Apparatus and method for controlling array antenna comprising a plurality of antenna elements with improved incoming beam tracking

In an apparatus and method for controlling an array antenna comprising a plurality of antenna elements arranged so as to be adjacent to each other in a predetermined arrangement configuration, a plurality of received signals received by the antenna elements is transformed into respective pairs of quadrature baseband signals, using a common local oscillation signal, wherein each pair of quadrature baseband signals is orthogonal to each other. Then predetermined first and second data are calculated based on each pair of transformed quadrature baseband signals, and are filtered using a noise suppressing filter. Respective elements of a transformation matrix for in-phase combining are calculated based on the filtered first and second data, and the received signals obtained from the each two antenna elements are put in phase based on the calculated transformation matrix. Thereafter, a plurality of received signals which are put in phase are combined in phase, and an in-phase combined received signal is outputted.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an apparatus and method for controlling an 
array antenna for use in communications, and in particular, to an 
apparatus and method for controlling an array antenna comprising a 
plurality of antenna elements with improved incoming beam tracking. 
2. Description of the Related Art 
There has been produced on trial a phased array antenna for use in 
satellite communications that is installed in a vehicle or the like and 
automatically tracks the direction of a geostationary satellite by 
Communications Research Laboratory of Japanese Ministry of Posts and 
Telecommunications, wherein the phase array antenna is referred to as the 
first prior art hereinafter. The phased array antenna of the first prior 
art is comprised of nineteen microstrip antenna elements, and is equipped 
with a total of eighteen microwave phase shifters each provided for each 
element except for one element so as to electrically scan the direction of 
a beam without any mechanical drive. In this case, there is provided a 
magnetic sensor that detects the direction of geomagnetism and calculates 
the direction of the geostationary satellite when seen from a vehicle, of 
which position has been previously known, serving as a sensor for 
controlling the directivity of the antenna and tracking the direction of 
an incoming beam as well as an optical fiber gyro that detects a 
rotational angular velocity of the vehicle and constantly keeps the 
direction of the beam with high accuracy. By combining these two sensors, 
the antenna directivity is directed to a predetermined direction 
regardless of the presence or absence of an incoming beam, so that the 
directivity is always kept constantly in an identical direction even when 
the vehicle moves. 
Furthermore, for a digital beam forming antenna for satellite communication 
using a digital phase modulation, a phase detection method for acquiring 
and tracking the incoming beam has been proposed by the present applicant, 
wherein the phase detection method is referred to as the second prior art 
hereinafter. The second prior art method is a method implemented by 
providing a carrier wave regenerating circuit employing a costas loop for 
each antenna element of an array antenna, controlling the phase of a 
voltage controlled oscillator (VCO) so that all the elements are put in 
phase, and then obtaining an array output through in-phase combining of 
the resulting signals. Further, according to the above-mentioned method, a 
phase uncertainty takes place at each antenna element in the carrier wave 
regenerating circuit, and consequently a great amount of power loss occurs 
when the signals are combined as they are. Therefore, a pull-in phase is 
detected from a baseband output of each antenna element, and a phase 
correction amount is calculated based on the detected pull-in phase, so 
that the phase uncertainty is corrected by a phase shifter prior to the 
above-mentioned in-phase combining process. According to the second prior 
art method, the directivity of the antenna is automatically directed to 
the incoming beam so long as a signal to be received is a phase-modulated 
wave, and therefore, no special sensor is required for perceiving the 
direction of the incoming beam. 
In the case of the phased array antenna of the first prior art, a magnetic 
sensor capable of detecting an absolute azimuth is used for directing the 
directivity of the antenna toward the satellite. However, in the case of a 
vehicle or the like, the body thereof is made of metal and is often 
magnetized, and this causes an error in the direction of the directivity 
of the antenna. In order to eliminate the above-mentioned problems, it is 
necessary to perform a calibration with magnetic data obtained by rotating 
the antenna by 360 degrees in a broad place free of any magnetized 
structure and so forth. Even though the calibration is effected 
satisfactorily for the achievement of acquiring and tracking of the 
direction of the satellite, the geomagnetism is often disturbed by 
surrounding buildings, the other vehicles and so forth, and therefore, it 
is difficult to track the direction of the incoming beam only by means of 
the magnetic sensor. For the above-mentioned reasons, the tracking is 
performed principally based on data obtained from the optical fiber gyro 
after the direction of the satellite is acquired. However, the optical 
fiber gyro detects only the angular velocity, not the absolute azimuth as 
performed by the magnetic sensor, and therefore, azimuth angle errors 
accumulate. In order to eliminate this problem, there is adopted a method 
of calibrating in a predetermined period the optical fiber gyro based on 
information obtained from the magnetic sensor, however, the control 
algorithm therefor becomes complicated, and also no highly accurate 
control algorithm has been developed yet. 
The phased array antenna of the first prior art has another drawback that, 
though the beam can be directed in the direction of a signal source when 
the direction of the signal source has been already known regardless of 
the presence or absence of the incoming beam, when the direction of the 
signal source has been unknown or the signal source itself moves as in the 
case of a satellite in a low-altitude earth orbit, the satellite cannot be 
tracked except for a case where the movement thereof can be estimated. As 
described above, the acquiring and tracking method utilizing an azimuth 
sensor has had such a problem that it has a complicated structure and 
limited capabilities. 
Furthermore, in the case of the phase detection method of the second prior 
art, a directivity is formed by regenerating a carrier wave for each 
antenna element. Therefore, the above-mentioned method has the 
advantageous feature that it requires neither an azimuth sensor as 
provided for the phased array antenna of the first prior art nor a 
complicated control algorithm. However, the carrier wave regenerating 
circuit employs a costas loop circuit for effecting phase-synchronized 
tracking in a closed loop, and this causes a problem that a certain time 
is required in achieving convergence in an initial stage of acquiring the 
incoming beam. In particular, when satellite communication is carried out 
with the antenna installed in a mobile body such as a vehicle, signal 
interruption frequently occurs due to trees, buildings and so forth, and 
therefore, the initial acquisition must be performed speedily within 
several symbols of received data. 
The phase detection method of the second prior art has another problem that 
a received signal-to-noise power ratio per antenna element is reduced when 
the array antenna has a great number of antenna elements, and therefore, a 
phase cycle slip occurs at each antenna element, consequently resulting in 
difficulties in regenerating a carrier wave and utilizing the gain of the 
array antenna. 
SUMMARY OF THE INVENTION 
An essential object of the present invention is therefore to provide an 
apparatus for controlling an array antenna, capable of acquiring and 
tracking an incoming beam speedily and stably without any mechanical drive 
nor sensor such as an azimuth sensor even in such a state that a received 
signal-to-noise power ratio at each antenna element is relatively low. 
Another object of the present invention is to provide a method for 
controlling an array antenna, capable of acquiring and tracking an 
incoming beam speedily and stably without any mechanical drive nor sensor 
such as an azimuth sensor even in such a state that a received 
signal-to-noise power ratio at each antenna element is relatively low. 
A further object of the present invention is to provide an apparatus for 
controlling an array antenna, capable of forming a transmitting beam in a 
direction of an the incoming beam based on a received signal at each 
antenna element obtained from an incoming wave transmitted from a signal 
source without using any azimuth sensor or the like even in such a case 
that the direction of the remote station of the other party which serves 
as the signal source has been unknown, and forming a single transmitting 
main beam only in the direction of a greatest received wave even in an 
environment in which a plurality of multi-path waves come or in such a 
case that a phase uncertainty takes place in a reception phase difference. 
A still further object of the present invention is to provide an apparatus 
for controlling an array antenna, capable of forming a transmitting beam 
in a direction of an incoming beam based on a received signal at each 
antenna element obtained from an incoming wave transmitted from a signal 
source without using any azimuth sensor or the like even in such a case 
that the direction of the remote station of the other party which serves 
as the signal source has been unknown, and forming a single transmitting 
main beam only in the direction of a greatest received wave even in an 
environment in which a plurality of multi-path waves come or in such a 
case that a phase uncertainty takes place in a reception phase difference. 
In order to achieve the above-mentioned objective, according to one aspect 
of the present invention, there is provided an apparatus for controlling 
an array antenna comprising a plurality of antenna elements arranged so as 
to be adjacent to each other in a predetermined arrangement configuration, 
said apparatus comprising: 
transforming means for transforming a plurality of received signals 
received by said antenna elements of said array antenna into respective 
pairs of quadrature baseband signals, respectively, using a common local 
oscillation signal, respective quadrature baseband signals of the pairs of 
quadrature baseband signals being orthogonal to each other; 
in-phase putting means, comprising a noise suppressing filter having a 
predetermined transfer function, the in-phase putting means using a 
predetermined first axis and a predetermined second axis which are 
orthogonal to each other and a transformation matrix for putting in phase 
received signals obtained from each two antenna elements of each 
combination of said plurality of antenna elements being expressed by a 
two-by-two transformation matrix including 
(a) second data on said second axis proportional to a product of a sine 
value of a phase difference between the received signals obtained from 
said each two antenna elements of each combination, and respective 
amplitude values of the received signals thereof, and 
(b) first data on said first axis proportional to a product of a cosine 
value of a phase difference between the received signals obtained from 
said each two antenna elements of each combination, and respective 
amplitude values of the received signals thereof, 
said in-phase putting means calculating said first data and said second 
data based on each pair of transformed quadrature baseband signals, 
passing the calculated first data and the calculated second data through 
said noise suppressing filter so as to filter said first and second data 
and output filtered first and second data, calculating respective element 
values of said transformation matrix based on the filtered first data and 
the filtered second data, and putting in phase said received signals 
obtained from said each two antenna elements of each combination based on 
said transformation matrix including said calculated transformation matrix 
elements; and 
combining means for combining in phase said plurality of received signals 
which are put in phase by said in-phase putting means, and outputting an 
in-phase combined received signal. 
In the above-mentioned apparatus, said combining means preferably 
comprises: 
calculating means for calculating respective correction phase amounts such 
that said plurality of received signals are put in phase based on said 
filtered first data and said filtered second data filtered by said 
in-phase putting means; 
first phase shifting means for shifting phases of said plurality of 
received signals respectively based on said respective correction phase 
amounts calculated by said calculating means; and 
first in-phase combining means for combining in phase said plurality of 
received signals whose phases are shifted by said first phase shifting 
means, and outputting an in-phase combined received signal. 
In the above-mentioned apparatus, said combining means preferably further 
comprises: 
correcting means for subjecting said respective correction phase amounts 
calculated by said calculating means to a regression correcting process so 
that, based on said arrangement configuration of said array antenna, said 
respective correction phase amounts are made to regress to a predetermined 
plane of said arrangement configuration, and outputting respective 
regression-corrected correction phase amounts, 
wherein said first phase shifting means shifts the phases of said plurality 
of received signals respectively by said respective regression-corrected 
correction phase amounts outputted from said correcting means. 
In the above-mentioned apparatus, said combining means preferably 
comprises: 
in-phase transforming means for transforming one of respective two received 
signals of each combination of said plurality of received signals so that 
said one of said received signals is put in phase with another one of said 
received signals thereof, using said transformation matrix including said 
transformation matrix elements calculated by said in-phase combining 
means; 
second in-phase combining means for combining in phase said respective two 
received signals of each combination comprised of a received signal which 
is not transformed by said in-phase transforming means, and another 
received signal which is transformed by said in-phase transforming means, 
and outputting an in-phase combined received signal; and 
control means for repeating the processes of said in-phase transforming 
means and said second in-phase combining means until one resulting 
received signal is obtained, and outputting the one resulting received 
signal combined in phase. 
The above-mentioned apparatus preferably further comprises: 
multi-beam forming means operatively provided between said transforming 
means and said in-phase putting means, for calculating a plurality of beam 
electric field values based on said plurality of received signals received 
by respective antenna elements of said array antenna, directions of 
respective main beams of a predetermined plural number of beams to be 
formed which are predetermined so that a desired wave can be received 
within a range of radiation angle, and a predetermined reception frequency 
of said received signals, and outputting a plurality of beam signals 
respectively having said beam electric field values; and 
beam selecting means operatively provided between said transforming means 
and said in-phase putting means, for selecting a predetermined number of 
beam signals having greater beam electric field values including a beam 
signal having a greatest beam electric field value among said plurality of 
beam signals outputted from said multi-beam forming means, and determining 
said beam signal having the greatest beam electric field value to be a 
reference received signal, and 
wherein said in-phase putting means puts in phase with said reference 
received signal, the other ones of said plurality of received signals 
selected by said beam selecting means, using said transformation matrix 
including said calculated transformation matrix elements. 
The above-mentioned apparatus preferably further comprises: 
amplitude correcting means operatively provided at a stage just before said 
combining means, for amplifying said plurality of received signals 
respectively which are put in-phase by said in-phase putting means with a 
plurality of gains proportional to signal levels of said plurality of 
received signals, thereby effecting amplitude correction. 
In the above-mentioned apparatus, said in-phase putting means preferably 
calculates elements of said transformation matrix by directly expressing 
said first data and said second data as the elements of said 
transformation matrix, and puts the other ones of said plurality of 
received signals except for one predetermined received signal in phase 
with said one predetermined received signal, using said transformation 
matrix including said calculated transformation matrix elements. 
In the above-mentioned apparatus, said in-phase putting means preferably 
calculates elements of said transformation matrix by directly expressing 
said first data and said second data as the elements of said 
transformation matrix, and puts respective two received signals of each 
combination in phase with each other, using said transformation matrix 
including said calculated transformation matrix elements. 
The above-mentioned apparatus preferably further comprises: 
distributing means for distributing in phase a transmitting signal into a 
plurality of transmitting signals; 
transmission phase shifting means for shifting phases of said plurality of 
transmitting signals respectively by either one of said respective 
correction phase amounts calculated by said calculating means and said 
respective regression-corrected correction phase amounts outputted from 
said correcting means; and 
transmitting means for transmitting said plurality of transmitting signals 
whose phases are shifted by said transmission phase shifting means, from 
said plurality of antenna elements. 
According to another aspect of the present invention, there is provided a 
method for controlling an array antenna comprising a plurality of antenna 
elements arranged so as to be adjacent to each other in a predetermined 
arrangement configuration, said method including the following steps of: 
transforming a plurality of received signals received by said antenna 
elements of said array antenna into respective pairs of quadrature 
baseband signals, respectively, using a common local oscillation signal 
respective quadrature baseband signals of the pairs of quadrature baseband 
signals being orthogonal to each other; 
putting in-phase received signals obtained from each two antenna elements 
of each combination of said plurality of antenna elements by using a 
predetermined first axis and a predetermined second axis which are 
orthogonal to each other and, a transformation matrix being expressed by a 
two-by-two transformation matrix including 
(a) second data on said second axis proportional to a product of a sine 
value of a phase difference between the received signals obtained from 
said each two antenna elements of each combination, and respective 
amplitude values of the received signals thereof, and 
(b) first data on said first axis proportional to a product of a cosine 
value of a phase difference between the received signals obtained from 
said each two antenna elements of each combination, and respective 
amplitude values of the received signals thereof, 
said step of putting in-phase received signals including calculating said 
first data and said second data based on each pair of transformed 
quadrature baseband signals; 
filtering the calculated first data and the calculated second data with a 
predetermined transfer function so as to provide filtered first and second 
data; 
calculating respective element values of said transformation matrix based 
on the filtered first data and the filtered second data; 
putting in phase said received signals obtained from said each two antenna 
elements of each combination based on said transformation matrix including 
said calculated transformation matrix elements; and 
combining in phase said plurality of received signals which are put in 
phase, and providing an in-phase combined received signal. 
In the above-mentioned method, said combining step preferably includes the 
following steps of: 
calculating respective correction phase amounts such that said plurality of 
received signals are put in phase based on said filtered first data and 
said filtered second data; 
shifting phases of said plurality of received signals respectively by said 
calculated respective correction phase amounts; and 
combining in phase said plurality of received signals whose phases are 
shifted, and providing an in-phase combined received signal. 
In the above-mentioned method, said combining step preferably further 
includes the following steps of: 
subjecting said calculated respective correction phase amounts to a 
regression correcting process so that, based on said arrangement 
configuration of said array antenna, said respective calculated correction 
phase amounts are made to regress to a predetermined plane of said 
arrangement configuration; and 
providing respective regression-corrected correction phase amounts, 
wherein said shifting step includes a step of shifting the phases of said 
plurality of received signals respectively by said respective 
regression-corrected correction phase amounts. 
In the above-mentioned method, said combining step preferably includes the 
following steps of: 
transforming one of respective two received signals of each combination of 
said plurality of received signals so that said one of said received 
signals is put in phase with another one of said received signals thereof, 
using said transformation matrix including said calculated transformation 
matrix elements; 
combining in phase said respective two received signals of each combination 
comprised of a received signal which is not transformed, and another 
received signal which is transformed, and providing an in-phase combined 
received signal; and 
repeating the processes of said transforming step and said combining step 
until one resulting received signal is obtained, and providing the one 
resulting received signal combined in phase. 
The above-mentioned method preferably further includes the following steps 
of: 
after the process of said transforming step and before the process of said 
combining step, calculating a plurality of beam electric field values 
based on said plurality of received signals received by respective antenna 
elements of said array antenna, directions of respective main beams of a 
predetermined plural number of beams to be formed which are predetermined 
so that a desired wave can be received within a range of radiation angle, 
and a predetermined reception frequency of said received signals, and 
providing a plurality of beam signals respectively having said beam 
electric field values; and 
after the processes of said transforming step and said calculating step, 
and before the process of said combining step, selecting a predetermined 
number of beam signals having greater beam electric field values including 
a beam signal having a greatest beam electric field value among said 
plurality of beam signals outputted at said multi-beam forming step, and 
determining said beam signal having the greatest beam electric field value 
to be a reference received signal, and 
wherein said combining step includes a step of putting in phase with said 
reference received signal, the other ones of said plurality of selected 
received signals, using said transformation matrix including said 
calculated transformation matrix elements. 
The above-mentioned method preferably further includes the following step 
of: 
just before the process of said combining step, amplifying said plurality 
of received signals respectively with a plurality of gains proportional to 
signal levels of said plurality of received signals, thereby effecting 
amplitude correction. 
In the above-mentioned method, said putting in phase step preferably 
includes the following steps of: 
calculating elements of said transformation matrix by directly expressing 
said first data and said second data as the elements of said 
transformation matrix; and 
putting the other ones of said plurality of received signals except for one 
predetermined received signal in phase with said one predetermined 
received signal, using said transformation matrix including said 
calculated transformation matrix elements. 
In the above-mentioned method, said putting in phase step preferably 
includes the following steps: 
calculating elements of said transformation matrix by directly expressing 
said first data and said second data as the elements of said 
transformation matrix; and 
putting respective two received signals of each combination in phase with 
each other, using said transformation matrix including said calculated 
transformation matrix elements. 
The above-mentioned method preferably further includes the following steps 
of: 
distributing in phase a transmitting signal into a plurality of 
transmitting signals; 
shifting phases of said plurality of transmitting signals respectively by 
either one of said calculated respective correction phase amounts and said 
respective regression-corrected correction phase amounts; and 
transmitting said plurality of transmitting signals whose phases are 
shifted, from said plurality of antenna elements. 
According to a further aspect of the present invention, there is provided 
an apparatus for controlling an array antenna comprising a plurality of 
antenna elements arranged so as to adjacent to each other in a 
predetermined arrangement configuration, said apparatus comprising: 
transforming means for transforming a plurality of received signals 
received by said antenna elements of said array antenna into respective 
pairs of quadrature baseband signals, using a common local oscillation 
signal, respective quadrature baseband signals of the pairs of quadrature 
baseband signals being orthogonal to each other; 
phase difference calculating means, based on said transformed two 
quadrature baseband signals transformed by said transforming means, for 
calculating the following data: 
(a) first data proportional to a product of a cosine value of a phase 
difference between two received signals obtained from a predetermined 
reference antenna element and another arbitrary antenna element, and 
respective amplitude values of said two received signals thereof, and 
(b) second data proportional to a product of a sine value of a phase 
difference between two received signals obtained from said each two 
antenna elements of each combination, and respective amplitude values of 
said two received signals thereof, and 
for calculating a reception phase difference between said each two antenna 
elements of each combination based on calculated first data and calculated 
second data; 
correcting means for correcting said reception phase difference so that a 
phase uncertainty generated such that the calculated reception phase 
difference between each of said two antenna elements of each combination 
calculated by said phase difference calculating means is limited within a 
range from -.pi. to +.pi. is removed from said reception phase difference, 
according to a predetermined phase threshold value representing a degree 
of disorder of a reception phase difference due to a multi-path wave, and 
for converting a corrected reception phase difference into a transmission 
phase difference by inverting a sign of said corrected reception phase 
difference; and 
transmitting means for transmitting a transmitting signal from said antenna 
elements with the transmission phase difference between said each two 
antenna elements of each combination converted by said correcting means 
and with the same amplitudes, thereby forming a transmitting main beam 
only in a direction of a greatest received signal. 
