Patent Publication Number: US-10333606-B2

Title: Method for estimating channel state and controlling transmission/reception signal by multiple antenna device, and multiple antenna device using same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS AND CLAIM OF PRIORITY 
     The present application claims priority under 35 U.S.C. § 365 to International Patent Application No. PCT/KR2016/000095 filed Jan. 6, 2016, entitled “METHOD FOR ESTIMATING CHANNEL STATE AND CONTROLLING TRANSMISSION/RECEPTION SIGNAL BY MULTIPLE ANTENNA DEVICE, AND MULTIPLE ANTENNA DEVICE USING SAME”, and through Japanese Patent Application No. 2015-074413, which was filed on Mar. 31, 2015, and Korean Patent Application No. 10-2015-0181075, which was filed on Dec. 17, 2015, each of which are incorporated herein by reference into the present disclosure as if fully set forth herein. 
     TECHNICAL FIELD 
     The present invention relates to a method of controlling transmission and reception of signals based on channel estimation in a multi-antenna apparatus. 
     BACKGROUND 
     Recently, a multi-antenna system has been attracting attention for achieving high frequency utilization efficiency in a limited frequency band. In order to implement the multi-antenna system, channel state information (CSI) may be required between a base station and a terminal. 
     Meanwhile,  FIG. 8  is a view of an example of a multi-antenna system that obtains CSI by feeding back CSI from a user terminal (UT) to a base station (BS). 
     Referring to  FIG. 8 , the base station may include a multi-antenna  201  configured by N antennas  201 - 1  to  201 -N, N transmitters Tx 1  to TxN, and N receivers Rx 1  to RxN respectively corresponding to the antennas  201 - 1  to  201 -N. Furthermore, the base station may include N circulators  205 - 1  to  205 -N and a controller  206  for respectively connecting transmitters Tx 1  to TxN and receivers Rx 1  to RxN to the antennas  201 - 1  to  201 -N. Meanwhile, the terminal may include an antenna  101  and a control unit  107 . 
     Referring to  FIG. 8 , in operation S 23 , the base station may start communication with the terminal through operation S 21  of transmitting a signal for estimating CSI from the base station to the terminal and operation S 22  of feeding back the signal for estimating CSI from the terminal to the base station. In addition, in the method of  FIG. 8 , CSI including information about a difference in amplitude and phase between a transmitter and a receiver may be estimated by feeding back the CSI. The number of times transmission and reception of signals for estimating CSI is performed increases depending on the number of antennas (the number of antenna elements) of the base station. Therefore, if the number of antennas of the base station or the number of users communicating with the base station increases, the amount of CSI feedback increases and communication efficiency may be greatly reduced. 
     SUMMARY 
     The present disclosure provides a method of controlling transmission and reception of signals based on channel estimation in a multi-antenna apparatus. 
     As a technical means to achieve the above-mentioned technical problem, some embodiments of the present disclosure may include, in a multi-antenna apparatus for controlling transmission and reception of signals based on channel estimation, a signal transmitter configured to transmit a first signal using a multi-antenna; a signal receiver configured to receive a second signal using the multi-antenna based on the transmitted first signal; a signal transferrer configured to receive a third signal received from the signal transmitter and provide the third signal to the signal receiver; and a controller configured to estimate a channel state of the multi-antenna based on the second signal and the third signal obtained from the signal receiver, and control transmission and reception of signals through the multi-antenna according to the estimated channel state. 
     The controller may include a calculator configured to calculate a calibration value of the multi-antenna based on the channel state, and the calibration value may be calculated based on a ratio of a comparison target value determined based on respective transfer functions of the second signal and third signal of a first antenna among the multi-antenna to a comparison target value of a second antenna among the multi-antenna. 
     The comparison target value may be determined by a ratio of the transfer function of the second signal of the first antenna to the transfer function of the third signal of the first antenna. 
     The comparison target value may be determined by a ratio of the transfer function of the second signal or the third signal of the first antenna to a transfer function of the third signal or the second signal of the second antenna. 
