JP3004015B1 - Arriving wave measuring method and arriving wave measuring device - Google Patents

Abstract

A method and apparatus for measuring an incoming wave that can measure the angle of arrival of an incoming wave satisfying physical conditions. When a pseudo-random signal is used for transmission, the received power obtained by integrating the product of the power of the arriving wave arriving at the angle of arrival θ and the antenna gain of the directional antenna 1 at the rotation angle α over the entire measurement interval Are obtained at the output end of the directional antenna 1. Power of the incoming wave, assuming that can be represented by the sum of the power incoming waves of the first to N having a specific arrival angle θ = ψ ₁ ~Ψ _N, with directional antennas from the average value of the received and measured received power, power c _1, c ₂ of each incoming wave, ..., c _N, and, angle of arrival _{ψ 1, ψ 2, ...,} ψ N
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Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an incoming wave measuring method and an incoming wave measuring device used for measuring radio wave propagation in mobile communication and the like. In particular, the present invention relates to measurement of an incoming wave received from a transmitting device through a complicated propagation path by multipath propagation.

[0002]

2. Description of the Related Art Conventionally, an angle of arrival, the number of arriving waves, and
The method of measuring the power of the arriving wave, etc. is to roughly measure how much arriving wave from which direction exists from the relation of only the received power at the antenna output end to the rotation angle of the antenna. Therefore, it has been considered difficult to obtain a measurement accuracy higher than the half-value angle of the antenna.

The half-value angle of the antenna means that the received power level is half (3d) around the angle at which the received power level is the maximum.
B decrease), which indicates the sharpness of the directional characteristics. In the case of a parabolic antenna, this half-value angle θ ₀ is represented by D = Cλ / θ ₀ where D is the diameter of the antenna, λ is the wavelength, and C is a constant of about 70. Therefore, when the directivity of the antenna is further sharpened, the antenna diameter becomes very large, which is not practical for measuring an incoming wave in mobile communication. For example, assuming that a parabolic antenna having a half-value angle of about 5 ° is made for a radio wave of about 3 GHz, an antenna having a diameter of 1.4 m or more, and a half-value angle of 1 ° requires a diameter of 5 × 1.4 m = 7 m or more. .

Further, the measurement accuracy is greatly degraded by side lobes of the parabolic antenna or by radio waves from the side of the antenna or from behind the antenna. In particular, radio waves from directions other than the direction of the antenna are also received due to side lobes, and as a result, sufficient values cannot be obtained as measurement accuracy. In addition, since the antenna system becomes large-scale, it is difficult to accurately detect an incoming wave when the propagation environment changes quickly due to movement around the vehicle or the like. When measuring while moving the antenna, the propagation environment changes quickly due to other moving objects such as vehicles, making accurate measurement difficult. For example, when an antenna having a sharp directivity is used, the antenna system is too large to obtain a sufficient rotation speed, so that it is impossible to follow the level change in the direction in which the antenna is not facing, and the incoming wave is fast. It was difficult to measure the change.

Therefore, the present applicant has proposed the following method of measuring an incoming wave as a method of improving the measurement accuracy, as disclosed in Japanese Patent Application No. Hei 10 (1999) -10-2.
No. 01426. A radio wave modulated by a pseudo random signal is transmitted from the transmitting side, and a parabolic antenna having directivity is used on the receiving side, and the power of the received signal of the parabolic antenna is measured. The analysis for improving the accuracy is based on the measurement interval (T1) for the arrival angle θ of the radio wave.
Is divided into M minute sections, and an angle θ _i is assigned corresponding to the i-th of each minute section with respect to the arrival angle θ (i = 1, 2, 3,..., M). The antenna is rotated to set the rotation angle to α, and the measurement section T2 is divided into M minute sections for the rotation angle α, and the rotation angle α
, An angle α _j (j = 1, 2, 3,..., M) is assigned corresponding to the j-th of the respective minute sections.

[0006] The average value of the received power measured for the angle of rotation αj and y (alpha _j), to the rotational angle alpha _j, the first matrix,

(Equation 9) And

Assuming that the gain of the parabolic antenna with respect to the angle θ _i −α _j is g (θ _i −α _j ), the second matrix is

(Equation 10) And the power of the arriving wave with respect to the angle θ _i is x (θ _i ), and the third matrix is

[Equation 11] And

GX = Y (4) That is,

(Equation 12) Into the third matrix

(Equation 13) , The number of arriving waves, and the angle and power of each arriving wave were obtained.

Here, in order to solve the simultaneous linear equations, the third matrix X is directly obtained by the Gaussian elimination method or the sweeping out method (Gauss-Jordan method). However,
In this method, x (θ) does not always take a positive value depending on the measurement error included in the measured received power y (α), and the power value may be negative. Was. If M = approximately 360, it is necessary to solve a simultaneous equation of 360 rows in order to solve the equation (5). In this case, a calculation error is accumulated due to a measurement error included in y (α). Therefore, there is a problem that the solution may diverge.

[0010]

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned conventional inconveniences and to provide an incoming wave measuring method and an incoming wave measuring apparatus capable of measuring the angle of arrival of an incoming wave satisfying physical conditions. It is intended to provide.

[0011]

According to a first aspect of the present invention, a directional antenna is rotated to receive one or more radio waves modulated by a pseudo random signal transmitted from a transmitting side. An arrival wave measuring method for measuring at least the arrival angle θ of the arrival wave of the directional antenna, wherein the measurement section is divided into M minute sections with respect to the rotation angle α of the directional antenna, and corresponds to the j-th of each minute section. The received power y (α _j ) of the received signal of the directional antenna is measured with respect to the rotation angle α _j (j = 1 to M) assigned as above, and the measurement of the angle of arrival θ is performed with respect to the angle of arrival θ. The section is divided into M minute sections, and the angle θ _i (i = 1 to M) assigned to the i-th of each minute section, and the rotation angle α _j , the angle θ _i −α _j, the gain of the directional antenna is g (θ _i −α _j ), The first matrix Y is

[Equation 14] And the second matrix G is

(Equation 15) And the power of the arriving wave at the angle of arrival θ _i is x (θ _i ),
The third matrix X is

(Equation 16) Is to solve an equation represented by GX = Y for the third matrix X. The power x (θ) of the arriving wave at the angle of arrival θ is represented by N an arbitrary natural number, Let x (θ) = c ₁ h (θ−ψ ₁ ) be an incoming wave of angle of arrival ψ ₁ and power c _{1 or} an incoming wave of angle of arrival ψ _N and power c _N.
+ C ₂ h (θ-ψ ₂ ) + ... + c _N h (θ-ψ _N )

[Equation 17]It is assumed that the directional antenna is
Received power y (α _j) Is the y obtained by the measurement.
(Α) so as to approximate the value of (α)
c₁, Ψ₁And sequentially, c_N, Ψ_NUp to
You. Therefore, even when a measurement error accompanies,
Arrival angle of arriving waves, etc. that satisfy the condition that the force is positive
Can be measured.

