DESCRIPTION,
MIMO COMMUNICATION SYSTEM HAVING DETERMINISTIC CHANNELS AND
METHOD .
Technical Field
[0001]
The present invention relates to a space-division multiplexing method (hereinafter, referred to as "MIMO
(Multiple-Input Multiple-Output)") and, more particularly to a MIMO communication system suitably applied to a line-of-sight fixed point microwave communication system. ..
Background Art [0002]
In recent years, a technique using a MIMO has become popular in the field of wireless communication, and the MIMO itself is becoming no longer a new technology. Conventional techniques using the MIMO mainly focus on a mobile communication, and application of the MIMO to a fixed communication has not been fully examined. In a.mobile communication radio channels, radio wave coming from a transmission antenna is reflected or scattered according to the surrounding terrain and reaches a receiver in the form of a group of waves, resulting in occurrence of fading phenomenon which has been an obstacle to achievement of high quality communication . The MIMO technique in a mobile communication does not demonize the fading phenomenon but considers it as environmental resources with great potential that are inherent in mobile communication radio propagation. In this point, the MIMO technique is regarded as a revolutionary technique. [0003]
Although smaller in the. amount of examples than the mobile communication, Non-Patent Document 1 discloses consequents of

application of such a MIMO technique to a line-of-sight fixed radio communication where radio channels are determined. [0004]
The mobile communication as described above deals with, channels as a probabilistic matrix. On the other hand, the line-of-sight fixed radio communication needs to deal with radio channels as deterministic radio channels where the geometrical positional relationship between transmission and reception antennas is fixed. [0005]
The above Non-Patent Document 1 describes, as follows, what effect is produced on a channel.matrix H constituting channels between transmission and reception antennas as a result of extension of antenna separation length on both the transmission side and reception side. [Numeral 1]

H.H''=« I

n

where n is the number of antennas, H" is the Hermitian transposed matrix of H, and I is a unit matrix. [0006]
According to Non-Patent Document 1, the phase rotation of a signal with respect to a transmission antenna i and reception antenna k linearly arranged so as to face each other between the transmission side and reception side is set by the following formula and thereby the transmission and reception antenna can be constituted by linear antennas. , [Numeral 2] ,

-■[i-k]
n
[0007]
Accordingly, when n=2 , the channel matrix H is represented by the following formula: [Numeral 3]

H

max

1 7 J 1

where j is a symbol representing an imaginary number. [0008]
In this case, an antenna configuration satisfying the condition of Numeral 1 is possible. Non-Patent Document 1 describes that when the condition of Numeral 1 is satisfied, channel capacity in the MIMO configuration becomes maximum by Hj11x •
[0009]
That is, an increase in channel capacity based on the MIMO can be expected not only in a mobile communication environment that is subject to'reflection or scattering but also in a deterministic line-of-sight communication environment. [0010]
On the other hand, a fixed point microwave communication system uses a frequency band of several GHz to several tens of

GHz, which corresponds to several mm to several cm in terms of wavelength. Therefore,, a significant phase rotation may occur due to movement in the antenna direction highly sensitive to a subtle change of weather condition such as wind or surrounding temperature. Under such a condition, it is difficult to ensure the deterministic channel matrix. [0011]
Note that theoretical analysis to be described later analytically reveals that the above increase in channel capacity can be achieved even when such a displacement in the highly sensitive antenna direction occurs. ■ [0012]
In the MIMO technique, a plurality of independent signals are transmitted/received at the same frequency band. Therefore, signal separation/detection is necessary. As a means for realizing this, there is a known a method (hereinafter, referred to as SVD method) based on matrix calculation using a unitary matrix which is obtained by Singular Value Decomposition (SVD). Assuming that feedback information for construction of the unitary matrix can ideally be send from a receiving end to transmission end in the SVD method. In this case, even when the above displacement in the highly sensitive antenna direction occurs, the unitary matrix acts so as to compensate for the displacement. As a result, large capacity fixed point microwave communication can be realized based on the MIMO.
Non-Patent Document 1: IEEE TRANSACTIONS ON COMMUNICATIONS , VOL.47, NO. 2, FEBRUARY 19 9 9 , PP. 173-176, On the Capacity Formula for Multiple Input-Multiple Output Wireless Channels : A Geometric Interpretation
Disclosure of the Invention. ;1:
Problems to be Solved by the Invention - ..

[0013]
However, the above feedback information may increase system overhead. In addition, it is necessary to prepare an inverse channel for exchanging the feedback information. Note that a modeling of a channel matrix H to be described later performs analysis including the displacement in the highly sensitive antenna direction. [0014]
When the singular value analysis is carried out for the line-of-sight fixed channels where channels are deterministic, there exists an inter-antenna position at which an eigenvalue is multiplicity condition to generate a singular point. Although the singularvalue is uniquely determined, singular vectors are not unique. This state,, which is particularly analytically troublesome, may cause significant transition of the singular vectors. . [0015]
However, by utilizing this phenomenon, various configurations can be possible. Various examples of configurations that take advantage of the characteristics will be described later. [0016]
As a maj or problem in the deterministic line-of-sight MIMO, there is a problem that carrier synchronization between antennas must be achieved on the transmission side or reception side in the above conventional method. That is, the phase difference between a plurality of antennas on the transmission side or reception side needs to be equal or needs to have a constant phase difference. [0017] On the other hand, in the fixed point microwave communication system, antenna separation length must be widened in view of a frequency to be used. Correspondingly, radio devices including