In the above-mentioned apparatus, said correcting means preferably 
calculates a reception phase difference between adjacent two antenna 
elements of each combination calculates a plurality of equi-phase linear 
regression planes corresponding to all proposed phases of the phase 
uncertainty of the reception phase difference between said two adjacent 
antenna elements of each combination according to a least square method, 
removes said phase uncertainty using a sum of squares of a residual 
between said reception phase difference and each of said equi-phase linear 
regression planes and a gradient coefficient of each of said equi-phase 
linear regression planes, and corrects said reception phase difference by 
specifying only one equi-phase linear regression plane corresponding to 
the greatest received wave. 
In the above-mentioned apparatus, said correcting means preferably derives 
an equation representing said equi-phase linear regression plane 
corresponding to all the proposed phases of said phase uncertainty by 
solving a Wiener-Hopf equation according to the least square method using 
a matrix comprised of reception phase differences corresponding to all the 
proposed phases of the phase uncertainty of the reception phase difference 
between said two adjacent antenna elements of each combination and a 
matrix comprised of position coordinates of the plurality of antenna 
elements of said array antenna, and calculates the plurality of equi-phase 
linear regression planes corresponding to all the proposed phases of said 
phase uncertainty. 
In the above-mentioned apparatus, said correcting means preferably 
determines a transmission phase difference by multiplying a reception 
phase difference calculated from said equi-phase linear regression plane 
from which said phase uncertainty is removed by a ratio of a transmission 
frequency to a reception frequency, thereby converting said reception 
phase difference into said transmission phase difference. 
According to a still further aspect of the present invention, there is 
provided a method for controlling an array antenna comprising a plurality 
of antenna elements arranged so as to adjacent to each other in a 
predetermined arrangement configuration, said method including the 
following steps of: 
transforming a plurality of received signals received by said antenna 
elements of said array antenna into respective pairs of quadrature 
baseband signals, using a common local oscillation signal, respective 
quadrature baseband signals of the pairs of quadrature baseband signals 
being orthogonal to each other; 
based on said transformed two quadrature baseband signals, calculating the 
following data: 
(a) first data proportional to a product of a cosine value of a phase 
difference between two received signals obtained from a predetermined 
reference antenna element and another arbitrary antenna element, and 
respective amplitude values of said two received signals thereof, and 
(b) second data proportional to a product of a sine value of a phase 
difference between two received signals obtained from said each two 
antenna elements of each combination, and respective amplitude values of 
said two received signals thereof; 
calculating a reception phase difference between said each two antenna 
elements of each combination based on calculated first data and calculated 
second data; 
correcting said reception phase difference so that a phase uncertainty 
generated such that the calculated reception phase difference between each 
of said two antenna elements of each combination is limited within a range 
from -.pi. to +.pi.0 is removed from said reception phase difference, 
according to a predetermined phase threshold value representing a degree 
of disorder of a reception phase difference due to a multi-path wave; 
converting a corrected reception phase difference into a transmission phase 
difference by inverting a sign of said corrected reception phase 
difference; and 
transmitting a transmitting signal from said antenna elements with said 
converted transmission phase difference between said each two antenna 
elements of each combination and with the same amplitudes, thereby forming 
a transmitting main beam only in a direction of a greatest received 
signal. 
In the above-mentioned method, said correcting step preferably includes the 
following steps of: 
calculating a reception phase difference between adjacent two antenna 
elements of each combination based on said calculated reception phase 
difference between said two antenna elements of each combination; 
calculating a plurality of equi-phase linear regression planes 
corresponding to all proposed phases of the phase uncertainty of the 
reception phase difference between said two adjacent antenna elements of 
each combination according to a least square method; 
removing said phase uncertainty using a sum of squares of a residual 
between said reception phase difference and each of said equi-phase linear 
regression planes and a gradient coefficient of each of said equi-phase 
linear regression planes; and 
correcting said reception phase difference by specifying only one 
equi-phase linear regression plane corresponding to the greatest received 
wave. 
In the above-mentioned method, said correcting step preferably includes the 
following steps of: 
deriving an equation representing said equi-phase linear regression plane 
corresponding to all the proposed phases of said phase uncertainty by 
solving a Wiener-Hopf equation according to the least square method using 
a matrix comprised of reception phase differences corresponding to all the 
proposed phases of the phase uncertainty of the reception phase difference 
between said two adjacent antenna elements of each combination and a 
matrix comprised of position coordinates of the plurality of antenna 
elements of said array antenna; and 
calculating the plurality of equi-phase linear regression planes 
corresponding to all the proposed phases of said phase uncertainty. 
In the above-mentioned method, said correcting step preferably includes a 
step of determining a transmission phase difference by multiplying a 
reception phase difference calculated from said equi-phase linear 
regression plane from which said phase uncertainty is removed by a ratio 
of a transmission frequency to a reception frequency, thereby converting 
said reception phase difference into said transmission phase difference. 
Accordingly, the first present invention have distinctive advantageous 
effects as follows. 
(1) Since no such feedback loop as in the second prior art is included, 
even when the carrier signal power to noise power ratio C/N per antenna 
element is relatively low, the incoming signal beam of a radio signal can 
be acquired automatically and rapidly without using any specific direction 
sensor, position data of the remote station of the other party, nor the 
like. Therefore, if a momentary interruption of the signal beam due to an 
obstacle or the like takes place, data to be lost can be suppressed in 
amount to the minimum. Further, in a burst mode communication system such 
as packet communication, a reduced preamble length can be achieved. 
Furthermore, for example, a received signal modulated with communication 
data can be directly used. Therefore, neither special training signal nor 
reference signal for effecting phase control is required, allowing the 
system construction to be simplified. 
(2) Since no such feedback loop as in the second prior art is included, 
even when the carrier signal power to noise power ratio C/N per antenna 
element is relatively low and the direction of an incoming signal beam 
changes rapidly, no phase slip occurs. Furthermore, since no such azimuth 
sensor as in the first prior art is provided, the apparatus is free of 
influence of external disturbance due to disarray of environmental lines 
of magnetic force and accumulation of tracking error. Therefore, an 
incoming signal beam of a radio signal can be tracked stably with high 
accuracy and, for example, quality of mobile communication can be 
improved. Furthermore, not only when the self-station moves but also when 
the remote station of the other party moves, the remote station of the 
other party can be tracked without any special information about the 
position of the remote station of the other party. Furthermore, in a burst 
mode communication system such as packet communication, a change of the 
direction of the incoming beam cannot be tracked in the course of burst 
according to a tracking system using a training signal (preamble). 
However, for example, a received signal modulated with communication data 
can be directly used in the present control apparatus, and therefore 
real-time tracking can be achieved even in the course of burst. 
Furthermore, based on the arrangement configuration of the array antenna, 
the calculated correction phase amount is subjected to the regression 
correction process so that the calculated correction phase amount is made 
to regress to the plane of the arrangement configuration, and the phases 
of the plurality of received signals are each shifted by the correction 
phase amount based on the correction phase amount obtained through the 
regression correction process. With the above-mentioned arrangement, the 
spatial information of the array antenna can be effectively utilized, so 
that the influence of the reduction of the carrier signal power to noise 
power ratio C/N per antenna element, which is problematic when a great 
number of antenna elements are employed, can be suppressed, thereby 
preventing the possible deterioration of the tracking characteristic and 
quality of communication. 
Furthermore, when the plurality of received signals are combined in phase 
to output the resulting received signal, by transforming one of two 
received signals of the plurality of received signals so that it is put in 
phase with the other received signal by means of a transformation matrix 
including the calculated transformation matrix elements, combining in 
phase two received signals of each combination of the received signal that 
is not transformed and the received signal that is transformed, and 
repeating the above-mentioned calculation, transformation and in-phase 
combining processes until the received signal obtained through the 
in-phase combining process is reduced in number to one, then the one 
received signal combined in phase is outputted. That is, the in-phase 
combining process is effected between the two element systems in advance 
without calculating a phase difference between adjacent antenna elements. 
Therefore, if there is an antenna element having a low reception level or 
a defective antenna element, the above-mentioned defect can be prevented 
from affecting the in-phase combining in the other antenna element 
systems. Therefore, it can be said that the present apparatus of the 
present invention has a tolerance to failure or the like of the antenna 
elements and the circuit devices connected thereto. 
Furthermore, just before the first data and the second data are calculated 
based on two transformed quadrature baseband signals of each combination, 
based on the plurality of received signals received by the antenna 
elements of the array antenna, the direction of each main beam of the 
predetermined plural number of beams to be formed predetermined so that 
the desired wave can be received within a predetermined range of radiation 
angle, and the predetermined reception frequency of the received signals, 
the following operations are performed. The plurality of beam electric 
field values are calculated so as to output a plurality of beam signals 
having the respective beam electric field values, and a predetermined 
number of beam signals having greater beam electric field values including 
the beam signal having the greatest beam electric field value among the 
plurality of outputted beam signals are selected. Then, the beam signal 
having the greatest beam electric field value is used as a reference 
received signal, a plurality of other selected received signals are put in 
phase with the reference received signal by means of a transformation 
matrix including the calculated transformation matrix elements, and the 
plurality of received signals are combined in phase with each other so as 
to output the resulting received signal. That is, the phase difference 
correction is effected after a beam signal having a high received signal 
to noise power ratio is formed through multi-beam formation and beam 
selection. Therefore, no influence is exerted on the phase difference 
correction accuracy even if the received signal to noise power ratio of 
each antenna element is relatively low, this means that there is 
theoretically no upper limit in number of antenna elements. Furthermore, 
when an intense interference wave or the like comes in another direction, 
such waves are spatially separated to a certain extent through beam 
selection, and this produces the effect that the apparatus is less 
susceptible to the interference waves. 
Furthermore, by amplifying the plurality of received signals with a 
plurality of gains direct proportional to the signal levels of the 
plurality of received signals before the in-phase combining process, there 
is effected amplitude correction or automatic amplitude correction. 
Therefore, the received signal having a deteriorated signal quality 
contributes less to the in-phase combining process. Therefore, even when 
there is a difference in received signal intensity between antenna 
elements owing to shadowing due to obstacles, fading due to reflection 
from buildings and the like, the possible lowering of the received signal 
to noise power ratio after the in-phase combining process can be 
suppressed, and deterioration in quality of communication can be 
prevented. 
Further, the first data and the second data are directly expressed as 
elements of the transformation matrix, and the elements of the 
transformation matrix are calculated. Otherwise, other received signals of 
the plurality of received signals except for one predetermined received 
signal are further put in phase with the one predetermined received signal 
by means of a transformation matrix including the calculated 
transformation matrix elements, the predetermined one received signal is 
combined in phase with the plurality of received signals put in phase, and 
the resulting received signal is outputted. With the above-mentioned 
operation or calculation, calculation of the elements of the 
transformation matrix used in effecting the in-phase combining process is 
remarkably simplified with a simplified circuit construction, thereby 
allowing the control apparatus to be compacted and reduced in weight. 
Furthermore, the transmitting signal is distributed in phase into a 
plurality of transmitting signals, and the phases of the plurality of 
transmitting signals are shifted by the respective calculated correction 
phase amounts or the regression-corrected correction phase amounts, and 
the resulting transmitting signals are transmitted from the plurality of 
antenna elements. Therefore, the transmitting beam can be automatically 
directed to the direction of the incoming beam, so that a transmitting 
antenna use beam forming apparatus can be simply constructed. 
Furthermore, the first present invention have further distinctive 
advantageous effects as follows. 
(1) The above-mentioned operations or calculations can be effected no 
matter whether the intervals of the arrangement of the antenna elements 
are regular intervals or irregular intervals and no matter whether the 
antenna plane is a flat plane or a curved plane. Accordingly, there is a 
great degree of freedom in regard to the arrangement of the antenna 
elements, so that an array antenna construction conforming to the 
configuration of each mobile body can be achieved. 
(2) The above-mentioned acquisition and tracking operations are all 
effected on the received signals by signal processing such as digital 
signal processing. The above-mentioned arrangement obviates the need of 
any such devices as microwave shifters corresponding in number to the 
antenna elements, sensors for acquisition and tracking and a motor for 
mechanical drive, thereby allowing the control apparatus to be compacted 
and inexpensive. 
Further, the second present invention has distinctive advantageous effects 
as follows. 
(1) Since neither a special azimuth sensor nor position data of the remote 
station of the other party as in the first prior art is required, the 
present apparatus receives no influence of the environmental magnetic 
turbulence, accumulation of azimuth detection errors and the like. 
Further, when the remote station of the other party moves, a transmitting 
beam can be automatically formed in the direction of the incoming wave 
transmitted from the remote station of the other party, while allowing 
downsizing and cost reduction to be achieved. 
(2) Instead of directly frequency-converting the reception phase difference 
of the reception antenna to make it a transmission phase difference as in 
the second prior art, the removal of the phase uncertainty is effected 
based on the least square method and the influence of the multi-path waves 
except for the greatest received wave is removed. Therefore, even when the 
greatest received wave comes in whichever direction in the multi-path wave 
environment, the transmitting beam can be surely formed in the direction 
in which the greatest received wave comes. Furthermore, even when there is 
a difference between the transmission frequency and the reception 
frequency, the possible interference exerted on the remote station of the 
other party can be reduced. 
(3) There can be achieved a construction free of any mechanical drive 
section for the antenna and any feedback loop in forming the transmitting 
beam. Therefore, upon obtaining a received baseband signal, the 
transmission weight can be immediately decided, so that the transmitting 
beam can be formed rapidly in real time. 
(4) The determination of the transmission weight can be executed in a 
digital signal processing manner. Therefore, by executing the transmitting 
beam formation in a digital signal processing manner, the baseband 
processing including modulation can be entirely integrated into a digital 
signal processor. When a device having a high degree of integration is 
used, the entire system can be compacted with cost reduction.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Preferred embodiments of the present invention will be described below with 
reference to the accompanying drawings. 
First preferred embodiment 
FIG. 1 is a block diagram of a receiver section of an automatic beam 
acquiring and tracking apparatus of an array antenna for use in 
communications according to the first preferred embodiment of the present 
invention. 
Referring to FIG. 1, according to the automatic beam acquiring and tracking 
apparatus of the array antenna for use in communications of the present 
preferred embodiment, a directivity of an array antenna 1 comprised of a 
plurality of N antenna elements A1, A2, . . . , Ai, . . . , AN arranged 
adjacently at predetermined intervals in an arbitrary flat plane or a 
curved plane is rapidly directed to a direction in which a radio signal 
wave such as a digital phase modulation wave or an unmodulated wave comes 
so as to perform tracking. In this case, in particular, the acquiring and 
tracking apparatus of the present preferred embodiment is characterized in 
comprising quasi-synchronous detectors QD-1 through QD- N and amplitude 
and phase difference correcting circuits PC-1 through PC-N. 
As shown in FIG. 1, the array antenna 1 is provided with N antenna elements 
A1 through AN and circulators CI-1 through CI-N which serve as 
transmission and reception separators. Further, each of receiver modules 
RM-1 through RM-N comprises a low-noise amplifier 2 and a down converter 
(D/C) 3 which frequency-converts a radio signal having a received radio 
frequency into an intermediate frequency signal having a predetermined 
intermediate frequency by means of a common first local oscillation signal 
outputted from a first local oscillator 11. 
The receiver section of the acquiring and tracking apparatus further 
comprises: 
(a) N analog-to-digital converters (referred to as A/D converters 
hereinafter) AD-1 through AD-N; 
(b) N quasi-synchronous detectors QD-1 through QD-N, each of which subjects 
each intermediate frequency signal obtained through an analog-to-digital 
conversion process (referred to an A/D conversion process hereinafter) to 
a quasi-synchronous detection process by means of a common second local 
oscillation signal outputted from a second local oscillator 12, and then 
converts the resulting signal into a pair of baseband signals orthogonal 
to each other, wherein a pair of baseband signals is referred to as 
quadrature baseband signals hereinafter; 
(c) N amplitude and phase difference correcting circuits PC-1 through PC-N, 
each of which calculates a phase difference estimation value between 
adjacent antenna elements of each combination and an intensity of a signal 
received by each of the antenna elements A1 through AN by means of the 
converted quadrature baseband signals, and then, executes an amplitude and 
phase correcting process for each of the antenna elements A1 through AN so 
as to effect weighting on all baseband signals so as to put the signals in 
phase; 
an in-phase combiner 4 which combines in phase output signals from the 
amplitude and phase difference correcting circuits PC-1 through PC-N; and 
a demodulator 5 which effects synchronous detection or delayed detection on 
a baseband signal outputted from the in-phase combiner 4 in a 
predetermined baseband demodulation process, extracts desired digital data 
therefrom, and then outputs the digital data as received data. 
In the above-mentioned receiver section, lines extending from the antenna 
elements A1 through AN of the array antenna 1 to the amplitude and phase 
difference correcting circuits PC-1 through PC-N are connected in series 
every antenna element system. The signal processings for respective 
antenna element systems of the receiver section are executed in a similar 
manner to that of one another, and therefore, the processing of the radio 
signal wave received by the antenna element Ai will be described. 
The radio signal wave received by the antenna element Ai is inputted to the 
down converter 3 via the circulator CI-i and the low-noise amplifier 2 of 
the receiver module RM-i. The down converter 3 of the receiver module RM-i 
frequency-converts the inputted radio signal into an intermediate 
frequency signal having the predetermined intermediate frequency using the 
common first local oscillation signal outputted from the first local 
oscillator 11, and then outputs the resulting signal to the 
quasi-synchronous detector QD-i via the A/D converter AD-i. The 
quasi-synchronous detector QD-i subjects the inputted intermediate 
frequency signal obtained through the A/D conversion process to a 
quasi-synchronous detection process using the common second local 
oscillation signal outputted from the second local oscillator 12 so as to 
convert the signal into each pair of quadrature baseband signals I.sub.i 
and Q.sub.i orthogonal to each other, and then outputs the signals to the 
amplitude and phase difference correcting circuit C-i and the adjacent 
amplitude and phase difference correcting circuit PC-(i+1). The amplitude 
and phase difference correcting circuit PC-i calculates a phase difference 
estimation value .delta.c.sub.i-1,i between adjacent antenna elements and 
the intensity of the signal received by each of the antenna elements A1 
through AN by means of the inputted quadrature baseband signals I.sub.i 
and Q.sub.i and quadrature baseband signals I.sub.i-1 and Q.sub.i-1 of an 
antenna element A-(i-1), and executes an amplitude and phase correcting 
process for the antenna element Ai by effecting phase difference 
correction (or phase shift) based on the above-mentioned calculated phase 
difference estimation value so that all the baseband signals are put in 
phase, and then effecting weighting on each baseband signal with an 
amplification gain proportional to the calculated received signal 
intensity. The baseband signals obtained through the above-mentioned 
processes are inputted to the in-phase combiner 4. 
A circuit processing of the amplitude and phase difference correcting 
circuit PC-i will be described in detail hereinafter. 
The in-phase combiner 4 combines in phase the baseband signals inputted 
from the amplitude and phase difference correcting circuits PC-1 through 
PC-N every channel, and thereafter, outputs the resulting signal to the 
demodulator 5. The demodulator 5 effects synchronous detection or delayed 
detection on each inputted baseband signal in a predetermined baseband 
demodulation process, extracts the desired digital data therefrom, and 
then, outputs the digital data as received data. 
FIG. 2 is a block diagram of a transmitter section of the above-mentioned 
automatic beam acquiring and tracking apparatus. 
Referring to FIG. 2, the transmitter section comprises N transmitter 
modules TM-1 through TM-N, N quadrature modulator circuits QM-1 through 
QM-N, and an in-phase divider 9. In the present case, each of the 
quadrature modulator circuits QM-1 through QM-N comprises a quadrature 
modulator 6 and a transmission local oscillator 10, while each of the 
transmitter modules TM-1 through TM-N comprises an up-converter (U/C) 7 
for frequency-converting the inputted intermediate frequency signal into a 
transmitting signal having a predetermined transmitting radio frequency, 
and a transmission power amplifier 8. In the present case, the 
transmission local oscillator 10 in each of the quadrature modulator 
circuits QM-1 through QM-N is implemented by, for example, an oscillator 
employing a DDS (Direct Digital Synthesizer) driven with an identical 
clock, and operates to generate a transmitting local oscillation signal 
having a phase corresponding to each phase correction amount based on 
phase correction amounts .DELTA..phi..sub.c1 through .DELTA..phi..sub.cN 
inputted from a least square regression correcting section 42. 