[0012] In the invention described in claim 2, the claim
2. The method for measuring an incoming wave according to claim 1, wherein₁, Ψ₁Seeking
Sequentially, c_N, Ψ_NThe first processing step
X (θ) = c₁h (θ-ψ₁)
Calculate the equation represented by GX = Y and obtain the result of the calculation.
Y (α) is y₁(Α) and obtained by the above measurement.
Δy relating to the difference from the value of y (α)₁= ｛Y
₁(Α₁) -Y (α₁)｝^Two+ ｛Y₁(Α_Two) -Y (α_Two)｝^Two
+ ... + y₁(Α_M) -Y (α_M)｝^TwoIs minimized
Mushroom c₁, Ψ₁To c₁≧ 0, the second processing
X (θ) = c_Twoh (θ-ψ_Two)age
To calculate the equation represented by GX = Y, and calculate the result.
The resulting y (α) is y_Two(Α) and y_Two(Α) already
Y calculated to₁(Α) and the above measurement
Δy relating to the difference from the value of y (α) obtained_Two=
｛Y₁(Α₁) + Y_Two(Α₁) -Y (α₁)｝^Two+ ｛Y
₁(Α_Two) + Y_Two(Α _Two) -Y (α_Two)｝^Two+ ... + y₁
(Α_M) + Y_Two(Α_M) -Y (α_M)｝^TwoIs minimum
Of c_Two, Ψ_TwoTo c_Two≧ 0, and hereinafter referred to as Nth
This is repeated until the processing step of
As a processing step of N, x (θ) = c_Nh (θ-ψ_N)
Calculate the equation represented by GX = Y and calculate
Y (α) obtained as a result of_N(Α) and y_N(Α)
Already calculated in₁(Α) or y_N-1(Α)
And the value of y (α) obtained by the above measurement
Value for minute Δy_N= ｛Y₁(Α₁) + Y_Two(Α₁) + ... +
y_N(Α₁) -Y (α₁)｝^Two+ ｛Y₁(Α_Two) + Y_Two(Α_Two)
+ ... + y_N(Α_Two) -Y (α_Two)｝^Two+ ... + y
₁(Α_M) + Y_Two(Α_M) + ... + y_N(Α_M) -Y (α_M)｝^Two
C when is minimum _N, Ψ_NAnd c_NUnder the condition of ≧ 0
. Therefore,
Arrival angle of arriving waves, etc. that satisfy the condition that the force is positive
Can be accurately measured.

[0013] In the third aspect of the present invention,
2. The method for measuring an incoming wave according to claim 1, wherein₁, Ψ₁Seeking
Sequentially, c_N, Ψ_NThe first processing step
The value of y (α) obtained by the above measurement is
When the value of α becomes large,₁And c₁= Y (ψ₁) / G
(0), and as a second processing step, y (α) −
c₁g (ψ₁−α) is the value of α when the value of_Two
As c_Two= ｛Y (ψ _Two) -C₁g (ψ₁−ψ_Two)｝ / G
(0), and thereafter, this is repeated until the Nth processing step.
And the N-th processing step includes y
(Α)-｛c₁g (ψ₁−α) + c_Twog (ψ_Two−α) +…
 + C_N-1g (ψ_N-1−α) α at which the value of｝ is maximum
The value of_NAs c_N= [Y (ψ_N)-｛C₁g (ψ₁−
ψ_N) + C _Twog (ψ_Two−ψ_N) + ... + c_N-1g (ψ_N-1−ψ
_N)｝] / G (0)
You. Therefore, the condition that the power is positive is satisfied
It is possible to easily measure the angle of arrival of incoming waves.

According to the fourth aspect of the present invention, the directional antenna is rotated to receive a radio wave modulated by the pseudo random signal transmitted from the transmitting side, and to determine at least the arrival angle θ of one or a plurality of arriving waves. An arriving wave measuring apparatus for measuring, with respect to a rotation angle α of the directional antenna, a measurement section of the rotation angle α is divided into M minute sections, and the measurement section corresponds to a jth of each minute section. Means for inputting and storing the measured reception power y (α _j ) of the reception signal of the directional antenna with respect to the assigned rotation angle α _j (j = 1 to M); The measurement section of the arrival angle θ is divided into M minute sections, and the angle θ _i (i = 1 to 1) assigned to the i-th of each minute section is assigned.
M) and means for outputting a gain g (θ _i -α _j ) of the directional antenna at an angle θ _i -α _{j with} respect to the rotation angle α _j , and a first matrix Y. 1, the second matrix G is equal to G according to claim 1, the power of the arriving wave at the arrival angle θ _i is x (θ _i ), and the third matrix G is equal to Y. Assuming that the matrix X is equal to X according to claim 1, the equation represented by GX = Y is
And computing means for solving the third matrix X. The power x (θ) of the arriving wave at the arriving angle θ is set to an arbitrary natural number N, and the arriving waves of N waves are arriving angles ψ ₁ , Power c ₁
, Or an arrival wave of arrival angle ψ _N and power c _N , x (θ) = c ₁ h (θ−ψ ₁ ) + c ₂ h (θ−ψ ₂ )
+... + C _N h (θ−ψ _N ) where the reception power y (α _j ) of the reception signal of the directional antenna is obtained by measurement based on the same assumption as in claim 1.
The above-mentioned c ₁ and ψ1 are _first determined so as to be close to the value of (α), and c _N and 順次_N are sequentially obtained. Therefore, even when a measurement error is involved, it is possible to measure the angle of arrival of an incoming wave that satisfies the condition that the power is positive.

