EP0752736B1 - Verfahren und Anordnung zur Ferneichung eines Gruppenantennensystems für die Satellitenkommunikation - Google Patents

Verfahren und Anordnung zur Ferneichung eines Gruppenantennensystems für die Satellitenkommunikation Download PDF

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Publication number
EP0752736B1
EP0752736B1 EP19960304973 EP96304973A EP0752736B1 EP 0752736 B1 EP0752736 B1 EP 0752736B1 EP 19960304973 EP19960304973 EP 19960304973 EP 96304973 A EP96304973 A EP 96304973A EP 0752736 B1 EP0752736 B1 EP 0752736B1
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Prior art keywords
signals
calibration
encoded signals
phased array
signal
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French (fr)
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EP0752736A1 (de
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Seth David Silverstein
Robert Leland Nevin
William Ernest Engeler
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Lockheed Martin Corp
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Lockheed Corp
Lockheed Martin Corp
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Priority claimed from US08/499,528 external-priority patent/US5572219A/en
Priority claimed from US08/499,796 external-priority patent/US5677696A/en
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q3/00—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system
    • H01Q3/26—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the relative phase or relative amplitude of energisation between two or more active radiating elements; varying the distribution of energy across a radiating aperture
    • H01Q3/267—Phased-array testing or checking devices

Definitions

  • Active phased array systems or smart antenna systems have the capability for performing programmable changes in the complex gain (amplitude and phase) of the elemental signals that are transmitted and/or received by each respective element of the phased array ⁇ system to accommodate different beam-forming scenarios.
  • Communications satellites equipped with phased array systems are desirable since satellites so equipped have an intrinsic performance advantage over satellites with conventional reflector antennas.
  • a communications satellite with a phased array system can offer the following advantages: reconfigurable beam patterns ranging from broad-uniform continental coverage down to narrow spot beam patterns with 3 dB widths of about 1°; flexibility in varying the level of effective isotropic radiated power (EIRP) in multiple communication channels; and means for providing graceful system performance degradation to compensate for component failures.
  • EIRP effective isotropic radiated power
  • the calibration process In order to obtain meaningful estimates of the respective complex gains for the elemental signals respectively formed in each element of the phased array system, the calibration process must be performed in a time window that is sufficiently short so that the complex gains for the respective elemental signals transmitted from each element are substantially quasi-stationary.
  • the relevant time windows are dominated by two temporally variable effects: changes in the transmitted elemental signals due to variable atmospheric conditions encountered when such signals propagate toward a suitable control station located on Earth; and changes in the relative phase of the transmitted elemental signals due to thermally induced effects in the satellite, such as phase offsets in the respective circuit components for each respective element of the phased array system, and physical warpage of a panel structure employed for supporting the phased array.
  • the thermally induced effects are caused primarily by diurnal variations of the solar irradiance on the phased array panel.
  • EP-A-0,642,191 there is described a digitally controlled beam former for a spacecraft which includes means for periodically calibrating the feed paths of the spacecraft's antenna array by measuring the apparent movement of the centre of a reference signal and a nominal signal and utilising the measured data to compensate for at least the phase drift in the antenna feed paths.
  • the measured data may also be used to compensate for amplitude and phase drift in the antenna feed paths.
  • Calibration techniques proposed heretofore are essentially variations on the theme of individually measuring, one at a time, the respective complex gain of each single element (SE) of the phased array system while all the other elements of the phased array system are turned off.
  • SE calibration techniques are conceptually simple, these SE calibration techniques unfortunately have some fundamental problems that make their usefulness questionable for meeting the calibration requirements of typical phased array systems for communications satellites.
  • One problem is the difficulty of implementing a multipole microwave switching device coupled at the front end of the respective electrical paths for each elemental signal so as to direct or route suitable test signals to any single element undergoing calibration.
  • This multipole switching device is typically necessary in the SE calibration techniques to measure the complex gain for the elemental signal respectively formed in any individual element undergoing calibration at any given time.
  • Another problem of the SE calibration techniques is their relatively low signal-to- noise ratio (SNR). This effectively translates into relatively long measurement integration times. At practical satellite power levels, the integration times required to extract the calibration measurements for the SE calibration techniques are often too long to satisfy the quasi- stationarity time window criteria described above. In principle, one could increase the effective SNR of the SE process by increasing the power of the calibration signals transmitted from each element.
