.

[0094]

K (v) = ln {E [exp (jv
^T x)]}

Here, j is an imaginary unit and E [·]
Is the mean value for the distribution of x, and ln {·}
Represents the natural logarithm. A plurality of random variables x ₁ , x ₂ ,
The n th order cumulant relating to x _n is derived as a coefficient of the n th order term when the above cumulant generation function is power series expanded with respect to the variables v ₁ , v ₂ , ..., v _n , and is defined as follows. To be done.

[0096]

[Equation 65]

Here are some examples of cumulants relating to the zero averaging process.

[0098]

[Equation 66] cum (x ₁ ) = 0

## EQU00006 ## cum (x ₁ ; x ₂ ) = E {x ₁ x ₂ }

[Equation 68] cum (x ₁ ; x ₂ ; x ₃ ) = E {x ₁ x ₂ x ₃ }

Cum (x ₁ ; x ₂ ; x ₃ ; x ₄ ) = E {x ₁ x ₂ x ₃ x ₄ } -cum (x ₁ ; x ₂ ) cum (x ₃ ; x ₄ ) -cum ( _{x 1; x 3) cum (} x 2; x 4) -cum (x 1; x 4) cum (x 2; x 3)

The output of the adaptive control type array antenna for the k-th iterative weighting coefficient vector c ^(k) is expressed by the following equation by the equation (19).

[0100]

[Equation 70]

Substituting the equations (70) and (15) into the equation (63), and the cumulant linearity (prior art 2), that is,
The following formula

[Number 71] _{cum (Σ i b i x i} ; ...) = Σ i b i cu
Considering m (x _i ; ...), the cumulant of Expression 63 is expressed as follows.

[0102]

[Equation 72]

For the definition of equation 57,

Β _n = cum (α _n (t): p; α
_{When n} ^* (t): q + 1) n = 1, ..., P + N is established, it is understood that the equation 72 completely matches the vector d ^(k) of the equation 61. Therefore, the following equation is obtained.

[0104]

D ^(k−1) = cum (z
^(K-1) (t): p; z ^{(k-1) *} (t): q; x
^* (T))

In conclusion, iterative weighting coefficient vector c
The associated equations for ^(k) are summarized as follows.

[0106]

[Equation 75]

D ^(k−1) = cum (z
^(K-1) (t): p; z ^{(k-1) *} (t): q; x
^* (T))

Z ^(k−1) (t) = (c ^(k−1) ) ^T x (t)

Note that the above weighting factor vector iteration equation holds for all sensor array antennas with arbitrary configurations and non-Gaussian source signals when blind adaptive beamforming is performed. In an actual communication signal, the probability distribution can be considered to be symmetric, so that an odd-order cumulant (that is, third-order, fifth-order, or seven-order when p ≠ q + 1) is obtained.
The next cumulant) is equal to zero. Therefore, in the present embodiment, the following Equation 7 is called a cumulant vector.
The vector d ^(k-1) of 6 uses p.
With the above integers, p first variables and q (q = p−
2p having the second variable of 1) and one third variable
In the following cumulant, p identical output signals z ^(k-1) (t) are included as a first variable, and (p-1) complex conjugate signals of the (p-1) output signals are included as a second variable. It is obtained by calculating a cumulant containing z ^{(k-1) *} (t) and containing the complex conjugate vector x ^* (t) of the received signal vector x as the third variable. Number 76
And calculating the weighting factors to direct the main beam of the array antenna in the direction of the desired wave and the null in the direction of the interference wave based on the higher order statistics of the received signals of the array antenna. it can.

Assuming that the noise associated with the array antenna is Gaussian and p + q ≧ 2,
By substituting 2 and formula 76 into formula 75, the following formula is obtained.

[0109]

[Equation 78]

This includes the fact that if p + q ≧ 2, the Gaussian noise cumulant defined by Eq. 73 is zero. From Eq. 78, the super-exponential iterative weighting coefficient vector of the blind adaptively controlled array antenna is always each optimal optimum associated with all corresponding spatial source signals specified by the Wiener-Hop equation. It can be seen that it is a linear combination of the weighting factor vectors. Equations (18) and (19) represent the gain vector of the i-th source signal of all independent source signals and noise components at the output of the optimal adaptive control array antenna as follows.

[0111]

[Equation 79]

It can be seen that the square of the norm of the gain vector ξ (θ _i ) represents the total output power of all the independent signal components.

[0113]

[Equation 80]

Based on the definition of Expression 56, Expressions 75 to 77
The iterative gain vector s ^(k) based on is expressed as:

[0115]

[Equation 81]

This means that the output gain vector of blind adaptive beamforming is also a linear combination of gain vectors for all associated optimal weighting coefficient vectors.

The convergent solution is based on the initial value c ⁽⁰⁾ of the complex weighting coefficient vector, the order p + q to be used, the signal environment including the power distribution of the source signals and the spatial correlation between the source signals. Dependent.