     The controller may include a transmission signal processor configured to control amplitude and phase of the first signal input to the signal transmitter based on the channel state. 
     The signal transmitter may include a variable attenuator configured to correct a power intensity of the multi-antenna using different power intensities for different antennas when transmitting and receiving the signals. 
     The signal transmitter may include: an oscillator configured to generate an electrical vibration; and a mixer configured to mix an output signal of the variable attenuator and an output signal of the oscillator. 
     The controller may include: a transmission signal controller configured to distribute a transmission signal to a plurality of transmission signals, to adjust intensities of the plurality of transmission signals, and to transmit the transmission signals to the signal transmitter for transmitting the transmission signal through the multi-antenna; and a reception signal controller configured to adjust intensities of a plurality of reception signals received through the multi-antenna and synthesize the plurality of reception signals into one reception signal. 
     The first signal may be a downlink pilot signal. 
     The number of times the second signal is sampled by the calculator may be equal to the number of antennas of the multi-antenna, and the calculator may calculate the calibration value of the multi-antenna by storing the third signal by the number of times the second signal is sampled. 
     When a calibration value of the first signal is calculated, the calculator may calculate a calibration value of the second signal by using the second signal received at an arbitrary time. 
     Furthermore, some embodiments of the present disclosure may include, in a method of controlling transmission and reception of signals based on channel estimation in a multi-antenna apparatus, transmitting a first signal from a signal transmitter; transferring a third signal received from the signal transmitter to a signal receiver; receiving a second signal using the multi-antenna based on the transmitted first signal; and estimating a channel state of the multi-antenna based on the received second signal and the transferred third signal, and controlling transmission and reception of signals through the multi-antenna according to the estimated channel state. 
     The method may further include calculating a calibration value of the multi-antenna based on the estimated channel state of the multi-antenna, and wherein the calibration value may be defined as a ratio of a comparison target value determined based on respective transfer functions of the second signal and the third signal of a first antenna among the multi-antenna to a comparison target value of a second antenna among the multi-antenna. 
     The comparison target value may be a ratio of a transfer function of the second signal of the first antenna to a transfer function of the third signal of the first antenna. 
     The comparison target value may be a ratio of the transfer function of the second signal or the third signal of the first antenna to a transfer function of the third signal or the second signal of the second antenna. 
     The method may further include controlling amplitude and phase of the first signal based on the estimated channel state. 
     The transferring of the third signal to the signal receiver may include correcting a power intensity of the multi-antenna using different power intensities for different antennas when transmitting and receiving the third signal. 
     The number of times the second signal is sampled may be equal to the number of antennas of the multi-antenna, and the method may include calculating the calibration value of the multi-antenna by storing the third signal by the number of times the second signal is sampled. 
     When a calibration value of the first signal is calculated, a calibration value of the second signal may be calculated by using the second signal received at an arbitrary time. 
     Furthermore, in some embodiments of the present disclosure, a non-transitory computer-readable recording medium has recorded thereon a program for executing the method of controlling transmission and reception of signals based on channel estimation in a multi-antenna apparatus. 
     As described above, a multi-antenna apparatus may control transmission and reception of signals by estimating a channel state without an external device, and thus communication efficiency can be increased without depending on the installation position and the surrounding environment. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a view of a multi-antenna apparatus of a time division duplex (TDD) system for controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
         FIG. 2  is a flowchart of a method of controlling transmission and reception of signals based on channel estimation in a multi-antenna apparatus, according to some embodiments of the present disclosure. 
         FIG. 3  is a view for explaining a method of using an antenna over time according to some embodiments of the present disclosure. 
         FIG. 4  is a view for explaining a signal transmitted by a transmitter of a multi-antenna apparatus, according to some embodiments of the present disclosure. 
         FIG. 5  is a view of a multi-antenna apparatus of a frequency division system for controlling transmission and reception of signals based on channel estimation, according to another embodiment of the present disclosure. 
         FIG. 6  is a view of radiation patterns of a multi-antenna where a horizontal axis represents an angle and a vertical axis represents relative power. 