  • each element of the phased array system is usually designed to operate at near maximum power, as dictated by the power-handling capacity and linearity constraints for the circuit components in each element, it follows that arbitrary additional increases in power levels are typically not feasible. Thus it is desirable to provide a calibration method that allows for overcoming the problems associated with SE calibration techniques.
  • a system comprising a plurality of N elements N being a positive integer number, and apparatus for remotely calibrating the system, comprising:
  • the calibration signal which is applied to each respective one of the plurality of N elements can be orthogonally encoded based on the entries of a predetermined invertible encoding matrix, such as a binary Hadamard matrix, to generate first and second sets of orthogonally encoded signals.
  • the first and second sets of encoded signals and the reference signal are transmitted to a remote location.
  • the transmitted first and second sets of encoded signals are coherently detected at the remote location.
  • the coherently detected first and second sets of encoded signals are then decoded using the inverse of the predetermined invertible encoding matrix to generate a set of decoded signals.
  • the set of decoded signals is then processed for generating calibration data for each element of the system.
  • FIG. 1 illustrates a communications satellite 10 that incorporates a phased array system 12 for transmitting and/or receiving radio frequency (RF) signals 14.
  • RF signals 14 can be received at a remote control station 18, such as an earth-based control station, through a receiving antenna 20.
  • a phased array system operates on the principle that the phase of the RF signals emitted from the elements of the array can be selectively adjusted to provide a desired interference pattern at locations that are spatially remote from each element of the phased array.
  • a phased array system operates on the principle that the phase of the RF signals emitted from the elements of the array can be selectively adjusted to provide a desired interference pattern at locations that are spatially remote from each element of the phased array.
  • an RF transmission from an N-element phased array system at wavelength ⁇ By way of example, choose a coordinate system with its origin at the center of the phased array.
  • the signals A( R i ), received at spatial points R i are the interference sum of N elemental signals, having waveforms
  • the relative values of the set of coefficients, ⁇ a(n) ⁇ give the relative complex gains associated with respective circuit components, such as phase shifters 50 (Fig. 2) and power amplifiers 80 (Fig. 2), for each element of the phased array. It can be shown that information merely obtained by spatially sampling any interference pattern transmitted and/or received by the phased array (but not encoded in accordance with the present invention) cannot easily extract phase offsets due to the relative positioning of the elemental horns of the phased array, such as transmitting horns 90 (Fig. 2).
  • the three different parameters include the spatial sampling ⁇ R i ⁇ , the elemental transmitting horn positions r n , and the relative values of the different propagation constants K i .
  • coherent signal encoding of the elemental signals provides a dramatic simplification as the encoded signals, which enable to form predetermined time multiplexed beam patterns, can be received at a single receiver point situated along a reference direction R 0 .
  • K 0 propagation constant
  • its value need not be known to determine the respective relative values of each complex gain.
  • the parameters of interest can be obtained without knowledge of the distance to the single receiver point. It is assumed that the projection angle of reference direction R 0 onto the uniform phase plane of the array is known to a precision commensurate with the desired calibration accuracy.
  • the projection angle can be measured using readily available attitude measurements from conventional celestial body sensors, such as Earth, Moon and Sun sensors.
  • t(m,n) represents the coefficients of a predetermined invertible, encoding matrix T , such as an unitary, encoding matrix
  • T a predetermined invertible, encoding matrix
  • the respective relative values of the product ⁇ a(n)e -j2 ⁇ r n ⁇ R 0 /( ⁇ R 0 ) ⁇ can be obtained directly from the inversion of matrix T which enables for solving a system of N linearly independent simultaneous equations.
  • the inverse of a unitary matrix U is equal to the Hermitian conjugate U * of the matrix U and thus U -1 ⁇ U * .
  • the rows and columns of a unitary matrix form a complete orthonormal set of basis vectors that span the vector space upon which matrix U is defined.
  • orthogonal transforms are formally defined as the subset of unitary transformations defined on real vector spaces. Orthogonal transforms have been used extensively in imaging applications; see, for example, technical paper by W. K. Pratt, J. Kane, and H. C. Andrews, "Hadamard Transform Image Coding", Proc. IEEE 57, No. 1, at 58-68, (January 1969).
  • a minimum variance encoding scheme can be achieved when using a renormalized unitary matrix where each matrix element has unit magnitude, i.e.,
  • 1.
