EP2153518A1 - Système de formation de faisceau multi-antennes pour transmettre des signaux d'enveloppe constants décomposés à partir d'un signal d'enveloppe variable - Google Patents

Système de formation de faisceau multi-antennes pour transmettre des signaux d'enveloppe constants décomposés à partir d'un signal d'enveloppe variable

Info

Publication number
EP2153518A1
EP2153518A1 EP08769633A EP08769633A EP2153518A1 EP 2153518 A1 EP2153518 A1 EP 2153518A1 EP 08769633 A EP08769633 A EP 08769633A EP 08769633 A EP08769633 A EP 08769633A EP 2153518 A1 EP2153518 A1 EP 2153518A1
Authority
EP
European Patent Office
Prior art keywords
signal
constant envelope
envelope signal
constant
variable
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP08769633A
Other languages
German (de)
English (en)
Inventor
Abbas Komijani
Aliazam Abbasfar
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Rambus Inc
Original Assignee
Rambus Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Rambus Inc filed Critical Rambus Inc
Publication of EP2153518A1 publication Critical patent/EP2153518A1/fr
Withdrawn legal-status Critical Current

Links

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0682—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission using phase diversity (e.g. phase sweeping)
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03F—AMPLIFIERS
    • H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
    • H03F1/02—Modifications of amplifiers to raise the efficiency, e.g. gliding Class A stages, use of an auxiliary oscillation
    • H03F1/0205—Modifications of amplifiers to raise the efficiency, e.g. gliding Class A stages, use of an auxiliary oscillation in transistor amplifiers
    • H03F1/0294—Modifications of amplifiers to raise the efficiency, e.g. gliding Class A stages, use of an auxiliary oscillation in transistor amplifiers using vector summing of two or more constant amplitude phase-modulated signals
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03F—AMPLIFIERS
    • H03F3/00—Amplifiers with only discharge tubes or only semiconductor devices as amplifying elements
    • H03F3/20—Power amplifiers, e.g. Class B amplifiers, Class C amplifiers
    • H03F3/24—Power amplifiers, e.g. Class B amplifiers, Class C amplifiers of transmitter output stages
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/02—Transmitters
    • H04B1/04—Circuits
    • H04B2001/0408—Circuits with power amplifiers