         FIG. 7  is a flowchart of a method of controlling transmission and reception of signals based on channel estimation in a multi-antenna apparatus, according to another embodiment of the present disclosure. 
         FIG. 8  is a view of an example of a multi-antenna system that obtains channel state information by feeding back channel state information from a terminal to a base station. 
         FIG. 9  is a view of an example of a multi-antenna system that does not feed back channel state information. 
         FIG. 10  is a view of an example of a multi-antenna apparatus using two loops to feed back channel state information. 
         FIG. 11  is a view of another example of a multi-antenna apparatus using two loops to feed back channel state information. 
         FIG. 12  is a flowchart for explaining a method of controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
         FIG. 13  is a block diagram for explaining a multi-antenna apparatus for controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
         FIG. 14  is a detailed block diagram for explaining a multi-antenna apparatus for controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     A multi-antenna apparatus for controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure, may include a signal transmitter configured to transmit a first signal using a multi-antenna, a signal receiver configured to receive a second signal using the multi-antenna based on the transmitted first signal, a signal transferrer configured to receive a third signal received from the signal transmitter and provide the third signal to the signal receiver, and a controller configured to estimate a channel state of the multi-antenna based on the second signal and the third signal obtained from the signal receiver, and control transmission and reception of signals through the multi-antenna according to the estimated channel state. 
     General and widely used terms have been employed herein, in consideration of functions provided in the disclosure, and may vary according to an intention of one of ordinary skill in the art, a precedent, or emergence of new technologies. Additionally, in some cases, an applicant may arbitrarily select specific terms, in which case, the applicant will provide the meaning of the terms in the description of the embodiments. Accordingly, It will be understood that the terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     Throughout the specification, it will be understood that when a unit is referred to as being “connected” to another element, it may be “directly connected” to the other element or “electrically connected” to the other element in a state in which intervening elements are present. In addition, it will be understood that when a unit is referred to as “comprising” another element, it may not exclude the other element but may further include the other element unless specifically oppositely indicates. In addition, terms such as “ . . . unit”, “ . . . module”, or the like refer to units that perform at least one function or operation, and the units may be implemented as hardware or software or as a combination of hardware and software. It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. 
     Throughout the specification, a “terminal” may refer to a personal computer (PC), a mobile phone, a smart phone, a TV, a tablet PC, a laptop computer, a personal digital assistant (PDA), a portable multimedia player (PMP), a navigation device, an MP3 player, or a digital camera. However, the present invention is not limited thereto. 
     In the present disclosure, an apparatus including a multi-antenna may refer to an apparatus including two or more antennas (or antenna elements). For example, a multi-antenna apparatus may be, but is not limited to, a base station. Further, a multi-antenna system may refer to a system including at least one multi-antenna apparatus. 
     Hereinafter, the present invention will be described in detail with reference to the accompanying drawings. 
       FIG. 9  is a view of an example of a multi-antenna system that does not feed back channel state information (CSI). 
     In  FIG. 9 , the same reference numerals as in  FIG. 8  denote the same elements, and descriptions thereof will not be given herein. In the multi-antenna system that does not feed back CSI of  FIG. 9 , in operation S 31 , a predetermined uplink signal is transmitted from a terminal UT to a base station BS, and in operation S 32 , uplink CSI is estimated according to the signal transmitted to the base station BT. In operation S 33 , communication starts between the base station BS and the terminal UT. Referring to  FIG. 9 , since only a control signal for estimating CSI is transmitted from the terminal UT to the base station BS, communication efficiency does not depend on the number of antenna elements of the base station BS. In addition, CSI feedback is unnecessary, so that communication efficiency may be improved as compared with the method shown in  FIG. 8 . However, the multi-antenna system of  FIG. 9  has to calculate a calibration value to correct a difference in amplitude and phase between transfer functions T k  and R k  of a transceiver provided in the base station BS. 