  • 2D two-dimensional discrete Fourier transforms
  • Hadamard matrices are notable examples of equal magnitude renormalized unitary matrices.
  • Fig. 2 shows a simplified schematic of an exemplary analog architecture for an N-element phased array system 12.
  • analog architectures being that digital beam-forming architectures can readily benefit from the teachings of the present invention.
  • present invention need not be limited to a phased array system being that any system that employs coherent signals, such as coherent electromagnetic signals employed in radar, lidar, communications systems and the like; or coherent sound signals employed in sonar, ultrasound systems and the like, can readily benefit from the teachings of the present invention.
  • Fig. 2 further shows a coherent signal generator 100 that supplies a reference tone or signal having a predetermined spectral relationship with respect to a calibration signal applied to each element of the phased array.
  • the reference signal can be offset in frequency by a predetermined factor from the calibration signal.
  • the reference signal and the calibration signal each passes through respective bandpass filters 72 having a predetermined passband substantially centered about the respective frequencies for the reference signal and the calibration signal.
  • coherent signal generator 100 is shown as supplying one reference signal, it will be appreciated that additional reference signals, if desired, could be readily obtained from coherent signal generator 100.
  • each phased array element further includes a respective power amplifier 80 and a respective horn 90.
  • Fig. 2 shows that the reference signal is transmitted from a separate horn 90', the reference signal can, with equivalent results, be transmitted from any of the phased array elements as long as the reference signal is injected into the electrical path after any of the phase shifters 50 1 -50 N so that the reference signal is unaffected by any encoding procedures performed by the phase shifters.
  • Fig. 2 shows a controller 300 which, during normal operation of the system, can issue switching commands for forming any desired beam patterns.
  • controller 300 further includes a calibration commands module 302 for issuing first and second sets of switching signals that allow the delay circuits 60 for encoding corresponding first and second sets of signals being transmitted by the N elements of the phased array system to a remote location, such as control station 18 (Fig. 1).
  • the controlled switching i.e., the encoding
  • the encoding matrix can be chosen to have a size NxN if N is an even number for which a Hadamard matrix can be constructed. If a Hadamard matrix of order N cannot be constructed, then the next higher order Hadamard construction can be conveniently used for the encoding.
  • this matrix construction technique is analogous to "zero-filling" techniques used in a Fast Fourier transform, for example.
  • H for the controlled switching (CS) procedure.
  • the power levels for the calibration signal are low enough so that the phase shifters can be treated as linear microwave devices.
  • the effect of switching-in or actuating a single delay circuit 60 such as the ⁇ th delay circuit in any nth phase shifter with a complex gain d ⁇ (n) simply imposes a complex gain as shown in Fig. 3a to an input signal x(n).
  • the effect of switching-in or actuating multiple delay circuits 60 and 60' simply generates the product of the respective complex gains for the multiple circuits switched-in. For example, as shown in Fig.
  • Fig. 4 shows a simplified schematic for coherent signal generator 100 used for generating coherent signals, such as the calibration signal and the reference signal.
  • coherent signals refers to signals having a substantially constant relative phase relation between one another.
  • a local oscillator 102 supplies an oscillator output signal having a predetermined frequency f o to respective frequency multipliers 104, 106 and 108 each respectively multiplying the frequency of the oscillator output signal by a respective multiplying factor such as N 1 , N 2 and N 3 , respectively.
  • the first mixer output signal can constitute the reference signal and the second mixer output signal can constitute the calibrated signal applied to each element of the phased array system.
  • Fig. 5 shows a simplified block diagram for a coherent detector 400 and a calibration processor 402 which can be situated at control station 18 (Fig. 1) for detecting and decoding, respectively, any sequences of encoded coherent signals being transmitted from the phased array system for determining calibration data which can then be conveniently "uplinked” to the satellite to compensate for changes in the various components which make up each respective element of the phased array system, such as power amplifiers, horns, and phase shifters.
  • Fig. 6 shows details about coherent detector 400 and calibration processor 402.
  • the received reference signal is supplied to a first mixer 406 and to a phase shifter 404, which imparts a phase shift of substantially 90° to the received coherent reference signal.
  • each orthogonally encoded signal is supplied to first and second mixers 406 and 408, respectively.
  • First mixer 406 mixes any received encoded signal with the reference signal to supply a first mixer output signal replicating the respective component of any received encoded signal that is in phase with the reference signal.