Definitions

  • Constant envelope signals are a popular way for transmitting wireless or over-the-air radio frequency (RF) signals.
  • RF radio frequency
  • the envelope of the carrier wave does not change in response to changes in the modulated signal.
  • the maximum and minimum amplitude of a constant envelope signal is kept at a constant level.
  • Constant envelope signaling schemes are advantageous in that they are efficient from a transmitted power standpoint. This is because constant envelope signals allow a transmitter's power amplifiers to operate at or near saturation levels, which correspond to the point whereby the power amplifiers operate at peak efficiency. Furthermore, due to the fact that the amplitude is maintained at a constant level, the power amplifiers only have to provide a steady amount of amplification.
  • variable envelope signals have envelopes that change over time.
  • Variable envelope signals can transmit a greater amount of data for the same occupied frequency bandwidth over a given amount of time as compared to constant envelope signals. This results in improved spectral efficiency.
  • power amplifiers for amplifying variable envelope signals operate at an average power level which is significantly less than their peak power. This means that the power amplifiers are mostly operating at a point which is less than ideal. This reduces the power efficiency of these variable envelope power amplifiers.
  • power amplifiers for variable envelope signals change the signals' amplitudes by varying amounts, depending on the instantaneous amplitudes of the signals.
  • Figure 1 shows an example of a system for transmitting a variable envelope signal as two constant envelope signals over two transmitter antennas.
  • Figure 2 shows a vector diagram used to illustrate the decomposition process used to perform spatial out-phasing.
  • Figure 3 shows constellations for transmitter antennas transmitting constant envelope signals and the constellation for a receiver antenna which receives an equivalent variable envelope signal.
  • Figure 4 shows a graph of output power and efficiency as functions of input power for a typical transmitter power amplifier.
  • Figure 5 shows a multi-antenna system having N number of transmitter antennas for transmitting N number of constant envelop signals, which represent an initial variable envelope signal.
  • Figure 6 shows a phased array antenna system for transmitting constant envelope signals decomposed from a variable envelope system.
  • Figure 7 is a flowchart describing the steps for the multi-antenna beam forming process for transmitting constant envelope signals decomposed from a variable envelope signal.
  • Figure 8 shows a system diagram for an embodiment of a multi-antenna system for transmitting decomposed constant envelope signals.
  • Embodiments in the present disclosure pertain to a multi-antenna beam- forming system.
  • a variable envelope signal is decomposed into two constant envelope signals through a process known as out-phasing.
  • the out-phasing process provides two signals of constant amplitude but of varying phase (e.g., "phasor fragments") to represent a single signal of varying phase and amplitude.
  • Each of the two constant envelope signals is amplified by a power amplifier and then transmitted wirelessly as an RF signal by a transmitting antenna. Because the power amplifiers are amplifying constant envelope signals, transmit power efficiency is achieved while any non-linearities associated with the power amplifiers are minimized.
  • the two constant envelope RF signals propagate over-the-air and are received by a one or more receiving antenna.
  • the combination of the two constant envelope RF signals received by one or more receiving antennas produces a variable envelope signal which matches that of the initial variable envelope signal before it was decomposed.
  • the received variable envelope signal results in superior spectral efficiency.
  • a delay can be introduced in the transmit path of one or more antennas to help steer the transmit signal to the location of a designated receiver antenna.
  • a variable envelope signal X(t) has changes in both amplitude and phase.
  • the variable envelope signal X(t) is decomposed into two constant envelope signals X c i and X c2 - This is accomplished by inputting the variable envelope signal X(t) into two mixers 101 and 104.
  • Mixer 101 changes the phase of the X(t) signal by ⁇ i to produce a constant envelope signal Xd .
  • the constant envelope signal Xd has a constant amplitude, but its phase varies as a function of X(t).
  • the constant envelope signal Xd is input to a power amplifier 102.
  • Power amplifier 102 amplifies the constant envelope signal Xd , which is then transmitted by antenna 103 over-the-air as an RF signal to a receiver antenna 107.
  • mixer 104 changes the phase of the variable envelope signal X(t) by ⁇ 2 to produce the constant envelope signal Xc2.
  • the constant envelope signal Xc2 has a constant amplitude, but its phase varies as a function of X(t).
  • the constant envelope Xc2 signal is input to power amplifier 105.
  • Power amplifier 105 amplifies the constant envelope signal Xc2, which is then transmitted by antenna 106 over-the-air as an RF signal to receiver antenna 107.
  • the two RF signals being transmitted by transmitter antenna 103 and 106 combine through superposition over-the-air, and the receiver antenna 107 receives a variable envelope signal that corresponds to the original variable envelope signal X(t).
  • This type of combining at least two constant envelope signals over-the-air to form a variable envelope signal is referred to herein as "spatial out-phasing.”