According to a fifth aspect of the present invention, in the arriving wave measuring apparatus according to the fourth aspect, a process for obtaining the c ₁ and ψ ₁ and sequentially obtaining up to c _N and ψ _N is performed. Calculates the equation represented by GX = Y, where x (θ) = c ₁ h (θ−ψ ₁ ), and converts y (α) obtained as a result of the calculation into y ₁ (α) And a value Δy ₁ = ｛y relating to the difference from the value of y (α) obtained by the above measurement
₁ (α ₁ ) −y (α ₁ )｝ ² + {y ₁ (α ₂ ) −y (α ₂ )} ²
+... + {Y ₁ (α _M ) −y (α _M )} ² where c ₁ and ψ ₁ are obtained under the condition of c ₁ ≧ 0, and the second processing means Is calculated as x (θ) = c ₂ h (θ−ψ ₂ ), the equation represented by GX = Y is calculated, and y (α) obtained as a result of the calculation is defined as y ₂ (α), and y ₂ (α)
And the value Δ regarding the difference between the value obtained by adding y ₁ (α) already calculated and the value of y (α) obtained by the measurement.
y ₂ = {y ₁ (α ₁ ) + y ₂ (α ₁ ) −y (α ₁ )} ² + Δy ₁
(Α ₂ ) + y ₂ (α ₂ ) −y (α ₂ )｝ ² +... + ｛Y
₁ (α _M ) + y ₂ (α _M ) −y (α _M )｝ ² , c ₂ and ψ ₂ are minimized under the condition of c ₂ ≧ 0.
Is intended to run repeatedly previous processing means, the processing means of the first N as _{x (θ) = c N h} (θ-ψ N), calculates the equation represented by the GX = Y, _Let y (α) obtained as a result of calculation be y _N (α), add y ₁ (α) to y _N−1 (α) already calculated to y _N (α), and The value Δy _N = ｛y ₁ (α ₁ ) + y ₂ (α ₁ ) +... + Y relating to the difference from the obtained value of y (α)
_N (α ₁ ) −y (α ₁ )｝ ² + ｛y ₁ (α ₂ ) + y ₂ (α ₂ ) +
... + y _N (α ₂ )-y (α ₂ )｝ ² + ... + ｛y ₁ (α _M )
+ Y ₂ (α _M ) +... + Y _N (α _M ) −y (α _M )｝ ^2, where c _N and に な る_N are minimized under the condition of c _N ≧ 0. Therefore, it is possible to accurately measure the arrival angle and the like of the incoming wave that satisfies the condition that the power of the incoming wave is positive.

According to a sixth aspect of the present invention, in the arriving wave measuring apparatus according to the fourth aspect, a process for obtaining the c ₁ and ψ ₁ and sequentially obtaining c _N and ψ _N is performed. Is the value of α when the value of y (α) obtained by the above measurement is the maximum, and _{1 1} , c ₁ = y (ψ ₁ ) /
g (0), and the second processing means includes:
Assuming that the value of α when the value of (α) −c ₁ g (α ₁ −α) is maximum is ψ ₂ , c ₂ = ｛y (ψ ₂ ) −c ₁ g (ψ ₁ −
ψ ₂ )｝ / g (0) is obtained, and thereafter, this processing is performed up to the N-th processing means.
(Α) − ｛c ₁ g (ψ ₁ −α) + c ₂ g (ψ ₂ −α) + ...
Α at which the value of + c _N-1 g ({ _N-1 -α)} becomes the maximum
As the value _{ψ N, c N = [y} (ψ N) - {c 1 g (ψ 1 -
ψ _N ) + c ₂ g (ψ ₂ −ψ _N ) + ... + c _N-1 g (ψ _N-1 −ψ
_N )｝] / g (0). Therefore,
It is possible to easily measure the arrival angle and the like of the arriving wave satisfying the condition that the power is positive.

[0017]

FIG. 1 is a block diagram for explaining an embodiment of an incoming wave measuring method according to the present invention. In the figure, 1 is a directional antenna, 2 is a turntable, 3 is a reception power measuring device, 4 is a first storage unit, 5 is a second storage unit, 6 is an analysis unit, 7 is a transmission antenna, and 8 is transmission. The device 9 is a pseudo-random signal generator. The block configuration itself is the same as in the prior art, but the analysis method in the analysis unit 6 is different from that in the prior art.

This embodiment relates to the power of one or a plurality of arriving waves (reception power of an arriving wave input to a parabolic antenna at a receiving point) transmitted through a multipath propagation path.
When a pseudo-random signal is used for transmission, the received power obtained by integrating the product of the power of the arriving wave arriving at the angle of arrival θ and the antenna gain of the directional antenna 1 having the rotation angle α over the entire measurement interval becomes the directivity. The focus is on what is obtained at the output end of the antenna 1. The measurement is performed for each minute section of the rotation angle α,
The relation between the power of the arriving wave, the antenna gain indicating the directional characteristics of the directional antenna 1 and the measurement result of the reception power at the antenna output end is expressed in the form of a matrix, and by performing an inverse calculation, the arrival of one or more arriving waves The angle θ, the received power, and the number of arriving waves are obtained. As a result, even if the directional characteristics of the directional antenna 1 are not good and there is a large side lobe, the incoming wave can be accurately obtained.

In the transmitting device 8, an experimental radio wave modulated by a pseudo random signal (for example, a PN signal) output from a high-speed pseudo random signal generating device 9 is transmitted from a transmitting antenna 7 such as a half-wave dipole. As the transmitting device, a transmitter of a delay profile measuring device described later can be used as it is. As the directional antenna 1, for example, a parabolic antenna is used. The directional antenna 1 is mounted on a turntable 2 and is driven to rotate. In addition, in this figure, an example in which the elevation angle changes by rotating around the horizontal axis is shown, but rotation around an arbitrary axis may be used, such as rotation around the vertical axis to change the azimuth.

A directional antenna 1 receives a signal modulated by a pseudo-random signal transmitted from a transmitting side. The signal received by the directional antenna 1 is measured by the reception power measuring device 3. The following can be said about the power of the arriving wave. Power incident from a certain direction × antenna gain in that direction = power of the antenna output end in that direction Then, the rotation angle (direction in which the directivity becomes maximum) of the antenna is α, and the arrival angle of the arriving wave is θ. I do. Further, the antenna gain in the direction of the angle of arrival θ at the rotation angle α is represented by g (θ−α).

Assuming that the power density with respect to the angle θ of the arriving wave within the minute angle dθ is f _in (θ), the antenna 1
The received power dy obtained at the output end of the above is expressed by dy = f _in (θ) g (θ−α) dθ (7)

Here, when the speed of the pseudo-random signal output from the pseudo-random signal generator 9 on the transmitting side is sufficiently high, multipath propagation is configured to be shorter than the 1-bit time width of the pseudo-random signal. The delay time difference between each wave is larger. The purpose of the conventional delay profile measuring device using a pseudo-random signal is to measure the delay time difference between multipath transmission paths of a signal transmitted from a transmitter, so that the time width of one bit of the pseudo-random signal is sufficient. Is set to short.