The baseband signal, or the transmitting data is inputted to the in-phase 
divider 9, and thereafter, the input signal is distributed in phase into a 
plurality of N baseband signals, which are inputted to the quadrature 
modulator 6 of each of the quadrature modulator circuits QM-1 through 
QM-N. For instance, the quadrature modulator 6 of the quadrature modulator 
circuit QM-1 effects a quadrature modulation such as a QPSK or the like on 
the transmitting local oscillation signal according to the transmitting 
baseband signal inputted from the in-phase divider 9. Thereafter, the 
intermediate frequency signal obtained through the quadrature modulation 
is inputted as a transmitting radio signal to the circulator CI-1 of the 
array antenna 1 via the up-converter 7 and the transmission power 
amplifier 8 of the transmitter module TM-1. Then, the transmitting radio 
signal is radiately transmitted from the antenna element A1. Further, 
similar signal processing is executed in each system of the transmitter 
section connected to the antenna elements A2 through AN. 
FIG. 3 shows a block diagram of one system corresponding to the i-th 
antenna element Ai (i=1, 2, 3, . . . , N) of the amplitude and phase 
difference correcting circuits PC-1 through PC-N shown in FIG. 1. 
Referring to FIG. 3, the amplitude and phase difference correcting circuit 
PC-i is a circuit for estimating and determining a phase difference 
.delta.c.sub.i-1,i between adjacent antenna elements of a received radio 
signal composed of a digital phase modulation wave, an unmodulated wave or 
the like, making the phase difference zero, i.e., effecting phase 
correction for each antenna element so as to put the signals in phase, and 
then, effecting amplification every system with a gain proportional to the 
signal intensity of the received radio signal so as to improve the 
received signal to noise power ratio when a plurality of N baseband 
signals are combined in phase. 
As shown in FIG. 3, the amplitude and phase difference correcting circuit 
PC-i comprises a phase difference estimation section 40, an adder 41, a 
least square regression correcting section 42, a delay buffer memory 43, a 
phase difference correcting section 44, and an amplitude correcting 
section 45. In the amplitude and phase difference correcting circuit PC-1, 
.DELTA..phi..sub.1 is set to zero without providing the phase difference 
estimation section 40 and the adder 41. 
The quadrature baseband signals I.sub.i and Q.sub.i, or the received 
signals inputted from the quasi-synchronous detector QD-1 (hereinafter, 
I.sub.i is referred to as an I-channel baseband signal, and Q.sub.i is 
referred to as a Q-channel baseband signal) are inputted to the phase 
difference estimation section 40 and the delay buffer memory 43. The phase 
difference estimation section 40 operates based on the quadrature baseband 
signals (sample values) I.sub.i and Q.sub.i and I.sub.i-1 and Q.sub.i-1 
outputted respectively from the quasi-synchronous detectors QD-i and 
QD-(i-1) of two adjacent antenna elements Ai and Ai-1 to estimate the 
phase difference .delta.c.sub.i-1,i between the systems of the two 
adjacent antenna elements Ai and Ai-1 at each sampling timing, and then 
output the estimated value to the adder 41. The adder 41 adds the 
estimated phase difference .delta.c.sub.i-1,i inputted from the phase 
difference estimation section 40 to an accumulative correction phase 
amount .DELTA..phi..sub.i-1 outputted from the adder 41 of the amplitude 
and phase difference correcting circuit PC-(i-1), and then, outputs the 
resulting accumulative correction phase amount .DELTA..phi..sub.i through 
the addition to the least square regression correcting section 42 and to 
the adder 41 of the next amplitude and phase difference correcting circuit 
PC-(i+1). 
The least square regression correcting section 42 outputs phase correction 
amounts .DELTA..phi..sub.c1 through .DELTA..phi..sub.cN of a reception 
phase difference relevant to the antenna elements A1 through AN for 
suppressing noises taking advantageous effects of a spatial characteristic 
of the array antenna based on the accumulative correction phase amounts 
.DELTA..phi..sub.1 through .DELTA..phi..sub.N of each antenna element 
obtained by successively accumulating the estimated phase difference 
.delta..sub.c.sub.i-1,i by means of the adder 41 every antenna element 
system to the phase difference correcting sections 44 of the amplitude and 
phase difference correcting circuits PC-1 through PC-N, and then, outputs 
the same phase correction amounts .DELTA..phi..sub.c1 through 
.DELTA..phi..sub.cN to the transmission local oscillators 10 inside the 
quadrature modulator circuits QM-1 through QM-N. The least square 
regression correcting section 42 is provided singly in the receiver 
section, and implemented by, for example, a DSP (Digital Signal 
Processor). 
On the other hand, the delay buffer memory 43 delays the quadrature 
baseband signals I.sub.i and Q.sub.i by a delay time for phase difference 
estimation corresponding to a time of operations or calculations of the 
phase difference estimation section 40, the adder 41, and the least square 
regression correcting section 42, and then, outputs the resulting signals 
to the phase difference correcting section 44. Subsequently, the phase 
difference correcting section 44 operates based on the correction amount 
.DELTA..phi..sub.ci of the reception phase difference outputted from the 
least square regression correcting section 42 to correct the phases of the 
quadrature baseband signals outputted from the delay buffer memory 43 by 
rotating the phases of the signals each by a phase shift amount 
corresponding to the correction amount .DELTA..phi..sub.ci, and then 
outputs the resulting signal to the amplitude correcting section 45. 
Thereafter, the amplitude correcting section 45 amplifies the quadrature 
baseband signals outputted from the phase difference correcting section 44 
with gains proportional to the signal intensity of the quadrature baseband 
signals, and then, outputs the resulting signals as quadrature baseband 
signals Ic.sub.i and Qc.sub.i to the in-phase combiner 4. 
Assuming now that sample values of the quadrature baseband signals at a 
certain time point after the quasi-synchronous detection process of the 
adjacent two antenna elements Ai-1 and Ai are respectively I.sub.i-1 and 
Q.sub.i-1 and I.sub.i and Q.sub.i, then an instantaneous phase difference 
.delta..sub.i-1,i calculated by the phase difference estimation section 40 
is expressed by an angle made by two vectors (I.sub.i-1, Q.sub.i-1) and 
(I.sub.i, Q.sub.i) in a phase plane. In the case of digital phase 
modulation, I.sub.i-1, Q.sub.i-1, I.sub.i and Q.sub.i are expressed by the 
following Equations (1) through (4). 
EQU I.sub.i-1 =a.sub.i-1 cos (.theta.) (1) 
EQU Q.sub.i-1 =a.sub.i-1 sin (.theta.) (2) 
EQU I.sub.i =a.sub.i cos (.theta.+.delta..sub.i-1,i) (3) 
EQU Q.sub.i =a.sub.i sin (.theta.+.delta..sub.i-1,i) (4) 
where a.sub.i-1 and a.sub.i represent the amplitudes of the baseband 
signals, and .theta. represents an arbitrary phase angle of each baseband 
signal varying according to modulated phase data. Therefore, by performing 
a baseband processing as expressed by the following Equations (5) and (6), 
values that are proportional to the sine and cosine of the phase 
difference .delta..sub.i-1,i and that do not at all depend on the 
modulated phase data can be obtained. 
EQU I.sub.i-1 .multidot.I.sub.i +Q.sub.i-1 .multidot.Q.sub.i =a.sub.i-1 a.sub.i 
cos.delta..sub.i-1,i (5) 
EQU I.sub.i-1 .multidot.Q.sub.i -I.sub.i .multidot.Q.sub.i-1 =a.sub.i-1 a.sub.i 
sin.delta..sub.i-1,i (6) 
According to the above-mentioned Equations, the instantaneous phase 
difference .delta..sub.i-1,i of the adjacent two antenna elements Ai-1 and 
Ai is expressed by the following Equation (7) to be calculated. 
##EQU1## 
The above-mentioned Equations depend neither on the modulated phase data of 
each signal nor the amplitudes a.sub.i-1 and a.sub.i. Therefore, the phase 
difference .delta..sub.i-1,i can be calculated independently of the 
modulation. In the present case, the transformation from Equations (1) 
through (4) to Equation (7) represents a transformation from the I-axis 
and the Q-axis that are perpendicular to each other into two axes that are 
perpendicular to each other for defining the phase difference 
.delta..sub.i-1,i, and this means a rotation of coordinates around an 
axial center. In the Equation (7), data of the denominator of the fraction 
of the right hand member is the left hand member of the Equation (5), and 
is directly proportional to the cosine of the phase difference 
.delta..sub.i-1,i as shown in the Equation (5). On the other hand, in the 
Equation (7), data of the numerator of the fraction of the right hand 
member is the left hand member of the Equation (6), and is directly 
proportional to the sine of the phase difference .delta..sub.i-1,i as 
shown in the Equation (6). 
In order to obtain a more correct phase difference by suppressing noises 
(which are mainly thermal noises of the receiver) included in the received 
radio signal, the two pieces of data obtained according to the Equation 
(5) and the Equation (6) are each passed or put through a predetermined 
digital filter included in the phase difference estimation section 40 to 
be filtered. In the present case, the filtering is effected prior to the 
calculating operations of division and tan.sup.-1 for the purpose of 
preventing the possible increase of errors in the calculations. A phase 
difference .delta.c.sub.i-1,i obtained through the filtering process is 
estimated according to the following Equation (8). 
##EQU2## 
where F(.multidot.) represents a transfer function of the digital filter. 
The digital filter can be implemented by any of a variety of filters such 
as a simple cyclic adder and a transversal filter provided with an 
adaptive tap coefficient. The phase difference estimation section 40 
calculates the phase difference .delta.c.sub.i-1,i obtained through the 
filtering process according to the Equation (8), and then, outputs the 
resultant to the adder 41. 
FIG. 4 shows a construction of an exemplified FIR (Finite Impulse Response) 
filter provided with fixed tap coefficients included in the phase 
difference estimation section 40. In the example shown in FIG. 4, the 
buffer size Buff=7. 
Referring to FIG. 4, an input signal x is inputted to an adder 70 via a tap 
coefficient multiplier 60, and also the input signal x is inputted to an 
input terminal of six delay circuits 51 through 56 connected in series. 
Signals outputted from the delay circuits 51 through 56 are inputted to 
the adder 70 via tap coefficient multipliers 61 through 66, respectively. 
In the present case, the multipliers 60 through 66 have respective tap 
coefficients k0 through k6, respectively, which are multiplication 
coefficients, and then outputs the inputted signals to the adder 70 by 
multiplying the signals with the respective tap coefficients. The adder 70 
sums up all the signals inputted thereto, and then, outputs the resultant 
sum signal as an output signal F(x). 
Assuming that the tap coefficients k0 through k6 are all one, the filter is 
a simple cyclic adder. The buffer size of each of the filters will be 
referred to merely as a buffer size Buff. 
Based-on the estimated phase difference .delta.c.sub.i-1, i calculated 
according to the Equation (8), the amount of phase to be corrected in each 
antenna element system (referred to as a correction phase amount 
hereinafter) .DELTA..phi..sub.i (i=1, 2, . . . , i, . . . , N) is 
expressed by the following Equations (9) and is calculated by the adder 41 
. 
EQU .DELTA..phi..sub.1 =0 
EQU .DELTA..phi..sub.2 =.DELTA..phi..sub.1 +.delta.c.sub.1,2 
EQU .DELTA..phi..sub.3 =.DELTA..phi..sub.2 +.delta.c.sub.2,3 - - - 
EQU .DELTA..phi..sub.i =.DELTA..phi..sub.i-1 +.delta.c.sub.i-1 - - - 
EQU .DELTA..phi..sub.N =.DELTA..phi..sub.N-1 +.delta.c.sub.N-1,N(9) 
In the Equations (9), it is assumed that the antenna element A1 is used as 
a phase reference (phase zero), and the phases of all the antenna elements 
A1 through AN are made to coincide with the phase of the antenna element 
A1. There can be selected several methods of setting an order for 
calculating the correction phase amounts as follows. 
In the case where the antenna elements A1 through AN are arranged in a 
linear array, there are a first method of using an antenna element A1 
located at either end as a phase reference and executing calculation 
sequentially therefrom as shown in FIG. 5(a), and a second method of using 
a certain antenna element Ai (1&lt;i&lt;N) as a phase reference and executing 
calculation parallel towards both ends thereof. The latter method achieves 
a higher calculation speed since the parallel processing that diverges 
into two branches is executed, however, two outputs are necessary at the 
element that serves as the phase reference. 
In the case where the antenna elements A1 through AN are arranged in a 
two-dimensional matrix array, assuming that input and output ports 
(referred to as an I/O ports hereinafter) are limited in number to three 
in total per element, there can be exemplified a method of using an 
antenna element A1 located diagonally at one end as a phase reference and 
summing up phase differences in a manner of divergence into branches as 
shown in FIG. 6. According to this method, there are executed three of 
accumulative additions in every branch. In a case where the antenna 
elements are arranged in another arbitrary array form, a speedy 
calculation can be achieved in a parallel calculation manner in accordance 
with the practices of the above-mentioned examples. 
In regard to the calculated correction phase amount .DELTA..phi..sub.i, 
noise components are suppressed by a digital filter of the phase 
difference estimation section 40 in each antenna element system. However, 
when a cut-off characteristic of the filter is made excessively steep, 
this results in an increased response delay, and accordingly, there is a 
limit in suppressing the noises by the filter. Therefore, by effecting 
linear, flat or curved plane regression correction on the correction phase 
amounts in array space signal processing by means of least square method 
as described below in the least square regression correcting section 42, 
the noise characteristic on the receiver side is improved. 
For simplicity, assuming that four antenna elements A1 through A4 are 
arranged at arbitrary intervals in line and one incoming beam of a radio 
signal wave is received in a certain direction, reception phases of the 
antenna elements A1 through A4 are as shown in FIG. 7. It is to be noted 
that no original noise is included in the incoming beam. In the present 
case, each reception phase can be obtained correctly if no receiver noise 
exists, and therefore, as indicated by a reference numeral 71 in FIG. 7, a 
reception relative phase amount .DELTA..phi..sub.i (x) of the i-th antenna 
element located in a position x becomes a linear function relative to the 
positions of antennas x. However, practically there are independent 
receiver noises (mainly thermal noises) in each of the systems of the 
antenna elements A1 through AN, and therefore, the phase amount (estimated 
value) .DELTA..phi..sub.i (x) to be calculated is as indicated by a 
reference numeral 72 in FIG. 7. In the present case, when a correction is 
effected by obtaining a regression line .DELTA..phi..sub.ci (x) such that 
it minimizes a sum of errors of squares resulting from the reception 
relative phase amount (estimated value) .DELTA..phi..sub.i (x) as 
indicated by a reference numeral 73 in FIG. 7, the receiver noises can be 
suppressed. 
The above-mentioned regression correcting process of phase amount can be 
managed similarly in a case where the antenna array is two-dimensional, 
and is applicable not only to a case where the antenna array is in a flat 
plane but also to a case where the antenna array is in an arbitrary curved 
plane. In the latter case, the curved plane is obtained from the 
configuration of the plane of the antenna array. Although the least square 
method is used in the regression correcting process, the present invention 
is not limited to this, and there may be used a numerical calculating 
method for obtaining an approximated line or curved plane through 
regression to one line or curved plane. 
An example of the calculation will be shown below when the antenna element 
array is in a linear plane. It is assumed that a position of an arbitrary 
natural number i-th antenna element (1.ltoreq.i.ltoreq.N) is expressed by 
(x, y) in an x-y plane, and an equi-phase regression plane 
.DELTA..phi..sub.ci (x, y) when an evaluation function J given by the 
following equation (10) becomes the minimum is calculated according to the 
following Equation (10). 
##EQU3## 
where .DELTA..phi..sub.i (x, y) is an estimated value (corresponding to 
the reference numeral 72 in FIG. 7) of the correction phase amount prior 
to the least square regression process. In the present case, it is assumed 
that the antenna element array is an equal-interval matrix array of 
x.sub.max .times.Y.sub.max, and a natural number N (=x.sub.max 
.times.y.sub.max) antenna elements are arranged at intersections of axes 
of x=1, 2, . . . , x.sub.max and y=1, 2, . . . , y.sub.max. The antenna 
plane is a flat plane, and therefore, the phase plane, i.e., the least 
square regression plane of correction phase amount is also a flat plane, 
and the regression plane .DELTA..phi..sub.ci (x, y) of the correction 
phase amount can be expressed by the following Equation (11). 
EQU .DELTA..phi..sub.ci (x, y)=ax+by+c, x=1, 2, . . . , x.sub.max ; y=1, 2, . . 
. , y.sub.max (11) 
where, a, b and c are parameters for determining the position of the plane. 
In the present case, a normalization equation which provides a condition 
for minimizing the evaluation function J is expressed by the following 
Equations (12). 
EQU .differential.J/.differential.a=0 
EQU .differential.J/.differential.b=0 
EQU .differential.J/.differential.c=0 (12) 
Then the Equations (12) can be transformed into the following Equation 
(13). 
##EQU4## 
From the Equation (13), the following Equation (14) is derived. 
##EQU5## 
where a matrix A and a matrix .PHI. are expressed by the following 
Equation (15). 
##EQU6## 
In the present case, the matrix A is a coefficient matrix depending on only 
the position coordinates of the antenna elements A1 through AN, and 
therefore, the inverse matrix A.sup.-1 can be preparatorily calculated, 
and this means that no real time calculation is required. For instance, 
when x.sub.max =y.sub.max =4, the inverse matrix A.sup.-1 can be expressed 
by the following Equation (16). 
##EQU7## 
Therefore, the parameters a, b and c for determining the position of the 
plane are expressed by the following Equation (17). 
##EQU8## 
Therefore, the regression plane .DELTA..phi..sub.ci (x, y) is determined by 
means of the estimated value .DELTA..phi..sub.i (x, y) of the correction 
phase amount, and correction phase amounts .DELTA..phi..sub.c1 
(=.DELTA..phi..sub.c1 (1,1)) through .DELTA..phi..sub.CN 
(=.DELTA..phi..sub.CN (x.sub.max, y.sub.max)) obtained through the 
regression correcting process for the respective systems of the antenna 
elements A1 through AN can be calculated by the least square regression 
correcting section 42. The above-mentioned calculation example is provided 
on an assumption that the antenna plane is a linear plane, however, the 
calculation can be applied to the case of a two-dimensional curved plane 
or the like. 
The above-mentioned process according to the least square method can be 
skipped while determining the correction phase amount .DELTA..phi..sub.ci 
(x, y)=.DELTA..phi..sub.i (x, y) when there is a small margin in operating 
speed. By using the thus obtained correction phase amount 
.DELTA..phi..sub.ci (=.DELTA..phi..sub.ci (x, y)), the quadrature baseband 
signals are each subjected to a phase correcting process in all the 
antenna element systems according to the following Equation (18) wherein 
it is assumed that .DELTA..phi..sub.ci =.DELTA..phi..sub.ci (x, y). 
##EQU9## 
where the left hand member of the Equation (18) is a matrix representing a 
vector of a received baseband signal of the i-th antenna element obtained 
through the phase correcting process, the first term of the right hand 
member of the Equation (18) is a phase rotation transformation matrix for 
effecting phase correction in order to put all the received baseband 
signals in phase, i.e., a transformation matrix for putting the signals in 
phase, and the second term of the right hand member is a matrix 
representing a vector of the received baseband signal prior to the phase 
correcting process. 
When there is a case where a reduction in power of a received signal occurs 
at some antenna elements due to multi-path fading or interruption, 
according to an equal-gain in-phase combining process for combining 
signals of all the antenna elements through equal weighting, a signal 
having a good quality and a signal having a degraded quality are summed up 
through equal weighting, and therefore, the signal to noise power ratio 
deteriorates after the in-phase combining process. In order to suppress 
the deterioration, the received baseband signals in the systems of the 
antenna elements A1 through AN are amplified with respective gains G 
directly proportional to the reception intensities of the signals in the 
amplitude correcting section 45 as expressed by the following Equations 
(19). The above-mentioned arrangement is intended to make each signal 
having a good quality contribute more and make each signal having a 
degraded quality contribute less. 
##EQU10## 
where k represents a proportional constant, and Ave () represents an 
average value in time. 