  • spatial out-phasing there is no need to have a physical adder circuit to add the two constant envelope signals together before RF transmission.
  • the constant envelope signals are separately amplified by separate power amplifiers, and each of the amplified constant envelope signals are transmitted wirelessly by their own dedicated antenna.
  • phase delay circuits any number of different types and designs of phase delay circuits, mixers, amplifiers, converters, switches, and other components can be used to implement the decomposition process. Furthermore, from the receiver side, no changes or modifications are needed. This provides for a standard-blind solution, whereby the multi-antenna system for transmitting constant envelope signals decomposed from a variable envelope signal will work for virtually any conventional receiver system.
  • Figure 2 shows a vector diagram used to illustrate the decomposition process used to perform spatial out-phasing.
  • Three vectors are shown.
  • One vector represents the variable envelope signal X(t).
  • the length of the X(t) vector represents the amplitude of the variable envelope signal.
  • the angle of the X(t) vector represents the phase of the variable envelope signal.
  • the amplitude and phase of the variable envelope signal may change. Consequently, the length and angle of the X(t) vector can change.
  • the X(t) vector can be decomposed into two vectors Xd and Xc2.
  • the Xd and Xc2 vectors represent constant envelope signals. For constant envelope signals, the amplitudes do not change.
  • the amplitudes of the constant envelope signals are denoted by the lengths of the Xd and Xc2 vectors. Consequently, the lengths of the Xd and Xc2 vectors are kept constant.
  • the angles of the Xd and Xc2 vectors represent their respective phases. By applying vector arithmetic, one can calculate the angles ( ⁇ 1 and ⁇ 2) for the Xd and Xc2 vectors such that when the Xd vector is combined with the Xc2 vector, the result is the X(t) vector. Any change in the phase of the variable envelope signal is represented by a corresponding change in the angle of the X(t) vector.
  • angles, ⁇ 1 and ⁇ 2, of the Xd and Xc2 vectors are changed (e.g., ⁇ 1 decreases while ⁇ 2 increases or ⁇ 1 decreases while ⁇ 2 increases) in response to the change in the angle of the X(t) vector.
  • the lengths of the Xd and Xc2 vectors need not be changed and can be kept constant. Consequently, changes in phase of a variable envelope signal are represented by changing the phases of the two corresponding constant envelope signals. [00017] Any change in the amplitude of the variable envelope signal is represented by a corresponding change in the length of the X(t) vector.
  • angles of the constant envelope to change accordingly, as represented by the angles of the Xd and Xc2 vectors.
  • the amplitude of the variable envelope signal were to decrease, this would be represented by a shorter X(t) vector.
  • Decomposing a shorter X(t) vector entails changing the angles, ⁇ 1 and ⁇ 2, of the Xd and Xc2 vectors.
  • the angles, ⁇ 1 and ⁇ 2 are increased when the length of the X(t) signal decreases.
  • the lengths of the Xd and Xc2 vectors cannot be shortened because they represent constant envelop signals having constant amplitudes.
  • the receiver antenna receives a variable envelope signal.
  • Figure 3 shows the constellations for the transmitter antennas and the constellation for the receiver antenna.
  • the constellation for one of the two transmitter antennas is depicted as 301.
  • the symbols are arranged equi-distant from the center, which indicates that a constant envelope signal having a constant amplitude is being transmitted.
  • the phase of the constant envelope signal can vary, as indicated by the various symbols located along the same radius, R1 , of the constellation.
  • the constellation for the other transmitter antenna is depicted as 302.
  • the symbols of constellation 302 are arranged equi-distant to the center by the radius R2. This indicates that a constant envelope signal having a constant amplitude, but varying phases, is being transmitted by the other transmitter antenna.
  • the constellation for the receiver antenna is depicted as 303.
  • Constellation 403 has symbols arranged along circles with different radii (R3, R4, and R5). The different radii indicates that the amplitude of the received signal varies over time. Furthermore, the symbols are arranged along various points of the circles. This means that the phase of the received signal also varies over time. Consequently, constellation 303 shows a received variable envelope signal.
  • the two transmitted signals having constellations 301 and 302 are combined over-the-air, through a process herein referred to as spatial out-phasing, and results in an antenna receiving a signal that corresponds to constellation 303, which characterizes a variable envelope signal.
  • a higher rate of data (e.g., greater bits per second) is being received by the receiver antenna as compared to a receiver that simply receives a constant envelope signal.
  • the transmitter's power amplifiers are amplifying constant envelope signals instead of variable envelope signals, power amplifier nonlineahties are minimized.
  • the receiver constellation 303 is uniform, and receiver errors are minimized.
  • the transmitter's power amplifiers are amplifying constant envelope signals (i.e., Xd and Xc2), these amplifiers can operate at or near their saturation level. This means that the transmitter's power amplifiers are operating at or near their peak efficiency.