│s _n ^(k) │ <1, n for k ≧ 1
= 1, ..., P + N, the exponent of the absolute value of the gain |
s _n ^(k) | ^{p + q} is smaller than the absolute value of the gain | s _n ^(k) |. The initial value weighting coefficient vector c ⁽⁰⁾ is

[Equation 82] When 1 ≦ n ₀ ≦ P holds, ∀p + q, | β _n | <+ ∞, n =
It is clear that for 1, ..., P + N, they converge as in the following equation.

[0119]

[Equation 83]

Here,

[Equation 84] Is

[Equation 85] Represents the phase angle of.

However, according to the equations 72 to 77,
p + q → ∞ means that the order of the cumulants used is infinite, which raises questions about the definition and existence of infinite order cumulants. On the other hand, the number 83
Implies that using higher order cumulants improves the performance of blind adaptive beamforming algorithms. Indeed, for a suitable order p + q, if the gain corresponding to the undesired source signal is less than the gain corresponding to the desired source signal, the blind adaptive beamforming algorithm is associated with a model such as the Wiener-Hop equation. It is possible to place the optimal adaptive beamformer in close proximity. This means that the initial condition of the iterative weighting coefficient vector is a proper value of the order p + q,

[Equation 86] Is satisfied,

[Equation 87] It is based on the fact that n = 1, ..., P + N, n ≠ n ₀ is obtained, which leads to

[Equation 88]

Here, ε _n ', n = 1, ..., P + N, n
≠ n ₀ and ε ″ are the numbers of smaller errors and complex error vectors that can take arbitrary values, respectively, and the absolute value of complex error vector ε ″ ‖ε ″ ‖ is a very small number. .

Next, two theorems will be proved in order to understand the behavior of this algorithm. Theorem 2 assumes that the SNRs of all source signals approach infinity, and Theorem 3 assumes that one source signal is spatially uncorrelated with another source signal.

<Theorem 2> When the noise associated with the array antenna has a Gaussian distribution and p + q ≧ 2, the following 2
If two equations are satisfied, the blind adaptive beamforming iterative algorithm specified by Eqs.
Performs complete suppression of interference.

[0125]

[Equation 89] i = 1, ..., P

[Equation 90]

Here, the coefficient β _n is defined by the equation 73.

Theorem 2 shows the best performance of the blind adaptive beamforming algorithm, which is the input S
This is useful for understanding the performance of this algorithm when NR is high. In fact, for high input SNRs, the blind algorithm causes the non-blind optimal adaptive beamformer, ie, the transmitting station and the receiving terminal, to generate the learning sequence signals and their minimum mean square error (MMSE). ) Approaches performance when adaptively controlled based on criteria such as

<Theorem 3> When the noise associated with the array antenna has a Gaussian distribution and p + q ≧ 2, the following two expressions are satisfied for a given n ₀ (1 ≦ n ₀ ≦ P). , 75 to 77, the blind adaptive beamforming iterative algorithm converges to the non-blind optimal adaptive beamformer specified by the Wiener-Hop equation.

[0129]

[Formula 91] n = 1, ..., P, n ≠ n ₀

[Equation 92] n ₀ ≠ m ₀ , 1 ≦ m ₀ ≦ P

The following notation is used here.

[Equation 93]

[Equation 94]

[Formula 95]

[Equation 96]

In practice, the problem of blind adaptive beamforming under the conditions of Theorem 3 can be solved by one-dimensional conventional digital beamforming, which is blind and in the case of a superposed signal environment. Often does not work. The purpose of Theorem 3 is that when the steering vector of the n _0th source signal is known, the blind algorithm is
Is theoretically shown to converge to the result of conventional digital beamforming (a non-blind optimal adaptive beamformer specified by the Wiener-Hop equation). This is an important property of blind adaptive beamforming algorithms.

<Proof of Theorem 2> Equation 60 and Equation 57 are transformed into Equation 5
Substituting 6 and considering the definition of Equation 12, the iterative gain vector s ^(k) of the signal by the iterative weighting coefficient vector at the output of the adaptive control array antenna is expressed by the following equation.

[0133]

[Numerical Expression 97]

Here, Δ ^(k-1) means the following equation.

[0135]

[Equation 98]

The cumulant of Gaussian noise is p + q ≧ 2
Since it is equal to zero when, the formula 97 is as follows.

[0137]

[Numerical expression 99]

Definition of Eq. 16 and Sherman-Morison-
Woodbury's formula (Prior Art 3 “GH Golub et a
l., "Matrix Computations", Third Edition, The John
s Hopkins University Press, p.50, 1996 ”)
The inverse matrix of the autocorrelation matrix R ^T based on Assumption A3 can be expressed as:

[0139]

[Equation 100]

Therefore, the following equation holds.

[0141]

[Equation 101]

Similarly, the following equation holds.

[Equation 102]

[0143]

[Equation 103] When i = 1, ..., P 1, the equations 101 and 102 approach the next result.

[0144]

## EQU00004 ## ^AT (.THETA.) ( ^RT ) ^{-1A *} (. THETA.) → I

Σ _ω (R ^T ) ⁻¹ A ^* (Θ) → 0

By substituting the equations 104 and 105 into the equation 99, the following equation is obtained.

[0146]

[Equation 106]

Here, Δ ^(k-1) means the following equation.