  • second mixer 408 mixes any received encoded signal with the phase shifted reference signal to supply a second mixer output signal replicating the respective component of any received encoded signal that is in quadrature (at 90°) with the reference signal.
  • calibration processor 402 can include register arrays 410 1 and 410 2 for storing, respectively, the in-phase components and the quadrature components supplied by A/D converters 409.
  • Calibration processor 402 can further include a memory 412 that can store entries for the inverse matrix H -1 which is used for decoding the respective quadrature components of the encoded signals.
  • Calibration processor 402 further includes an arithmetic logic unit (ALU) 412 for performing any suitable computations used for decoding the respective quadrature components of the encoded signals.
  • ALU 412 can be used for computing a difference between each quadrature component for the first and second sets of orthogonally encoded signal, and computing the product of the resulting difference with the inverse matrix H -1 .
  • Fig. 7 shows a flow chart for an exemplary calibration method in accordance with the present invention.
  • step 204 allows for generating coherent signals, such as the calibration signal and reference signal generated by coherent signal generator 100 (Figs 2 and 4).
  • the calibration signal is applied to each element of an N-element coherent system, such as the phased array system of Fig. 2.
  • Step 206 allows for encoding the calibration signal applied to each element of the coherent system to generate, for example, first and second sets of encoded signals.
  • the encoding can be advantageously performed using controlled switching or toggling of the delay circuits in each element of the phased array system, that is, no additional or separate encoding hardware is required being that the encoding is performed based on the specific delay circuits that are actuated in response to the switching signals from calibration commands module 110 (Fig. 2).
  • the reader is referred to our US patent application Serial No. 08/499,796 (RD-24,492), from which the present application claims priority.
  • Step 208 allows for transmitting the first and second sets of encoded signals and the reference signal to a remote location, such as control station 18 (Fig 1).
  • Step 210 allows for coherently detecting the transmitted first and second sets of encoded signals at the remote location.
  • Step 212 allows for decoding the detected first and second sets of encoded signals to generate a set of decoded signals which can be conveniently processed in step 214, prior to end of operations in step 216, for generating calibration data for each element of the phased array system.
  • Fig. 8 shows a flow chart, which can be conveniently used for performing encoding step 206 (Fig. 7) in the phased array system of Fig. 2.
  • step 224 allows for generating a first set of switching signals based upon entries of invertible, binary matrix H .
  • Step 226 allows for applying the first set of switching signals to actuate respective ones of the p delay circuits in each element of the phased array system to generate the first set of encoded signals.
  • the second set of switching signals uses - H for the controlled switching which in turn generates the second set of encoded signals.
  • step 230 allows for applying the second set of switching signals to actuate respective ones of the p delay circuits in each element of the phased array to generate the second set of encoded signals.
  • This switching procedure using a Hadamard control matrix effectively generates an exact unitary (orthogonal) transform encoding of the calibration signal applied to each of the phased array elements.
  • this switching scheme is particularly advantageous being that the delay circuits themselves provide the desired encoding, and thus no additional encoding hardware is required.
  • Fig. 9 shows a flowchart that can be used for performing, respectively, detecting step 210 and decoding step 212 (Fig. 7).
  • step 242 allows for measuring, with respect to the reference signal, respective in-phase and quadrature components for the first and second sets of orthogonally encoded signals which are received at the remote location.
  • coherent detector 400 (Fig. 6) allows for measuring both in-phase components and quadrature components of any received encoded signals. This can further include measuring, with respect to the reference signal, the phase and amplitude for each first and second sets of orthogonally encoded signals which are received at the remote location.
  • Step 244 allows for computing a respective difference between each respective measured in-phase and quadrature components for the first and second sets of orthogonally encoded signals which are received at the remote location.
  • H -1 H T /N used in the controlled switching encoding.
  • Fig. 10 shows a flowchart which provides further details about transmitting step 208 (Fig. 7) which allows for calibrating the full set of N(p+1) state variables associated with, for example, the N elements for the phased array system of Fig. 2. It will be shown that the controlled switching calibration procedure in accordance with the present invention generally requires a total of 2N(p+2) individual sequential transmissions, or N(p+2) sequential transmission pairs, that is, sequentially transmitting N(p+2) pairs of the first and second sets of orthogonally encoded signals.