  • Figure 4 shows a graph of the output power and efficiency as functions of input power for a typical transmitter power amplifier.
  • variable envelope signals For constant envelope signals, the amplitude is constant. Consequently, the average power for constant envelope signals is approximately equal to its peak power. This corresponds to higher efficiency. Conversely, because the amplitude of the variable envelope signal varies over time, its average power is less than that of its peak power. Its average power is backed off from its peak. This results in a lower power efficiency. For a typical power amplifier, the efficiency for variable envelope signals can be 5%, whereas the typical efficiency for constant envelope signals can be 50%. Thus, by decomposing variable envelope signals into constant envelope signals, embodiments of the present disclosure can improve power amplifier efficiency by upwards of ten-fold. [00020] In other embodiments, more than two transmitter antennas are utilized.
  • variable envelope signal is decomposed into three or more constant envelope signals, each of which is separately amplified by power amplifiers and sent over-the-air as RF signals by transmitter antennas.
  • Figure 5 shows a multi- antenna system having N number of transmitter antennas for transmitting N number of constant envelop signals which represent an initial variable envelope signal.
  • the initial variable envelope signal X(t) is simultaneously input to N number of mixers.
  • the N number of mixers independently changes the phase by ⁇ i to ⁇ N .
  • the outputs from the mixers are N number of constant envelope signals, X c i to X CN -
  • Each of these N number of constant envelope signals are amplified by N number of power amplifiers, PAi to PA N , and then transmitted as RF signals by the N number of antennas.
  • the multi-antenna systems of the above embodiments are applicable to circumstances whereby the receiver antenna is located equi-distant from each of the transmitter antennas.
  • the constant envelope signal corresponding to the transmitter antenna(s) that are further away will take longer to reach the receiver antenna. This extra delay may cause errors in phase to occur.
  • One solution is to introduce extra delay(s) in the transmit path(s) corresponding to the closer transmitter antenna(s) so that their constant envelope signal will synchronize and arrive "on time" with that of the constant envelope signal of the transmitter antenna that is further away. For example, if there are two transmitter antennas with one transmitter antenna driven by X c -i(t), and the other transmitter antenna driven by X C 2(t), then at the receiver antenna, the summation is correct if the delays from the two transmitter antennas are the same. This occurs at one angle.
  • the delay can be adjusted by a feedback from the receiver to the transmitter.
  • X C2 (t) can be adjusted for phase, while keeping its amplitude constant.
  • the phase adjustment can direct the transmitted signal to any desired angle by:
  • a phased array antenna system is used to transmit the decomposed, out-phased constant envelope signals.
  • a phased array antenna system uses multiple antennas to transmit multiple RF signals.
  • the phased array antenna system can point or steer a beam to the specific location of a receiver antenna. This beam forming functionality is desirable for security reasons.
  • the directivity is advantageous because more RF power can be directed to the receiver antenna, which increases the distance by which data can be reliably transmitted.
  • the location information of the receiver is fedback to the transmitter so that the transmitter can adjust the delays to compensate for the location of that receiver. Feeding back the receiver location is performed for mobile or portable receiver applications. Alternatively, if the locations of the transmitter and receiver are fixed, the delays can be calculated based on the fixed locations and stored in the memory of the transmitter system. Location information can also be input from a user or downloaded from a network. Embodiments of the present disclosure can be applied to a phased array antenna system. [00026] For example, Figure 6 shows a phased array antenna system for transmitting constant envelope signals decomposed from a variable envelope system. The variable envelope signal X(t) is input to the constant envelope decomposition block 601.
  • the constant envelope decomposition block 601 decomposes the variable envelope signal X(t) into two constant envelope signals, Xd and Xc2, according to the out-phasing decomposition process described in detail above. After constant envelope decomposition, beam steering delays are introduced into the X C i and X C2 signal paths before they are amplified by the power amplifiers. More specifically, one of the X C i signal paths 602 does not have any added beam steering delay.
  • the Xci signal is input to power amplifier 606. Power amplifier 606 amplifies the Xci signal for RF transmission by transmitter antenna 610. The Xci signal is also transmitted over an additional N number of transmit paths in the phased array antenna system.
  • the beam steering delays are incrementally larger for each successive Xci transmit path.
  • the last transmit path 604 of the Xci signal has an added beam steering delay of ⁇ 2N - 2 -
  • the X C i signal with the added beam steering delay of ⁇ 2N - 2 is amplified by power amplifier 608 and then transmitted as an RF signal by antenna 612.
  • the ⁇ delays are incorporated into the phases (e.g., ⁇ i - ⁇ 2 N-2 ) ⁇
  • one of the transmit paths 603 has an added beam steering delay of ⁇ -i.