[0148]

[Equation 107]

Expression 106 is based on the same situation as Theorem 1. The conclusion of Theorem 1 proves the conclusion of Theorem 2. This proves Theorem 2.

<Proof of Theorem 3> Similar to the proof of Theorem 2,
When the noise associated with the array antenna is Gaussian distributed, the iterative gain vector s ^(k) of Eq. 99 is now rewritten as:

[0151]

[Equation 108]

Here, the following two notations are used.

[0153]

[Equation 109]

R _i = A _i (Θ) A _i ^H (Θ) + σ _ω ² I

[0154]

[Equation 111] The following equation is derived from the condition that n = 1, ..., P, n ≠ n ₀ .

[0155]

[112]

According to equation 16, the autocorrelation matrix R can be expressed as follows.

[0157]

[Equation 113]

According to the Sherman-Morison-Woodbury formula (Prior Art 3), the inverse matrix of the autocorrelation matrix R can be expressed by the following equation.

[0159]

[Equation 114]

Similarly, the matrix

[Equation 115] By using the Sherman-Morison-Woodbury formula for and the equation 112, the following equation is obtained.

[0161]

[Equation 116]

Therefore, the following equation holds.

[0163]

[Expression 117]

Substituting the number 117 into the number 108, and the number 11
Using 2, the following equation is obtained.

[0165]

[Equation 118]

Here, the following two notations are used.

[0167]

[Equation 119]

[Equation 120]

According to equation 118, the following inequality holds.

[0169]

[Equation 121] n = 1, ..., P, n ≠ n ₀

[Equation 122]

[Equation 123] l = 1, ..., N

The gain s _{P + 1} ^(k) , l = 1, ..., N is
Gain ^{_{s n (k), n =}} 1, ..., but it can be seen that depend on P, gain What we are interested s _n
^(K) , n = 1, ..., P is only the behavior of iteration.
If the following equation holds,

[Equation 124] That is, for n = 1, ..., P,

[Equation 125] Then, the following relation is obtained.

[0171]

[Equation 126] n = 1, ..., P, n ≠ n ₀

[Equation 127]

[Equation 128]

Here,

[Numerical Expression 129] n = 1, ..., P, n ≠ n ₀

[Equation 130]

[Equation 131] When 1 ≦ r ₀ ≦ P, the following equation is obtained.

[0173]

[Equation 132] n = 1, ..., P

[Expression 133] n = 1, ..., P, n ≠ n ₀

[Equation 134]

By repeating the above, the following iterative equation is obtained.

[0175]

[Equation 135]

[Equation 136] n = 1, ..., P + N, n ≠ n ₀

[Equation 137]

Therefore, the following inequality holds.

[0177]

[Equation 138] n = 1, ..., P, n ≠ n ₀

[0178]

[Equation 139] Then, if k → ∞, the next term converges to zero exponentially (that is, at the exponentiation speed of the exponentiation).

[0179]

[Equation 140]

According to equation 117, equation 140 implies the following.

[0181]

[Expression 141]

[Equation 142]

Therefore, from the equation 118, the following equation is established.

[0183]

[Numerical Expression 143]

The vector s ^(k) approaches the gain vector of the optimum adaptive filter until it becomes the maximum complex phase coefficient representing rotation. Above, Theorem 3 is proved.

Next, the objective function of blind adaptive beam forming is formulated. The objective function or the cost function is always necessary when executing the adaptive filtering algorithm. The most widely used objective function in blind separation and blind equalization is the inverse filter criterion of the following equation, which indicates the performance of the array antenna to operate as an inverse filter for extracting a desired wave (Prior Art Document 4 "O. . Shalv
i et al., "New criteria for blind deconvolution of
nonminimum phase systems (channels) ", IEEE Transa
ction on Information Theory, Vol. 36, No. 2, pp.31
2-321, March 1990 ").

[0186]

[Expression 144]

The following notation is used here.

[0188]

[Equation 145]

E (k) represents the output of the associated blind equalizer, m + n> 2. The numerator of Expression 144 is an m + nth order cumulant represented by Expression 145, and the denominator of Expression 144 is the power of the signal e (k).
In the absence of noise, the objective function is limited by the maximum modulus of the cumulant of the signal associated with the array antenna (envelope of the desired wave signal) (4). In principle, there is no difficulty in using the objective function for blind adaptive beamforming. In the meaning of the expressions 17 to 19, when e (k) is replaced with the output signal z (t) of the array antenna, the expression 144 is expressed by the following expression.

[0190]

[Expression 146]

Here, the following notation is used.

[0192]

[Expression 147]

Hereinafter, description will be made based on the mathematically modified term on the right side of Expression 146. According to Equation 14, the following equation is obtained.

[0194]

Γ _l ^(1,1) = cum {α _l (t), α
_l ^* (t)} = E {| α _l (t) | ² } = 1

The following equation

[Equation 149] Represents the root mean square of the total output power of the adaptive control array antenna, the equation 146 can be expressed as follows.