     The calibration value indicates a value used for correcting a difference in phase and amplitude between branches, i.e., correcting phase and amplitude of a branch based on the other branch. For example, the calibration value in  FIG. 9  may be obtained as a ratio between branches of T k /R k  according to a transfer function of each transceiver. Where, T k  is a transfer function of a k th  transmitter Txk, and R k  is a transfer function of a k th  receiver Rxk. K=1 to N, and N indicates the number of elements of a multi-antenna. Furthermore, each of the transfer functions T k  and R k  is complex amplitude and includes a phase component and an amplitude component. For example, a calibration value of a transceiver # 2  having a transceiver # 1  as a reference may be defined as T 2 /R 2  divided by T 1 /R 1 . Also, a comparison target value (T k /R k  in this example) when a calibration value is obtained is referred to as a comparison target value. 
     Meanwhile, an embodiment for implementing a correction according to a calibration value may include a method in which the base station BS and the terminal UT obtain CSI in both directions in advance before starting communication and use the difference as a calibration value. However, according to the method, the calibration value may not be stably obtained when the terminal UT moves or when the terminal UT is outdoors and a propagation environment changes. 
     Another example of performing a correction using a calibration value may include a method of obtaining a calibration value using two loops (Loop A and Loop B) in order to feed back a portion of a transmission signal to a receiving side in the base station BS. 
       FIG. 10  is a view of an example of a multi-antenna apparatus using two loops to feed back CSI. 
     Referring to  FIG. 10 , since an external device is not used, a calibration value may be obtained without depending on a place where the base station BS is installed or a surrounding environment. 
     In the configuration of  FIG. 10 , the base station BS includes a multi-antenna apparatus  301  having at least two antenna elements  301 - 1  and  301 - 2 , and a transmitter Tx 1  and a receiver Rx 1  and a transmitter Tx 2  and a receiver Rx 2  respectively corresponding to the antenna element  301 - 1  and the antenna element  301 - 2 . Furthermore, the base station BS includes time division duplex (TDD) switches  302 - 1  and  302 - 2  which selectively connect the transmitter Tx 1  or receiver Rx 1  or the transmitter Tx 2  or receiver Rx 2  to the antenna element  301 - 1  or  301 - 2 . The base station BS further includes a directional coupler  303 - 1  for feeding back a portion of a transmission signal of the transmitter Tx 1  to the receiver Rx 2  and a directional coupler  303 - 2  for feeding back a portion of a transmission signal of the transmitter Tx 2  to the receiver Rx 1 . In the configuration of  FIG. 10 , a loop that feeds back a portion of the transmission signal of the transmitter Tx 1  to the receiver Rx 2  using a distributor or the like (not shown) is Loop A. Furthermore, a loop that feeds back a portion of the transmission signal of the transmitter Tx 2  to the receiver Rx 1  is Loop B. 
     Meanwhile, in the configuration of  FIG. 10 , a transfer function LA of Loop A and a transfer function LB of Loop B may be represented as follows when a calibration value is obtained as a ratio of the value T k /R k  corresponding to each transceiver.
 
L A =T 1 R 2  
 
L B =T 2 R 1   [Formula 1]
 
     Here, T 1  and T 2  are transfer functions of the transmitters Tx 1  and Tx 2 , and R 1  and R 2  are transfer functions of the receivers Rx 1  and Rx 2 . 
     A relationship between the transfer function LA and the transfer function LB and a calibration value D 2,1  of the transceiver # 2  having the transceiver # 1  as a reference may be represented as follows. 
     
       
         
           
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     Formula 2 represents that a value obtained by dividing a value T 2 /R 2  to be compared to the transceiver # 2  (a combination of the transmitter Tx 2  and the receiver Rx 2 ) by a value T 1 /R 1  to be compared to the transceiver # 1  (a combination of the transmitter Tx 1  and the receiver Rx 1 ) becomes the calibration value D 2,1  of the transceiver # 2  having the transceiver # 1  as a reference. 
     Meanwhile, a multi-antenna apparatus of  FIG. 11  may prevent the configuration from being complicated when the number N of antenna elements of the base station BS increases. 
       FIG. 11  is a view of another example of a multi-antenna apparatus using two loops to feed back CSI. 