When a radio wave BPSK-modulated by such a pseudo random signal is multiplexed by multipath propagation, a plurality of radio waves passing through each path are 1 bi.
Since they are delayed by t or more, they can be regarded as mutually independent stochastic events. That is, the electric fields of the arriving waves are f ₁ , f ₂ ,..., F _n, and the variance of the multiplex wave (f ₁ + f ₂ +... + F _n ) = the variance of f ₁ + the variance of f ₂ + the variance of + f _n (8) holds.

The relationship of the above equation (8) relates to the dispersion of the electric field. The dispersion of the electric field corresponds to the electric power. As described above, since the electric field dispersion and the electric power have similar properties,
The following can be said about equation (7). The received power y (α) at the output end of the directional antenna 1 at the rotation angle α facing the direction of α is: y (α) = power (dispersion) at the antenna output end = (f ₁ + f ₂ +... + f antenna output terminal of the power of _n) (dispersion) = f ₁ of the antenna output terminal of the power (variance) + f ₂ of the antenna output terminal of the power (variance) + ............ + f _n of the antenna output terminal of the power (variance)

Therefore,

(Equation 18) That is,

[Equation 19]

As can be seen from the above-described calculation process of the expression (9), the expression (10) indicates that when a pseudo random signal arrives, the delay time difference between the paths is delayed by 1 bit or more of the pseudo random signal. In addition, y (α) can be read by the power meter of the reception power measuring device 3 as the sum of the electric power of the radio waves arriving from each path. For example, the power of a received signal received by the directional antenna 1 is measured. In the integration section, -π to π are selected in equation (10), and the entire circumference is set as the measurement section. However, it is possible to exclude a section where an incoming wave does not exist. Alternatively, a section where the antenna gain is considered to be sufficiently small can be excluded. For example, if a parabolic antenna or the like having a sharp directivity is used, the integration interval of Expression (10) can be limited to a small range.

The above equation (10) can be transformed into the following approximate equation. For sufficiently large M, y (α) = f in (θ 1) g (θ 1 -α) Δθ + f in (θ 2) g (θ 2 -α) Δθ ··· + f in (θ M) g (θ _M− α) Δθ (11) Here, Δθ is an angle when the measurement section T1 is divided into sufficiently small sections, and when the measurement section of the arrival angle θ is −π to π, Δθ = 2π / M (12) Given by Also, θ ₁ , θ ₂ ,..., Θ _M are obtained by dividing the measurement section of the arrival angle θ into M minute sections,
Is the center point for the angle assigned corresponding to the i-th of each microsection. In addition, in the above-described equations (10) and (11), the directional antenna 1 has a rotation angle α.
Are obtained as the output of the received power measuring device 3.

In the equation (11), f _in (θ ₁ ) Δθ,
_{f in (θ 2) Δθ,} ..., f in (θ M) Δθ , respectively,
θ _1, θ _2, ..., is the power of the incoming wave in the period of Δθ arriving at an angle of theta _M, this value, respectively x
_{Assuming that} (θ ₁ ), x (θ ₂ ),..., X (θ _M ), the received power y (α) can be replaced with the following form. y (α) = x (θ ₁ ) g (θ ₁ -α) + x (θ ₂ ) g (θ ₂ -α) ... + x (θ _M ) g (θ _M -α) (13)

The equation (13) is based on M unknowns x (θ ₁ ),
x (θ _2), ···, is an equation which is x (θ _M), in order to solve this equation, rotates the directional antenna 1, M number of points (α _1, α _2, ··· , Α _M ). Here, α _j is obtained by dividing the measurement section T ₂ of the directional antenna into M minute sections and assigning the rotation assigned to the j-th of each minute section with respect to the rotation angle α of the directional antenna. Is the corner. This measurement result is stored in the first storage unit 4.

[0030] In analyzing unit 6, using the first measurement results stored in the storage unit 4 and a second antenna gain is stored in the storage unit 5, theta _1, theta _2, ..., the theta _M Received power x (θ ₁ ), x (θ ₂ ),..., X in the section of angle Δθ
Solve (θ _M ). That is, equation (7) can be expressed as follows with respect to the rotation angles α ₁ , α ₂ ,..., Α _M of the _M antennas. y (α ₁ ) = x (θ ₁ ) g (θ ₁ −α ₁ ) + x (θ ₂ ) g (θ ₂ −α ₁ ) + x (θ _M ) g (θ _M −α ₁ ) y ( α ₂ ) = x (θ ₁ ) g (θ ₁ −α ₂ ) + x (θ ₂ ) g (θ ₂ −α ₂ ) + x (θ _M ) g (θ _M −α ₂ ) ... Y (α _M ) = x (θ ₁ ) g (θ ₁ −α _M ) + x (θ ₂ ) g (θ ₂ −α _M )... + X (θ _M ) g ( θ _M −α _M ) (14)

Equation (14) is described above using a matrix (5)
It can be represented by an equation. Equation (5) is obtained from equations (2) and (3).
According to the equations (6) and (6), it can be expressed as GX = Y expressed by the equation (4). By solving this equation (4) for X, the incoming wave can be separated with respect to the angle θ.
As a result, the arrival angle and power of each arriving wave and the number of arriving waves can be obtained. In addition, as mentioned above,
The equation outputs the received power x (θ) in a section of Δθ at an angle of θ without separating the incoming waves even when a plurality of arriving waves shifted in time are multiplexed.

Since the above equation (4) is a system of linear equations, it can be directly solved using a well-known Gaussian elimination method or a sweeping-out method (Gauss-Jordan method). But,
In the embodiment of the arriving wave measuring method of the present invention, instead of directly solving equation (4), a solution that satisfies the laws of physics is obtained by using the physical properties of the arriving wave.

FIG. 2 is a schematic diagram for explaining the principle of an embodiment of an incoming wave measurement method according to the present invention. In the figure, the horizontal axis is the angle of the rotation angle α of the directional antenna 1, the vertical axis is the measured value of the received power of the received signal of the antenna (solid line pattern),
The received power of the received signal of the directional antenna when only the first arriving wave is present (pattern of the dashed line);
The reception power of the reception signal of the directional antenna when only the third arriving wave is present (the pattern indicated by the dashed line) is shown. A case will be described in which it is assumed that N waves (N is an arbitrary natural number) are received, but only two waves are shown in FIG.