[0196]

[Equation 150]

Most of the complex envelope signal waveforms used in communications and radar (eg, QPSK modulated signals)
Since we have a symmetric probability distribution, we find that all their odd moments, all their odd cumulants and all those cumulants with asymmetric definitions are equal to zero. In the following, m
Consider the situation where = n> 1. Therefore, the number 14
The value of the objective function of 6 is, using Equation 65, in a 2mth order cumulant having m first variables and m second variables, m identical above A cumulant of the output signal z containing the output signal z and containing, as a second variable, a complex conjugate signal z ^* of the m output signals;
By calculating the power of the output signal z and the ratio of the cumulant of the output signal z to the calculated power of the output signal z. In order that the objective function J of Expression 146 serves as the inverse filter reference of the array antenna, it is necessary to set the parameters of the orders of the cumulants of Expression 76 and Expression 146 to be equal (that is, p = q + 1 = m = n).

Based on this situation, the equation 150 is transformed into the following equation.

[0199]

[Expression 151]

From _equation 151, given n 0,1 ≦ n
_{For 0} ≤ P,

[Equation 152] The necessary and sufficient conditions for being

[Expression 153] , And s _n = 0, n = 1, ..., P + N, n ≠ n ₀ , which is a condition of the complete processing mentioned in Theorem 2 and is rarely satisfied by the adaptive beamformer. There is no such thing. In fact, the blind adaptive beamformer

[Equation 154] When n = 1, ..., P + N, n ≠ n ₀ , and 1 ≦ n ₀ ≦ P, Expression 151 can be expressed by the following equation.

[0201]

[Equation 155]

Here, the ratio

[Equation 156] Becomes smaller as m becomes larger. This is
The larger m, ie the higher the order of the cumulants used, the terms γ _n ^(m) , n = 1, ..., P + N, n
Of _{≠ n 0, 1 ≦ n 0} ≦ P, means that the contribution to be more reduced with respect to the objective function value _J 2m (c). Term

[Equation 157] Represents the suppression ratio of the adaptive filter for the l-th unwanted source signal. The larger the suppression ratio, the smaller the contribution of the l-th unwanted source signal to the objective function.

The gradient regarding the weighting coefficient vector c of the objective function is derived as in the following equation.

[0204]

[Equation 158]

Here, sgn (C _{m, m} {z (t)}) represents the positive or negative sign of the cumulant C _{m, m} {z (t)}. The fixed point of equation 155 is

[Equation 159] It is located where The next theorem proves that the algorithm given by Eqs. 75 to 77 converges to the stationary point of Eq.

<Theorem 4> The hyperexponential iterative algorithm specified by the equations 75 to 77 has the objective function number 155.
Converge to the fixed point of. However, in Eqs. 76 and 146, the cumulant order parameter is p = q + 1
= M = n.

<Proof of Theorem 4> When the hyper-exponential iterative algorithm converges, Equations 75 to 77 can be expressed as follows.

[0208]

[Equation 160]

D = cum (z (t): m; z ^* (t):
m-1; x ^* (t))

Z (t) = c ^T x (t)

By substituting the equation 160 into the equation 158, the following equation is obtained.

[0210]

[Expression 163]

Here c ^T Rc ^* = 1 is used. Based on the linearity of the cumulant (Prior Art 2) and using the equations 161 and 162, the following equation holds.

[0212]

[Equation 164]

This is

165 means sgn (C _{m, m} {z (t)}) = + 1. Therefore, the following equation holds.

[0214]

[Equation 166]

Thus, Theorem 4 is proved.

Since analytic signals (complex envelopes) in communications, radar, etc. often have symmetrical probability distributions, this embodiment uses a cumulant having symmetrical components based on the definition of the prior art document 2. ing. p = q + 1
= M = n = 2,3,4 associated with cumulants, ie numbers 76, 146 and 158 with orders (2,2), (3,3) and (4,4) The equation is given below.

[0217]

167 cum (z (t): 2; z ^* (t): 2)
= E (| z (t) | ⁴ ) -2 (E (| z (t) | ² ))
^Two

Cum (z (t): 2; z ^* (t); x ^*
(T)) = E (| z (t) | ² z (t) x ^* (t))-
2E (| z (t) | ² ) E (z (t) x ^* (t))

169 cum (z (t): 3; z ^* (t): 3)
= E (| z (t) | ⁶ ) -9E (| z (t) | ⁴ ) E
(| Z (t) | ² ) +12 (E (| z (t) | ² )) ³

Cum (z (t): 3; z ^* (t): 2;
x ^* (t)) = E (| z (t) | ⁴ z (t) x
^* (T))-3E (| z (t) | ⁴ ) E (z (t) x ^*
(T))-6E (| z (t) | ² ) E (| z (t) | ²
z (t) x ^* (t)) + 12 (E (| z (t) | ² ))
² E (z (t) x ^* (t))

171 cum (z (t): 4; z ^* (t): 4)
= E (| z (t) | ⁸ ) -16E (| z (t) | ⁶ ) E
(| Z (t) | ² ) -18 (E (| z (t) | ⁴ )) ²
+ 144E (| z (t) | ⁴ ) (E (| z (t)
| ² )) ² -144 (E (| z (t) | ² )) ⁴