When the signals obtained through the amplitude correcting process are 
combined in phase in all the systems of the antenna elements A1 through 
AN, relative in-phase combining outputs of the quadrature baseband signals 
are expressed by the following Equations (20). 
##EQU11## 
In regard to the amplitude correcting process effected by the amplitude 
correcting section 45, when differences in power between the antenna 
elements A1 through AN have no serious problem, the gain G is set to 1 and 
the process can be skipped. When the in-phase combining output signal is 
inputted to an arbitrary baseband processing type demodulator 5, a desired 
digital data can be obtained. 
On the other hand, the weight for controlling the directivity of the 
transmitting array antenna does not include an amplitude component and is 
required to have only a phase component. Therefore, the correction phase 
amount .DELTA..phi..sub.ci calculated by the least square regression 
correcting section 42 can be directly used as a weight for controlling the 
directivity of the transmitting array antenna, thereby allowing the 
transmitting beam to be automatically directed to the direction of the 
incoming beam. It is to be noted that, depending on cases, it is required 
to perform a simple transformation process at need in a manner as 
described below. 
For instance, in a case where the array antenna 1 is used commonly for 
transmission and reception when there is a difference in radio wavelength 
between transmission and reception, a phase shift amount 
.DELTA..phi..sub.Ti (x, y) in each transmitting antenna element system is 
expressed by the following Equation (21). 
##EQU12## 
It is to be noted that .lambda..sub.T and .lambda..sub.R are free space 
wavelengths in transmission and reception, respectively. The 
above-mentioned transformation is not necessary when independent antenna 
elements are used for transmission and reception and the intervals between 
the elements are the same in terms of wavelength or when the antenna 
elements are commonly used for transmission and reception but the 
transmission and reception frequencies are equal to each other. 
The following will describe a calculation result of a simulation carried 
out to confirm effects produced in receiving an incoming beam by means of 
the automatic beam acquiring and tracking apparatus for array antenna of 
the present preferred embodiment having the above-mentioned construction. 
Conditions for the simulation are shown in Table 1. 
TABLE 1 
______________________________________ 
Modulation system 
QPSK 
Bit rate 16 kbps 
Modulation 32 kHz 
frequency 
Sampling rate 128 kHz 
Added noise Gauss noise 
Array antenna 4-element linear array with a point 
radiation source 
Antenna element 
Half wavelength 
interval 
Transmission 10-tap FIR filter, 
low-pass filter 
cut-off frequency = 8 kHz 
Transmission 51-tap FIR filter, 
band-pass filter 
cut-off frequency = 16 kHz 
Reception 51-tap FIR filter, 
band-pass filter 
cut-off frequency = 16 kHz 
Reception 10-tap FIR filter, 
low-pass filter 
cut-off frequency = 8 kHz 
Remarks Neither interference wave nor 
frequency fluctuation occurs 
______________________________________ 
A digital filter for use in estimating a correction phase amount is a 
simple cyclic adder (FIR filter having each tap coefficient=1), and an 
addition buffer size Buff corresponding to the number of taps of the 
filter was changed so as to examine the effects. It is to be noted that 
powers received by the antenna elements are same, and no amplitude 
correction is effected. Further, no least square regression is effected. 
Further, in the simulation, the phase difference correcting operation is 
not effected every sample, however, the frequency of effecting the 
operation is reduced to a frequency of once in nine samples. With the 
above-mentioned arrangement, not only an operation load of DSP (Digital 
Signal Processor) is reduced but also a correlation of noise signals 
between the calculation samples is reduced, and therefore, more effective 
noise suppression by means of the digital filter can be achieved. 
FIGS. 8A and 8B each show a variation in time of an antenna relative gain 
in a direction in which a signal beam comes when a phase difference 
estimating operation or calculation is performed every sampling (sampling 
frequency =128 kHz) together with an I-channel modulation baseband signal 
(modulation data). In the present case, FIG. 8A shows a case where a 
reception C/N per antenna element is 4 dB, while FIG. 8B shows a case 
where C/N is -2 dB. In this regard, C/N represents a ratio of a carrier 
signal power to noise power (referred to as a carrier signal power to 
noise power ratio hereinafter). 
As shown in FIGS. 8A and 8B, it is assumed that generation of an output of 
a transmitting signal starts when an accumulative sampling number of 
times=0, input and calculation of the transmitting signal starts when the 
accumulative sampling number of times=100, the signal is subjected to a 
shadowing process (which is interruption of the reception signal) when the 
accumulative sampling number of times=700 to 1000, and the direction of 
the incoming signal beam varies at an angle of 90.degree./sec. 
Assuming herein that an operation from the start of the calculation to a 
time when the antenna relative gain exceeds -3 dB is referred to as "rough 
acquisition" and an operation to a time when the antenna relative gain 
exceeds -0.5 dB is referred to as "precise acquisition" the accumulative 
sampling number of times required for the precise acquisition is about 80 
in the case of FIG. 8A, and about 300 in the case of FIG. 8B. Therefore, 
the accumulative sampling number of times required for the precise 
acquisition depends on the carrier signal power to noise power ratio C/N. 
On the other hand, the accumulative sampling number of times required for 
the rough acquisition does not significantly depend on the carrier signal 
power to noise power ratio C/N, and the incoming signal beam is acquired 
when the accumulative sampling number of times is 30 to 50. After the 
acquisition, as shown in FIG. 8B, the variation of the antenna relative 
gain increases when the carrier signal power to noise power ratio C/N is 
low. That is, it can be found that the incoming signal beam is stably 
tracked in both the cases of FIGS. 8A and 8B. The reason why such fast 
acquisition and stable tracking are achieved even when the reception 
carrier signal power to noise power ratio C/N is low is that a phase 
control of the systems of the antenna elements A1 through AN are effected 
in a feedforward manner. 
FIGS. 9A and 9B each show a variation in time of an antenna pattern when a 
signal beam is acquired under the same conditions as those of FIGS. 8A and 
8B. In FIGS. 9A and 9B, dotted lines indicate an antenna pattern when the 
accumulative sampling number of times is 8, one-dot chain lines indicate 
an antenna pattern when the accumulative sampling number of times is 26, 
and solid lines indicate an antenna pattern when the accumulative sampling 
number of times is 35 (in the case of FIG. 9A) or 125 (in the case of FIG. 
9B). 
As is apparent from FIGS. 9A and 9B, the antenna pattern rapidly converges 
when the antenna pattern changes its state from a random state (when the 
accumulative sampling number of times is 8) to a state in which a signal 
beam incident at an angle of -45.degree. is acquired (when the 
accumulative sampling number of times is 35 (in the case of FIG. 9A) or 
125 (in the case of FIG. 9B)). 
FIGS. 10A and 10B each show a variation in time of an antenna pattern based 
on an assumption that an estimated maximum rotation speed in a normal land 
mobile body or the like is 90 degrees per second under the same conditions 
as those of FIGS. 8A and 8B, where the antenna pattern varies with a 
change in direction of an incoming signal beam. In FIGS. 10A and 10B, each 
antenna pattern indicated by one-dot chain lines is obtained after an 
elapse of 1/3 second from the antenna pattern indicated by dotted lines, 
and each antenna pattern indicated by solid lines is obtained after an 
elapse of 1/3 second from the antenna pattern indicated by the one-dot 
chain lines. 
As is apparent from FIGS. 10A and 10B, it can be found that the main beam 
of the array antenna is approximately correctly tracking the incoming 
signal beam even when the direction of the incoming signal beam changes. 
FIG. 11 shows tracking characteristics in the times of rough acquisition 
and precise acquisition of the incoming signal beam with respect to the 
carrier signal power to noise power ratio C/N when the buffer size Buff is 
used as a parameter. In the present case, the calculation period Topr is 
fixed to 1. 
As is apparent from FIG. 11, it can be found that the rough acquisition 
depends scarcely on the carrier signal power to noise power ratio C/N and 
the buffer size Buff, and is able to constantly obtain a stable 
acquisition characteristic. On the other hand, in regard to the precise 
acquisition, the accumulative sampling number of times to the achievement 
of acquisition increases with promotion of deterioration of the carrier 
signal power to noise power ratio C/N. That is, a time required for the 
achievement of acquisition increases resulting in a dull acquisition, and 
then this means that the precise acquisition depends greatly on the 
carrier signal power to noise power ratio C/N. In the present case, a 
faster acquisition can be achieved with a smaller buffer size Buff, 
however, as described in detail hereinafter, the tracking becomes 
unstable. Therefore, in selecting the buffer size Buff, there is required 
a trade-off (consideration for picking up and discarding several 
conditions that cannot be concurrently satisfied) between acquisition and 
tracking taking actual communication conditions into account. 
FIG. 12 shows a tracking characteristic with respect to the carrier signal 
power to noise power ratio C/N when the buffer size Buff is used as a 
parameter, where the axis of ordinates represents the sampling number of 
times that are effective when the relative gain of the array antenna 
becomes below -0.5 dB until the accumulative sampling number of times 
becomes 8000, and indicates the frequency of occurrence of a formed main 
beam deviating from the intended direction. In the present case, the 
calculation period Topr is fixed to 1. 
As is apparent from FIG. 12, it can be found that the stability of tracking 
at a relatively low carrier signal power to noise power ratio C/N is 
remarkably improved by increasing the buffer size Buff. 
FIG. 13 shows tracking characteristics in times of precise acquisition and 
rough acquisition with respect to the carrier wave signal to noise power 
ratio C/N when the calculation period Topr is used as a parameter. In the 
present case, the buffer size Buff is fixed to 30. 
As is apparent from FIG. 13, the tracking characteristic of the rough 
acquisition depends scarcely on the calculation period Topr, whereas, in 
regard to the precise acquisition, it can be found that the smaller the 
calculation period Topr is, the faster the acquisition is. However, in 
this case, the tracking becomes unstable as described in detail 
hereinafter. Therefore, in selecting the calculation period Topr, there is 
required a trade-off between acquisition and tracking taking actual 
communication conditions into account. 
FIG. 14 shows a tracking characteristic with respect to the carrier signal 
power to noise power ratio C/N when the calculation period Topr is used as 
a parameter, where the axis of ordinates represents the sampling number of 
times that are effective when the relative gain of the array antenna 
becomes below -0.5 dB until the accumulative sampling number of times 
becomes 8000, and indicates the frequency of occurrence of a formed main 
beam deviating from the intended direction. In the present case, the 
buffer size Buff is fixed to 30. 
As is apparent from FIG. 14, it can be found that the stability of tracking 
at a relatively low carrier signal power to noise power ratio C/N is 
remarkably improved by increasing the calculation period Topr similarly to 
the case where the buffer size Buff is increased (See FIG. 12). It is to 
be noted that, when the calculation period Topr is excessively prolonged, 
this results in a slow response to the change of the direction of the 
incoming signal beam, and this leads to an increase of tracking errors. 
From the above-mentioned simulation results in connection with the 
automatic beam acquiring and tracking apparatus of the present preferred 
embodiment, it can be understood that a more stable tracking 
characteristic can be obtained by setting both the buffer size Buff and 
the calculation period Topr to relatively small values so as to increase 
the speed of acquisition under a radio communication line condition in 
which the carrier signal power to noise power ratio C/N is relatively 
high, and setting both the buffer size Buff and the calculation period 
Topr to relatively great values under a radio communication line condition 
in which the carrier signal power to noise power ratio C/N is relatively 
low. 
As described above, the automatic beam acquiring and tracking apparatus of 
the present preferred embodiment produces the following distinctive 
effects. 
(1) An incoming beam is acquired by correcting the phase difference between 
the received signals received at the antenna elements A1 through AN in a 
feedforward manner instead of including a feedback loop as in the second 
prior art. Therefore, the incoming beam of a radio signal comprised of a 
digital phase modulation wave, an unmodulated wave or the like can be 
acquired automatically and rapidly even when the carrier signal power to 
noise power ratio C/N is relatively low, so that a delay time for 
convergence as in the second prior art can be remarkably reduced while 
obviating the need of a training signal or a reference signal for 
executing phase control. Therefore, a simple system construction can be 
achieved. 
(2) The incoming beam is tracked by correcting the phase difference between 
the received signals received at the antenna elements A1 through AN in a 
feedforward manner, instead of including a feedback loop as in the second 
prior art. Therefore, the incoming beam of a radio signal comprised of a 
digital phase modulation wave, an unmodulated wave or the like can be 
tracked stably with high accuracy even when the carrier signal power to 
noise power ratio C/N is relatively low and the direction of the incoming 
signal beam changes rapidly. Therefore, the present apparatus is almost 
free of phase slip, influence of external interference due to the 
surrounding electromagnetic environment, and accumulation of tracking 
errors as seen in the prior art method. 
(3) Spatial information of the array antenna can be effectively utilized by 
further effecting least square regression correction on the correction 
phase amount in each antenna element system. Therefore, influence of the 
reduction of the carrier signal power to noise power ratio C/N per antenna 
element, which is problematic when there are many antenna elements, can be 
suppressed. 
(4) The above-mentioned acquisition and tracking are all effected on the 
received signals by, for example, signal processing such as digital signal 
processing. Therefore, the present apparatus does not require at all any 
microwave shifter, sensor for the acquisition and tracking, motor for 
mechanical movement or the like as in the phased array antenna of the 
first prior art. 
A modification example of the first preferred embodiment will be described 
below based on a case where the regression correction according to the 
least square method is not effected in the first preferred embodiment. In 
the present case, instead of obtaining a phase difference between adjacent 
antenna elements according to the Equation (8), the numerator and the 
denominator of the Equation (8) are calculated with respect to a 
predetermined reference antenna element, and the numerator of the Equation 
(8) is substituted into sin.DELTA..phi..sub.ci in the Equation (18), and 
the denominator of the Equation (8) is similarly substituted into 
cos.DELTA..phi..sub.ci in the Equation (18) for processing. With the 
above-mentioned operation or calculation, the left hand member of the 
Equation (18) can be obtained without calculating tan.sup.-1 in the 
Equation (8) on the reception side, so that the amount of calculation can 
be reduced, and amplitude correction for not only phase correction but 
also maximum ratio combining can be automatically effected. In the present 
case, an equation for effecting phase correction of the quadrature 
baseband signals is expressed by the following Equation (22). 
##EQU13## 
where the left hand member of the Equation (22) is a matrix representing a 
vector of the received baseband signal of the i-th antenna element 
obtained through the phase correcting process, the first term of the right 
hand member thereof is a phase rotation transformation matrix for the 
phase correction process, i.e., a transformation matrix for putting the 
signals in phase, and the second term of the right hand member is a matrix 
representing a vector of the received baseband signal prior to the phase 
correcting process. It is to be noted that, in the modification example, a 
calculating operation is not effected between adjacent two antenna 
elements but effected in a manner as follows. That is, by assuming that an 
antenna element to be used as a phase reference is, for example, A1, and 
effecting a calculating operation between a received signal of the antenna 
element A1 and a received signal of each of the other antenna elements A2 
through AN so as to execute processing between the signals. Although the 
reference antenna element is assumed to be A1 in the present modification 
example, the present invention is not limited to this, and another antenna 
element may be used as the reference antenna element. 
An advantageous effect in executing the above-mentioned processing 
operation or calculation is that the calculation of the Equation (22) is 
capable of performing not only phase transformation but also amplitude 
transformation so that the maximum ratio combining is executed at the same 
time. In other words, the Equation (22) can be approximated to the 
following Equation (23) according to the Equation (5) and the Equation (6) 
by means of approximation expressions (24). 
##EQU14## 
As is apparent from the Equation (23), a product of the third term and the 
fourth term of the right hand member of Equation (23) is multiplied by a 
product F(a.sub.1).multidot.F(a.sub.i) of the filtered amplitude 
coefficients. In the present case, when the amplitude coefficient a.sub.1, 
amplitude coefficient a.sub.i and the cosine value cos.delta..sub.1,i of 
the phase difference can be assumed in a short term to be mutually 
independent variables that vary at random in time about a certain average 
value due to thermal noise, the following Expressions (24) can be obtained 
. 
EQU F(a.sub.1 a.sub.i 
cos.delta..sub.1,i).apprxeq.F(a.sub.1).multidot.F(a.sub.i).multidot.F(cos. 
delta..sub.1,i) F(a.sub.1 a.sub.i 
sin.delta..sub.1,i).apprxeq.F(a.sub.1).multidot.F(a.sub.i).multidot.F(sin. 
delta..sub.1,i) (24) 
The Expressions (24) hold for a reason as follows. Assuming now that 
variables u and v are independent variables that vary at random in time 
and average values of the respective variables are avr(u) and avr(v), the 
variables can be expressed by the following Equations (25). 
EQU u=avr(u)+eu 
EQU v=avr(v)+ev (25) 
where eu and ev are random components each expressing a component that vary 
at random in time about an average value of 0. When the above-mentioned 
digital filter is, for example, a predetermined low-pass filter, then 
F(.multidot.) is a transfer function of the low-pass filter, and 
therefore, the following Expressions (26) can be derived from Equations 
(25). 
EQU F(u).apprxeq.avr (u) 
EQU F(v).apprxeq.avr (v) 
EQU F(eu).apprxeq.0 
EQU F(ev).apprxeq.0 (26) 
When the following Expression (27) holds between the variables u and v, the 
Expressions (24) can hold. 
EQU F(u.multidot.v).apprxeq.F(u).multidot.F(v) (27) 
When the Equations (25) are substituted into the left hand member of the 
Expression (27) and then the Expression (27) is transformed by means of 
the Expressions (26), the following Expression (28) can be obtained. 
##EQU15## 
In the above-mentioned Expressions, the random components eu and ev can be 
assumed to be mutually independent and have no correlation and a mutual 
correlation function R(.tau.) is always zero. Therefore, by assuming that 
.tau.=0, the following Equation (29) holds. 
##EQU16## 
The Equation (29) means that a time average of (eu.multidot.ev) is 
approximately zero. Therefore, F(eu.multidot.ev).apprxeq.0, and according 
to this expression and the Expression (28), there hold Expression (27) and 
Expressions (24). It is to be noted that Expressions (24) hold with high 
accuracy in particular in a case of a constant envelope modulation system 
where the envelope is constant. When the envelope varies depending on 
information symbols, this results in a deteriorated approximation 
accuracy. 
Otherwise, assuming that the calculating operation of the Equation (22) is 
effected within the system of the reference antenna element A1 itself, the 
following Expression (30) holds when the received signal to noise power 
ratio S/N is sufficiently high. 
##EQU17## 
As is apparent from the Equation (23) and the Expression (30), it can be 
found that amplitude transformation coefficients of received signals at 
the antenna elements are directly proportional to filter outputs 
F(a.sub.i) (i=1, 2, . . . , N) of the amplitudes of the respective 
received signals. Combining the results of calculating operations of the 
Equation (22) and the Expression (30) according to the Equations (20) is 
consequently the same operation as the operation of effecting the maximum 
ratio combining, and therefore, the received signal to noise power ratio 
achieved through combining a plurality of received signals can be 
remarkably improved. In the present case, the calculating operation as 
expressed by the Equations (19) is unnecessary, so that the phase 
difference correcting section 44 and the amplitude correcting section 45 
shown in FIG. 3 can be integrated with each other. It is to be noted that, 
when a random component of the amplitude coefficient a.sub.1 is assumed to 
be eal and a calculation of a filter output F(a.sub.1.sup.2) is performed 
similarly to the Expression (28), the following Equation (31) is obtained. 
EQU f(a.sub.1.sup.2)=F.sup.2 (a.sub.1)+F(ea.sub.1.sup.2) (31) 
That is, as is apparent from the Equation (31), the second term of the 
right hand member of the Equation (31) cannot be ignored when the received 
signal power to noise power ratio S/N is low, and therefore, this causes a 
problem that the approximation error of the Expression (30) increases. 
When there is no multi-path and no regression correction when the least 
square method is effected, the same result is obtained when the Equation 
(8) and the Equation (18) are used and when the Equation (22) and the 
Expression (30) are used. 
Second preferred embodiment 
FIG. 15 is a block diagram of a part of a receiver section of an automatic 
beam acquiring and tracking apparatus of an array antenna for use in 
communications according to the second preferred embodiment of the present 
invention. 
In the second preferred embodiment, adjacent two antenna element systems 
are paired, and an amplitude and phase difference correcting process is 
effected so that quadrature baseband signals obtained therefrom are put in 
phase with each other. Thereafter, a process of in-phase combining (i.e., 
maximum ratio combining) between two antenna element systems of each pair 
is effected, resulting adjacent outputs are paired, and then, an amplitude 
and phase difference correcting process and a process of in-phase 
combining (maximum ratio combining) of the paired outputs are effected 
again. By repeating the above-mentioned operations, there is eventually 
obtained only one array antenna output formed by combining in phase at the 
maximum ratio the signals received by all the antenna elements. 