Since the arriving waves can be regarded as plane waves, each of the first to N-th arriving waves has a specific arriving angle θ = ψ _{1 to} Ψ _N. In addition, the power of each arriving wave has a non-negative value. As described in the derivation process of Equation (9), the received power of the multiplex wave composed of a plurality of arriving waves modulated by the pseudo random signal is represented by the single arriving wave x (θ) (where (15) to (15)
Equation (18) should hold. x (θ) = c ₁ h (θ−ψ ₁ ) + c ₂ h (θ−ψ ₂ )... + c _N h (θ−ψ _N ) (15)

(Equation 20)

In the embodiment of the arriving wave measuring method according to the present invention, on the assumption that the arriving wave is represented by the above equation, the reception power y (α of the reception signal of the directional antenna is assumed.
_j) is, as a value approximate to the obtained value of y (alpha) by the measurement, first determine the c _1, [psi ₁ large incoming wave power, sequentially, a small incoming wave power c _N , seeking to [psi _N, the average value of the received power measured by received by the directional antenna, power c _1, c ₂ of each incoming wave, ..., c _N, and the angle of arrival [psi _1, [psi ₂ , ..., ψ _N. Note that the reception power y (α) of the reception signal of the directional antenna
_j ) uses a time-averaged value.

Next, a description will be given of a first embodiment of an incoming wave measurement method according to the present invention. Y In this embodiment, as the first process step, as _{x (θ) = c 1 h} (θ-ψ 1) (19), which calculates the GX = Y, resulting from the calculation
(Α) is again referred to as y ₁ (α).

On the other hand, y (α) obtained by measurement is directly used as y (α), and y ₁ (α) obtained as a result of calculation is obtained.
And the square error of the difference between the measured value y (α) and Δy ₁ , Becomes

Δy ₁ is obtained by adding the square of the difference between the measured value of the antenna reception power and the antenna reception power of the first arriving wave in FIG. 2 for the entire section of the angle α. When this Δy ₁ becomes minimum, c ₁ , ψ ₁ is c ₁ ≧
Determined under the condition of 0. The coefficient c ₁ obtained at this time is
While satisfying the physical condition of c ₁ ≧ 0, a plurality of incoming waves x
(Θ) corresponds to the largest power. Because it is better to exclude the arriving wave with the largest power (20)
This is because the expression indicates the minimum value.

As a second processing step, x (θ) = c_Twoh (θ-ψ_TwoGX = Y (Equation 4) is calculated as (21), and the calculation result is obtained.
Y (α) is replaced by y _Two(Α), while measuring
The obtained y (α) is referred to as y (α) as it is. Total
Y obtained as a result of the operation_TwoY already calculated in (α)₁(Α)
And the square error of the difference between the measured value y (α) and
To Δy_TwoThen, Δy_Two= ｛Y₁(Α₁) + Y_Two(Α₁) -Y (α₁)｝^Two + ｛Y₁(Α_Two) + Y_Two(Α_Two) -Y (α_Two)｝^Two + ... + y₁(Α_M) + Y_Two(Α_M) -Y (α_M)｝^Two C when (22) becomes minimum_Two, Ψ_TwoTo c_TwoUnder the condition of ≧ 0
Ask.

In FIG. 2, Δy ₂ is the measured value of the antenna reception power and (the antenna reception power of the first arriving wave +
This is the sum of the square of the difference from the second arriving wave antenna reception power) over the entire interval of the angle α. The coefficient c ₂ obtained at this time corresponds to the second largest power among a plurality of arriving waves while satisfying the physical condition of c ₂ ≧ 0. The first largest arriving wave is already represented by y ₁ (α). At this time, by further removing the second largest arriving wave from y (α), equation (42) shows the minimum. is there. Hereinafter, this operation is repeated until the Nth processing step.

As the Nth processing step, x (θ) = c_Nh (θ-ψ_NGX = Y (Equation 4) is calculated as (23), and the result of the calculation is obtained.
Y (α) is replaced by y _N(Α), while measuring
The obtained y (α) is directly used as y (α),
Y obtained as a result of the operation_NY already calculated in (α)₁(Α)
~ Y_N-1(Α) and the measured value y (α)
Δy is the square error of the difference_NThen, Δy_N= ｛Y₁(Α₁) + Y_Two(Α₁) + ... + y_N(Α₁) -Y (α₁)｝^Two + ｛Y₁(Α_Two) + Y_Two(Α_Two) + ... + y_N(Α_Two) -Y (α_Two)｝^Two + ... + y₁(Α_M) + Y_Two(Α_M) + ... + y_N(Α_M) -Y (α_M)｝^Two (24) c when is minimized_N, Ψ_NTo c_NUnder the condition of ≧ 0
Ask. C thus obtained₁, C_Two, ..., c_N,
ψ₁, Ψ_Two,…, Ψ_NWhen the expression (15) is calculated using
In this case, GX = Y is represented within the range of a practically allowable error.
Equation (4) holds.

Next, a description will be given of a second embodiment of the arriving wave measuring method according to the present invention. In this embodiment, the first
Is the rotation angle α when the measured value y (α) of the received power becomes the maximum value is the arrival angle ψ of the first arriving wave.
₁ and the maximum value of the measured value of the received power at this time is considered to be equal to the received power of the received signal of the directional antenna when only the first arriving wave is present and received. is there.

That is, in FIG. 2, it is assumed that the first arriving wave is incident from the direction of the rotation angle α at which the measured value of the antenna reception power is maximum, and the antenna reception power at this time is all , The power of the first arriving wave. Therefore, the rotation angle α when the reception power y (α) of the reception signal of the directional antenna indicates the maximum value is the first rotation angle α.
Arrival angle theta = [psi ₁ next to the incoming wave and the received power of the directivity of the antenna in the rotation angle alpha = [psi ₁ when only the first arriving wave is _{received, y (ψ 1) = g} ( ψ ₁ −α) c ₁ h (θ−ψ ₁ ) = g (0) c ₁ (25) By transforming the equation, c ₁ = y (ψ ₁ ) / g (0) (26)

Ψ obtained in the first processing step
_When y (α) −c ₁ g (ψ ₁ −α) (27) is calculated using ₁ and c ₁ , this value is obtained from the measured value of the antenna reception power in FIG. Is subtracted from the reception power of the antenna when it is assumed that only the arriving wave has been received, and the value is 0 at the arrival angle α = ψ1 of the _first arriving wave. As a result, the peak of the first arriving wave having the largest received power is removed from the measured value y (α) of the antenna received power.