     Referring to  FIG. 11 , a plurality of loops including Loop A and Loop B are formed to obtain a comparison target value between adjacent elements. In the configuration of  FIG. 11 , switches  304 - 2  and  304 - 3  provided to obtain a comparison target value between adjacent elements may be realized by only a two-branch switch. 
     The base station BS also includes the multi-antenna apparatus  301  having a plurality of antenna elements such as antenna elements  301 - 2  and  301 - 3 , and a plurality of the transmitter Tx 2  and receiver Rx 2 , and a transmitter Tx 3  and a receiver Rx 3  respectively corresponding to the antenna elements  301 - 2  and  301 - 3 . The base station BS also includes the TDD switch  302 - 2  for selectively connecting the transmitter Tx 2  or the receiver Rx 2  to the antenna element  301 - 2 , and a TDD switch  302 - 3  for selectively connecting the transmitter Tx 3  or the receiver Rx 3  to the antenna element  301 - 3 . The base station BS further includes the switch  304 - 2  for feeding back a portion of the transmission signal of the transmitter Tx 1  to the receiver Rx 3  or Rx 1 , and the switch  304 - 3  for feeding back a portion of a transmission signal of the transmitter Tx 3  to the receiver Rx 2  or a receiver Rx 4 . In the configuration of  FIG. 11 , a loop that feeds back a portion of the transmission signal of the transmitter Tx 2  to the receiver Rx 3  is Loop A. Furthermore, a loop that feeds back a portion of the transmission signal of the transmitter Tx 3  to the receiver Rx 2  is Loop B. 
     If T k  is the transfer function of the k th  transmitter Txk and R k  is the transfer function of the k th  receiver Rxk, a transfer function of Loop A may be represented by T 2 R 3  and a transfer function of Loop B by T 3 R 2 . 
     A calibration value D 3,2  of a transceiver # 3  having the transceiver # 2  as a reference may be represented by the following Equation. 
     
       
         
           
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               Formula 
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     Furthermore, a calibration value D 3,1  of the transceiver # 3  having the transceiver # 1  as a reference may be obtained from the calibration value D 3,2  of the transceiver # 3  based on the transceiver # 2 , and the calibration value D 2,1  of the transceiver # 2  having the transceiver # 1  as a reference through Formula 4. 
     
       
         
           
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     That is, since the multi-antenna of  FIGS. 10 and 11  do not use an external device, a comparison target value may be obtained without depending on a place where the multi-antenna is installed or a surrounding environment. 
     However, since the multi-antenna  301  of  FIGS. 10 and 11  have the transmitter Tx 1  and the receiver Rx 1  as references, a plurality of calibration procedures are required. In particular, in the multi-antenna apparatus  310  of  FIG. 11 , when a comparison target value is calculated from adjacent elements, a value including an error is accumulated when the error occurs in a transmitter or a receiver, thereby causing a problem. 
     Furthermore, when power of a transmission signal transmitted from the transmitter Tx is different from power of a reception signal obtained by the receiver Rx, it is necessary to perform calibration between the transmitter and the receiver using power output from the transmitter Tx. However, the multi-antenna apparatus  310  of  FIGS. 10 and 11  have no countermeasure when power of the transmission signal is different from power of the reception signal. 
     Similarly, when forming a transmission radiation pattern with a multi-antenna using CSI, different powers are applied to respective antennas. If different powers are applied to respective antennas, it is necessary to perform calibration between the transmitter and the receiver using different powers. However, the multi-antenna apparatus  310  of  FIGS. 10 and 11  have no countermeasure thereto. 
     In addition, in the multi-antenna apparatus  310  of  FIGS. 10 and 11 , a guarantee of transmission/reception isolation and a countermeasure when calibration is not performed have not been examined. 