Consequently, the array antenna performs acquisition and tracking of an 
incoming signal beam. An amount of calculation required for the amplitude 
and phase difference correction process and the in-phase combining process 
are substantially equal to that of the first preferred embodiment. In the 
present case, the maximum ratio combining or the maximum ratio in-phase 
combining is to combine the signals in phase so that the obtained received 
signal to noise power ratio is maximized. 
FIG. 15 shows a construction in a case where the present apparatus has nine 
quasi-synchronous detector circuits QD-1 through QD-9, including stages 
that are subsequent to the quasi-synchronous detector circuits QD-1 
through QD-9 and prior to the demodulator 5. 
Referring to FIG. 15, quadrature baseband signals I.sub.1 and Q.sub.1 
relevant to the antenna element A1 outputted from the quasi-synchronous 
detector circuit QD-1 are inputted to an in-phase combiner 81 and an 
amplitude and phase difference correcting circuit PCA-1. Quadrature 
baseband signals I.sub.2 and Q.sub.2 relevant to the antenna element A2 
outputted from the quasi-synchronous detector circuit QD-2 are inputted to 
the amplitude and phase difference correcting circuit PCA-1. Similarly, 
quadrature baseband signals I.sub.3 and Q.sub.3 relevant to the antenna 
element A3 outputted from the quasi-synchronous detector circuit QD-3 are 
inputted to an in-phase combiner 82 and an amplitude and phase difference 
correcting circuit PCA-2. Quadrature baseband signals I.sub.4 and Q.sub.4 
relevant to the antenna element A4 outputted from the quasi-synchronous 
detector circuit QD-4 are inputted to the amplitude and phase difference 
correcting circuit PCA-2. On the other hand, quadrature baseband signals 
I.sub.5 and Q.sub.5 relevant to the antenna element A5 outputted from the 
quasi-synchronous detector circuit QD-5 are inputted to an in-phase 
combiner 83 and an amplitude and phase difference correcting circuit 
PCA-3. Quadrature baseband signals I.sub.6 and Q.sub.6 relevant to the 
antenna element A6 outputted from the quasi-synchronous detector circuit 
QD-6 are inputted to the amplitude and phase difference correcting circuit 
PCA-3. On the other hand, quadrature baseband signals I.sub.7 and Q.sub.7 
relevant to the antenna element A7 outputted from the quasi-synchronous 
detector circuit QD-7 are inputted to an in-phase combiner 84 and an 
amplitude and phase difference correcting circuit PCA-4. Quadrature 
baseband signals I.sub.8 and Q.sub.8 relevant to the antenna element A8 
outputted from the quasi-synchronous detector circuit QD-8 are inputted to 
the amplitude and phase difference correcting circuit PCA-4. On the other 
hand, quadrature baseband signals I.sub.9 and Q.sub.9 relevant to the 
antenna element A9 outputted from the quasi-synchronous detector circuit 
QD-9 are inputted to an amplitude and phase difference correcting circuit 
PCA-5. 
The amplitude and phase difference correcting circuit PCA-1 calculates 
transformation matrix elements (which are transformation matrix elements 
of the Equation (22)) for putting in phase two received signals of 
adjacent antenna elements by means of the quadrature baseband signals 
I.sub.1 and Q.sub.1 relevant to the antenna element A1 outputted from the 
quasi-synchronous detector circuit QD-1, the quadrature baseband signals 
I.sub.2 and Q.sub.2 relevant to the adjacent antenna element A2 and a 
specific filter for removing noises. Based on the transformation matrix 
(See the Equation (22)) including the calculated transformation matrix 
elements, the detector circuit PCA-1 effects phase difference correction 
(or phase shift) so that the baseband signals of the antenna elements A1 
and A2 are put in phase with each other. Further, by effecting weighting 
with an amplification gain directly proportional to the calculated 
received signal intensity similarly to the amplitude correcting section 45 
of the first preferred embodiment, the detector circuit PCA-1 executes the 
amplitude and phase difference correcting process, and then, outputs the 
baseband signal obtained through the above-mentioned processes to the 
in-phase combiner 81. The in-phase combiner 81 combines in phase the 
quadrature baseband signals I.sub.1 and Q.sub.1 relevant to the antenna 
element A1 with a quadrature baseband signal outputted from the amplitude 
and phase difference correcting circuit PCA-1 every channel, and then, 
outputs the resulting signal to the in-phase combiner 86 and an amplitude 
and phase difference correcting circuit PCA-6. It is to be noted that the 
in-phase combiners 81 through 88 each combine in phase two pairs of 
inputted baseband signals every channel. 
The amplitude and phase difference correcting circuit PCA-2 executes an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1 by means of the 
quadrature baseband signals I.sub.3 and Q.sub.3 relevant to the antenna 
element A3 inputted from the quasi-synchronous detector circuit QD-3 and 
the quadrature baseband signals I.sub.4 and Q.sub.4 relevant to the 
adjacent antenna element A4, and then, outputs the baseband signal 
obtained through the above-mentioned processes to the in-phase combiner 
82. The in-phase combiner 82 combines in phase the quadrature baseband 
signals I.sub.3 and Q.sub.3 relevant to the antenna element A3 with a 
quadrature baseband signal outputted from the amplitude and phase 
difference correcting circuit PCA-2, and then, outputs the resulting 
signal to the amplitude and phase difference correcting circuit PCA-6. 
The amplitude and phase difference correcting circuit PCA-3 executes an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1 by means of the 
quadrature baseband signals I.sub.5 and Q.sub.5 relevant to the antenna 
element A5 inputted from the quasi-synchronous detector circuit QD-5 and 
the quadrature baseband signals I.sub.6 and Q.sub.6 relevant to the 
adjacent antenna element A6, and then, outputs the baseband signal 
obtained through the above-mentioned processes to the in-phase combiner 
83. The in-phase combiner 83 combines in phase the quadrature baseband 
signals I.sub.5 and Q.sub.5 relevant to the antenna element A5 with a 
quadrature baseband signal outputted from the amplitude and phase 
difference correcting circuit PCA-3, and then, outputs the resulting 
signal to the in-phase combiner 87 and the amplitude and phase difference 
correcting circuit PCA-7. 
The amplitude and phase difference correcting circuit PCA-4 executes an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1 by means of the 
quadrature baseband signals I.sub.7 and Q.sub.7 relevant to the antenna 
element A7 inputted from the quasi-synchronous detector circuit QD-7 and 
the quadrature baseband signals I.sub.8 and Q.sub.8 relevant to the 
adjacent antenna element A8, and then, outputs the baseband signal 
obtained through the above-mentioned processes to the in-phase combiner 
84. The in-phase combiner 84 combines in phase the quadrature baseband 
signals I.sub.7 and Q.sub.7 relevant to the antenna element A7 with a 
quadrature baseband signal outputted from the amplitude and phase 
difference correcting circuit PCA-4, and then, outputs the resulting 
signal to the in-phase combiner 85 and the amplitude and phase-difference 
correcting circuit PCA-5. 
The amplitude and phase difference correcting circuit PCA-5 executes an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1 by means of a 
quadrature baseband signal outputted from the in-phase combiner 84 and the 
quadrature baseband signals I.sub.9 and Q.sub.9 relevant to the antenna 
element A9 inputted from the quasi-synchronous detector circuit QD-9, and 
then, outputs the baseband signal obtained through the above-mentioned 
processes to the in-phase combiner 85. The in-phase combiner 85 combines 
in phase the quadrature baseband signal outputted from the in-phase 
combiner 84 with the quadrature baseband signal outputted from the 
amplitude and phase difference correcting circuit PCA-5, and then, outputs 
the resulting signal to the amplitude and phase difference correcting 
circuit PCA-7. 
The amplitude and phase difference correcting circuit PCA-6 executes an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1 by means of the 
quadrature baseband signal outputted from the in-phase combiner 81 and the 
quadrature baseband signal outputted from the in-phase combiner 82, and 
then, outputs the baseband signal obtained through the above-mentioned 
processes to the in-phase combiner 86. The in-phase combiner 86 combines 
in phase the quadrature baseband signal outputted from the in-phase 
combiner 81 with a quadrature baseband signal outputted from the amplitude 
and phase difference correcting circuit PCA-6, and then, outputs the 
resulting signal to the in-phase combiner 88 and the amplitude and phase 
difference correcting circuit PCA-8. 
The amplitude and phase difference correcting circuit PCA-7 executes an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1 by means of the 
quadrature baseband signal outputted from the in-phase combiner 83 and a 
quadrature baseband signal outputted from the in-phase combiner 85, and 
then, outputs the baseband signal obtained through the above-mentioned 
processes to the in-phase combiner 87. The in-phase combiner 87 combines 
in phase the quadrature baseband signal outputted from the in-phase 
combiner 83 with a quadrature baseband signal outputted from the amplitude 
and phase difference correcting circuit PCA-7, and then, outputs the 
resulting signal to the amplitude and phase difference correcting circuit 
PCA-8. 
The amplitude and phase difference correcting circuit PCA-8 executes an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1 by means of a 
quadrature baseband signal outputted from the in-phase combiner 86 and a 
quadrature baseband signal outputted from the in-phase combiner 87, and 
then, outputs the baseband signal obtained through the above-mentioned 
processes to the in-phase combiner 88. The in-phase combiner 88 combines 
in phase the quadrature baseband signal outputted from the in-phase 
combiner 86 with a quadrature baseband signal outputted from the amplitude 
and phase difference correcting circuit PCA-8, and then, outputs the 
resulting signal to the demodulator 5. In the present case, the quadrature 
baseband signal outputted from the in-phase combiner 88 is a quadrature 
baseband signal that corresponds to the quadrature baseband signal 
outputted from the in-phase combiner 4 of the first preferred embodiment 
shown in FIG. 1, and is obtained by executing the amplitude and phase 
difference correcting process based on all the quadrature baseband signals 
relevant to all the antenna elements. 
FIG. 16 is a block diagram of the amplitude and phase difference correcting 
circuit PCA-s (s=1, 2, . . . , 8) shown in FIG. 15. The amplitude and 
phase difference correcting circuit PCA-s of the second preferred 
embodiment shown in FIG. 16 differs from the amplitude and phase 
difference correcting circuit PCA-i of the first preferred embodiment 
shown in FIG. 3 in the following points. 
(1) A phase difference estimation section 40a calculates transformation 
matrix elements (which are the transformation matrix elements of the 
Equation (22)) from which noises are removed for putting in phase received 
signals of two antenna elements i and j based on the quadrature baseband 
signals I.sub.i and Q.sub.i and I.sub.j and Q.sub.j relevant to the two 
antenna elements i and j, and then outputs the transformation matrix 
including the calculated transformation matrix elements to a phase 
difference correcting section 44a. 
(2) The phase difference correcting section 44a corrects the phase 
difference by shifting the phase of the quadrature baseband signal 
inputted from a delay buffer memory 43 based on the transformation matrix 
inputted from the phase difference estimation section 40a, and then 
outputs the resulting signals to an amplitude correcting section 45. 
(3) Neither adder 41 nor the least square regression correcting section 42 
is provided. 
It is to be noted that the delay buffer memory 43 and the amplitude 
correcting section 45 operate similarly to those of the first preferred 
embodiment. 
Therefore, the amplitude and phase difference correcting circuit PCA-s 
shown in FIG. 15 calculates transformation matrix elements (which are the 
transformation matrix elements of the Equation (22)) for putting in phase 
two received signals of adjacent antenna elements by means of the 
quadrature baseband signals I.sub.i and Q.sub.i relevant to the antenna 
element Ai inputted from the quasi-synchronous detector circuit QD-i, the 
quadrature baseband signals I.sub.j and Q.sub.j relevant to the adjacent 
antenna element Aj and a specific filter for removing noises. Thereafter, 
based on the transformation matrix including the calculated transformation 
matrix elements, the circuit PCA-s effects phase difference correction, or 
phase shift so that the two baseband signals of the antenna elements Ai 
and Aj are put in phase with each other. Further, by effecting weighting 
with an amplification gain directly proportional to the calculated 
received signal intensity similarly to the amplitude correcting section 45 
of the first preferred embodiment, the circuit PCA-s executes the 
amplitude and phase difference correcting process, and then, outputs 
baseband signals Ic.sub.i and Qc.sub.i obtained through the 
above-mentioned processes to an in-phase combiner (one of the in-phase 
combiners 81 through 88). 
In the above-mentioned amplitude and phase difference correcting circuit 
PCA-s of the second preferred embodiment, when a transformation operation 
using the transformation matrix for putting the signals in phase is 
performed according to the Equation (22) and the Expression (30) in the 
amplitude and phase difference correcting circuits PCA-1 through PCA-8 
shown in FIG. 15, the phase difference correcting section 44a and the 
amplitude correcting section 45 shown in FIG. 16 can be integrated with 
each other. According to the integrated arrangement, a phase difference 
correcting process for putting the signals in phase and an amplitude 
correcting process can be simultaneously achieved, with which a plurality 
of received signals received by the array antenna 1 can be combined at the 
maximum ratio and corrected in amplitude, so that one combined received 
signal can be outputted. 
As a modification example of the second preferred embodiment, there may be 
a construction as follows similarly to the processing in the first 
preferred embodiment. The phase difference estimation section 40a 
estimates an instantaneous phase difference .delta..sub.i,j of the 
received signal received by the two antenna elements i and j based on the 
quadrature baseband signals I.sub.i and Q.sub.i and I.sub.j and Q.sub.j 
relevant to the two antenna elements i and j according to the Equation 
(7), removes noises, and then, outputs an estimated phase difference 
.delta..sub.ci,j obtained through the removal of noises (See the Equation 
(8)) to the phase difference correcting section 44a. Then, the phase 
difference correcting section 44a corrects the phase difference by 
shifting the quadrature baseband signals inputted from the delay buffer 
memory 43 by the estimated phase difference .delta..sub.ci,j based on the 
estimated phase difference .delta..sub.ci,j inputted from the phase 
difference estimation section 40a, and then, outputs the resulting signals 
to the amplitude correcting section 45. 
The second preferred embodiment has advantageous effects as follows in 
comparison with the first preferred embodiment. In the first preferred 
embodiment, the phase at each antenna element system relative to the 
reference antenna is calculated by summing up the phase differences 
between adjacent antenna element systems of all the combinations, and 
maximum ratio in-phase combining is finally effected collectively. 
Therefore, if there is an antenna element having a low reception level or 
a defective antenna element, there are not only the possibility that the 
estimation of phase relevant to the antenna element cannot be effected but 
also the possibility that it affects the estimation of phase of the other 
antenna element systems. In contrast to the above, in the second preferred 
embodiment, instead of summing up the phase differences between adjacent 
antenna elements of all the combinations, the signals are combined in 
phase at the maximum ratio between the two element systems in advance. 
Therefore, if there is an antenna element having a low reception level or 
a defective antenna element, the above-mentioned defect can be prevented 
from affecting the in-phase combining in the other antenna element 
systems. Therefore, it can be found that the second preferred embodiment 
has a greater tolerance to failures or the like of the antenna elements 
and the circuit devices connected thereto than the first preferred 
embodiment. It is to be noted that the phase difference correction can be 
effected in a parallel processing manner in all the antenna element 
systems in the first preferred embodiment, whereas the second preferred 
embodiment requires a serial processing to be effected by a number of 
times corresponding to approximately log.sub.2 (the number of antenna 
elements), resulting in a long calculating operation time. 
Third preferred embodiment 
FIG. 17 is a block diagram of a part of a receiver section of an automatic 
beam acquiring and tracking apparatus according to the third preferred 
embodiment of the present invention. 
In the third preferred embodiment, received signals of antenna elements are 
inputted to a multi-beam forming circuit 90 which operates based on 
two-dimensional fast Fourier transform (FFT) or discrete Fourier transform 
(DFT). Among a plurality of obtained M beam signals BE-1 through BE-M, a 
predetermined plural number of L beam signals BES-1 through BES-L are 
selected by a beam selecting circuit 91 in order of magnitude of signal 
intensity from a beam signal having the greatest signal intensity, i.e., 
the greatest sum of squares of beam electric field values. Thereafter, an 
amplitude and phase difference correcting process is effected between the 
beam signals BES-1 through BES-L in amplitude and phase difference 
correcting circuits PCA-1 through PCA-(L-1) and then the resulting signals 
are subjected to an in-phase combining (maximum ratio combining) process 
in an in-phase combiner 92. As a result, the array antenna performs 
acquisition and tracking of an incoming beam. 
Referring to FIG. 17, the multi-beam forming circuit 90 calculates beam 
electric field values EI.sub.m and EQ.sub.m (m=1, 2, . . . , M) comprised 
of a plurality of M beams based on received quadrature baseband signals 
I.sub.i and Q.sub.i (i=1, 2, . . . , N) based on the quasi-synchronous 
detector circuits QD-1 through QD-N, a direction vector d.sub.m 
representing the direction of each main beam of a predetermined plural 
number of M beam signals to be formed predetermined so that a desired wave 
can be received within a range of radiation angle, and a reception 
frequency fr of the received signal, and then outputs beam signals having 
the beam electric field values EI.sub.m and EQ.sub.m to the beam selecting 
circuit 91. That is, the plurality of M directions of beams of a 
multi-beam to be formed are predetermined in correspondence with the 
incoming direction of the desired wave, and the directions are expressed 
by direction vectors d.sub.1, d.sub.2, . . . , d.sub.M (represented by 
reference character d.sub.m hereinafter) viewed from a predetermined 
origin. In the present case, M represents the number of the direction 
vectors d.sub.m which is set so that the desired wave can be received by 
means of the array antenna 1, the number being preferably not smaller than 
four and not greater than the number of the antenna elements A1 through 
AN. Further, position vectors r.sub.1, r.sub.2, . . . , r.sub.N 
(represented by reference character r.sub.n hereinafter) of the antenna 
elements A1 through AN of the array antenna 1 are predetermined as the 
direction vectors viewed from the predetermined origin. Then, according to 
the following Equation (32) and Equation (33), the multi-beam forming 
circuit 90 calculates a plurality of 2N beam electric field values 
EI.sub.n and EQ.sub.n corresponding to the direction vectors d.sub.n 
expressed by respective combinatorial electric fields, and then, outputs 
beam signals having the beam electric field values EI.sub.n and EQ.sub.n 
to the beam selecting circuit 91. 
##EQU18## 
where c is the velocity of light, (d.sub.m .multidot.r.sub.n) is the inner 
product of the direction vector d.sub.m and the position vector r.sub.n. 
Therefore, the phase a.sub.mn is a scalar quantity. 
Then, the beam selecting circuit 91 calculates a sum of squares 
EI.sub.m.sup.2 +EQ.sub.m.sup.2 (m=1, 2, . . . , M) of the plurality of M 
beam electric field values EI.sub.m and EQ.sub.m of the beam signals BE-1 
through BE-M outputted from the multi-beam forming circuit 90, selects a 
predetermined plural number of L beam signals BES-1 through BES-L having 
greater sums of squares of beam electric field values in the order of 
magnitude from the beam signal having the greatest sum of squares of beam 
electric field values, and thereafter, outputs the plurality of beam 
signals BES-1 through BES-L to the in-phase combiner 92 and (L-1) 
amplitude and phase difference correcting circuits PCA-1 through 
PCA-(L-1). In the present case, L is a natural number not greater than the 
plural number of M and is predetermined. It is to be noted that the beam 
selecting circuit 91 is provided for the purpose of removing a received 
signal having an extremely low level and a deteriorated S/N. The sum of 
squares of the beam electric field values is calculated in the 
above-mentioned calculating operation, however, the present invention is 
not limited to this. It is acceptable to calculate a square root of the 
sum of squares of the beam electric field values corresponding to the 
absolute values of the beam electric field values. 
A quadrature baseband signal of the beam signal BES-1 which has the sum of 
squares of the greatest beam electric field values and serves as a 
reference beam signal is inputted to the in-phase combiner 92 and the 
amplitude and phase difference correcting circuit PCA-1. A quadrature 
baseband signal of the beam signal BES-2 which has the sum of squares of 
the second greatest beam electric field values is inputted to the 
amplitude and phase difference correcting circuit PCA-1. A quadrature 
baseband signal of the beam signal BES-3 which has the sum of squares of 
the third greatest beam electric field values is inputted to the amplitude 
and phase difference correcting circuit PCA-2. Likewise, a quadrature 
baseband signal of the beam signal BES-L which has the sum of squares of 
the L-th greatest beam electric field values is inputted to the amplitude 
and phase difference correcting circuit PCA-(L-1). In the present case, 
the amplitude and phase difference correcting circuit PCA-s (s=1, 2, . . . 