  • step 262 allows for sequentially transmitting N pairs of orthogonally encoded signals, such as corresponding to the first and second sets of orthogonally encoded signals, wherein each ⁇ th delay circuit is switched in accordance with predetermined encoding rules based upon entries of matrix H, while each remaining delay circuit in each element of the phased array system is switched-out.
  • Each sequentially received transmission pair is conveniently expressed in vector form as,
  • the first subscript index ⁇ on Y ⁇ 0 indicates that a predetermined delay circuit, such as the ⁇ th delay circuit, is toggled in accordance with predetermined encoding rules based upon entries of Hadamard matrix H .
  • the second subscript (zero) on these vector signals indicates that these are the signals received when each remaining delay circuit, other than the ⁇ th delay circuit, is switched-out.
  • N transmission pairs of orthogonally encoded signals corresponding to the N elements of the phased array system are sequentially transmitted and received at the remote location.
  • Any mth sequentially received transmission pair of the first and second sets of orthogonally encoded signals is, respectively, represented by,
  • the encoding coefficients D ⁇ (mn), D R / ⁇ (mn) are dictated by the status of the delay circuits that are switched according to the following Hadamard encoding rules:
  • decoding can be conveniently performed at the remote location by computing the difference of received signal vectors Y ⁇ 0 , Y ⁇ 0 and multiplying the resulting vector difference by the inverse of the same Hadamard matrix that was used in the controlled switching performed onboard the satellite.
  • a decoded vector signal Z ⁇ 0 such that,
  • Step 264 allows for transmitting N(p-1) pairs of orthogonally encoded signals wherein each ⁇ th delay circuit is toggled in accordance with the predetermined encoding rules while another predetermined delay circuit other than the ⁇ th delay circuit, say the vth delay circuit, is permanently switched-in on each of the elements of the phased array.
  • another predetermined delay circuit other than the ⁇ th delay circuit say the vth delay circuit
  • any mth received transmission pair of the first and second sets of orthogonally encoded signals is represented, respectively, by
  • the first subscript index ⁇ on any component y ⁇ indicates that the ⁇ th delay circuit is toggled in accordance with the predetermined encoding rules based upon entries of the predetermined Hadamard matrix H while the second subscript index (here the ⁇ index) indicates that the vth delay circuit is switched-in on each of the elements of the phased array system.
  • the resulting set of decoded signals are represented in vector form by a decoded vector Z ⁇ , such that
  • step 264 allows for transmitting N(p-1) pairs of first and second sets of orthogonally encoded signals wherein the predetermined ⁇ th delay circuit is toggled in accordance with the predetermined encoding rules, while each remaining vth delay circuit in each phase-shifting element of the phased array is sequentially switched-in.
  • Step 266 allows for transmitting N pairs of first and second sets of orthogonally encoded signals wherein any delay circuit other than the ⁇ th delay circuit, for example the ⁇ th delay circuit ( ⁇ th ⁇ ⁇ th), is toggled in accordance with the predetermined encoding rules, while each remaining delay circuit in each element of the phased array system is switched out.
  • Step 268 allows for transmitting N pairs of first and second sets of orthogonally encoded signals wherein the ⁇ th delay circuit is toggled in accordance with the predetermined encoding rules, while the predetermined ⁇ th delay circuit in each phase shifter of the phased array system is switched in.
  • An Nth order Hadamard matrix is not unique, as any permutation of the rows or columns also produces an additional Nth order Hadamard matrix.
  • the "natural form" Hadamard matrix of order 2N can be constructed from the Nth order Hadamard matrix using,

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Claims (10)

  1. System enthaltend eine Anzahl N von Elementen (501, 502,...50N), wobei N eine positive ganze Zahl ist, und eine Einrichtung (300) zum Ferneichen des Systems, enthaltend:
    einen kohärenten Signalgenerator (100) zum Erzeugen eines Eichsignals und eines Refrenzsignals, die eine vorbestimmte spektrale Beziehung zueinander haben,
    eine Einrichtung (65) zum Zuführen des Eichsignals zu jedem entsprechenden der Anzahl N von Elementen,
    eine Einrichtung (60) zum Kodieren des Eichsignals, das jedem entsprechenden der Anzahl N von Elementen zugeführt ist, um einen Satz von kodierten Signalen zu generieren,
    eine Einrichtung (801, 802,...80N; 901, 902...90N) zum Senden des Satzes von kodierten Signalen und des Referenzsiganls an einen entfernten Ort,
    eine Einrichtung (412) zum Dekodieren des kohärent detektierten Satzes von kodierten Signalen, um einen Satz von dekodierten Signalen zu generieren, und
    einen Signalprozessor (402) zum Verarbeiten des Satzes dekodierter Signale zum Generieren von Eichdaten für jedes Element des Systems.