Then, as a second step, (2
As shown in equation (7), the reception power of the difference obtained by subtracting the reception power of the directional antenna when only the first arriving wave is received from the measured value of the antenna reception power is:
The rotation angle α at the maximum value is the arrival angle ψ2 of the second arriving wave having the next highest received power, and the difference of the received power is that when only the second arriving wave is received. It is assumed that it is equal to the reception power of the antenna.

That is, assuming that the rotation angle α when the difference received power has the highest value is ψ2, the maximum value y (ψ
₂ ), y (ψ ₂ ) −c ₁ g (ψ ₁ −ψ ₂ ) = g (ψ ₁ −α) c ₂ h (θ−ψ ₂ ) = g (0) c ₂ (28) When deformed, c ₂ = {y (ψ ₂ ) −c ₁ g (ψ ₁ −ψ ₂ )} / g (0) (29)

The value obtained by the second processing step is as follows:
Using ψ ₁ , ψ ₂ and c ₁ , c ₂ , y (α) −c ₁ · g (ψ ₁ −α) −c ₂ · g (ψ ₂ −α) (30) The value is such that the largest peak and the next largest peak are removed from y (α).

When this process is repeated, the last N-th process is as follows. Using ψ ₁ , ψ ₂ ,..., Ψ _N-1 and c ₁ , c ₂ ,..., C _N-1 obtained in the processing up to the (N−1) th processing, y (α) − ｛c ₁ · g ( ψ ₁ −α) + c ₂ · g (ψ ₂ −α) +... + c _N−1 · g (ψ _N-1 −α)｝ The value of α when the value of (31) is the maximum is denoted by ψ _N I do.

The contrast value y (ψ _N) of the maximum _{value, y (ψ N) - {} c 1 g (ψ 1 -ψ N) + c 2 g (ψ 2 -ψ N) + ... + c N-1 g (Ψ _N−1 −ψ _N )｝ = g (ψ _N− α) c _N h (θ−ψ _N ) = g (0) c _N (32) When deformed, c _N = [y (ψ _N ) − {C ₁ g (ψ ₁ −ψ _N ) + c ₂ g (ψ ₂ −ψ _N ) +... + C _N−1 g (ψ _N−1 −ψ _N )}] / g (0) (33) Become.

By the above processing, y (α) = c ₁ · g (ψ ₁ -α) + c ₂ · g (ψ ₂ -α) +... + C _N · g (ψ _N -α) (34) be able to. Equation (34) indicates that each c _i · (ψ _i −
α) is the arriving wave c _i h of the received power c _i of the i-th magnitude
(Θ-ψ _i) it is, represents the received power at the output end of the directional antenna when arriving at the arrival angle [psi _i, whole expression, respectively power c _1, c _2, ..., multiple waves of c _N Is the angle of arrival ψ ₁ ,
ψ ₂ , ..., ψ _N represents the case of arrival.

Next, with reference to FIG. 3 and FIG. 4, a simulation result using the embodiment of the incoming wave measuring method of the present invention will be described. FIG. 3 shows an antenna gain pattern converted into a logarithmic representation. In the figure, the horizontal axis represents the angle of the rotation angle α of the directional antenna 1, and the vertical axis represents the antenna gain. FIG.
FIG. 4 is a diagram illustrating an example of analyzing an incoming wave assuming a measurement result of the reception power measurement device. In the figure, the horizontal axis indicates the angle of the rotation angle α of the directional antenna 1, and the vertical axis indicates the reception level in dBm. 0 dBm corresponds to 1 mW of power.

In this simulation, assuming that the result measured by the signal level measuring device 3 with respect to the antenna gain pattern shown in FIG. Is an analysis of Here, each of the three arriving waves is a pseudo random signal 1b.
It is assumed that the time has arrived with a delay of at least it. The first arriving wave is at a level of +3 dBm from the angle of + 1.0 °, and the second arriving wave is at -10 dB from the angle of −1.5 °.
At the level of m, the third arriving wave arrives at the level of 0 dBm from the angle of + 22.5 °.

The first to third arriving waves are theoretically given by logarithmically expressing the following equation. y (α) = 0.1 g (−1.5−α) +2.0 g (+ 1.0−α) +1.0 g (+ 22.5−α) + measurement error (mW) (35) The value of the error is a case where the number of significant digits of y (α) is two.

The analysis means 6 solves GX = Y (Equation 4) for X. As the analysis means 6, the method of the first embodiment of the incoming wave measurement method of the present invention was analyzed using a general-purpose computer. The analysis was performed for α and θ in FIG.
° step. That is, the analysis is performed with M = 360. The analysis result for the arriving wave shown in FIG. 4 (indicated by a thick solid line with ● in the figure) is -10d
It represents that three incoming waves are reproduced above B. For example, the level of the incoming wave for an angle of -1.5 [deg.] Is about 0.
Although an error of about 4 dB occurs, there is no practical problem. Also,
It appears that a plurality of arriving waves exist around -20 dB, but this is a false arriving wave generated because the number of significant digits is set to two as a measurement error. This spurious incoming wave is of a sufficiently low level and does not pose a practical problem. When the arriving wave is analyzed, the same calculation is repeated N times. When the reliable arriving wave is no longer output, the calculation may be stopped.

In FIG. 4, the curve shown by the thin solid line is
This is a reception pattern reproduced based on the analysis result. It turns out that it is very close to the measurement result shown by □. Moreover, only from the measurement results indicated by □, -10 dB at an angle of -1.5 °
The existence of an incoming wave near m is not identified, but the presence of the incoming wave is clearly seen from the analysis result by the method of the present invention.

As described above, if the arriving wave measuring method of the present invention is used, the angle of the arriving wave, the received power, and the number of arriving waves can be obtained with high accuracy even if the directivity of the antenna is not so sharp. As a result, for example, when the present invention is applied using a parabolic antenna having a half-value angle of about 5 °, the influence of the sub-lobe is reduced even though the sub-lobe is about 14 dB below the main lobe, and there is no practical problem. An incoming wave can be determined. This means that relatively high accuracy can be obtained even when an antenna having a large half-value angle θ ₀ is used, and high accuracy can be realized even when a small antenna is used. Therefore, since a small antenna can be used, it is possible to rotate the antenna at a higher speed than in a change in the surrounding radio wave environment. In other words, if you use an antenna that rotates at a high speed,
Changes in the surrounding radio environment can be considered as stationary,
It is also possible to accurately measure the time characteristic of an incoming wave that constantly changes under the influence of a moving vehicle or the like.