local oscillators are installed.near antennas. That is, the problem of the necessity of achievement of carrier synchronization between antennas imposes severe restriction on construction of the fixed point microwave communication system. [0018]
An object of the present invention is therefore to provide
MIMO communication system having deterministic channels wherein
the MIMO is applied to line-of-sight channels having a fixed
geometrical positional relationship so as to increase the channel
capacity and its method.
[0019] , ■ : .
Another object of the present invention is to provide a MIMO communication system capable of offering performance equivalent to a conventional SVD method without feedback information that needs.to be sent from a reception end to transmission end for construction of a unitary matrix in the SVD method. [0020]
Further, the main object of the present invention is to provide a MIMO communication system in which the problem of the necessity of achievement of carrier synchronization between antennas which imposes severe restriction on construction of the fixed point microwave communication system is solved. [0021]
Still another object of the present invention is to provide a MIMO communication system capable of offering performance equivalent to an SVD method even under the condition that it is difficult to ensure a deterministic channel matrix due to a significant phase rotation caused by movement in the antenna direction highly sensitive to a subtle change of weather condition such as wind or surrounding temperature.
.'[0022] ":1;"1■:■■■
..'.,, The MIMO according to. the, present invention is a.

line-of-sight communication, so that there is some correlation between signals of a plurality of antennas and, in this point, differs from MIMO used in a conventional mobile communication. That is, a conventional mobile communication or indoor wireless LAN system is realized based on the assumption that there is no correlation between signals of a plurality of antennas . Therefore, it should be noted that, unlike the MIMO according the present invention, conventional MIMO does not operate in a state where there is some correlation between antennas.
Means for Solving the Problems [0023]
To solve the above problems, according to the present invention, there is provided a line-of-sight MIMO communication system including a plurality of channels characterized by comprising: a channel matrix calculation processing section on a transmission or reception side or both of the transmission and reception sides, wherein the channel matrix calculation processing section updates an orthogonal channel formation matrix in accordance with a fluctuation of a transmission antenna position (e.g., a transmission antenna, light-emitting device, speaker, and the like used in electric wave propagation) or reception antenna (e.g., a reception antenna, light-receiving device, microphone, and the like used in electric wave propagation) or a fluctuation of the channels. [0024]
For formation of virtual orthogonal channels, geometric parameters of the channels are set so that the eigenvalue of the channel matrix become multiplicity condition, and calculation of a unitary matrix constituted based on an eigenvector obtained from the eigenvalue or an eigenvector obtained from the linear sum of eigenvector is performed on one of the transmission side or reception side.

[0025]
The MIMO communication system is a fixed point microwave :;ommunication system using a plurality of antennas and is constituted by using local oscillators provided independently for respective antennas on one or both of the transmission and reception sides. [0026]
The MIMO communication system includes a means for detecting a fluctuation of a transmission antenna position or reception antenna position or a fluctuation of the channels and, based on a detection result from the means, updates a virtual orthogonal channel formation matrix.
Advantages of the Invention
[0027] ,. ■
, The MIMO communication system according to the present invention includes a plurality of channels. Further, the system includes a channel matrix calculation processing section on a transmission or reception side or both of the transmission and reception sides. The channel matrix arithmetic processing section updates an orthogonal channel formation matrix in accordance with a fluctuation of a transmission antenna position or reception antenna position or a fluctuation of the channels. With this configuration, it is possible to absorb a fluctuation of a transmission antenna position or reception antenna position or a fluctuation of the channels, thereby providing a MIMO communication system capable of achieving the maximum communication capacity. [0028].
Further, for formation of virtual' orthogonal channels, geometric parameters of the channels are set so that the eigenvalue of the channel matrix is multiplicity condition, and calculation of a unitary matrix constituted based on an eigenvector obtained

from the eigenvalue or an eigenvector obtained from the linear sum of eigenvector is performed on one of the transmission side or reception side. This enables flexible system design and can realize a configuration in which there is no need to use an inverse channel for exchanging the feedback information and.a configuration in which only transmission processing is performed. [0029]
Further, the MIMO communication system is a fixed point microwave communication system using a plurality of antennas and constituted by using local oscillators provided independently for respective antennas on one or both of the transmission and reception sides . With this configuration , it is possible to solve the problem of the necessity of achievement of carrier synchronization between antennas that imposes severe restriction on construction of the fixed point microwave communication system. [0030]
Further, matrix calculation processing for formation of the virtual orthogonal channels may be performed only on the reception side. With this configuration, a MIMO communication system where there is no need to use an inverse channel for periodically and frequently exchanging the feedback information can be provided. [0031]
Further, the MIMO communication system includes a means
for detecting a fluctuation of a transmission antenna position
or reception antenna position or a fluctuation of the channels
and uses a detection result from the means to update a virtual
orthogonal channel formation matrix. With this configuration,
a problem-free MIMO communication system with satisfactory
installation condition and rigid structure can be provided.
[0032] . ■ - ■ --
Further, the MIMO communication system includes a means for. transmitting pilot signals from the transmission side to

reception side, detects a fluctuation of a transmission antenna position or reception antenna position or a fluctuation of the channels by the pilot signals, and updates a virtual orthogonal channel formation matrix based on a result of the detection . With this configuration, a problem-free MIMO communication system with satisfactory installation condition and rigid structure can be provided. [0033] .
Further, the MIMO communication system includes a means for transmitting pilot signals of respective antennas from the transmission side to reception side and, based on the pilot signals , performs matrix calculation processing for formation of the virtual orthogonal channels only on the reception side. With this simple' processing, a MIMO communication system where there is no need to use an inverse channel for periodically and frequently exchanging the feedback information can be provided. [0034]
Further, the pilot signals to be transmitted from the transmission side to reception side are generated before processing performed by the local oscillators. With this configuration, phase noise between local oscillators generated on the transmission side can be detected on the reception end, and the generated phase noise can be compensated for by updating the matrix. [0035]
Further, the detection of the pilot signals that have been
transmitted from the transmission side'to reception side is
performed after processing performed by the local oscillators
on the reception side. With this configuration, phase noise
between, local oscillators-generated, on the reception side can
be detected on the reception end, and the generated phase noise
can be compensated for by,updating the matrix.
.[0036] ' ■ ■ • ■ •

Further, thepilot signals transmitted from the transmission side to reception side are orthogonal between transmission antennas . With this configuration , phase,noise between the local oscillators and a displacement in the highly sensitive antenna direction caused due to weather condition can be detected by a simple correlator, and the detected phase noise or displacement can be compensated for by updating the matrix. [0037]
Further, the line-of-sight channels may be used as optical channels or acoustic channels , as well as electrical wave channels . Also in this case, the MIMO communication system can be provided. [0038]
Further, one or both of the separation length between a plurality of transmission antennas or a plurality of reception antennas and direction of a plurality of transmission antennas or a plurality of reception antennas are made changeable. With this configuration, a MIMO communication system where the maximum communication capacity can always be achieved by controlling one or both of the separation length between the transmission antennas or a reception antennas and axial direction of the transmission antennas or reception antennas, regardless of the type of a geometric form of the line-of-sight channels. [0039]
In the present invention, the abovementioned effects need not be achieved simultaneously but at least one of the effects may be achieved.
Brief Description of the Drawings
[0040] : .
FIG. 1 is a view showing .a configuration example of a line-of-sight MIMO where an SVD method in which antenna separation length is arbitrarily set and a fluctuation of antenna position inithe highly sensitive- antenna direction is taken.into

consideration;
FIG . 2 is a view showing a first example (first configuration example) of the line-of-sight. MIMO according to the present invention, where matrix calculation based on a unitary matrix V is performed only on the transmission side;
FIG. 3 is a view showing a second example (second configuration example) of the line-of-sight MIMO according to the present invention , where matrix calculation based on a unitary matrix is performed only on the transmission side and where virtual orthogonal channels have different values;
FIG. 4 is a view showing a third example (third configuration example) of the line-of-sight MIMO according to the present invention, where matrix calculation based on a unitary matrix is performed only on the reception side and where local oscillators are provided independently for respective antennas on the transmission side;
FIG. 5 is a view showing a fourth example (fourth configuration example) of the line-of-sight MIMO according to the present invention , where matrix calculation based on a unitary matrix is performed only on the reception side and where local oscillators are provided independently for respective antennas both on the transmission and reception sides;
FIG. 6 is a view showing a fifth example (fifth configuration example) of the line-of-sight MIMO according to the present invention, where matrix calculation based on a unitary matrix is performed only on the reception side, where virtual orthogonal channels have different values, and where local oscillators are provided independently for respective antennas both on the transmission and reception sides;
FIG. 7 is a view showing a sixth example (sixth configuration
example) of the line-of-sight MIMO according to the present '
invention, where three antennas are installed respectively on
..the. transmission and reception sides , and where local oscillators

are provided independently for respective antennas both on the transmission and reception sides;
FIG. 8 is a view showing a seventh example (seventh configuration example) of the line-of-sight MIMO according to the present invention, where four antennas are installed respectively on the transmission and reception sides, and where local oscillators are provided independently for respective antennas both on the transmission and reception sides;
FIG. 9 is a view showing comparison between SNRs of virtual orthogonal channels based on respective methods in terms of antenna separation length;
FIG. 10 is a view showing a configuration example in which antenna separation lengths differ from each other between transmission and reception sides;
FIG. 11 is a view showing a modeling of the channels of FIG. 10;
FIG. 12 is a view showing communication capacity in the case of FIG. 10 where antenna separation lengths differ from each other between transmission and reception sides;
FIG. 13 is a view showing a configuration example in which antenna arrangement betvveen the transmission and reception sides is formed in diamond shape;
FIG. 14 is a view showing a configuration example in which antenna arrangement between the transmission and reception sides is formed in diamond shape and where matrix calculation based on a unitary matrix is performed only on reception side;
FIG. 15 is a view showing a case where antenna arrangement between the transmission, and reception sides is formed in an arbitrary geometric form;
FIG . 16 is a view showing ah example in which optical channels
are used as deterministic; channels ;,,
FIG. 17 isa view showing an example in whichacoustic channels are used as deterministic channels;

FIG. 18 is a view showing an configuration example of an antenna used in a configuration in which antenna arrangement between the transmission and reception sides is formed in an arbitrary geometric form;
FIG. 19 is a view showing eigenvalues on the virtual orthogonal channels; and
FIG. 20 is a view showing an application example of a configuration in.which matrix calculation is performed only on transmission side.
Explanation of Reference Symbols [0041]
101, 201: Matrix calculation processing section based on unitary matrix V
102, 108, 402, 502, 510, 602, 610: Frequency conversion section
103, 105, 109, 111, 403, 407, 503, 507, 511, 515, 603, 607, 611, 615: Mixer
104, 110, 404, 405, 504, 505, 512, 513,'604, 605, 612, 613: Local oscillator
106, 107, 202, 203, 302, 303, 408, 409, 508, 509, 608, 609: Fixed
antenna section
112, 410, 517: Matrix calculation processing section based on
unitary matrix U
301: Matrix calculation processing section based on matrix V
401, 501, 601: Pilot signal generation section
406, 506, 514, 606, 614: Modeling of phase noise caused due to
absent of synchronization between carriers >
516, 616: Pilot detection section
1601 1602 1701 1702
617: Matrix calculation processing section based on matrix U
Laser diode (LD) Photodetector (PD) Ultrasonic oscillator 1Ultrasonic microphone

1803 1804 2001 2002 2003
1801, 1802:_Antenna element
Connection bar
Hinge
Transmission station
Reception station 1
Reception station 2

Best Mode for Carrying Out the Invention [0042]
An exemplary embodiment of the present invention will be described with reference to the accompanying formulas and accompanying drawings. Before that, a theoretical reasoning for the fact that channel capacity in. the MIMO configuration becomes maximum even with deterministic line-of-sight channels will be explained. [0043]
The channel capacity of virtual orthogonal channels based on the MIMO configuration is represented by eigenvalues of respective paths. Then,,eigenvalue analysis is performed for a configuration using two antennas . The following modeling, whose antenna configuration and reference symbols are shov/n in FIG. 1, takes the displacement in the highly sensitive antenna direction into consideration. Although a case where two antennas are used will be described for convenience, the same calculation may be applied regardless of the number of antennas. [0044] .
The propagation loss and common phase shift based on a transmitter-receiver distance R are not essential so those terms are ignored. The channel difference between diagonal channel and straight channel is represented by Numeral 4. . [Numeral 4] ..

{{A0)
if-(l-cos(A1))=.i?-1i1J = i?jA(1)1j = 1 v1:.tan(A1)«(A1), atd,=d.
0045]
Phase rotation a based on the channel difference is represented by Numeral 5. [Numeral 5]

a = 271

J
2R

y 1

[0046]
Incidentally, assuming that RF frequency=30GHz, R=5000m, mtenna separation length dT=dR=5m, a is satisfied. [Numeral 6]

a =

n
n
TT d
.8
R -.
r R (3-10')/(30-10") 5000 2

[0047]
Therefore, channel matrix H considering phase shift O based on the fluctuation of a transmission antenna position for transmitting a signal S2 which is one of two transmission antennas for transmitting signals si and S2 provided on the transmission side is' represented by Numeral,,.? . '

[Numeral 7]

H =

1

e -e
JO
l-e

[0048]
Therefore, Numeral 8 is satisfied. [Numeral 8] .

■,j°

1 e-1°.e-1"1

2 e1'1ie'"+€-'")

e111.g-y* g-y*

2
2 • cos or •e-'*
2-cosa-e'-''1 2

[0049]
As a result, eigenvalues 1i and /t-2 representing channel ■capacity of the virtual orthogonal channels can be calculated as follows.' In the following formula, H1 is the Hermitian transposed matrix of the channel matrix H. [Numeral 9]

2~Pi 2-cosa-e1

= X\+4-4Z-4cos1a = X1 -4Z-4sin1 a = 0

.: Z = 2±yl4-4sm1a=2±2

cos a

[0050]
A calculation result of Numeral ,9 is shown in FIG.. 19. The numerical result in FIG. 19 shows a case where unit power is

transmitted per one antenna and, therefore, channel capacity is double as same as the number of antennas. It should be noted here that the modeling used in the'above calculation includes a displacement in the highly sensitive antenna direction . Despite this, the displacement component does not appear in a result of •the eigenvalue representing a final channel capacity. That is, an increase in the channel capacity is possible by MIMO even in the line-of-sight fixed radio communication where radio channels are determined. The channel capacity is determined by the antenna separation length not relevant to the highly sensitive antenna displacement. [0051],
A case where two antennas are used has been described above. In the, following, a case where three or more antennas are used will be described. [0052]
A phase rotation between a linearly arranged transmission antenna and reception antenna, which is based on the channel difference between orthogonal channel and straight channel, is obtained from Numeral 5. Assuming that the antenna separation length is a common value of d-, the phase rotation is represented by Numeral 10., [Numeral 10]
7t_ d1
r R
[0053]
,,, [Numeral 11]

TV d1
■m—11 W

n

R

L
3

Thus , when d and transmitter-receiver distance R are defined so that the above Numeral 11 is satisfied and a configuration in which three antennas are used is considered, a channel matrix H3 represented by Numeral 12 can be obtained. [Numeral 12]

1 3

H. =

3
X
3
y4

,j1
'J

[0054]
Therefore, Numeral 13 is satisfied. [Numeral 13]

H
n = H3" -H3 =

e

.X

e

.X

3
.X

-]-.

e

-J4-.
3
X 3 0 0
3 — 0 3 0 0 0 3

Thus, it can be understood that three eigenvalues corresponding to the channel capacity of the virtual orthogonal channels are all "3" and that the entire channel capacity is three times as same as the number of antennas. [0055]
[Numeral 14]

1 d 71 d' _r
r 1 4 R 4
similarly, when d and transmitter-receiver distance R are defined so that a configuration in which four antennas are used is considered, a channel matrix H4 represented by Numeral 15 can
be obtained. [0056]
[Numeral 15]

e

e

-1"4

e

-1'f

H4

.*
-)-

«

.«
-y
1
-4

/41
■'1

[0057] . ■
Therefore, Numeral 16 is satisfied. [Numeral 16]

1 e * e * 1 i'-* e ■• e * 4 0 0 0
n = H/ -H,- ■A*
e * 1 e * 1 1*7 - e * e * 1 1 ■A'
e * = 0 0 4 0 0 0 4 0
e * e * e * 1 e * e-'1 1 0 0 0 4
Thus, it can be understood that four eigenvalues corresponding to the channel capacity of the virtual orthogonal channels are all "4" and that the entire channel capacity is four times as same as the number of antennas. [0058]
That is, it can be understood that even when the number of antennas exceeds 2, the channel capacity of deterministic line-pf-sight channels is.increased to an: extent corresponding .to the number of "antennas which is equivalent to the maximum capacity of MIMO. Note that although a case where two- antennas

are used will be described for convenience in the following examples , it.goes without saying that the same is applied to a case where the number of antennas exceeds 2. [0059]
Next, as a signal separation/detection method in MIMO, a method (hereinafter, referred to as SVD method) based on matrix calculation using a unitary matrix which is obtained by Singular Value Decomposition will be described. In the SVD method, matrix calculation using a unitary matrix V on the transmission side and matrix calculation using a unitary matrix U on the reception side are required. In order to perform the matrix calculation using the unitary matrix V, feedback information for construction of a unitary matrix needs to be sent from the reception end to transmission end. [0060]
An exemplary embodiment of the present invention will be described in detail below with reference to the accompanying formulas and accompanying drawings. [0061]
In FIG. 1, transmission signals processed by a transmission (transmitter) side matrix calculation processing section 101 based on the unitary matrix V are frequency converted into signals of a radio frequency by a transmission side frequency conversion section 102 including a local oscillator 104, a mixer 103, and a mixer 105 and then transmitted from a fixed antenna section 106 including a plurality of antennas as Si and 82. The notation of the Si and S2 is based on equivalent baseband representation. [0062]
It should be noted here that carrier synchronization between antennas is achieved by a local oscillation signal supplied from one local oscillator 104 to the mixers 103 and 105. This results from a restriction on a space-division multiplexing fixed point microwave communication system:that deterministic channels are

determined based on the phase difference between paths . However , as described later, the local oscillators may be provided independently for respective antennas. [0063]
The signals thus transmitted are received by a reception (receiver) side fixed antenna section 107 including a plurality of antennas as ri and ra. The notation of the ri and ra is based on equivalent baseband representation.. The reception signals ri and T2 are frequency converted into signals of a baseband frequency by a reception side frequency conversion section 108 including a local oscillator 110, a mixer 109, and a mixer 111 and then processed by a reception side matrix calculation processing section 112 based on the unitary matrix U, whereby signal separation/detection in MIMO is completed. [0064]
It should be noted here that carrier synchronization between antennas is achieved by a local oscillation signal supplied from one local oscillator 110 to the mixers 109 and 111. This results from a restriction on a space-division multiplexing fixed point microwave communication system that deterministic channels are determined based on the phase difference betv/een paths. [0065] - . .
Also in this case , as described later , the local oscillators
may be provided independently for respective antennas as in the
case of the transmission end. The antennas to be used are not
particularly limited and may be a parabola antenna or a horn antenna .
The matrix calculation processing sections 101 and 112 may be
realized by program control or constructed by hardware such as
ASIC (Application Specific Integrated Circuit) or the like.
,.[0066]. ' 11. ' ■
Next, a method of calculating the unitary matrixes V and U using the following channel matrix H considering a given antenna ...separation length and highly sensitive antenna displacement will

concretely be described with reference to formulas. [0067]
Channel matrix H of line-of-sight channels used here is represented by Numeral 17. " [Numeral 17]

<,-}'
H =

1 e-'-'-e'1
\-e'*

n dr,
where; flr = — {aidj=dA, O; phase change caused by displacement
Y R

[0068]
Singular value orthogonal matrix A ■'•11 based on the eigenvalue is represented by Numeral 18. [Numeral 18]

2-sin
A'" =

V2 + 2ci)sor 0

v2—ZcosaJ

.co{f)

(f]J

{e1+e ')

-Ke

l+cosa = 2cos l-cosa = 2si«i'

(f)
(!)

[0069]
The unitary matrix V and unitary matrix U are calculated using the above channel matrix H in the order mentioned. [0070]
[Unitary matrix V]
First, calculation of the unitary matrix V will be described. It is assumed that an eigenvector corresponding to the channel matrix H represented by Numeral 19 is represented by Numeral 20. [Numeral 19]

.-J"
H

1 e-1'1-e1
j
\-e

[Numeral 20]
a b
In this case, Numeral 21 is satisfied, [Numeral 21] '

H
n=H" H-

2 I'CQsa-e11

Thus, from Numeral 22, Numeral 23 can be obtained. [Numeral 22]

2-vl I'Cosa-e11
l1cosa-e'11 2-/1

a b

0

[Numeral 23]

jo
a =

b =
2-X
I'Cosa-e-11 , cosa-e
±cosa

b = ±e1'1-b V ;i = 2±2cosa

[0071]
When both sides of Numeral 24 are multiplied by v" from the left. Numeral 25 is obtained. [Numeral ,24]
n-v = k'[Numeral 25]

H
\" n-V1yl

[0072]
'■ . . Then, orthogonal "v" are collected and Numeral 26 is obtained. ■,...,.;'.

[Numeral 26]
V"ft-V = A .-. ft = V.AV"
[0073]
From Numeral 27, Numeral 28 is satisfied. [Numeral 27]
H = U«A''1V"
[Numeral 28]
S2 = H"H=V.A"1U*UA"'V''=VA.V''
Thus, the eigenvectors each represented by Numeral 29 are collected to obtain Numeral 30. [Numeral 29]
a
v =
[Numeral 30]

v =

X
xe

-j

y

-jO

i0074]
Here , whenNumeral 31 is set as a special solution considering normalization and orthogonality. Numeral 32 is obtained. [Numeral 31]

x =

y =
J2' -1"72

[Numeral 32]


_1_
-y*
V:=

,-;*
— e
L V2 V2

.-. V" =

[0075] . 1 ■■
[Unitary matrix U]
Next, calculation of the unitary matrix U will be described. -It is assumed that-an eigenvector u is represented'by Numeral

34 based on Numeral 33. [Numeral 33]

a'=H H'' =

1 e-'1-e1''

,J'1
e1'1-e'1'1 he--''1

2 2-cosflr
2-cosQr 2

[Numeral 34]
a b
In this case, from Numeral 35, Numeral 36 is obtained, [Numeral 35]
=0
2' cos a 2 — X
[Numeral 36]
-2*cosa_ cosa . .. . 1.1
a = -b = ———b = ±b VA = 2±2cosa
2-A +coscr
.[0076]

- When both sides of Numeral 37 are multiplied by u** from the lefty Numeral 38 is obtained. [Numeral 37]' • . , -.-„■■■.
fl*-u = 1 • u
[Numeral 38]
u"-n'u = ;i
[0077]
Then, orthogonal "u"s are collected and Numeral 39 is obtained. -[Numeral 39J
U"0'-U = A •. n'=U-AU"
Thus, the eigenvectors each represented by Numeral 40 are collected to obtain Numeral" 41.' [Numeral. 40]

u

a ±a

[Numeral 41]

U =

X y X -y

[0078]
Here , when Numeral 42 is set as a special solution considering normalization and orthogonality. Numeral 43 is obtained. [Numeral 42]

-7
x =

je
4i ''~ 4i

[Numeral 43]

.
l-e

1 -J.e1 ■J \e1

[0087]
Here, Numeral 48 is satisfied,. [Numeral 48]

n=H H1 =

1 -j-e''1 1 J "2 0
-J he'"1 B j-e--'1 l1e-''1 0 2

Thus, from Numeral 49, eigen equation has multiplicity condition. In this case, the following conversion can be possible.
[Numeral 49]

2-X 0 0 2-A

= (2 - X)

[0088] ..' . ;, : •
Numeral 50 is satisfied for a given eigenvector u1 with
respect to eigenvalue ?i . ; :-'t ';■"
.[Numeral 50] 1 • ,' :; 11.. ' 1. , ;■ ■
O'Uj =lui
[0089]
Similarly, Numeral 51 is satisfied for a given eigenvector U2 with respect to eigenvalue A . [Numeral 51]
H'-Uj -A'VL1
[0090]
Therefore, Numeral 52 is satisfied for the linear sum of both the eigenvectors. Accordingly, linear sum (ci • U1+C2 •U2) becomes an eigenvector. [Numeral 52]
n''(c, U, +C2 ■U2)=>l(Ci U, +C2 uj
[0091]
It is assumed that an asymptotic eigenvector based on another
3 condition is set for the multiple root as Numeral 53. \ ,-. [Numeral 53]

a b
In this case, from Numeral 54, Numeral 55 is satisfied, [Numeral 54]

2-cosa 2-A

.

a b

0

[Numeral,55]
— 2'COSQr 1 cos Of , , 1 1 . 1
fl = lf = b-±b V A = 2±2cosa
2 — X ± cos a
[0092]
When both sides of Numeral 56 are multiplied by u" from the left. Numeral 57 is obtained. [Numeral 56]

n'-u = 1 u
[Numeral 57]
u" Sl'u = X
[0093]
Then, orthogonal "u"s are' collected and Numeral 58 is obtained.
[Numeral 58]
U"a*-U = A .. fl»=UA U"
[0094]
Here, Numeral 59 is satisfied. [Numeral 59] ■
Q'1HH" =:U A'1'V" V A'1 U" =U A U"
Thus, the above eigenvectors represented by Numeral 6 0 are collected to obtain Numeral 61 with normalization and

orthogonality taken into consideration, [Numeral 60]

u =

a ±a

[Numeral 61]

«1 =

X X

u

X -X

[0095]
Here, when considering sum and difference as linear combination. Numeral 62 is satisfied. [Numeral 62]

U, +U2 =

0

u, -u, =

0 2x

From Numeral 62, Numeral 63 is obtained [Numeral 63]

u =

1 0 0 1

[00,96]
Further, since Numeral 64 is satisfied. Numeral 65 is satisfied.
[Numeral 64] ' '

H=U'A''1-V1 =

1 -ye1- "1 0" 1/2 0
-j he''' 0 1 0 V2

V

H

[Numeral 65]

y1 =

4i
0

0
1
4i

1 -j-e11
-J

1
4i -J
j1

4i 42

[0097]
As a trial, when the channel matrix H is calculated using the obtained matrixes U, A''-''1, and v". Numeral 66 is satisfied. [Numeral 66]

1/2
H = U-A"'-V" =

1 0 0 1

V2 0'
0 1/2

1 -
42
-j

j-e
4i
42

y*

J-e

J1

As can be seen from Numeral 66,. the channel matrix H is effected. However,, this is merely an example, and various decomposition methods can be considered based on the same approach, depending on the singular point corresponding to the multiple root.
First Example [0098]
(Case where matrix calculation is performed only on transmission side)
As a first example (first configuration example) of the present invention, a configuration example in which the matrix calculation is performed only on the transmission side will be described. [0099]
[Singular value orthogonal matrix A''1''1]
In this case, the virtual orthogonal channels have the same value , so that singular value orthogonal matrix A.111 is represented by Numeral 67.
[Numeral 67]

Ml
A"' =

0 V1

V2 + 2cosa 0
0 v2~2cosa

V2 0'
0 V2

[0100]
[Channel matrix H] ,
Thus, the channel matrix H is represented by Numeral 68.
[Numeral 58]

1
H = U A

1/2

[1 0]
V" = 0 1 •

V2 0 0 V2

j-e
V2
V2
. V2 V2

/*

( 1 2 \ 2R
V =
111 112
V V
/ 21 '1 22
where; a = 27r

y
A/2 V2 A/2 V2 ,
I y - R -
r /?

U« = C/l2 , 1
0 0
1
;?r
2

[0101]
A configuration obtained based on the above result is shown in FIG. 2. In FIG. 2, transmission signals processed by a transmission side matrix calculation processing section 201 based on the unitary matrix V are transmitted from a fixed antenna section 202 including a plurality of antennas as Si and S2. The notation of the si and S2 is based on equivalent baseband representation, and the frequency conversion processing is omitted here for avoiding complexity.
[0102]
The signals thus transmitted are received by a reception side fixed antenna section 203 including a plurality of antennas as Xi and r2. The notation of the ri and ra is based on equivalent baseband representation, and the frequency conversion processing into a signal of a baseband frequency is omitted here for avoiding complexity. The point is that receiving side matrix calculation processing based on the unitary matrix U is not performed at all, .

but all matrix calculations are done on the transmission side. [0103]
As can be seen from Numeral 68 , in the case where the matrix calculation is performed only on the transmission side, the matrix includes a fluctuation between the channels caused due to external factors such as a fluctuation (modeledby *I> inFIG., 2) of an antenna position highly sensitive to a subtle change of weather condition such as wind or surrounding temperature. Thus, even when the displacement in the highly sensitive antenna direction occurs, the unitary matrix acts so as to compensate for the displacement. [0104]
In this configuration, the feedback information for construction of the.V matrix needs to be sent from the reception end to transmission end. The thiclc arrows of FIG . 2 denote virtual orthogonal channels in which channel qualities thereof are proportional to V~2 and -12 . The antennas to be used are not particularly limited andmay be a parabola antenna or a horn antenna . The matrix calculation processing section 201 may be realized by program control or constructed by hardware such as ASIC or the like.
Second.Example [0105]
(Case of virtual orthogonal channels having paths with different widths where matrix calculation is performed only on transmission side)
As a second example (second configuration example) of the present invention, a configuration example in which the matrix calculation is performed only on the transmission side in the virtual orthogonal channels having paths with different widths will be described..
[0106].-,1 ;' 1 '■:, ; . .■
.■[Singular value orthogonal matrix A-'-11.]

In this case , the virtual orthogonal channels have different values, so that singular value orthogonal matrix k.'1'1 is represented by Numeral 69. - ■ , [Numeral 69] ,

V1 0 1 11/2 + 2cosa

12-2

cos a

2cos) ~

2 sin — U

.•<» .T
-/(1'-'J1)

[0107]
[Channel matrix H]
Thus, the channel matrix H is represented by Numeral.7 0 [Numeral 70]

>-}'1
H = U-A"'-V= =

/*
1 1'"-e1
1-e

1 0 0 1

a
(e 2+e 2) 0

0
— -/—

V"

Thus, matrix V1 is represented by Numeral 71 [Numeral 71]
n-1

+ e1)
yH _

(1 2 _L 1 2

0

e"1" . e'"1

-J
0

J(e'"

e 2)

,-j1

l-e

ji>

[0108]
Here, Numeral 72 is satisfied, so that Numeral 73 can be
obtained as the matrix v". "/1
[Numeral 72]

i
1
a a
(e1i +e'12") 2-cos

1a1'
K1J

.a ,a
J-z -J.
I

[Numeral 73]

2-cos e
1" =

1
2•cos —
0

0
2-sin

a

1

/&
e-1"-e1
1-e

1
e-J" -e1
a) 1 fa)
2-cos —
2) [2
>J1
a
2-sin —
2-sin — \2J

[0109]
Here, the square norm of the vector is represented by Numeral
74
[Numeral 74]

1 1
1"j 2 • sin 1 (or)
+
4-cos1
~\ 4-sm' — 16-sin — -cos —

Thus, the V is no longer a unitary matrix. Therefore, in order to calculate the matrix V, inverse matrix calculation is required. [0110]- ■ ; . :
As a trial, when, the channel matrix H is calculated using

the obtained matrixes U, k'1''1, and V1, Numeral 75 is satisfied. [Numeral 75]


H = U-A"''-V« =

I 0 0 1

2-cos — 2;
0 2-sinl-
u.

1 e-1".e1

■ As can be seen from Numeral 75, the channel matrix H is effected. [0111]
Next, inverse matrixV of v'1 is considered. A given matrix A represented by Numeral 7 6. is assumed. [Numeral 76]

A =

«11 «12 121 122

The inverse matrix A' of the above matrix A is represented by Numeral 77 . [Numeral 77]

A-'=-

1 «22
«tl«22-«12<»21




i- 1 ■ «22 1 an«22-aua2i
0 0 <'u«22-«12a2..
<'ll«22-<'l2 "ii




«11«22-<»12«21

[0112]

Therefore, Numeral 78 is obtained as the matrix V. [Numeral 78]

V =

1
o fa 2-cos —
U
2-sm — 2

e -'" -e1
( «1
2. cos 2]
-.(f

1
1 , e1» e--'°-e-1 2.1(f)
2-co{1] 2.sm[|] 2.cos[|]

=,/*
2-sin[|
'o ■ r«
2-sin —

2-cosj—
1 2■cos —
u

a
2- 2-sm
2-sm
f)
-J%a
m — • cos —
1-e

./a m —
u
2-sin

2 CO!
-;«
2-cos

or
a

\-e-

cos

a

u

-e ' sin
-jf,
1 —

e1 coa —
\2
- e"-** COS

-sin

!
7 sin a

-sin —
Kf)
a
-£--1cos[-| «-1«1°sin|-

. j„ cos(a/2) jsm[al2)
sin a sin cr
sincr
y1--1 cos(ff / 2) - je-'1e1" sin(a' / 2)
smcr

where; or = 2ff

2J?

iy =

y R

A configuration obtained based on the above result is shown
in FIG. 3. ■
[0113]
in FIG. 3, transmission signals processed by a transmission side matrix calculation processing section 301 based on the unitary matrix V are transmitted from a fixed antenna section 3 02 including a plurality of antennas as si and sz. The notation of the Si and S2 is based on equivalent baseband representation, and the frequency conversion processing is omitted here for avoiding complexity. [0114] ; . . :
The signals thus transmitted are received by a reception side fixed antenna section 303. including a plurality of antennas as r.i and rz. Thenotation of the ri and rz is based on equivalent-. baseband representation, and the frequency conversion processing into a signal of a baseband frequency is omitted here for avoiding

complexity. The point is.that receiving side matrix calculation
processing based on the unitary matrix U is not performed at all,
but all matrix calculations are done on'the transmission side.
[,0115] ..'■,;■.
As can be seen from Numeral 78, in the case where the matrix
calculation is performed only on the transmission side, the matrix
includes a fluctuation between the channels caused due to external
factors such as a fluctuation (modeledby 1 in FIG. 3) of an antenna
position highly sensitive to a subtle change of weather condition
such as wind or surrounding temperature. Thus, even.when the
displacement in the highly sensitive antenna direction occurs,
the transmission side matrix acts so. as to compensate for the,
displacement.
[0116] . ■ ■ ,
In this configuration, the feedback information for construction of the V matrix needs to be sent from the reception end to transmission end. The antennas to be used are not particularly limited aridmay be a parabola antenna or a horn antenna . The matrix calculation processing section 301 may be realized by program control or constructed by hardware such as ASIC ot the like. , ■ [0117]
Thus , it can be understood that it is possible to form virtual orthogonal channels regardless of whether the optimum position (R=500 0m and dT=dR=5m) is achieved or not and by the matrix
calculation processing only on the transmission side. [0118] .
An application of the configuration in which the matrix
•- calculation- is performed only on the transmission side-is shown
'in FIG. 20. As shown in FIG. 20, a plurality of antennas are
provided, in a transmission station 2001 located near, a backbone;
network, and one antenna is provided in. reception stations 2002
, and 2003 . located near a, user, network ,/respectively.. The

reception . station 2001 and reception station 2003 are located far away from each other and, therefore, matrix calculation cannot be performed. On the.other hand, the transmission station 2001 can perform the matrix calculation . Thus, it is possible to apply the configuration in which the matrix calculation is performed only on the transmission side to the configuration of FIG. 20. Such a concept in "one station to many stations" configuration may be applied to "many stations to one station" configuration to be described later as a configuration in which the matrix, calculation is performed only on the reception side.
Third Example
[0119] ;.- . ■ - ..
(Case where unitary matrix calculation is performed only on reception side and where local oscillators on transmission side are provided independently for respective antennas)
As a third example (third configuration example) of the present invention, a configuration example in which the unitary matrix calculation is performed only on the reception side will be described. This third configuration has the. following features: the feedback information to be sent from the reception end to transmission end is not required; local oscillators may be provided independently for respective antennas on the transmission side; and exactly the same characteristics as those of the SVD method can be shown. [0120]
[Singular value orthogonal matrix A''-'1]
In this case, the virtual orthogonal channels have the same value , so that singular value orthogonal matrix A''"'1 is represented by Numeral 79. .[Numeral 79]

A111 =

A1 0

+ 2cosa 0
0 Jz—lcosa

\[2 0 ' 0 V2

[0121] 'I:.
[Channel matrix H] , ,
Thus, Numeral 80, can be obtained, as the channel matrix H,
[Numeral ,80] 1

u =
H = U-A"1-V" =U'

V2 0' ,0 V2
1 -j-e

1 0
0 1

1/V2 0 0 1/V2

where; O = ; + O1
.I/V2 -j-e1l4l -3l4i e1lS