, L-1) is constructed in a manner similar to that of the amplitude and 
phase difference correcting circuits PCA-s of the second preferred 
embodiment shown in FIG. 16. 
In the third preferred embodiment, the amplitude and phase difference 
correcting circuit PCA-1 uses the quadrature baseband signal of the 
reference greatest beam signal BES-1 and a specific filter for removing 
noises to calculate transformation matrix elements for putting the two 
beam signals in phase with each other, and effects phase difference 
correction so that the baseband signals of the two beam signals are put in 
phase with each other based on a transformation matrix including the 
calculated transformation matrix elements, i.e., effects phase shift. The 
circuit PCA-1 further executes an amplitude and phase difference 
correcting process by effecting weighting with an amplitude gain directly 
proportional to the calculated received signal intensity similarly to the 
amplitude correcting section 45 of the first preferred embodiment, and 
then, outputs the processed baseband signal to the in-phase combiner 92. 
The amplitude and phase difference correcting circuit PCA-2 uses the 
quadrature baseband signal of the reference greatest beam signal BES-1 and 
the quadrature baseband signal of the beam signal BES-3 to execute an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1, and then, outputs 
the processed baseband signal to the in-phase combiner 92. Likewise, the 
amplitude and phase difference correcting circuit PCA-(L-1) uses the 
quadrature baseband signal of the reference greatest beam signal BES-1 and 
the quadrature baseband signal of the beam signal BES-L to execute an 
amplitude and phase difference correcting process similarly to the 
amplitude and phase difference correcting circuit PCA-1, and then, outputs 
the processed baseband signal to the in-phase combiner 92. The in-phase 
combiner 92 combines in phase the inputted plurality of L baseband signals 
every channel, and then, outputs the resulting signal to the demodulator 
5. 
In the third preferred embodiment, all the selected beam signals are put in 
phase with the beam signal having the greatest signal intensity. In other 
words, the beam signal having the greatest signal intensity is used as a 
reference received signal, and the phases of the other selected beam 
signals are corrected with respect to the reference signal. In the present 
third preferred embodiment, the amplitude and phase difference correcting 
process and the in-phase combining process are each permitted to be 
effected "(the number L of the selected beams) -1" times. However, it is 
required to incorporate the multi-beam forming circuit 90 and the beam 
selecting circuit 91. 
In the amplitude and phase difference correcting circuits PCA-s of the 
third preferred embodiment, when a transforming calculation using a 
transformation matrix for the in-phase combining process is executed 
according to the Equation (22) and Expression (30) in the amplitude and 
phase difference correcting circuits PCA-1 through PCA-(L-1) shown in FIG. 
7, the phase difference correcting section 44a and the amplitude 
correcting section 45 shown in FIG. 16 can be integrated with each other. 
According to the integrated construction, the phase difference correction 
for the in-phase combining process and the amplitude correction can be 
effected simultaneously, by which the plurality of received signals 
received by the array antenna 1 can be combined at the maximum ratio and 
the combined one received signal can be outputted. 
Further, as a modification example of the third preferred embodiment, there 
may be a construction as follows similarly to the processing operations of 
the first preferred embodiment. The phase difference estimation section 
40a estimates an instantaneous phase difference .delta..sub.i,j of the 
received signals received by two antenna elements i and j based on the 
quadrature baseband signals I.sub.i and Q.sub.i and I.sub.j and Q.sub.j 
relevant to the two antenna elements i and j according to the Equation 
(7), removes noises, and then outputs an estimated phase difference 
.delta..sub.ci,j (See FIG. 8) from which the noises are removed to the 
phase difference correcting section 44a. Then, the phase difference 
correcting section 44a corrects the phase difference by shifting the 
quadrature baseband signals inputted from the delay buffer memory 43 by 
the estimated phase difference .delta..sub.ci,j based on the estimated 
phase difference .delta..sub.ci,j inputted from the phase difference 
estimation section 40a, and then, outputs the resultant to the amplitude 
correcting section 45. 
The third preferred embodiment has advantageous effects as follows in 
comparison with the first and second preferred embodiments. In the first 
and second preferred embodiments, the received signal to noise power ratio 
per antenna element is reduced accordingly as the number of the antenna 
elements constituting the array antenna increases resulting in a 
deteriorated accuracy in the phase difference correcting process, and then 
there is a limitation in the number of antenna elements. In contrast to 
the above, according to the third preferred embodiment, the amplitude and 
phase difference correcting process is effected after a beam having a high 
received signal to noise power ratio is formed by the multi-beam forming 
circuit 90 and the beam selecting circuit 91. Therefore, no influence is 
exerted on the phase difference correction accuracy even if the received 
signal to noise power ratio of each antenna element is relatively low, 
this means that there is theoretically no limitation on the number of 
antenna elements. Furthermore, when an intense interference wave or the 
like comes in another direction, the first and second preferred 
embodiments try to combine all the signals including the interference 
wave, and therefore, the combined received signal is sometimes distorted 
or disturbed in regard to its directivity. However, in the third preferred 
embodiment, such waves are spatially separated to a certain extent through 
beam selection, and therefore, the apparatus is less susceptible to the 
interference waves. However, in the first and second preferred 
embodiments, the beam formation is effected by making effective use of the 
received signals inputted from all the antenna elements so that the 
maximum gain can be achieved in the direction of the incoming beam in the 
first and second preferred embodiments, and therefore, the tracking 
operation is effected with the maximum gain maintained even when the 
direction of the incoming beam changes. In contrast to the above, there is 
a power loss in the time of beam selection when there is a reduced number 
of beams in the third preferred embodiment, and this causes a problem that 
a fluctuation is generated in the gain when the direction of the incoming 
beam changes. 
Fourth preferred embodiment 
FIG. 18 is a block diagram of a receiver section of an automatic beam 
acquiring and tracking apparatus of an array antenna for use in 
communications according to the fourth preferred embodiment of the present 
invention. 
Referring to FIG. 18, in the automatic beam acquiring and tracking 
apparatus of the array antenna for use in communications of the present 
preferred embodiment, a directivity of an array antenna 1 comprised of a 
plurality of N antenna elements A1, A2, . . . , Ai, . . . , AN arranged 
adjacently at predetermined intervals of, for example, either one half of 
the wavelength of a reception frequency, one half of the wavelength of a 
transmission frequency or one half of an average value of the wavelength 
of a reception frequency and the wavelength of a transmission frequency in 
an arbitrary flat plane or a curved plane is rapidly directed to a 
direction in which a radio signal wave such as a digital phase modulation 
wave or an unmodulated wave comes so as to perform tracking. In this 
arrangement, in particular, the acquiring and tracking apparatus of the 
present preferred embodiment is characterized in comprising a digital beam 
forming section (referred to as a DBF section hereinafter) 104 and a 
transmission weighting coefficient calculation circuit 30. Even when the 
azimuth of the remote station of the other party serving as a signal 
source has been unknown, a transmitting beam is formed in a direction of 
the incoming wave based on a baseband signal of each antenna element 
obtained from the incoming wave transmitted from the signal source. 
Further, in an environment or state in which a plurality of multi-path 
waves come, or in a case where a phase uncertainty takes place in a 
reception phase difference, influence of the multi-path waves and the 
phase uncertainty are removed, and a single transmitting main beam is 
formed only in the direction of a greatest received wave. 
As shown in FIG. 18, the array antenna 1 comprises a plurality of N antenna 
elements A1 through AN and circulators CI-1 through CI-N which serve as 
transmission and reception separators. Each of receiver modules RM-1 
through RM-N comprises a low-noise amplifier 2 and a down converter (D/C) 
3 which frequency-converts a radio signal having a received radio 
frequency into an intermediate frequency signal having a predetermined 
intermediate frequency by means of a common first local oscillation signal 
outputted from a first local oscillator 11. 
The receiver section of the present beam acquiring and tracking apparatus 
further comprises: 
(a) N A/D converters AD-1 through AD-N; 
(b) N quasi-synchronous detector circuits QD-1 through QD-N which subject 
the intermediate frequency signal obtained through an A/D conversion 
process to a quasi-synchronous detection process by means of a common 
second local oscillation signal outputted from a second local oscillator 
12 so as to convert the resulting signal into a pair of baseband signals 
orthogonal to each other, wherein a pair of baseband signals is referred 
to as quadrature baseband signals hereinafter; 
(c) the DBF section 104 which calculates reception weights W.sub.1.sup.RX, 
W.sub.2.sup.RX, . . . , W.sub.N.sup.RX for the quadrature baseband signals 
such that the maximum ratio combining is achieved based on the transformed 
quadrature baseband signals, multiplies the quadrature baseband signals by 
the calculated reception weights W.sub.1.sup.RX, W.sub.2.sup.RX , . . . , 
W.sub.N.sup.RX, and thereafter, combines in phase the resulting signals to 
output the resulting signal to a demodulator 5; 
(d) a transmission weighting coefficient calculation circuit 30 which 
calculates transmission weights W.sub.1.sup.TX, W.sub.2.sup.TX, . . . , 
W.sub.N.sup.TX according to a method of the present invention based on the 
reception weights W.sub.1.sup.RX, W.sub.2.sup.RX, . . . , W.sub.N.sup.RX 
calculated by the DBF section 104, and then, outputs the resulting signals 
to a transmission local oscillator 10; and 
(e) a demodulator 5 which effects synchronous detection or delayed 
detection in a predetermined baseband demodulation process from the 
baseband signal outputted from the DBF section 104, extracts desired 
digital data, and then, outputs the digital data as received data. 
In the above-mentioned receiver section, lines extending from the antenna 
elements A1 through AN in the array antenna 1 to the DBF section 104 are 
connected in series in each antenna element system. The signal processing 
operation for each antenna element system in the present receiver section 
is executed in a similar manner, and therefore, the processing operation 
of the radio signal wave received by an antenna element Ai (one of the 
antenna elements A1 through AN is represented by Ai) will be described. 
A radio signal wave received by the antenna element Ai is inputted via the 
circulator CI-i and the low-noise amplifier 2 of the receiver module RM-i 
to the down converter 3. The down converter 3 of the receiver module RM-i 
frequency-converts the inputted radio signal into an intermediate 
frequency signal having a predetermined intermediate frequency using the 
common first local oscillation signal outputted from the first local 
oscillator 11, and then, outputs the resulting signal to the 
quasi-synchronous detector circuit QD-i via the A/D converter AD-i. The 
quasi-synchronous detector circuit QD-i subjects the inputted intermediate 
frequency signal obtained through the A/D conversion process to a 
quasi-synchronous detection process using the common second local 
oscillation signal outputted from the second local oscillator 12 so as to 
convert the resulting signal into each pair of quadrature baseband signals 
I.sub.i and Q.sub.i orthogonal to each other, and then, outputs the 
signals to the DBF section 104. 
The DBF section 104 calculates reception weights W.sub.1.sup.RX, 
W.sub.2.sup.RX, . . . , W.sub.N.sup.RX for the quadrature baseband signals 
such that the maximum ratio combining is achieved based on the transformed 
quadrature baseband signals, multiplies the quadrature baseband signals by 
the calculated reception weights W.sub.1.sup.RX, W.sub.2.sup.RX, . . . , 
W.sub.N.sup.RX, and thereafter, combines in phase the resulting signals to 
output the same to the demodulator 5. Further, the transmission weighting 
coefficient calculation circuit 30 forms a transmitting beam in the 
direction of the direct wave according to a method of the present 
invention based on the reception weights W.sub.1.sup.RX, W.sub.2.sup.RX. . 
. , W.sub.N.sup.RX calculated by the DBF section 104. Further, in an 
environment in which a plurality of multi-path waves come, or in a case 
where a phase uncertainty takes place in a reception phase difference, the 
circuit 30 calculates transmission weights W.sub.1.sup.TX, W.sub.2.sup.TX, 
. . . , W.sub.N.sup.TX so that the influence of the multi-path waves and 
the phase uncertainty are removed and a single transmitting main beam is 
formed only in the direction of the greatest received wave, and then, 
outputs the resulting signals to the transmission local oscillator 10. The 
demodulator 5 effects synchronous detection or delayed detection in a 
predetermined baseband demodulation process from a baseband signal 
outputted from the DBF section 104, extracts the desired digital data, and 
then, outputs the digital data as the received data. The DBF section 104 
and the transmission weighting coefficient calculation circuit 30 will be 
described in detail hereinafter. 
FIG. 19 is a block diagram of a transmitter section of the present beam 
acquiring and tracking apparatus. 
Referring to FIG. 19, the transmitter section includes N transmitter 
modules TM-1 through TM-N, N quadrature modulator circuits QM-1 through 
QM-N, and an in-phase divider 9. In the present case, each of the 
quadrature modulator circuits QM-1 through QM-N comprises a quadrature 
modulator 6 and the transmitting local oscillator 10, while each of the 
transmitter modules TM-1 through TM-N comprises an up-converter (U/C) 7 
for frequency-converting the inputted intermediate frequency signal into a 
transmitting signal having a predetermined transmitting radio frequency 
and a transmission power amplifier 8. In the present case, the 
transmitting local oscillator 10 of each of the quadrature modulator 
circuits QM-1 through QM-N is implemented by an oscillator using a DDS 
(Direct Digital Synthesizer) driven by an identical clock, and operates, 
based on the transmission weights W.sub.1.sup.TX, W.sub.2.sup.TX, . . . , 
W.sub.N.sup.TX inputted from the transmission weighting coefficient 
calculation circuit 30, to generate N transmitting local oscillation 
signals having phases corresponding to the weights. 
A transmitting baseband signal S.sup.TX, or transmitting data is inputted 
to the in-phase divider 9, and thereafter, the inputted transmitting 
baseband signal S.sup.TX is divided in phase, each divided signal being 
inputted to the quadrature modulator 6 of each of the quadrature modulator 
circuits QM-1 through QM-N. For instance, the quadrature modulator 6 of 
the quadrature modulator circuit QM-1 effects a quadrature modulation such 
as a QPSK or the like on the transmitting local oscillation signal 
generated by the transmitting local oscillator 10 according to the 
transmitting baseband signal S.sup.TX inputted from the in-phase divider 
9, and thereafter, obtains the intermediate frequency signal through the 
quadrature modulation as a transmitting radio signal to the circulator 
CI-1 of the array antenna 1 via the up-converter 7 and the transmission 
power amplifier 8 of the transmitter module TM-1. In the present case, the 
quadrature modulator 6 subjects the inputted transmitting baseband signal 
S.sup.TX to a serial to parallel conversion process so as to convert the 
signal into a transmitting quadrature baseband signal, and thereafter, 
combines the transmitting local oscillation signals having a mutual phase 
difference of 90.degree. according to the transmitting quadrature baseband 
signal so as to obtain the intermediate frequency signal. Then, the 
transmitting radio signal is radiately transmitted from the antenna 
element A1. Further, a similar signal processing operation is executed in 
each system of the transmitter section connected to the antenna elements 
A2 through AN. Consequently, transmitting signals weighted with the 
transmission weights W.sub.1.sup.TX, W.sub.2.sup.TX, . . . , 
W.sub.N.sup.TX are radiated from the antenna elements A1 through AN. In 
the present preferred embodiment, the transmitting signals transmitted 
from the antenna elements Ai are weighted with the transmission weights 
W.sub.1.sup.TX, W.sub.2.sup.TX, . . . , W.sub.N.sup.TX in a manner as 
described in detail hereinafter, when the signals are transmitted with 
same amplitudes with the phases thereof merely varied through the 
weighting. 
In the present preferred embodiment, for example, N=16 antenna elements A1 
through A16 are arranged at predetermined intervals in a lattice 
configuration. The above-mentioned interval is, as described hereinbefore, 
either half wavelength of the transmission frequency, half wavelength of 
the reception frequency, or half wavelength of the average value of them. 
Each of the antenna elements A1 through AN is, for example, a circular 
patch microstrip antenna. In a linear array antenna of a modification 
example, four antenna elements A1 through A4 are arranged in a line so as 
to be separated apart from each other at the above-mentioned intervals. 
FIG. 21 is a block diagram showing a signal processing operation of the DBF 
section 104. The DBF section 104 of the present preferred embodiment 
effects the signal processing on a quadrature baseband signal comprised of 
an I component and a Q component obtained through the A/D conversion 
process and the quasi-synchronous detection process for each of the 
antenna elements A1 through AN. In the present case, assuming that the 
number of the antenna elements of the array antenna 1 is N, baseband 
signals S.sub.r and S.sub.i respectively of an antenna element Ar which 
serves as a phase reference and an arbitrary antenna element Ai 
(1.ltoreq.r.ltoreq.N, 1.ltoreq.i.ltoreq.N) including the antenna element 
Ar are expressed by complex numbers as follows. In the present case, the 
baseband signal S.sub.r is referred to as a reference baseband signal, 
while the baseband signal S.sub.i is referred to as a processing baseband 
signal. The antenna element that serves as the phase reference (referred 
to as an antenna element Ar hereinafter) is a predetermined one of the N 
antenna elements. An antenna element that has received the baseband signal 
S.sub.i is referred to as an processing antenna element Ai. 
##EQU19## 
where a.sub.r is an amplitude component of the reference baseband signal, 
a.sub.i is an amplitude component of the processing baseband signal, and 
.phi..sub.m is a modulation phase. Further, .theta..sub.r is a phase 
difference between the reference baseband signal S.sub.r and the local 
oscillation signal generated by the second local oscillator 12, 
.theta..sub.i is a phase difference between the processing baseband signal 
S.sub.i and the local oscillation signal generated by the second local 
oscillator 12, and .DELTA..theta..sub.r,i is a phase difference between 
the reference baseband signal S.sub.r and the processing baseband signal 
S.sub.i. 
In the present case, a reception signal power .vertline.S.sub.i 51 .sup.2 
at the processing antenna element Ai can be expressed by the following 
Equation (37). 
EQU .vertline.S.sub.i.vertline..sup.2 =I.sub.i.sup.2 +Q.sub.i.sup.2 
=a.sub.i.sup.2 (37) 
In the present preferred embodiment, it is preferable to compare reception 
signal powers with each other obtained at the processing antenna elements 
Ai and determine the antenna element at which the maximum reception signal 
power is obtained as the phase reference for the in-phase combining in 
terms of in-phase combining accuracy. However, actually a phase skip 
occurs when the reference antenna element is changed in the course of 
communication, and therefore, the reference antenna element is 
predetermined and fixed. Then, .phi..sub.m and .theta..sub.r in the 
Equation (35) and the Equation (36) can be canceled by means of an 
operation or calculation expression of a complex conjugate product 
expressed by the following Equation (38). 
EQU S.sub.r *.multidot.S.sub.i =a.sub.r a.sub.i .multidot.exp 
(j.DELTA..theta..sub.r, i) (38) 
where * represents a complex conjugate. A complex conjugate product 
calculation section 21 as shown in FIG. 21 executes the operation or 
calculation of the Equation (38). 
The real number component and the imaginary number component of the 
Equation (38) are expressed by the following Equations (39) and (40), 
respectively. 
##EQU20## 
Therefore, by multiplying the complex conjugate (S.sub.r 
*.multidot.S.sub.i)* of (S.sub.r .multidot.S.sub.i) in the Equation (38) 
by the baseband signal S.sub.i of the antenna element Ai, the processing 
baseband signal S.sub.i is put in phase with the reference baseband signal 
S.sub.4, and a processing baseband signal S.sub.i, obtained through the 
in-phase combining process can be expressed by the following Equation 
(41). 
##EQU21## 
In the above-mentioned Equations, .vertline.S.sub.r .vertline. represents 
the amplitude of the reference baseband signal S.sub.r of the reference 
antenna element Ar. By multiplying the complex conjugate commonly by an 
inverse number of the amplitude for each antenna element Ai in a manner as 
shown in the Equation (41), the level of each processing baseband signal 
S.sub.i is standardized by the total reception power received by the array 
antenna 1. If the Equation (41) is expressed by a vector, the following 
Equation (43) holds. 