Cum (z (t): 4; z ^* (t): 3;
x ^* (t)) = E (| z (t) | ⁶ z (t) x
^* (T))-4E (| z (t) | ⁶ ) E (z (t) x ^*
(T))-12E (| z (t) | ² ) E (| z (t) |
⁴ z (t) x ^* (t))-18E (| z (t) | ⁴ ) E
(| Z (t) | ² z (t) x ^* (t)) + 72E (| z
(T) | ⁴ ) E (| z (t) | ² ) E (z (t) x
^* (T)) + 72 (E (| z (t) | ² )) ² E (| z
(T) | ² z (t) x ^* (t))-144 (E (| z
(T) | ² )) ³ E (z (t) x ^* (t))

From Theorem 4, it can be seen that the fixed point is not specified, which means that if a given initial condition is given and satisfied, the super-exponential blind algorithm will find all constants of the objective function. It implies to converge to the point of absence. According to Theorem 4, the adaptive control process that realizes the perfect super-exponential blind adaptive beamforming algorithm is formulated as in the flowchart shown in FIG.

Referring to FIG. 2, as an initial setting before the adaptive control processing, for example, a threshold constant ρ of convergence accuracy is set to ρ
= 10 ⁻⁵ , the cumulant order used in Eqs. 76 and 146 is set to (2, 2), and the cumulant order parameter is set to p = m = n = 2 and q = 1. . In step S1, the adaptive controller 10 measures the received signal vector x (t) having the received signals x ₁ , ..., X _N received by the antenna elements 1-1 to 1- _N as components, 16 is used to calculate the autocorrelation matrix R. In step S2, the initial value c ^{(0 )} of the weighting coefficient vector is output to the multipliers 5-1 to 5-N and set. Then, at step S3, (see number 77) to measure the weight coefficient vector ^{c (0)} to based on the output signal ^{z (0)} (t), the output signal ^{z (0)} (t) objective based on the function value J ( z ⁽⁰⁾ (t)) = J (c ⁽⁰⁾ )
6 (provided that m = n = 2) is used.
In step S4, the step number k of the iteration is initialized to 1, and then in step S5, the output signal z
^{(K−1) Based on} (t) and the received signal vector x (t), the cumulant vector d
^(K-1) is calculated, and then based on this cumulant vector d ^(k-1) and the autocorrelation matrix R,
Is used to calculate the weighting coefficient vector c ^(k) , which is output to the multipliers 5-1 to 5-N to be set. Step S
6, the output signal z ⁽ based on the weighting coefficient vector c ^(k)
k) (t) is measured (see equation 77), and the output signal z
^(K) the objective function value ^J based on the ^{(t) (z (k)} (t))
= J (c ^(k) ) is calculated using equation 146. next,
In step S7, it is determined whether the difference between the objective function value J (c ^(k-1) ) and the objective function value J (c ^(k) ) is smaller than the threshold constant ρ. When the difference between the objective function values is equal to or larger than the threshold constant ρ, the step number k is incremented by 1 in step S8, and the process returns to step S5.
On the other hand, when the difference between the objective function values is smaller than the threshold constant ρ, the adaptive control process ends.

[0220]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present inventors performed a computer simulation to confirm the effectiveness of the proposed blind adaptive beamforming algorithm. The simulation uses a uniform linear array antenna consisting of 6 elements with half wavelength spacing. The linear array antenna is not calibrated, which implies that the complex gain of each antenna element is perturbed from their nominal value, eg, 1. Complex gain perturbations actually exist and are generally considered to be very slow, irregular fluctuations due to factors such as ambient temperature, humidity, and so on. Here, it is assumed that the perturbed gain is unknown, but remains constant during the period relevant to the simulation. Nominal values for amplitude and phase are 1 (0 dB) and 0 radians, respectively. We assume that the perturbed gain is a random sample that follows a uniform distribution, with a standard deviation in amplitude of 0.1 and a standard deviation in phase of 0.1 radian. The perturbed gain vector thus set was multiplied by the components of the steering vector of the array antenna by using the values in the following table in the simulation.

[0221]

[Table 1] ―――――――――――――――――――――――――――――――――――― 1.0236-0.1233j 0.8636-0.0075j 1.1470 + 0.1185j 1.0491-0.0626j 0.8854-0.1041j 1.1536 + 0.1937j ――――――――――――――――――――――――――――――――――――

Consider the case where there are three source signals transmitted from the far field to the array antenna.
It is assumed that all source signals are QPSK modulated.
Assuming that the source signal having the strongest power is the desired source signal, 12.3 from the broad side of the array antenna.
Located at °. For convenience, the power of the desired source signal is always 0.5 dB higher than the power of the second source signal located 16.5 ° from the broadside, and the power of the third source located −1.7 ° from the broadside. Assume 2 dB above the power of the source signal.

As described above, the initial value of the weighting coefficient vector is important for the convergence result. Here, the following initial values of two different weighting coefficient vectors are used.

[0224]

[Numerical Expression 173]

C ⁽⁰⁾ = [1,0,0,0,0,0] ^T

Therefore, under the first initial value condition of Expression 173, the initial value of the weighting coefficient vector forms a beam toward the desired signal source, and under the second initial value condition of Expression 174, Then, the array antenna response is omnidirectional. Although a blind beamformer using the first initial value condition as the initial value of the weighting coefficient vector is expected to have better performance, there is a priori information about the spatial signature waveform signal of the desired source signal. In practice, the second initial value condition is generally used because it does not exist.