In the present invention, the rotation angle of the directional antenna 1 is considered two-dimensionally and only one of the azimuth angle and the elevation angle is changed. Exactly the same method can be applied. In this case, it is preferable to stop the change of one angle, change the other angle and perform the processing according to the present invention, and then change the stopped angle and repeat the same processing.

As can be seen from the above analysis, in the arriving wave measuring method of the present invention, even when a measurement error is involved, the analysis result does not diverge abnormally and becomes negative power. Inconvenience is not caused, and a result having no practical problem can be obtained.

[0059]

As is apparent from the above description, the arriving wave measuring method and arriving wave measuring apparatus according to the present invention have an effect that the arriving angle and the like of the arriving wave satisfying the physical conditions can be measured. . There is an effect that the angle of arrival, the level, the number of incoming waves, and the like of the incoming waves can be measured with extremely high accuracy with a low-cost and relatively simple configuration. Also, when using a parabolic antenna, etc.
An incoming wave can be identified with a resolution higher than an order of magnitude. Moreover, in the analysis of the measurement result, there are no problems such as a negative power or a divergence of the solution. In addition, a small antenna can be used to enable measurements with high accuracy,
In this case, by rotating the small antenna at a higher speed than the change in the surroundings, it is possible to catch the temporal change of the arriving wave.

[Brief description of the drawings]

FIG. 1 is a block diagram for explaining a first embodiment of an incoming wave measurement method of the present invention.

FIG. 2 is a schematic diagram for explaining the principle of an embodiment of an incoming wave measurement method of the present invention.

FIG. 3 is a diagram of a logarithmic antenna gain pattern.

FIG. 4 is a diagram showing an example in which an incoming wave is analyzed assuming a measurement result of the reception power measuring device.

[Explanation of symbols]

REFERENCE SIGNS LIST 1 directional antenna, 2 turntable, 3 received power measuring device, 4 first storage unit, 5 second storage unit, 6 analysis unit

Continuation of the front page (56) References JP-A-11-142497 (JP, A) JP-A-11-52037 (JP, A) JP-A-11-38058 (JP, A) JP-A-11-23688 (JP, A) JP-A-8-201498 (JP, A) JP-A-7-140221 (JP, A) JP-A-5-259727 (JP, A) Patent 2991234 (JP, B1) (58) Int.Cl. ⁷ , DB name) G01S 3/00-3/76 H04B 17/00

Claims (6)