##EQU22## 
By executing the above-mentioned vector rotating operation for every 
antenna element Ai, all the processing baseband signals S.sub.i are 
relatively put in phase with each other. The method of the present 
preferred embodiment of the present invention executes no tan.sup.-1 
operation but uses the results of the Equation (39) and the Equation (40) 
directly as rotational matrix elements. Therefore, as evident from the 
Equation (43), the matrix is automatically multiplied by the amplitude 
.vertline.a.sub.i .vertline. of the processing baseband signal S.sub.i 
which serves as a coefficient. Therefore, to perform combining of the 
resultants for all the antenna elements Ai is to execute nothing but the 
maximum ratio combining (MRC). In actual communication, there is caused an 
error or amplitude fluctuation in putting signals in phase due to receiver 
noise, modulation components, band limitation and so forth, and according 
to these factors, each weight for the maximum ratio combining has a 
greater error. In order to suppress the influence of the above-mentioned 
factors, the Equation (43) is replaced by the following Equation 4 by 
means of low-pass filters 22 and 23 which are digital filters having a 
filter coefficient F(.multidot.). 
##EQU23## 
Cut-off frequencies of the low-pass filters 22 and 23 will be described 
hereinafter. The low-pass filters 22 and 23 shown in FIG. 21 are each 
implemented by a digital filter such as an FIR filter or an IIR filter. 
The higher the cut-off frequency is, the more the reception noises exert 
influence. Therefore, when the reception power per antenna element is 
relatively low, the acquiring and tracking accuracy tends to deteriorate. 
Conversely, the lower the cut-off frequency is, the less the reception 
noises exert influence. Therefore, acquisition and tracking can be 
performed even when the reception power per antenna element is low. 
However, the time constant of a band-pass filter increases accordingly as 
the bandwidth is made narrower, and therefore, this results in a dull or 
slow trackability with respect to an abrupt change of the direction in 
which the reception wave comes. A change of the direction in which the 
reception wave directly comes in normal mobile communication or the like 
is sufficiently slower than the calculating operation time for beam 
formation, and therefore, the reception noises are dominant. Therefore, 
the cut-off frequencies of the low-pass filters 22 and 23 can be 
determined depending on the received signal power to noise power ratio. 
When the reception power is relatively small as in satellite 
communications, it is preferable to set the cut-off frequencies of the 
low-pass filters 22 and 23 as low as possible within a permissible range 
of hardware. The cut-off frequencies of the low-pass filters 22 and 23 are 
each practically set to about one hundredth to one thousandth of the 
sampling frequency. 
It is to be noted that delay buffer circuits 24 and 25 for adjusting timing 
so that two signals inputted to multipliers 26 and 27 are put in phase 
with each other are inserted into the DBF section 104 taking into account 
the delay effected by the low-pass filters 22 and 23. 
Construction and operation of the above-mentioned DBF section 104 will be 
described hereinafter with reference to FIG. 21. 
Referring to FIG. 21, the reference baseband signal S.sub.r is inputted to 
an absolute value calculation section 20 and a complex conjugate product 
calculation section 21, and also the reference baseband signal S.sub.r is 
inputted to the multiplier 26 via the delay buffer circuit 24. On the 
other hand, the processing baseband signal S.sub.i is inputted to the 
complex conjugate product calculation section 21 and is also inputted to 
the multiplier 27 via the delay buffer circuit 25. The absolute value 
calculation section 20 calculates the absolute value .vertline.S.sub.r 
.vertline. based on the reference baseband signal S.sub.r, and then, 
outputs a signal representing the absolute value .vertline.S.sub.r 
.vertline. to dividers 28a and 28b via the low-pass filter (LPF) 22. On 
the other hand, the complex conjugate product calculation section 21 
executes an operation of (S.sub.r .multidot.S.sub.i *) based on the 
reference baseband signal S.sub.r and the processing baseband signal 
S.sub.i, and then, outputs a signal representing the operation result to 
the multiplier 27 and the divider 28b via the low-pass filter 23. The 
multiplier 26 multiplies the inputted two signals by each other, and then, 
outputs a signal representing the multiplication result as a processed 
reference baseband signal S.sub.r '. On the other hand, the multiplier 27 
multiplies the inputted two signals by each other, and then, outputs a 
signal representing the multiplication result to the divider 28a. The 
divider 28a divides the signal inputted from the multiplier 27 by the 
signal inputted from the low-pass filter 22, and then, outputs a signal 
representing the division result as a processed in-phase processing 
baseband signal S.sub.i ' to an in-phase combiner 29. The divider 28b 
divides the signal inputted from the low-pass filter 23 by the signal 
inputted from the low-pass filter 22, and then, outputs a signal 
representing the division result as a reception weight W.sub.i.sup.Rx to a 
transmission weighting coefficient calculation circuit 30. Then, the 
in-phase combiner 29 combines in phase all of N processed in-phase 
processing baseband signals S.sub.i ' (i=1, 2, . . . , N), and then, 
outputs the resulting signal to the demodulator 5. Therefore, as is 
apparent from FIG. 21 and the above description, weighting for the maximum 
ratio combining is automatically effected in the process of putting the 
signals in phase with each other, and therefore, the DBF section 104 has a 
very simple construction. 
On the other hand, since a quasi-synchronous detection process is used for 
the detection of the baseband signals as shown in FIG. 18, the output 
signal of the DBF section 104 is not synchronized with the second local 
oscillation signal for reception. Therefore, it is required to connect the 
baseband processing type demodulator 5 in the stage subsequent to the DBF 
section 104 so as to synchronize the signal Phase with the carrier phase. 
Further, when symbol delay of a multi-path wave signal is significantly 
great, a further appropriate adaptive equalizer (EQL) (not shown) must be 
incorporated. As a result of these processing operations, the present 
apparatus of the present preferred embodiment simultaneously forms a 
plurality of main beams in the directions of the direct wave and a 
multi-path delayed wave (referred to as a multi-path wave hereinafter), 
combines the main beams appropriately in terms of carrier signal power to 
noise power ratio (reception CNR), and tracks the beams. Since the present 
apparatus uses no feedback loop for the beam formation, the apparatus can 
operate stably and speedily even at a low reception CNR similarly to the 
second prior art. 
Next, retro-directive transmitting beam formation to be executed by the 
transmission weighting coefficient calculation circuit 30 shown in FIG. 23 
will be described hereinafter. First of all, here is considered a case 
where the interval of the antenna elements of the transmission array 
antenna and the interval of the antenna elements of the reception array 
antenna are equal to each other in terms of wavelength. In the present 
case, in order to form a transmitting beam in the same direction as that 
of the received incoming beam, it is normally proper to use the reception 
weight W.sub.i.sup.RX that is used on the reception side as a transmission 
weight W.sub.i.sup.TX, as follows. 
EQU S.sub.i.sup.TX =W.sub.i.sup.TX .multidot.S.sup.TX 
=(W.sub.i.sup.RX).multidot.S.sup.TX (45) 
EQU W.sub.i.sup.RX ={1/F(.vertline.S.sub.r .vertline.)}.multidot.F(S.sub.r 
.multidot.S.sub.i *) (46) 
where S.sup.TX is a transmitting baseband signal inputted to the present 
apparatus, Si.sup.TX is a transmitting baseband signal supplied to the 
antenna element Ai, and W.sub.i.sup.TX is a transmission weight for the 
antenna element Ai. As a result, a transmitting beam having a form 
identical to that of the received beam is to be formed. When a relatively 
great multi-path delayed wave exists, a beam is to be formed not only in 
the direction of the direct wave but also in the direction of delayed 
waves. When it is possible to assume that same frequencies are used and 
both paths are approximately equal to each other in reception and 
transmission in such a case as TDD (Time Division Duplex) by which 
reception and transmission are performed alternately at an identical 
frequency, the above-mentioned arrangement is enough, this allows a 
diversity transmission and reception system to be easily constructed. 
However, when there are used different frequencies in reception and 
transmission, the phase difference between the paths becomes unequal. 
Therefore, no diversity transmission and reception system can be 
constructed, and it is required to suppress transmission in the direction 
of the delayed waves as far as possible. Therefore, on an assumption that 
the direct wave has the greatest level among a plurality of multi-path 
waves, a method for forming a single main beam in the direction of the 
direct wave while eliminating the influence of the delayed waves will be 
described below. 
According to the Equation (39) and the Equation (40), a reception phase 
difference .DELTA..theta..sub.r,i between the reference antenna element Ar 
and the arbitrary antenna element Ai is expressed by the following 
Equation (47). 
EQU .DELTA..theta..sub.r,i =tan.sup.-1 {F(I.sub.r .multidot.Q.sub.i -I.sub.i 
.multidot.Q.sub.r)/F(I.sub.r .multidot.Q.sub.i)} (47) 
It is to be noted that .DELTA..theta..sub.r,i obtained here is within a 
range of -.tau. to +.tau.. Therefore, the phase difference rotates several 
times (i.e., becomes an integral multiple of 2.tau.) accordingly as the 
antenna element interval increases, and this causes a phase uncertainty. A 
method for removing the phase uncertainty will be described in detail 
hereinafter, however, it is assumed now that the phase uncertainty has 
been already removed. Assuming that there is neither delayed wave nor 
noise, the phase difference .DELTA..theta..sub.r,i is to be in a certain 
linear phase plane. However, when there is a delayed wave or noise, the 
phase difference is to be dispersed about the plane. It is now considered 
that, by using a value formed by making the phase difference regress to 
the phase plane as an excitation phase and effect excitation with an 
identical amplitude, a single transmitting main beam is formed only in the 
direction in which the direct wave having the greatest level comes. As a 
method for making the phase difference regress to the linear phase plane, 
a regression analysis method using the least square method (LSR) can be 
used. First of all, a linear phase regression plane is set as follows. 
EQU .DELTA..theta..sub.r,i.sup.LSR =ax+by+c (48) 
In the present case, the array antenna 1 is assumed to be located in an 
xy-plane of an xyz-coordinate system as shown in FIG. 22. The coefficients 
a, b and c can be obtained by solving the following Wiener-Hopf equation 
(49). 
##EQU24## 
In the present case, the coordinates of the antenna element Ai of the array 
antenna 1 are (x.sub.i, y.sub.i) (i=1, 2, . . . , N), where x is a matrix 
depending on the arrangement of the antenna element Ai, A is a matrix 
comprised of the coefficients a, b and c representing the above-mentioned 
linear phase regression plane, .THETA. is a matrix comprised of the phase 
difference .DELTA..theta..sub.r,i of the antenna elements Ai. The matrix A 
in the Equation (49) can be expressed by the following Equation (53) by 
rewriting the Equation (49). 
EQU A=(X.sup.T .multidot.X).sup.-1 .multidot.X.sup.T .multidot..THETA.(53) 
In the Equation (53), (X.sup.T .multidot.X).sup.-1 .multidot.X.sup.T 
represents a matrix of 3.times.N depending on the element arrangement of 
the array antenna 1, and therefore, (X.sup.T .multidot.X).sup.-1 
.multidot.X.sup.T can be preparatorily calculated. The parameter A of the 
regression plane can be obtained by executing a product-sum operation 
every N times from the phase matrix .THETA. obtained according to the 
Equation (47). On the other hand, the phase difference 
.DELTA..theta..sub.r,.sub.i obtained according to the Equation (47) in a 
manner as described above has a phase uncertainty. When such an 
uncertainty exists, even when the least square regression process is 
executed, the correct phase regression plane cannot always be obtained. 
Therefore, the following three ways of phase uncertainty and phase 
correction in the cases are put into execution. 
(a) Correction case (I): 
EQU .DELTA..theta.'.sub.i-1,i =.DELTA..theta..sub.i-1,i (no correction)(54) 
(b) Correction case (II): 
EQU if .DELTA..theta..sub.i-1,i &lt;-k, .DELTA..theta.'.sub.i-1,i 
=.DELTA..theta..sub.i-1,i +2 .pi. 
otherwise, 
EQU .DELTA..theta.'.sub.i-1,i =.DELTA..theta..sub.i-1,i (no correction)(55) 
(c) Correction case (III): 
EQU if k.ltoreq..DELTA..theta..sub.i-1,i, .DELTA..theta.'.sub.i-1,i 
=.DELTA..theta..sub.i-1,i -2 .pi. 
otherwise, 
EQU .DELTA..theta.'.sub.i-1,i =.DELTA..theta..sub.i-1,i (no correction)(56) 
where the phase difference .DELTA..theta..sub.i-1,i represents a phase 
difference between most adjacent antenna elements of each combination, and 
is expressed by the following Equation (57). 
EQU .DELTA..theta..sub.i-1,i =.DELTA..theta..sub.r,i -.DELTA..theta..sub.r,i-1( 
57) 
On the other hand, k exists within a range of 0&lt;k&lt;.pi., and is a phase 
threshold value representing a degree of disorder or disturbance of the 
reception phase difference due to a multi-path wave, the value is set 
according to an estimated intensity of the multi-path wave. Setting of the 
phase threshold value k in checking the reception phase uncertainty will 
be described below. 
In the present preferred embodiment, the three ways of phase uncertainty 
and phase correction processes are executed according to the Equation (54) 
through the Equation (56), and the positive phase threshold value k (&gt;0) 
is set therein. The positive phase threshold value K becomes a parameter 
for determining a sensitivity of the phase correction. That is, the 
smaller the value k is, the higher the correction sensitivity becomes, and 
the maximum sensitivity is achieved when k=0. Conversely, the greater the 
value k is, the lower the correction sensitivity becomes, and almost no 
phase correction is effected when k is not smaller than .pi.. Therefore, 
when the received signal wave is only the direct incoming wave and the 
reception intensity of the multi-path incoming wave is sufficiently 
smaller than that of the direct incoming wave, it is preferable that 
k.apprxeq.0. However, when the reception intensity of the multi-path 
incoming wave is great and the direction in which the direct wave comes is 
close to the front of the antenna, a correction error may occur due to the 
fact that the reception phase plane is not flat as shown in FIG. 30. The 
above is because the correction sensitivity is too high. Therefore, by 
making the correction sensitivity slightly dull by setting the value k to 
a value within a range of k&gt;0, the correct correction phase is to be 
obtained. By setting the phase threshold value k to about .pi./6, correct 
phase correction can be achieved even when a multi-path incoming wave 
having the same level as that of the direct incoming wave is received. 
Therefore, in the present preferred embodiment, the phase threshold value 
k is preferably set to .pi./6. 
When the array antenna 1 is arranged in the xy-coordinate system as shown 
in FIG. 22, the phase plane is expressed by the following Equation (58). 
EQU .DELTA..theta..sub.r,i.sup.LSR =ax+by+c (58) 
In the present case, there are three correction methods (I) through (III) 
in the x-axis direction, while there are three correction methods (I) 
through (III) in the y-axis direction. Therefore, a total of nine types of 
phase regression planes are obtained. Hereinbelow, for example, a 
correction case (I-II) represents a phase regression plane in a case where 
the correction case (I) is effected in the x-axis direction (practically 
no correction is effected) and the correction case (II) is effected in the 
y-axis direction. Each axis corresponds to three types of phase 
uncertainty, and totally nine phase regression planes expressed by the 
following Equations (59) are obtained. 
(a) In the correction case (I-I), 
EQU .DELTA..theta..sub.r,i.sup.LSR(I-I) =a.sub.I x+b.sub.I y+c 
(b) In the correction case (I-II), 
EQU .DELTA..theta..sub.r,i.sup.LSR(I-II) =a.sub.I x+b.sub.II y+c 
(c) In the correction case (I-III), 
EQU .DELTA..theta..sub.r,i.sup.LSR(I-III) =a.sub.I x+b.sub.III y+c 
(d) In the correction case (II-I), 
EQU .DELTA..theta..sub.r,i.sup.LSR(II-I) =a.sub.II x+b.sub.b y+c 
(e) In the correction case (II-II), 
EQU .DELTA..theta..sub.r,i.sup.LSR(II-II) =a.sub.II x+b.sub.II y+c 
(f) In the correction case (II-III), 
EQU .DELTA..theta..sub.r,i.sup.LSR(II-III) =a.sub.II x+b.sub.III y+c 
(g) In the correction case (III-I), 
EQU .DELTA..theta..sub.r,i.sup.LSR(III-I) =a.sub.III x+b.sub.I y+c 
(h) In the correction case (III-II), 
EQU .DELTA..theta..sub.r,i.sup.LSR(III-II) =a.sub.III x+b.sub.I y+c 
(i) In the correction case (III-III), 
EQU .DELTA..theta..sub.r,i.sup.LSR(III-III) =a.sub.III x+b.sub.III y+c(59) 
In the present case, residual sums of squares are defined by the following 
Equations (60). 
(a) In the correction case (I-I), 
##EQU25## 
(b) In the correction case (I-II), 
##EQU26## 
(c) In the correction case (I-III), 
##EQU27## 
(d) In the correction case (II-I), 
##EQU28## 
(e) In the correction case (II-II), 
##EQU29## 
(f) In the correction case (II-III), 
##EQU30## 
(g) In the correction case (III-I), 
##EQU31## 
(h) In the correction case (III-II), 
##EQU32## 
(i) In the correction case (III-III), 
##EQU33## 
According to the above-mentioned equations, the phase uncertainty is 
removed through a phase regression plane selecting process shown in FIGS. 
25 through 27 by means of the residual sum of squares 
SS=.SIGMA.(.DELTA..theta..sub.r,i -.DELTA..theta..sub.r,i.sup.LSR).sup.2 
and phase gradients .vertline.a.vertline. and .vertline.b.vertline. of the 
regression plane, so that one equi-phase regression plane is selected. 
The phase regression plane selecting process in a two-dimensional array 
will be described hereinafter with reference to flowcharts of FIGS. 25 
through 27. 
Referring to FIG. 25, in step S11, residual sums of squares SS.sub.(I-I), 
SS.sub.(I-II), SS.sub.(II-I) and SS.sub.(II-II) in the correction cases 
(I-I), (I-II), (II-I) and (II-II) are compared with each other. When the 
residual sum of squares SS.sub.(I-I) is the minimum in step S12, the phase 
regression plane in the correction case (I-I) is selected in step S21, and 
then, the present process is completed. When the residual sum of squares 
SS.sub.(I-II) is the minimum in step S13, gradients 
.vertline.b.vertline..sub.(I-II) and .vertline.b.vertline..sub.(I-III) of 
the regression planes in the correction cases (I-II) and (I-III) are 
compared with each other in step S22. Subsequently, when 
.vertline.b.vertline..sub.(I-II) &lt;.vertline.b.vertline..sub.(I-III) in 
step S23, the phase regression plane in the correction case (I-II) is 
selected in step S24, and then, the present process is completed. When 
.vertline.b.vertline..sub.(I-II) .gtoreq..vertline.b.vertline..sub.(I-III) 
in step S23, the phase regression plane in the correction case (I-III) is 
selected in step S25, and then, the present process is completed. 
When the answer in step S13 is negative or NO and when the residual sum of 
squares SS.sub.(II-I) is the minimum in step S14 in FIG. 26, gradients 
.vertline.a.vertline..sub.(II-I) and .vertline.a.vertline..sub.(III-I) of 
the regression planes in the correction cases (II-I) and (III-I) are 
compared with each other in step S26. Subsequently, when 
.vertline.a.vertline..sub.(II-I) &lt;.vertline.a.vertline..sub.(III-I) in 
step S27, the phase regression plane in the correction case (II-I) is 
selected in step S28, and then, the present process is completed. When 
.vertline.a.vertline..sub.(II-I) .gtoreq..vertline.a.vertline..sub.(III-I) 
in step S27, the phase regression plane in the correction case (III-I) is 
selected in step S29, and the then, present process is completed. 
When the answer in step S14 is NO, gradients 
.vertline.a.vertline..sub.(II-II) and .vertline.a.vertline..sub.(III-II) 
of the regression planes in the correction cases (II-II) and (III-II) are 
compared with each other in step S30 in FIG. 27. Subsequently, when 
.vertline.a.vertline..sub.(II-II) &lt;.vertline.a.vertline..sub.(III-II) in 
step S31, gradients .vertline.b.vertline..sub.(II-II) and 
.vertline.b.vertline..sub.(II-II) of the regression planes in the 
correction cases (II-II) and (II-III) are compared with each other in step 
S40. Subsequently, when .vertline.b.vertline..sub.(II-II) 
&lt;.vertline.b.vertline..sub.(II-III) in step S41, the phase regression 
plane in the correction case (II-II) is selected in step S42, and then, 
the present process is completed. When .vertline.b.vertline..sub.(II-II) 
.gtoreq..vertline.b.vertline..sub.(II-III) in step S41, the phase 
regression plane in the correction case (II-III) is selected in step S43, 
and then, the present process is completed. 