  2. System nach Anspruch 1, wobei die N Elemente des Systems eine phasengesteuerte Array bilden.
  3. System nach Anspruch 2, wobei jedes der N Elemente der phasengesteuerten Array ein Anzahl von p Verzögerungsschaltungen aufweist.
  4. System nach Anspruch 2, wobei jedes der N Elemente in der phasengesteuerten Array eine Anzahl von p Verzögerungsschaltungen (d1, .....dp) enthält und wobei die Kodiereinrichtung enthält:
    eine Einrichtung (302) zum Generieren eines Satzes von Eichschaltsignalen, die auf Einträgen einer vorbestimmten umstellbaren binären Matrix H basieren, und
    eine Einrichtung (300) zum Zuführen des Satzes von Eichschaltsignalen, um entsprechende der p Verzögerungsschaltungen in jedem der N Elemente zu betätigen, um den ersten Satz von kodierten Signalen zu generieren.
  5. System nach Anspruch 4, wobei die umstellbare binäre Matrix H eine binäre Matrix mit wenigstens einer Grösse NxN aufweist.
  6. System nach Anspruch 4, wobei die Kodiereinrichtung ferner enthält:
    eine Einrichtung (302) zum Generieren eines zweiten Satzes von Eichschaltsignalen, die auf Einträgen von einem anderen umstellbaren Feld basieren, das durch das Produkt (-1)H definiert ist, und
    eine Einrichtung (300) zum Zuführen des zweiten Satzes von Eichschaltsignalen, um entsprechende der p Verzögerungsschaltungen in jedem der N Elemente zu betätigen, um so den zweiten Satz von kodierten Signalen zu generieren.
  7. System nach Anspruch 6, wobei die Sendeeinrichtung (801,...80N;901,...90N) im Betrieb eine Gesamtzahl von N(p+2) Paaren der ersten und zweiten Sätze von orthogonal kodierten Signalen sendet.
  8. System nach Anspruch 1, wobei der Satz kodierter Signale, der durch die Kodiereinrichtung generiert ist, einen Satz orthogonal kodierter Signale aufweist, und wobei der kohärente Detektor Mittel zum Messen, in Bezug auf das Referenzsignal, entsprechender in-Phase- und Quadratur-Komponenten für den Satz orthogonal kodierter Signale aufweist, die an dem entfernten Ort empfangen sind.
  9. System nach Anspruch 8, wobei die Dekodiereinrichtung enthält:
    Mittel zum Berechnen des Produktes von jeder entsprechenden Differenz zwischen den gemessenen in-Phase- und Qudratur-Komponenten mit der inversen Matrix H-1 der Matrix H.
  10. System nach Anspruch 8, wobei die Einrichtung zum Messen entsprechender in-Phase- und Quadratur-Komponenten für den Satz orthogonal kodierter Signale Mittel zum Messen des Referenzsignals, der Phase und Amplitude des Satzes orthogonal ko-. dierter Signale aufweist, die an dem entfernten Ort empfangen sind.
EP19960304973 1995-07-07 1996-07-05 Verfahren und Anordnung zur Ferneichung eines Gruppenantennensystems für die Satellitenkommunikation Expired - Lifetime EP0752736B1 (de)

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
US499528 1995-07-07
US499796 1995-07-07
US08/499,528 US5572219A (en) 1995-07-07 1995-07-07 Method and apparatus for remotely calibrating a phased array system used for satellite communication
US08/499,796 US5677696A (en) 1995-07-07 1995-07-07 Method and apparatus for remotely calibrating a phased array system used for satellite communication using a unitary transform encoder

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EP0752736A1 EP0752736A1 (de) 1997-01-08
EP0752736B1 true EP0752736B1 (de) 2002-05-02

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JPH09121195A (ja) 1997-05-06
EP0752736A1 (de) 1997-01-08
CA2180051C (en) 2005-04-26
CA2180051A1 (en) 1997-01-08

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