The output S of the desired wave signal with respect to the input SNR under the first and second initial value condition of the weighting coefficient vector
Graphs representing the INR are plotted in FIGS. 3 and 4, respectively. Here, the number of samples used is 5000, and the convergence accuracy constant ρ = 1 × 10 ⁻⁵ . In these figures, "BB" stands for the blind adaptive beamforming algorithm proposed herein. From these figures, when the input SNR is not too low (input SNR> -5 dB), the higher order is used,
It is clear that the blind adaptive beamforming algorithm is closer to the optimal solution with MMSE. It can also be seen that the result based on the first initial value condition is slightly better than the result based on the second initial value condition. On the other hand, when the input SNR is high, the order (2,
2), blind adaptive beamforming algorithm for both first and second initial value conditions with cumulants of (3,3) and (4,4) (ie, cumulants for p = q + 1 = m = n) All of the results approach to the state where there is almost no difference in the case of MMSE.

FIGS. 5 and 6 are graphs showing the convergence performance of the blind algorithm represented by the output SINR of the desired wave signal with respect to the number of iterations of the adaptive control processing, for each of the first and second initial value conditions, Here, input S
The results are shown when NR is assumed to be 10 dB and 5000 samples are used. From these figures it can be seen that both initial values of the two weighting coefficient vectors give similar convergence rates.

To examine the effect of the number of samples on the performance of the blind algorithm, FIGS.
In the graph, the graph showing the output SINR of the desired wave signal with respect to the number of samples of the symbol rate used is plotted. Here, it is assumed that the input SNR is 10 dB. It can be seen that for a larger number of samples, the blind algorithm based on both the first and second initial value conditions converges closer to the optimal result. However, since the power of the second source signal is close to the desired source signal, under the second initial value condition, the present algorithm will be the second one, as can be seen in the case of 1000 samples in FIG. May converge close to the optimal weighting coefficient vector for the source signal of. This is natural because all blind algorithms are blind to the order of the incoming signal, unless other information is available to distinguish the signals.

Finally, FIGS. 10 and 11 show a beam pattern represented by the amplitude of the gain pattern based on the first and second initial value conditions of the weighting coefficient vector.
Here we are using 5000 samples with an input SNR of 10 dB. It can be seen that under the initial values of both weighting factor vectors, the convergent beam pattern is very close to that of the optimal MMSE beamformer.

FIGS. 3 to 11 show the second initial value condition and the order (2, 2) in blind adaptive beamforming.
It clearly shows that the use of these cumulants is effective.

In FIG. 1, the array antenna 100 is
In the embodiment disclosed in the specification of the present application, a plurality of N antenna elements 1-1 to 1-N are arranged side by side on a straight line to form a linear array antenna, but other arrangements (one-dimensional, 2 Dimensionally or three-dimensionally arranged shape)
Does not limit the use of. Further, in the present embodiment, it is assumed that the signal to be transmitted is QPSK modulated, but the adaptive control process according to the present invention uses QPSK.
Not limited to modulation, it can be performed for any modulation method that has a non-zero cumulant.

The advantages of the array antenna control method according to the present embodiment will be shown below by comparison with some conventional blind control methods. First, in blind adaptive filtering, a known constant modulus algorithm (CMA) is used for an array antenna, in which the characteristic that the envelope of a digital communication signal is constant is used instead of using a learning sequence of a desired wave signal in designing an equalizer. This is realized by expansion (Prior Art Document 5 “JJ Shynk et al.,“ The constant mo
dulus array for cochannel signal copy and directio
n finding ", IEEE Transaction on Signal Processing,
Vol. 44, No. 3, pp. 652-660, March 1996 ").
The analysis result shows that, for example, when a plurality of source signals have high SNRs and the angles of arrival are not close to each other, C
The steady state and convergence performance of the MA-based blind adaptive beamforming algorithm is shown to be very close to that obtained from the non-blind scenario associated with the learning sequence signal. However, CMA-based blind beamformers typically result in poor performance if such conditions are not met, and
The array antenna control method according to the present embodiment, which can operate under more relaxed conditions, is superior.

On the other hand, instead of that, the MUSIC algorithm proposed in 1979 (Prior Art Document 6 "R.
O. Schmidt, "Multiple emitter location and signal
parameter estimation ", Proceedings of RADC Spectru
m Estimation Workshop, pp.243-258, Griffith Air Force Base, NY 1979. IEEE Transaction o
n Antennas Propagation, Vol. AP-34, pp.276-280, 1
According to Reprint, March 986 "), the steering vector of the desired source signal is obtained using the estimated directions of arrival (DOA) of multiple spatial source signals coming from each source simultaneously. be able to.
However, this algorithm is sensitive to modeling errors in the array signal. When the array antennas associated with the control algorithm are not well calibrated, DOA estimation introduces large errors without knowledge of the spatial and temporal channel response. That is, the steering vector of the desired wave signal should be estimated with a large error. Therefore, also in this respect, the method of controlling the array antenna according to the present embodiment, which does not require knowledge of the channel response of the array antenna or strict calibration of the array antenna, is excellent.