Further, when .vertline.a.vertline..sub.(II-II) 
.gtoreq..vertline.a.vertline..sub.(III-II) in step S31, gradients 
.vertline.b.vertline..sub.(III-II) and .vertline.b.vertline..sub.(III-III) 
of the regression planes in the correction cases (III-II) and (III-III) 
are compared with each other in step S32. Subsequently, when 
.vertline.b.vertline..sub.(III-II) in step S33, the phase regression plane 
in the correction case (III-II) is selected in step S44, and then, the 
present process is completed. When .vertline.b.vertline..sub.(III-II) 
.gtoreq..vertline.b.vertline..sub.(III-III) in step S33, the phase 
regression plane in the correction case (III-III) is selected in step S45, 
and then, the present process is completed. 
Next, a method for removing the phase uncertainty will be described based 
on a case of a linear array antenna (modification example) for simplicity. 
That is, when N antenna elements Ai are arranged in line, the phase plane 
is expressed by the following Equation (61). 
EQU .DELTA..theta..sub.r,i.sup.LSR =ax+c (61) 
In the present case, by applying the Equation (61) to each of the cases of 
the Equation (54) through the Equation (56), the following three phase 
regression planes can be obtained. 
(a) In correction case (I), 
EQU .DELTA..theta..sub.r,i.sup.LSR(I) =a.sub.Ii X+c.sub.I 
(b) In correction case (II), 
EQU .DELTA..theta..sub.r,i.sup.LSR(II) =a.sub.II X+c.sub.II 
(c) In correction case (III), 
EQU .DELTA..theta..sub.r,i.sup.LSR(III) =a.sub.III X+c.sub.III (62) 
In the present case, residual sums of squares of the correction cases are 
defined by the following Equations (63). 
(a) In correction case (I), 
##EQU34## 
(b) In correction case (II), 
##EQU35## 
(c) In correction case (III), 
##EQU36## 
With the above-mentioned arrangement, the phase uncertainty is removed 
through the phase regression plane selecting process shown in FIG. 24 by 
means of the residual sum of squares SS=.SIGMA.(.DELTA..theta..sub.r,i 
-.DELTA..theta..sub.r,i.sup.LSR).sup.2 and the phase gradient 
.vertline.a.vertline. of the regression plane, so that one equi-phase 
regression plane is selected. 
The phase regression plane selecting process in the case of the linear 
array will be described hereinafter with reference to FIG. 24. 
Referring to FIG. 24, the residual sums of squares SS.sub.(I) and 
SS.sub.(II) in the correction cases (I) and (II) are compared with each 
other in step S1. When SS.sub.(I) &lt;SS.sub.(II) in step S2, the phase 
regression plane in the correction case (I) is selected in step S3, and 
then, the present process is completed. When SS.sub.(I) 
.gtoreq.SS.sub.(II) in step S2, gradients .vertline.a.vertline..sub.(II) 
and .vertline.a.vertline..sub.(III) in the correction cases (II) and (III) 
are compared with each other in step S4. When 
.vertline.a.vertline..sub.(II) &lt;.vertline.a.vertline..sub.(III) in step 
S5, the phase regression plane in the correction case (II) is selected in 
step S6, and then, the present process is completed. When 
.vertline.a.vertline..sub.(II) .gtoreq..vertline.a.vertline..sub.(III) in 
step S5, the phase regression plane in the correction case (III) is 
selected in step S7, and then, the present process is completed. 
FIG. 28 shows an explanatory view of a regression process to linear plane 
by the least square method of reception phase, while FIG. 29 is an 
explanatory view of check and removal of phase uncertainty in the 
above-mentioned case. 
Referring to FIG. 28, when only the direct wave is received, the reception 
phase difference .DELTA..theta..sub.r,i between antenna elements Ai of 
each combination is located in a line depending on the position of the 
antenna elements Ai. However, when a multi-path wave is further received, 
the reception phase difference deviates from the line. 
Referring to FIG. 29, there is shown a case where the phase regression 
plane of the correction case (II) is selected when the program flow 
reaches step S6. 
Through the above-mentioned phase regression plane selecting process, the 
phase plane corresponding to the direction of the direct wave having the 
greatest intensity can be estimated and detected. In any other phase 
plane, the residual sum of squares increases and the phase gradient is 
steep. From the thus-determined reception phase difference 
.DELTA..theta..sub.r,i.sup.LSR, the transmission weight W.sub.i.sup.TX can 
be calculated according to the following Equation (64). 
##EQU37## 
In the present case, the amplitude component of the transmission weight is 
made to 1 commonly for all the antenna elements Ai so as to uniform the 
wave source distribution. Further, when the array antenna 1 is used 
commonly for transmission and reception, and different frequencies are 
used in transmission and reception, a transmitting main beam can be formed 
correctly in the direction of the direct incoming wave by multiplying the 
excitation phase by a frequency ratio. That is, the above-mentioned 
operation or calculation can be expressed by the following Equation (65), 
where f.sup.TX and f.sup.RX are transmission frequency and reception 
frequency, respectively. 
##EQU38## 
FIG. 23 is a block diagram showing a transmitting weighting coefficient 
calculation circuit 30 for executing the above-mentioned processes. 
Referring to FIG. 23, a phase difference calculation section 31-i (i=1, 2, 
. . . , N) calculates a phase difference .DELTA..theta..sub.r,i by 
executing a tan.sup.-1 operation of the reception weight W.sub.i.sup.RX 
based on the reception weight W.sub.i.sup.RX inputted from the DBF section 
104, and then, outputs the resultant to a least square regression 
processing section 32-j (j=1, 2, . . . , 9). The least square regression 
processing section 32-j (j=1, 2, . . . , 9) is provided with nine 
processing sections corresponding to the nine phase regression planes 
expressed by the Equation (59). Each least square regression processing 
section 32-j calculates the coefficients a, b and c of the phase plane set 
therefor by solving the Wiener-Hopf equation expressed by the Equation 
(49), calculates the reception phase difference .DELTA..theta.r,i.sup.LSR 
(i=1, 2, . . . , N) on the phase regression plane by substituting the 
calculated coefficients a, b and c into the Equation (59), and then, 
outputs the resultant to a selector 34. On the other hand, a phase 
regression plane selecting section 33 executes the phase regression plane 
selecting process shown in FIGS. 25 through 27 based on the phase 
regression planes calculated by the least square regression processing 
sections 32-j to determine the phase regression plane to be selected, and 
then, outputs information of the phase regression plane determined to be 
selected to the selector 34. The selector 34 selects only N reception 
phase differences .DELTA..theta..sub.r,i.sup.LSR inputted from the least 
square regression processing section 32-k corresponding to the phase 
regression plane determined to be selected, and then, outputs the 
resultant to a transmission weighting coefficient calculation section 35. 
In response to the above-mentioned operation or calculation, the 
transmission weighting coefficient calculation section 35 calculates the 
transmission weight W.sub.i.sup.TX (i=1, 2, . . . , N) by executing the 
calculation of the Equation (65) based on the inputted N reception phase 
differences .DELTA..theta..sub.r,i.sup.LSR. 
A result of simulation on the apparatus having the above-mentioned 
construction performed by the present inventor will be further described 
below. In order to evaluate the apparatus of the present preferred 
embodiment, a numerical simulation was performed under the conditions 
shown in Table 2. As the array antenna 1, a basic four-element 
half-wavelength interval linear array antenna of a modification example 
was used, and a modulation system was assumed to be a quarterly phase 
shift keying modulation QPSK (transmission rate: 16 kbps). Further, as the 
low-pass filters 22 and 23 for putting received signals in phase with each 
other, a secondary narrow-band IIR (Infinite Impulse Response) filter was 
used. 
TABLE 2 
______________________________________ 
Simulation specifications 
______________________________________ 
Modulation 16-kbps QPSK with differential encoded 
system synchronous detection 
Modulation 32 kHz (used as intermediate 
frequency frequency) 
Sampling 128 kHz (16 samples/symbol) 
frequency 
A/D resolution 
8 bits 
Added noise Gauss noise 
Antenna 4-element linear array with a point 
radiation source 
Antenna Half wavelength of carrier wavelength 
element 
interval 
Roll-off 10-tap FIR filter, roll-off rate: 50%, 
filter cut-off frequency: 8 kHz 
Transmission Bandwidth bit length product BT = 2 
band-pass 
filter 
Reception Bandwidth bit length product BTm = 1 
band-pass 
filter 
Carrier Feed-forward phase estimation 
regenerating 
method 
Clock Decision directed method 
generating 
method 
______________________________________ 
FIG. 31 shows a comparison of a directivity pattern obtained through 
maximum ratio combining (MRC) reception in a case where a direct wave 
comes in the direction of -45.degree. and a multi-path wave having a level 
of -3 dB and a phase difference of .pi./2 (at the center of the array 
antenna 1) with respect to the direct wave comes in the direction of 
+15.degree. between a case of equal gain combining (EGC) in which received 
signals received by the antenna elements Ai are combined with each other 
with equal gain and a case where no multi-path wave exists. The reception 
carrier signal power to noise power ratio (referred to as a reception CNR 
hereinafter) of the direct wave is 4 dB. In the equal gain combining 
process, the multi-path wave exerts less influence on the directivity 
pattern. However, in the maximum ratio combining process, a beam is formed 
in the direction in which the multi-path wave comes. Consequently, it can 
be found that directional diversity for taking in both the direct wave and 
the multi-path wave and recombining them is achieved. 
FIGS. 32 and 33 show directivity patterns when the phase of the multi-path 
wave varies relative to that of the direct wave, where a phase delay value 
is at 0, .pi./2 or (3.pi.)/2, and .pi.. The fact that the phase delay 
value=0 means that the phases of the two waves are in phase at the center 
of the antenna. In order to clarify the characteristic of the directivity 
pattern, the reception CNR of the direct wave is set at 30 dB. In the case 
of FIG. 32 where the direction of the direct wave and that of the 
multi-path wave are relatively close to each other (when the direction in 
which the multi-path wave comes is -15.degree.), it can be found that the 
two waves are acquired by an identical beam when the phase delay value=0, 
whereas the waves are acquired by adjacent beams when the phase delay 
value=.pi. (anti-phase) in beam formation. On the other hand, in the case 
of FIG. 33 where the incident directions of the two waves are separated 
apart from each other (when the direction in which the multi-path wave 
comes is 30.degree.), it can be found that there is a shift by one beam of 
the beam used for acquisition between the case where the waves are 
incident in phase and the case where the waves are incident in anti-phase, 
however, the beam formation is achieved in the direction in which the 
waves are effectively acquired within the range of the limited degree of 
freedom of the antenna. In other words, directional diversity for 
combining the direct wave with the multi-path wave by giving both of them 
directivities corresponding to the powers thereof is achieved. 
FIG. 34 shows a simulation result of a bit error rate (BER) in the maximum 
ratio combining reception process under the same conditions as those of 
FIG. 31. It is assumed that the symbol delay of the multi-path wave 
relative to the direct wave can be ignored. It can be found that the bit 
error rate (BER) in a case where one multi-path wave comes is improved by 
a degree of about 1.5 dB in comparison with a case where only the direct 
wave comes, and the value of the degree of improvement comes close to a 
theoretically expected value (about 1.8 dB) through the maximum ratio 
combining process. 
Next, a simulation result of transmitting beam formation will be described. 
FIGS. 35 and 36 show a case where a transmitting beam is formed when two 
waves of a direct wave and a multi-path wave come by means of the 
apparatus of the present preferred embodiment. In the present case, there 
are shown two cases where the directions in which the two waves come are 
changed. FIG. 35 shows a case where the directions in which the direct 
wave and the multi-path wave come are -45.degree. and +15.degree., 
respectively. FIG. 36 shows a case where the directions in which the 
direct wave and the multi-path wave come are -15.degree. and +30.degree., 
respectively. The array antenna 1 is commonly used for transmission and 
reception, and the transmission frequency is 1.066 times as great as 
reception frequency. In each case, it can be found that the transmitting 
main beam is formed only in the direction of the direct wave while 
receiving no influence of the multi-path wave, and radiation in the 
direction of the multi-path wave is suppressed to about the side lobe 
level at most. 
As described above, the present preferred embodiments of the present 
invention have distinctive advantageous effects as follows. 
(1) Since neither a special azimuth sensor nor position data of the remote 
station of the other party as in the first prior art is required, the 
present apparatus of the present preferred embodiments receives no 
influence of the environmental magnetic turbulence, accumulation of 
azimuth detection errors and the like. Further, when the remote station of 
the other party moves, a transmitting beam can be automatically formed in 
the direction of the incoming wave transmitted from the remote station of 
the other party, while allowing downsizing and cost reduction to be 
achieved. 
(2) Instead of directly frequency-converting the reception phase difference 
of the reception antenna to make it a transmission phase difference as in 
the second prior art, the removal of the phase uncertainty is effected 
based on the least square method and the influence of the multi-path waves 
except for the greatest received wave is removed. Therefore, even when the 
greatest received wave comes in whichever direction in the multi-path wave 
environment, the transmitting beam can be surely formed in the direction 
in which the greatest received wave comes. Furthermore, even when there is 
a difference between the transmission frequency and the reception 
frequency, the possible interference exerted on the remote station of the 
other party can be reduced. 
(3) As shown in the apparatus of the preferred embodiment, there can be 
achieved a construction free of any mechanical drive section for the 
antenna and any feedback loop in forming the transmitting beam. Therefore, 
upon obtaining a received baseband signal, the transmission weight can be 
immediately decided, so that the transmitting beam can be formed rapidly 
in real time. 
(4) Further, as shown in the apparatus of the preferred embodiment, the 
determination of the transmission weight can be executed in a digital 
signal processing manner. Therefore, by executing the transmitting beam 
formation in a digital signal processing manner, the baseband processing 
including modulation can be entirely integrated into a digital signal 
processor. When a device having a high degree of integration is used, the 
entire system can be compacted with cost reduction. 
Fifth preferred embodiment 
FIG. 20 is a block diagram of a transmitter section of an automatic beam 
acquiring and tracking apparatus of an array antenna for use in 
communications according to the fifth preferred embodiment of the present 
invention. The other components are constructed similarly to those of the 
fourth preferred embodiment. A point different from that of the fourth 
preferred embodiment shown in FIG. 19 will be described in detail below. 
Referring to FIG. 20, a transmitting local oscillator 10a is, for example, 
an oscillator using a DDS (Direct Digital Synthesizer) driven by an 
identical clock, and operates to generate a transmitting local oscillation 
signal having a predetermined frequency. On the other hand, a transmitting 
baseband signal S.sup.TX, or transmission data is inputted to the in-phase 
divider 9 to be divided in phase into N transmitting baseband signals 
S.sup.TX, and then, the signals are inputted respectively to phase 
correcting sections 13-1 through 13-N. Each phase correcting section 13-i 
(i=1, 2, . . . , N) multiplies the inputted transmitting baseband signal 
S.sup.TX by the transmission weights W.sub.1.sup.TX, W.sub.2.sup.TX, . . . 
, W.sub.N.sup.TX, and then, outputs a transmitting baseband signal 
S.sub.i.sup.TX (i=1, 2, . . . , N) of the multiplication result to a 
quadrature modulator 6a-i. The quadrature modulator 6a-i subjects the 
inputted transmitting baseband signal to a serial to parallel conversion 
process so as to convert the signal into a transmitting quadrature 
baseband signal, and then, combines the transmitting local oscillation 
signals having a mutual phase difference of 90.degree. according to the 
transmitting quadrature baseband signal through a quadrature modulation 
process so as to obtain the above-mentioned intermediate frequency signal. 
Then, the intermediate frequency signal obtained through the quadrature 
modulation process is inputted as a transmitting radio signal to the 
circulator CI-i in the array antenna 1 via the up-converter 7 and the 
transmission power amplifier 8 in the transmitter module TM-i. Then, the 
transmitting radio signal is radiated from the antenna element Ai. 
Consequently, transmitting signals weighted by the transmission weights 
W.sub.1.sup.TX, W.sub.2.sup.TX, . . . , W.sub.N.sup.TX are radiated from 
the antenna elements A1 through AN. Therefore, the transmitter section of 
the fifth preferred embodiment operates similarly to that of the fourth 
preferred embodiment, while producing a similar effect. 
FIG. 37 shows a transmission weighting coefficient calculation circuit 30a 
of a modification of the preferred embodiment. 
Referring to FIG. 37, an operation of the circuit 30a will be described 
below. In the Equation (47), r is replaced with i, and then, based on the 
following Equation (66), there is calculated the phase difference between 
the antenna elements A(i-1) and the Ai, namely, the phase difference 
.DELTA..theta..sub.i-1,i between the adjacent antenna elements A(i-1) and 
Ai. 
##EQU39## 
where S.sub.i =I.sub.i +jQ.sub.i, i=1, 2, . . . , N, (N is the number of 
the antenna elements) is a reception baseband signal received by the 
antenna element Ai. This processing is performed by phase difference 
calculation sections 31a-1 through 31a-(N-1). Then by using adders 36-1 
through 36-(N-2), the output signals from the phase difference calculation 
sections 31a-1 through 31a-(N-1) are accumulatively added sequentially, 
according to the following Equations (67) so as to obtain the phase 
difference .DELTA..theta..sub.1,i between the antenna elements A1 and Ai. 
##EQU40## 
Since the distance between the adjacent antenna elements is often set to 
half the wavelength, normally, the phase difference .DELTA..theta.i-1,i 
does not include any phase uncertainty. Due to this, the accumulatively 
added phase difference .DELTA..theta..sub.1,i also does not include any 
phase uncertainty. In this preferred embodiment, the phase plane 
regression correction using the least square method is performed to this 
phase difference .DELTA..theta..sub.1,i by a least square regression 
processing section 32. That is, in a manner similar to that of the 
Equation (48), the linear plane regression plane is now expressed by the 
following Equation (68). 
EQU .DELTA..theta..sub.i,i.sup.LSR =ax+by+c (68) 
Then the matrix A is calculated according to the Equation (53), this 
results in obtaining the parameters a, b and c of the regression plane, 
and also obtaining the regression-corrected phase difference 
.DELTA..theta..sub.1,i.sup.LSR. It is noted that the matrixes X, A and 
.THETA. can be calculated, respectively, according to the Equations (50) 
and (51) and the following Equation (69). 
##EQU41## 
The matrix X is a known matrix which has been previously determined by the 
arrangement or portion information of the antenna elements, and therefore, 
the matrix X is previously inputted to the least square regression 
processing section 32. 
The regression-corrected phase differences .DELTA..theta..sub.1,i.sup.LSR 
are inputted to the transmission weighting coefficient calculation section 
35, which performs the following calculations in a manner similar to that 
of the Equations (64) and (65), and then outputs the transmission 
weighting coefficients W.sub.i.sup.TX (i=1, 2, . . . N). 
That is, in the case where the transmission frequency is equal to the 
reception frequency and the transmission and reception antennas are 
commonly used as one antenna, and in the case where the transmission 
frequency is different from the reception frequency, the transmission 
antenna is provided separately from the reception antenna, the distances 
between the adjacent antenna elements are equal to each other between the 
transmission and reception in terms of wavelength, the transmission 
weighting coefficients W.sub.i.sup.TX are calculated according to the 
following Equation (70). 
EQU W.sub.i.sup.TX =exp (j.theta..sub.i.sup.TX)=.sub.i.sup.TX exp 
(-j.DELTA..theta..sub.1,i.sup.LSR) (70) 
Further, in the case where the transmission frequency is different from the 
reception frequency and the transmission and reception antennas are 
commonly used as one antenna, the transmission weighting coefficients 
W.sub.i.sup.TX are calculated according to the following Equation (71). 
EQU W.sub.i.sup.TX =a.sub.i exp (-j (f.sup.TX 
/f.sup.RX).DELTA..theta..sub.1,i.sup.LSR) (71 ) 
where a.sub.i.sup.TX is a transmission excited amplitude in the antenna 
element Ai. Normally, a.sub.i.sup.TX is set to one, however, it can be set 
to any distribution for the purpose of side-lobe suppression. 
The results of the transmission beam forming by this method becomes equal 
to those of the phase correction method using the condition branch 
according to the fifth preferred embodiment. However, it is noted that the 
weighting coefficients W.sub.i.sup.RX obtained by the receiver side can 
not be utilized, and it is necessary to again calculate the value of the 
above-mentioned Equation (66) based on the reception baseband signal 
S.sub.i =I.sub.i +jQ.sub.i. In this case, the calculation amount is 
decreased. Further, the above-mentioned processing can be performed in a 
similar manner in both cases when the array antenna is a linear array 
antenna and when the array antenna is a two-dimension plane array antenna. 
Although the present invention has been fully described in connection with 
the preferred embodiments thereof with reference to the accompanying 
drawings, it is to be noted that various changes and modifications are 
apparent to those skilled in the art. Such changes and modifications are 
to be understood as included within the scope of the present invention as 
defined by the appended claims unless they depart therefrom.