  • the X C2 signal that has the added beam steering delay of ⁇ i is input to power amplifier 607 which amplifies the signal before being transmitted over- the-air by antenna 611.
  • the Xc2 signal is also transmitted over an additional N number of transmit paths in the phased array antenna system. For each of the N number of Xc 2 paths, additional beam steering delays are added. The beam steering delays are incrementally larger for each successive Xc2 transmit path.
  • the last transmit path 605 of the Xc2 signal has an added beam steering delay of ⁇ 2N-i-
  • the Xc 2 signal with the added beam steering delay of ⁇ 2N -i is amplified by power amplifier 609 and then transmitted as an RF signal by antenna 613.
  • the phased array antenna system can have many transmit paths, power amplifiers, and transmitter antennas for transmitting the constant envelope signals. However, for purposes of illustration and explanation, only four of the multiple transmitter paths, power amplifiers, and transmitter antennas are shown in detail in Figure 6. Increasing the number of transmit paths, power amplifiers, and transmitter antennas in the phased array antenna system increases its gain, thereby extending its transmit range. By selectively controlling the beam steering delays, the beam can be directed to any location corresponding to a receiver antenna. In other words, the beam can be electronically steered to a receiver antenna.
  • Figure 7 is a flowchart describing the steps for the multi-antenna beam forming process for transmitting constant envelope signals decomposed from a variable envelope signal.
  • step 701 the variable envelope signal is generated.
  • This variable envelope signal is decomposed into at least two constant envelope signals, step 702.
  • the amplitudes of the constant envelope signals are kept constant, but their phases varies as a function of the amplitude and phase of the variable envelope signal.
  • step 703 one or more delays can be added to one or more of the transmit signal paths corresponding to one or both of the constant envelope signals.
  • Step 703 is optional and is used to steer the beam to the known location of a receiver antenna. For implementation in a phased array antenna system, the delays are successively staggered for successive antennas.
  • each of the transmit paths associated with the constant envelope signals are amplified by separate power amplifiers.
  • FIG. 8 shows a system diagram for an embodiment of a multi-antenna system for transmitting decomposed constant envelope signals.
  • the multi-antenna system 802 can send and receive data from a network 801 (e.g., the Internet) through an I/O interface 803.
  • a network 801 e.g., the Internet
  • the I/O interface 803 is also coupled to a user interface 810 which enables users to input data and commands to the multi-antenna system 802 and also to obtain data for display from the multi-antenna system 802.
  • Any data designated for transmission by transmitter 806 is initially processed as a variable envelop signal.
  • the data can originate as input from a user through Ul 810, obtained through the network 801 , read from memory 805, or generated by processor 804.
  • the variable envelope signal is then processed by out-phasing decomposition block 807 which outputs constant envelope signals. Delays are added in block 808 to certain ones of the constant envelope signals for purposes of bean steering.
  • the constant envelope signals are then amplified by power amplifiers in block 809.
  • the amplified constant envelope signals are steered and transmitted over-the-air to one or more receiving antennas.
  • An example of a receiving system is shown as 811.
  • the receiving system 811 has a receiver 812, which is designed to receive and demodulate variable envelope signals.
  • a processor 813 processes the received data.
  • the data can then be stored in memory 814 or sent out via I/O interface 815 for display or playback on user interface 817 or sent over a network 816.
  • the processor 813 of receiving station 811 can send location information back to the transmitter 806 of multi-antenna system 802. This location information is used to adjust the delays of delay circuit 808 to compensate for the location of receiving system 811.
  • This information can be sent back wirelessly, especially for mobile or portable receiver applications.
  • the location information can be input by the user, stored in memory, or downloaded from a network or server.
  • the multi-antenna system directly generates the constant envelope signals without having to actually generate any variable envelope signal.
  • the constant envelope signals are modeled after an imaginary or virtual variable envelope signal. It should be noted that this system supports any type of point-to-point or multicast data communications.
  • the distance between the transmitter and receiver can be as short as ten times the distance between the transmitter antennas and can be as far away as practically supported by the power amplifiers and number of antennas.
  • variable envelope signals e.g., Differential Quadrature Phase Shift Keying, spread spectrum signals, etc.
  • constant or near-constant envelope signals e.g., Frequency Shift Keying, Orthogonal Frequency Division Multiplexing, etc.
  • the multi-antenna system is not limited by frequency; it can work in any frequency range.
  • the multi- antenna system can be used in a wide range of different applications (e.g., as a repeater, for transmitting television signals including high definition, high-speed digital data link, audio/voice/cellular communications, etc.).