(57) [Claims] 1. A directional antenna is rotated and transmitted from a transmitting side.
Receives the radio wave modulated by the transmitted pseudo random signal
At least the angle of arrival θ of one or more arriving waves
An arriving wave measuring method, wherein the number of measurement sections is M for the rotation angle α of the directional antenna.
Is divided into small sections of
The correspondingly assigned rotation angle α_j(J = 1 to M)
And the reception power y of the reception signal of the directional antenna.
(Α_j) Is measured, and with respect to the angle of arrival θ, there are M measurement sections of the angle of arrival θ.
It is divided into minute sections, and the i-th pair of each minute section
Angle θ assigned_i(I = 1 to M), and
The rotation angle α_jFor the angle θ_i−α_jSaid orientation in
G (θ_i−α_j), The first matrix Y is given by:And the second matrix G is given by:And the angle of arrival θ_iX (θ_i), And the third matrix X is given by:An equation represented by GX = Y is given by
The power x (θ) of the arriving wave at the angle of arrival θ is represented by N
The number of arriving waves, N,₁, Power c₁Incoming waves,
No, the angle of arrival ψ_N, Power c_NX (θ) = c₁h (θ-ψ₁) + C_Twoh (θ-ψ_Two) +…
 + C_Nh (θ-ψ_N) However,It is assumed that the directional antenna is
Received power y (α _j) Is the y obtained by the measurement.
(Α) so as to approximate the value of (α)
c₁, Ψ₁And sequentially, c_N, Ψ_NArriving wave measurement method. 2. The method according to claim 1, wherein₁, Ψ₁And sequentially, c_N, Ψ_NMa
X (θ) as the first processing step of the processing for obtaining
= C₁h (θ-ψ₁), The equation represented by GX = Y is calculated, and the calculation result is obtained.
Y (α) is given by y ₁(Α)
Δy relating to the difference from the obtained value of y (α)₁= ｛Y₁(Α₁) -Y (α₁)｝^Two+ ｛Y₁(Α_Two)-
y (α_Two)｝^Two+ ... + y₁(Α_M) -Y (α_M)｝^Two C when is minimum₁, Ψ₁To c₁Under the condition of ≧ 0
X (θ) = c as a second processing step_Twoh (θ−
ψ_Two), The equation represented by GX = Y is calculated, and the calculation result is obtained.
Y (α) is given by y _Two(Α) and y_Two(Α) already
Calculated y₁(Α) and the above measurement
The value Δy relating to the difference from the obtained value of y (α)_Two= ｛Y₁(Α₁) + Y_Two(Α₁) -Y (α₁)｝^Two+
｛Y₁(Α_Two) + Y_Two(Α_Two) -Y (α_Two)｝^Two+ ... + ｛y
₁(Α_M) + Y_Two(Α_M) -Y (α_M)｝^Two C when is minimum_Two, Ψ_TwoTo c_TwoUnder the condition of ≧ 0
Thereafter, this is repeated until the Nth processing step.
In the Nth processing step, x (θ) = c_Nh (θ
−ψ_N), The equation represented by GX = Y is calculated, and the calculation result is obtained.
Y (α) is given by y _N(Α) and y_N(Α) already
Calculated y₁(Α) or y_N-1(Α) added
And the difference between the value of y (α) obtained by the measurement
Value Δy_N= ｛Y₁(Α₁) + Y_Two(Α₁) + ... + y_N(Α₁)-
y (α₁)｝^Two+ ｛Y₁(Α_Two) + Y_Two(Α_Two) + ... + y
_N(Α_Two) -Y (α_Two)｝^Two+ ... + ｛y₁(Α_M) + Y
_Two(Α_M) + ... + y_N(Α_M) -Y (α_M)｝^Two C when is minimum_N, Ψ_NAnd c_NUnder the condition of ≧ 0
The method for measuring an incoming wave according to claim 1, further comprising the step of: 3. The first processing step of obtaining c ₁ and ψ ₁ and sequentially obtaining up to c _N and ψ _N is performed when the value of y (α) obtained by the measurement is maximum. Is set to ψ ₁ and c ₁ = y (ψ ₁ ) / g (0) is obtained. As a second processing step, y (α) −c ₁ g (ψ ₁ −
As ₂ values ψ of alpha when the value of alpha) is maximum, c ₂ =
{Y (ψ ₂ ) −c ₁ g (ψ ₁ −ψ ₂ )} / g (0) is obtained, and thereafter, this is repeated until the Nth processing step. As the Nth processing step, y (Α) − ｛c ₁ g (ψ ₁ −α) + c ₂ g (ψ ₂ −α) +
... Α at which the value of + c _N-1 g ({ _N-1 −α)} becomes maximum
Values for the [psi _{N of, c N = [y (ψ} N) - {c 1 g (ψ 1 -ψ N) + c 2 g (ψ 2
−ψ _N ) +... + C _N-1 g (ψ _N-1 −ψ _N )｝] / g (0)
The method according to claim 1, further comprising the step of: 4. The directional antenna is rotated and transmitted from the transmitting side.
Receives the radio wave modulated by the transmitted pseudo random signal
At least the angle of arrival θ of one or more arriving waves
Arrival wave measuring device for the directional antenna, regarding the rotation angle α, the rotation angle α
The measurement section is divided into M minute sections, and each minute section
Rotation angle α assigned corresponding to the j-th section_j(J
= 1 to M), the measured reception of the directional antenna
Received power y (α_j) Is input and stored. Regarding the angle of arrival θ, the number of measurement sections of the angle of arrival θ is M
It is divided into minute sections, and the i-th pair of each minute section
Angle θ assigned accordingly_i(I = 1 to M), and
And the rotation angle α_jFor the angle θ_i−α_jSaid in
The gain g of the directional antenna (θ_i−α_j) Output means,
And the first matrix Y isAnd the second matrix G is given by:And the angle of arrival θ_iX (θ_i), And the third matrix X is given by:An equation represented by GX = Y is given by
And computing means that solves the power x (θ) of the arriving wave at the arriving angle θ.
Let N be the incoming wave, and the angle of arrival ψ₁, Power c₁The arrival of
Wave, or angle of arrival ψ_N, Power c_NWhen the arrival wave of
x (θ) = c₁h (θ-ψ₁) + C_Twoh (θ-ψ_Two) +…
 + C_Nh (θ-ψ_N) However,It is assumed that the directional antenna is
Received power y (α _j) Is the y obtained by the measurement.
(Α) so as to approximate the value of (α)
c₁, Ψ₁And sequentially, c_N, Ψ_NUp to
A arriving wave measuring device, characterized in that: 5. The method according to claim 1, wherein₁, Ψ₁And sequentially, c_N, Ψ_NMa
The first processing means for executing the processing for obtaining
= C₁h (θ-ψ₁), The equation represented by GX = Y is calculated, and the calculation result is obtained.
Y (α) is given by y ₁(Α)
Δy relating to the difference from the obtained value of y (α)₁= ｛Y₁(Α₁) -Y (α₁)｝^Two+ ｛Y₁(Α_Two)-
y (α_Two)｝^Two+ ... + ｛y₁(Α_M) -Y (α_M)｝^Two C when is minimum₁, Ψ₁To c₁Under the condition of ≧ 0
The second processing means is x (θ) = c_Twoh (θ-ψ_Two)age
Then, the equation expressed by GX = Y is calculated, and the calculation result is obtained.
Y (α) is given by y _Two(Α) and y_Two(Α) already
Calculated y₁(Α) and the above measurement
Δy related to the difference from the obtained value of y (α)_Two= ｛Y₁(Α₁) + Y_Two(Α₁) -Y (α₁)｝^Two+
｛Y₁(Α_Two) + Y_Two(Α_Two) -Y (α_Two)｝^Two+ ... + ｛y
₁(Α_M) + Y_Two(Α_M) -Y (α_M)｝^Two C when is minimum_Two, Ψ_TwoTo c_TwoUnder the condition of ≧ 0
And repeat this until the Nth processing means
And the N-th processing means calculates x (θ) = c_Nh (θ
−ψ_N), The equation represented by GX = Y is calculated, and the calculation result is obtained.
Y (α) is given by y _N(Α) and y_N(Α) already
Calculated y₁(Α) or y_N-1(Α) added
And the difference between the value of y (α) obtained by the measurement
Value Δy_N= ｛Y₁(Α₁) + Y_Two(Α₁) + ... + y_N(Α₁)-
y (α₁)｝^Two+ ｛Y₁(Α_Two) + Y_Two(Α_Two) + ... + y
_N(Α_Two) -Y (α_Two)｝^Two+ ... + ｛y₁(Α_M) + Y
_Two(Α_M) + ... + y_N(Α_M) -Y (α_M)｝^Two C when is minimum_N, Ψ_NAnd c_NUnder the condition of ≧ 0
5. The method according to claim 4, wherein
Arrival wave measuring device. 6. The c ₁ and ψ ₁ are obtained, and c _N and ψ _N are sequentially determined.
The first processing means for executing the processing of determining the value of ま で₁ , where の₁ is the value of α when the value of y (α) obtained by the measurement is the maximum, is c ₁ = y (ψ ₁ ) / g. The second processing means calculates the value of α when the value of y (α) −c ₁ g (ψ ₁ −α) is the maximum as ψ ₂ , and c ₂ = ｛ y (ψ ₂ ) −c ₁ g (ψ ₁ −ψ ₂ )} / g (0) is obtained, and this is executed up to the Nth processing means. The Nth processing means (Α)-｛c ₁ g (ψ ₁ -α)
+ C ₂ g (ψ ₂ −α) +... + C _N−1 g ({ _N−1 −α)} The value of α when the value is the maximum is defined as ψ _N , and c _N = [y (ψ _N ) − ｛C ₁ g (ψ ₁ −ψ _N ) + c ₂ g (ψ ₂
−ψ _N ) +... + C _N-1 g (ψ _N-1 −ψ _N )｝] / g (0)
The arriving wave measuring apparatus according to claim 4, wherein: