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TITLE:
ARRAY ANTENNA SYSTEM
TECHNICAL FIELD
The invention refers to a method for an antenna system comprising a transmitting phase array antenna comprising a transmitting antenna subarray comprising a number Q antenna elements transmitting on a first frequency and a receiving phase array antenna comprising a receiving antenna subarray comprising a number P antenna elements. The transmitting antenna subarray antenna is positioned at a distance relative the receiving antenna subarray antenna. The transmitting antenna suban'ay antenna transmits a first signal at a first time period and the receiving antenna subarray antenna receives the first signal at least partly within the first time period causing a coupling between the transmitting antenna subarray antenna and the receiving antenna subarray antenna.
BACKGROUND ART
In today's antenna system comprising a transmitting array antenna and a receiving array antenna, there is coupling between the transmitting antenna and the receiving antenna when they are used at the same time. This is a problem since the transmitting antenna could be too "loud" for a receiving antenna. In prior ari: the problem with coupling have been solved by introduction of physical obstacles such as walls, etc.
Coupling between subarrays in an array antenna may constitute a major problem since a transmitting antenna subarray may make another subarray for receive more or less useless because of interference.
Reduction of the suban-ay coupling is not an easy task. The large bandwidth of broadband array antennas is a result of strong element coupling.

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The possibility to use existing adaptive beam-forming techniques to reduce the coupling is known in far field pattern, but the previously known technique do not reduce the subarray coupling.
The conclusion is that traditional adaptive beam-forming techniques are not appropriate for reduction of subarray coupling.
SUMMARY
In view of prior art there still exists a need for an antenna system, comprising a transmitting array antenna and a receiving array antenna, where frie mutual coupling between subarrays within a combined transmitting and receiving array antenna or between a transmitting an^ay antenna and a receiving array antenna are nullified or at least reduced. The Invention refers to a method where a transmitting antenna uses adaptive beam-forming functions with a constraint based on the knowledge of coupling between the antenna elements in the transmitting antenna and the receiving antenna, where a scattering matrix between the transmitting antenna and the receiving antenna is used. The scattering matrix comprises a coupling coefficient between each antenna element in the transmitting antenna and each antenna element in the receiving antenna element.
In the description of the invention the transmitting array antenna is described as a transmitting antenna subarray antenna and the receiving antenna is described as a receiving antenna subarray antenna, since the invention refers to an antenna system comprising a transmitting antenna and a receiving antenna regardless of whether if they are comprised in a combination array antenna or whether if they are two separate units.
The scattering matrix Is thus used as constraint in an equation to modify a
quiescent excitation ^° In the transmitting antenna subarray antenna in order to get nulls at the elements in the receiving antenna subarray antenna by controlling the elements in the transmitting antenna subarray antenna to

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transmit a signal that nullifies the coupling energy in the receiving antenna subanray antenna.
Hence, the invention refers to a new method for subarray coupling reduction.
The invention refers to nullifying transmitted energy from a transmitting antenna in an area connected to a receiving antenna.
The position of each antenna element in the transmitting antenna subarray antenna relative each element in the receiving antenna subaray antenna is not important per se since according to one example, the coupling can be measured without knowledge of the position in order to create the scattering matrix. However, If the position is changed after the measurement, a new measurement has to be done in order to create a new scattering matrix. Hence, the position must be fixed for each measurement If the relative position and thus distance is known, it is possible to calculate the scattering matrix. The measurement has the advantage over the calculation that it becomes more precise and that reflections in surrounding stnjctures will be part of the measurement. Both the measurement and the calculation techniques are known from prior art.
The invention refers to a mathematical algorithm that calculates how the transmitting antenna shall use the apertures in order to create the nullified area(s) in the transmitting pattern at the receiving antenna.
The method can dynamically shift the nullifying pattern in order to cover different receiving antennas at different points in time.
A coupling matrix must be detemnined for use In the algorithm. The coupling matrix can be decided using measurements or calculation. Measurement in situ is preferable since reflections from the surrounding structure will then inherently be part of the coupling matrix.
The invention can be used on both group antennas of multifunction type and on a number of separated group antennas.

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The invention has the following advantages:
The method gives a better performance of an already existing group antenna used for both transmitting and receiving.
The method is forceful and simple to implement since there is only calculations on already existing devices.
The method has very little impact on the radiation diagram of the transmitting antenna.
No extra hardware is needed. The already existing functions, in the group antenna, regarding control of amplitude and phase are used. The control of amplitude and phase for the different elements in the antenna system for beam fomiing purposes is well known in the prior art.
The method gives increased antenna performance.
The method gives increased field of application of array antennas.
The invention can be used in all type of phased array antennas where the coupling between subarrays within multifunction array antennas or between array antennas needs to be reduced
The invention relies on the possibility to detect or calculate the coupling between the subarray of the transmitting antenna and the subarray of the receiving antenna and to use the scattering matrix between the subarrays as a constraint with an antenna pattern synthesis method, in order to reduce the coupling. A constraint with the least mean square pattern synthesis method is used in the invention.
One example on how to use the constraint is tiie least mean square pattem synthesis method as described below, but other solutions could be possible with another method for solving a problem aiming to modify the quiescent

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excitation in tlie transmitting antenna subarray in order to get nulls at the elements In the receiving antenna subarray.
In order to explain the invention further an example will be described below where the antenna system is one of many possibilities, but where the calculations can be used on all the possible antenna system referring to the invention, i.e. a transmitting anray antenna and a receiving array antenna where the coupling from the transmitting antenna to the receiving antenna needs to be reduced.
The example refers to an array where the antenna elements are arranged in a planar rectangular lattice with element spacing d in both spatial directions and is used in the derivation of the method according to the invention. The final result that shows how to modify the array excitation coefficients is valid for any type of planar or non-planar array lattice.
Assume that a transmitting antenna subarray TX is used as a transmitting antenna and that a receiving antenna subarray RX is used as the receiving antenna. The goal is to reduce the coupling from the transmitting antenna subarray TX to the receiving antenna subarray RX with as little effect as possible on the transmitting antenna subarray TX far-field pattern. The transmitting antenna subarray TX far-field pattern is described by the array factor
m n
w = sin<9cos^ v = sin^sin^
Where ^■■"' (^ in vector fomri) is the complex excitation of element (m, n) in transmitting antenna subarray TX, d is the element spacing, k is the wavenumber, A is the wavelength and (6.9) is the direction in space in spherical coordinates. The array normal direction is given by G=0 degrees.

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Let ^0 be the quiescent pattern of the transmitting antenna subarray obtained when no constraints regarding nulls in receiving antenna subarray RX have been applied
(2)
where ^O""' (^o in vector fonn) is the corresponding quiescent excitation.
Let " be the approximate pattern obtained when constraints regarding nulls have been applied
" " . (3)
where ^'™'" (*" in vector form) is the corresponding excitation. Let " be the
closest approximation, in the least mean square sense, to the quiescent
p pattern ".
The coupling, b, from the elements in transmitting antenna subarray TX to the elements in receiving antenna subarray RX is
b = Ss^x^ (4)
where ^i^ is the scattering-matrix with the transmitting antenna subarray TX
to receiving antenna subarray RX mutual coupling coefficients. «^ is a P^Q matrix, where P and Q is the number of elements in receiving antenna subarray RX and transmitting antenna suban^ay TX respectively.
The synthesis problem can then be stated as: find the approximate partem " such that the mean square difference

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A. A. f(/;)=4 7 j^F,{u,v)-F,{u,vfdvdu = mm
2d "U , (5)
subject to the constraint
Parseval's identity on equation (5) gives A. JL
j2 2rf Id
4^J=^ I ]\FoM-F„iu,vfdvdu = J^YMo«..-Xa»J =
•^ J ^ m It
2d 2d
Where the horizontal bar symbol denote complex conjugate. Superscript T denotes transpose. Parseval's identity is known per se in prior art.
The synthesis problem now becomes
The solution to this optimization problem can be obtained by using "Lagrange's multipliers"
a ( I' —- £ix„h2^jgjixj =0,i = L.Q. (10)
where yS is a complex vector to be determined. Element index m, n has for simplicity been replaced by the single index /, j is the receiving antenna suban-ay RX element index. Lagrange's multipliers are known per se in prior art. Substitution of equation (8) and equation (9) in equation (10) gives

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d ( r- r- T- r- '' 1
-Xo+f„+(/?%J=Oo
where superscript * denote conjugate transpose. /? is determined from equation (9) and (11)
— / • v *' ^/
P -^BA^BA) ^BA^Q
Substitution of equation (12) in equatibn (11) finally gives
^a-^0~^BA^BA^BA) ^BA^O = Y ~ ^BA\^BA^»A} ^BATO ^ (-j 3where / is the identity matrix. Equation (13) shows how to modify the
quiescent excitation ^o in transmitting antenna subarray TX in order to get nulls at the elements in the receiving antenna subarray RX.
Some of the properties of the method according to the invention are:
• It is used on the transmitting antenna subarray TX. The only information needed in order to use the method is the scattering matrix between the transmitting antenna subarray TX and the receiving antenna subarrays RX. Information about the excitation of the receiving antenna suban^ay RX is not needed. Since the method is used on the transmitting antenna suban-ay TX it does not affect beam-forming on ttie receiving antenna subarray RX.

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• The term between the parentheses on the right hand side of equation (13) is independent of the array antenna scan direction and needs to be calculated only once for each frequency. The frequency independency is true if the coupling coefficients between the elements in the transmitting antenna subarray TX and the receiving antenna subarray RX do not change with time.
• The best way to determine the coupling coefficients from the transmitting antenna suban'ay TX to the receiving antenna subarray RX is probably to measure them w^en the array has been integrated since the coupling to the environment (radome etc) close to the array then will be included in the coupling coefficients. It may be possible to use the calibration function, if any, in ttie array to determine the coupling coeffidents.
• If the number of elements in the transmitting antenna subarray TX and receiving antenna subarray RX is Q and P respectively then P < Q is a necessary condition since the number of free variables is Q.
BRIEF DESCRIPTION OF DRAWINGS
The invention will below be described in connection to a number of drawings, In which:
Fig. 1 schematically shows an antenna system comprising a combination array antenna according to the invention comprising a transmitting antenna subarray and a receiving antenna subarray;
Fig. 2 schematically shows an antenna system according to the invention comprising a separate transmitting antenna subarray and a separate receiving antenna subarray facing essentially in the same direction;

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Fig, 3 schematically shows an antenna system according to the invention comprising a separate transmitting antenna subarray and a separate receiving antenna subarray facing essentially in the opposite directions;
Fig. 4 schematically shows a flow chart of the method according the invention;
Figs. 5a and 5b show the power coupling from the transmitting antenna suban-ay TX and receiving antenna subarrays RX over a 1 GHz frequency band at 10 GHz for the transmitting antenna subarray TX scan direction (0o,
where *""' (* in vector form) is the complex excitation of element (m, /?) in transmitting antenna subarray TX, d is the element spacing, k is the wavenumber, A is the wavelength and (9,(p) is the direction in space in spherical coordinates. The array normal direction is given by 9=0 degrees.
■p Let 0 be the quiescent pattern transmitting antenna suban-ay TX obtained
when no constraints regarding nulls in receiving antenna subarray RX have
been applied
(2)
where •^«'"" (^o in vector form) is the corresponding excitation.
■p Let " be the approximate pattern obtained when constraints regarding nulls
have been applied

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(3)
where "^ ( " in vector form) is the corresponding excitation. Let " be the closest approximation, in the least mean square sense, to the quiescent
pattern «.
The coupling, b, from the elements in transmitting antenna subarray TX to the elements In receiving antenna subarray RX is
w^here '>'* is the scattering-matrix with the transmitting antenna subarray TX
to receiving antenna subarray RX mutual coupling coefficients. "^^-^ is a P'o)={^°,0°).
The position of the elements or the geometrical features or the material in the transmitting antenna subarray or the receiving antenna subarray are not important per se for the invention but are implicitly taken into consideration during the coupling measurements or must be known when the coupling should be calculated.
Figures 9a-9d schematically shows the transmitting antenna subarray TX power coupled to the receiving antenna subarray RX for a 9.5-10.5 GHz frequency band with and without the method according to the invention and for the four different centre distances D in figure 8. Figure 9a shows the result for the sub-to-sub centre distance 37d. Figure 9b shows the result for the sub-to-sub centre distance 51 d. Figure 9c shows the result for the sub-to-sub

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centre distance 65d. Figure 9b shows the result for the sub-to-sub centre distance 79d.
Figures 9a-9d show the transmitting antenna subarray TX power coupled to the Receiving antenna subarray RX with use of the method according to the invention, i.e. equation (13), shown with the lower continuous line WM in figures 9a-9d and without the use of the method according to the invention shown with the upper continuous line NM in figures 9a-9d. The excitation according to equation (13) has been detemriined at the center frequency 10 GHz and has thereafter been used for the whole frequency band.
Sub-array size:
Figure 10 schematically shows five different sized transmitting antenna subarrays TX and a fixed sized and position of the receiving antenna subarray RX. The coupling from transmitting antenna subarrays TX with 24x24, TX1, 32x32, TX2, 40x40, TX3. 48x48, TX4, and 56x56, TX5, elements to a 16x16 element receiving antenna subarray RX is investigated in this section. Figure 10 shows that the transmitting antenna subarrays TX are positioned in one of the corner of the array and the receiving antenna subarray RX is positioned at the opposite corner. Observe that the centre distance D between the transmitting antenna subarray TX and the receiving antenna subarray RX decreases with increased transmitting antenna subarray TX size. The transmitting antenna subarrays TX have uniform taper and are steered to (0o,etween the
transmitting antenna subarray antenna (TX) and the receiving antenna
subarray antenna (RX),
characterized in that the coupling between the antenna elements in the transmitting antenna subarray antenna (TX) and the antenna elements in the receiving antenna subarray antenna (RX) are decided in a scattering-matrix
'^*^ and that the scattering matrix ^"^ is used as a constraint in order to
modify a quiescent excitation ^° in the transmitting antenna subarray (TX) in order to get nulls at the elements (5) in the receiving antenna subarray (RX) by controlling the elements (3) in the transmitting antenna subarray antenna (TX) to transmit a signal that nullifies the coupling energy in the receiving antenna subarray antenna (RX).
2. A method according to claim 1, wherein Q is greater than P.
3. A method according to any one of claims 1 or 2, wherein the coupling is decided by transmitting on one antenna element (3) at a time in the transmitting antenna subarray antenna (TX) and receiving the signal on one antenna element (5) at a time for every transmission of the antenna element (3) in the transmitting antenna subarray antenna (TX), and wherein the

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transmitted signal is measured in the receiving antenna subarray antenna (RX) giving the scattering matrix SBA comprising Q times P measurements representing the coupling.
4. A method according to any one of claims 1-2, wherein the coupling is decided by a numerical calculation by use of data regarding the distance from each element (3) in the transmitting antenna suban-ay (TX) to each element (6) in the receiving antenna suban'ay antenna (RX) and data regarding material and shape of the transmitting antenna suban-ay (TX) and the receiving antenna subarray antenna (RX).
5. A method according to any one of the preceding claims, wherein a
modification of the quiescent excitation ^° in transmitting antenna subarray (TX) is calculated by the following steps:
a transmitting antenna subarray (TX) far-field pattern is described by the array factor
m It
u=sinOcos^ v = sin^sin^
where ^»"' (^ in vector fonn) is the complex excitation of element m, n (3) in the transmitting antenna subarray antenna (TX), d is the element (3) spacing, k is the wavenumber, X is the wavelength and (G,(p) is the direction in space in spherical coordinates. The transmitting antenna subarray antenna (TX) normal direction is given by 9=0 degrees.
p Let 0 be the quiescent pattern of the transmitting antenna subarray (TX)
obtained when no constraints regarding nulls in the receiving antenna
subarray (RX) have been applied

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" " . (2)
where ^o™" (^o in vector form) is the corresponding excitation.
Let " be the approximate pattern obtained when constraints regarding nulls have been applied
" " , (3)
where <»"' ( " in vector form) is the corresponding excitation. Let " be the
closest approximation, in the least mean square sense, to the quiescent
p pattern ".
The coupling, b, from the elements in transmitting antenna subarray (TX) to the elements in receiving antenna subarray (RX) is
^ = ^SA^ ^ (4)
where ^i^' is the scattering-matrix with the transmitting antenna subarray
(TX) to receiving antenna subarray (RX) mutual coupling coefficients. "^"-^ is a P^Q matrix, where P and Q is the number of elements in receiving antenna subarray (RX) and fransmitting antenna subarray (TX) respectively.
The synthesis problem can then be stated as: find the approximate pattern
p " such that the mean square difference
A. 1.
id'Id , (5)
subject to the constraint

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Parseval's identity on equation (5) gives
i_ A. ^(^„)=^ J \\PMv)~FXu,vfdvdu = Y,lLV