A method of realizing blind adaptive beamforming by using a higher order statistic of a communication signal, that is, a cumulant (Prior Art 2) or using a cyclic stationary characteristic of a communication signal is described as follows. It is a new method of estimating the spatial signature waveform signal of the desired signal source without knowledge. However, the method once proposed is limited to some applications. For example, kurtosis (4th cumulant)
Maximization algorithm (Prior Art Document 7 “Z. Ding et a
l., "Stationary points of a Kurtosis maximization
algorithm for blind signal separation and antenna
beamforming ", IEEE Transaction on Signal Processin
g, Vol. 48, No. 6, pp.1587-1596, 2000 6
The moon ") converges globally only in the absence of noise. Four
Blind adaptive beamforming based on the following cumulants (Prior Art Document 8 “MC Dogan et al.,“ Cumulant-ba
sed blindoptimum beamforming ", IEEE Transaction on
Aerospace Electronics System, Vol. 30, No. 3, pp.7
22-741, July 1994 ") assumes that the interfering signal is Gaussian distributed or that the incoming signal is coherent (or is an independent signal with the same fourth order cumulant). . Blind Adaptive Beamforming Based on Periodic Correlation Function (Prior Art Document 9 “Q. Wu
et al., "Blind adaptive beamforming for cyclostati
onary signals ", IEEE Transaction on Signal Process
ing, Vol. 44, No. 11, pp. 2757-2767, 1996 11
Moon ”) requires a priori information of the cycle frequency of the associated signals.

As described above, according to the array antenna control method of the embodiment of the present invention, global convergence is achieved even in the presence of noise, and the interference wave signal is Gaussian distributed. , The assumption that the incoming signal is coherent (or independent signals with the same fourth-order cumulant), and without the need for a priori knowledge of the frequency of multiple signal cycles, Since the array antenna can be adaptively controlled so as to direct the null toward the desired wave and toward the interference wave, it is superior to the control method according to the related art.

In this embodiment, the super-exponential blind adaptive beamforming algorithm extended from the super-exponential blind separation theory is formulated and presented. Also we
We proved the conditions for the proposed blind algorithm to approach the case of the optimal adaptive beamformer, and derived the relation between the inverse filter criterion and the proposed algorithm. The simulation results show that the proposed algorithm is not sensitive to the initial value of the weighting coefficient vector, and that using an omnidirectional array antenna pattern for the initial value makes the initial value of the weighting coefficient vector consistent with the desired wave signal It shows that the performance does not deteriorate so much as compared with the case where it is used. It is sufficient to use a cumulant of order (2,2) to approach the optimal steady-state performance, but higher order cumulants can be used to perform more computations and improve convergence performance. be able to.

A formulation of a super-exponential blind adaptive beamforming algorithm has been presented herein. The above algorithm is an extension of the cumulant-based super-exponential blind deconvolution theory (Prior Art 1) presented by Shalvi and Weinstein. With this formulation, we show two different sets of conditions,
Under the above set of conditions, each blind adaptive beamforming algorithm proved to perform complete suppression of the undesired source signal and converge to the optimal weighting coefficient vector associated with the Wiener-Hop equation. . Simulation results show the effectiveness of this algorithm.

[0238]

As described above in detail, the array according to the present invention is
-According to the antenna control method, a plurality of N antenna elements
In an array antenna consisting of children, each of the above antenna elements
Predetermined for each received signal received by each child
Output signal of the result of multiplying and adding the weighting factors of
Outputs z and has a 2m-th order cumulan with 2m variables
The output signal z and the output as variables.
Signal z of the complex conjugate of the signal ^*And each received signal as a component
Complex conjugate vector x of received signal vector x^*including
Calculate the cumulant vector d and calculate the received signal vector
The autocorrelation matrix R of Le x and the cumulant vector d
Based on
To calculate and set the weighting coefficient vector c
By returning it, the main beam of the above array antenna is located.
Point the null towards the wanted wave and towards the interfering wave
Adaptive control.

Therefore, according to the above array antenna control method, the main beam of the array antenna is directed in the direction of the desired wave and null in the direction of the interference wave by using a simple circuit configuration without requiring the reference signal. The array antenna can be adaptively controlled so as to point to. In addition, the adaptive control process can converge at a high speed exponentially (at the speed of exponentiation) to derive an optimum weighting coefficient. This optimal weighting factor converges to the solution specified by the Wiener-Hop equation under given conditions.

In the above array antenna control method, preferably, each time the output signal z is output,
In a cumulant of order 2m with 2m variables,
The cumulant of the output signal z including the output signal z and the complex conjugate signal z ^{* of the} output signal as its variable is calculated, the power of the output signal z is calculated, and the power of the calculated output signal z is calculated. The value of the cumulant ratio of the output signal z is calculated as the value of the objective function, and the difference between the value of the calculated objective function and the value of the objective function calculated based on the output signal z output last time. When is smaller than a predetermined threshold value, the adaptive control process is stopped. Therefore,
When the inverse filter criterion associated with the blind adaptive beamforming is used as the objective function of the adaptive control process, the optimal weighting factor described above causes the main beam of the array antenna to produce the desired wave of the desired wave so as to maximize the objective function. A null can be directed in the direction and in the direction of the interference wave.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an array antenna device according to an embodiment of the present invention.