Abstract

La présente invention concerne, selon ses modes de réalisation, un système de formation de faisceau multi-antennes pour transmettre des signaux d'enveloppe constants décomposés à partir d'un signal d'enveloppe variable. Le signal d'enveloppe variable est décomposé en deux signaux d'enveloppe constants. Chacun des signaux d'enveloppe constants est amplifié séparément par des amplificateurs de puissance et transmis par des antennes séparées. Des temporisations d'orientation du faisceau peuvent être ajoutées aux voies de transmission des signaux d'enveloppe constants pour orienter le faisceau vers l'emplacement d'un récepteur. Les signaux d'enveloppe constants transmis se combinent par déplacement de phase spatiale de telle manière que l'antenne de réception reçoive un signal d'enveloppe variable.
EP08769633A 2007-05-25 2008-05-22 Système de formation de faisceau multi-antennes pour transmettre des signaux d'enveloppe constants décomposés à partir d'un signal d'enveloppe variable Withdrawn EP2153518A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US93169907P 2007-05-25 2007-05-25
PCT/US2008/064572 WO2008147908A1 (fr) 2007-05-25 2008-05-22 Système de formation de faisceau multi-antennes pour transmettre des signaux d'enveloppe constants décomposés à partir d'un signal d'enveloppe variable

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EP2153518A1 true EP2153518A1 (fr) 2010-02-17

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FR3080732A1 (fr) * 2018-04-27 2019-11-01 Orange Procedes de reception et d'emission, et dispositifs recepteur et emetteur d'un systeme de communication sans fil
JP2020156022A (ja) * 2019-03-22 2020-09-24 古河電気工業株式会社 増幅装置
EP3876420A1 (fr) * 2020-03-02 2021-09-08 Nokia Solutions and Networks Oy Transmission de fréquence radio

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JPH07162224A (ja) * 1993-12-02 1995-06-23 Nippon Telegr & Teleph Corp <Ntt> アンテナ合成回路
EP1511181B1 (fr) * 2002-05-31 2009-12-09 Fujitsu Limited Compensateur de distorsion
JP4368592B2 (ja) * 2003-02-19 2009-11-18 シャープ株式会社 デジタル放送受信用チューナ及びこれを備えた受信装置
JP3747922B2 (ja) * 2003-07-03 2006-02-22 三菱電機株式会社 移動体通信装置
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JP2010530657A (ja) 2010-09-09
WO2008147908A1 (fr) 2008-12-04

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