FIG. 2 is a flowchart showing an adaptive control process executed by the adaptive control type controller 10 of FIG.

3 is a simulation result of the array antenna apparatus of FIG. 1, showing the output SIN of the desired wave signal with respect to the input SNR under the condition of the first initial value of the weighting coefficient vector.
It is a graph which shows R.

FIG. 4 is a simulation result of the array antenna apparatus of FIG. 1, showing the output SIN of the desired wave signal with respect to the input SNR under the second initial value condition of the weighting coefficient vector.
It is a graph which shows R.

5 is a simulation result of the array antenna apparatus of FIG. 1, showing convergence performance represented by output SINR of a desired wave signal with respect to the number of iterations of adaptive control processing under the first initial value condition of the weighting coefficient vector. It is a graph.

6 is a simulation result of the array antenna apparatus of FIG. 1, showing a convergence performance represented by an output SINR of a desired wave signal with respect to the number of iterations of the adaptive control process under the second initial value condition of the weighting coefficient vector. It is a graph.

FIG. 7 is a graph showing a simulation result of the array antenna apparatus of FIG. 1, showing the output SINR of the desired wave signal with respect to the number of samples of the used symbol rate under the first initial value condition of the weighting coefficient vector.

8 is a simulation result of the array antenna apparatus of FIG. 1, showing the use of (2,2) th order and (3,3) th order blind beam forming algorithms and the second initial value condition of the weighting coefficient vector. 7 is a graph showing an output SINR of a desired wave signal with respect to the number of samples of a selected symbol rate.

FIG. 9 is a simulation result of the array antenna apparatus of FIG. 1, showing the number of samples of the symbol rate used in the (4, 4) th order blind beam forming algorithm and the second initial value condition of the weighting coefficient vector. 5 is a graph showing an output SINR of a desired wave signal with respect to.

FIG. 10 is a graph showing simulation results of the array antenna apparatus of FIG. 1, showing a converged directivity pattern represented by the amplitude of a gain pattern under the first initial value condition of the weighting coefficient vector.

FIG. 11 is a graph showing a simulation result of the array antenna apparatus of FIG. 1, showing a converged directivity pattern represented by the amplitude of a gain pattern under the second initial value condition of the weighting coefficient vector.

[Explanation of symbols]

1-1 to 1-N ... Antenna element, 2-1 to 2-N ... Low noise amplifier, 3-1 to 3-N ... Down converter, 4-1 to 4-N ... A / D converter, 5-1 to 5-N ... Multiplier, 6 ... adder, 7 ... Demodulator, 10 ... Adaptive control type controller, 100 ... array antenna.

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Zhang Yimin             United States 19085 Bi, Pennsylvania             Lanova, Lancaster Avenue 800             Number, Vila Nova University, Depar             Statement of Electrical Anne             De computer engineering (72) Inventor Tada Yui             Taiwan 30013 Hsinchu City Gwangbokro 2nd dan No. 101 National Qing             Hua University F term (reference) 5J021 AA05 AA06 CA06 DB01 EA07                       FA13 FA16 FA26 FA29 FA30                       FA32 GA02 GA06 HA06 HA10                 5K059 CC03 CC04 DD31

Claims (2)

[Claims] 1. A method of controlling an array antenna comprising a plurality of N antenna elements arranged in close proximity in a predetermined arrangement shape, wherein a plurality of N elements received by the respective antenna elements are provided.
A first step of calculating an autocorrelation matrix R of a received signal vector x having a number of received signals as components; and a plurality of N predetermined weighting factors for the received plurality of N received signals, respectively. After the multiplication, a second step of outputting an output signal z as a result of adding the respective signals of the multiplication results, m being an integer of 2 or more, and the m first variables and (m-
1) 2 with one second variable and one third variable
In the m-th order cumulant, m identical output signals z are included as a first variable and (m-
1) A third step of calculating a cumulant vector d containing the same complex conjugate signal z ^* of the output signals and containing the complex conjugate vector x ^* of the received signal vector x as a third variable; Autocorrelation matrix R of the calculated received signal vector x
And the cumulant vector d calculated above, the following equation By repeating the fourth step of calculating and setting the weight coefficient vector c having each weight coefficient as a component and the second to fourth steps,
Fifth, the adaptive control is performed so that the main beam of the array antenna is directed to the desired wave and the null is directed to the interference wave.
And a method of controlling an array antenna. 2. In a 2m-th order cumulant having m first variables and m second variables each time the output signal z is output, m identical first variables are provided. Calculating the cumulant of the output signal z including the output signal z of the above and including, as a second variable, the signal z ^* of the complex conjugate of m identical output signals, calculating the power of the output signal z, Calculating the ratio of the cumulant of the output signal z to the calculated power of the output signal z as the value of the objective function, the value of the calculated objective function, and the output signal z output last time The step of stopping the process of the fifth step when the difference from the value of the objective function calculated by the above is smaller than a predetermined threshold value, the array antenna according to claim 1. Control method.