       FIG. 1  is a view of a multi-antenna apparatus  10  of a time division duplex (TDD) system for controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
     Referring to  FIG. 1 , the multi-antenna apparatus  10  may perform communication according to the TDD system. That is, the multi-antenna apparatus  10  may transmit and receive signals by the TDD system using an identical frequency. The multi-antenna apparatus  10  may further include a multi-antenna  1 , N TDD switches  2 - 1  to  2 -N, a signal transferrer  3 , a signal transmitter including N transmitters Tx 1  to TxN, a signal receiver including N receivers Rx 1  to RxN, and a controller  4 . The signal transferrer  3  may include N directional couplers  31 - 1  to  31 -N, a 1:N divider (a synthesizer of N-input and 1-output)  32 , a variable attenuator  33 , an ON/OFF switch  34 , a 1:N divider (a distributor of 1-input and N-output)  35 , and N dividers  36 - 1  to  36 -N. Furthermore, the controller  4  may include a transmission signal controller  41 , a transmission signal processor  43 , a calculator  44 , and a reception signal controller  45 . 
     The multi-antenna  1  has at least two N antenna elements  1 - 1  to  1 -N arranged in a predetermined order. The TDD switches  2 - 1  to  2 -N are provided corresponding to the antenna elements  1 - 1  to  1 -N, respectively. The TDD switches  2 - 1  to  2 -N are connected to the transmitters Tx 1  to TxN or the receivers Rx 1  to RxN through the directional couplers  31 - 1  to  31 -N or dividers  36 - 1  to  36 -N by time division, with respect to the antenna elements  1 - 1  to  1 -N. 
     The directional couplers  31 - 1  to  31 -N receive signals output from the transmitters Tx 1  to TxN and respectively output a portion of the signals to N inputs of the divider  32 , and then output the remaining signals to input terminals of the TDD switches  2 - 1  to  2 -N, respectively. The dividers  36 - 1  to  36 -N are connected to output terminals of the switches  2 - 1  to  2 -N and output terminals of the divider  35 , respectively. The dividers  36 - 1  to  36 -N synthesize output signals of the antenna elements  1 - 1  to  1 -N received through the switches  2 - 1  to  2 -N and N output signals of the divider  35 , and output them to the receivers Rx 1  to RxN, respectively. 
     The variable attenuator  33  and the ON/OFF switch  34  form a series circuit and connect the divider  32  and the divider  35 . The variable attenuator  33  is an attenuator capable of changing attenuation, and the attenuation is controlled by the controller  4 . When the ON/OFF switch  34  is turned ON, the divider  32  and the divider  35  are connected to each other. When the ON/OFF switch  34  is turned OFF, the divider  32  and the divider  35  are isolated from each other. 
     The transmitters Tx 1  to TxN amplify input signals received from the controller  4  and input them to the corresponding antenna elements  1 - 1  to  1 -N. N signals output from the transmission signal controller  41  are input to the transmitters Tx 1  to TxN, respectively. Furthermore, the N signals output from the transmission signal controller  41  may be a result of scaling weight coefficients of a complex number, according to an instruction from the transmission signal processor  43 . 
     The receivers Rx 1  to RxN amplify respective output signals of the corresponding antenna elements  1 - 1  to  1 -N and input them to the controller  4 . The signals output from the receivers Rx 1  to RxN are input to N inputs of the reception signal controller  45 , respectively. The reception signal controller  45  scales the weight coefficients of the complex number for the N signals input from the receivers Rx 1  to RxN, and synthesizes the scaling result into one reception signal, and outputs the one reception signal according to the instruction from the transmission signal processor  43   
     The transmission signal processor  43  controls a radiation pattern of the multi-antenna  1  by weighting amplitudes and phases to signals respectively input to the plurality of transmitters Tx 1  to TxN. The transmission signal processor  43  controls the radiation pattern of the multi-antenna  1  by weighting amplitudes and phases to signals respectively output from the plurality of receivers Rx 1  to RxN. Here, the transmission signal processor  43  calibrates weight coefficients of amplitudes and phases according to a calibration value of each branch calculated by the calculator  44 . 
     The calculator  44  calculates a calibration value of amplitudes and phases of a branch of each of the antenna elements  1 - 1  to  1 -N according to each reception signal obtained by the N receivers Rx 1  to RxN through two dividers  32  and  25 . The calculator  44  receives a predetermined signal output from the transmission signal controller  41  and receives each reception signal input to the reception signal controller  45 . Then, the calculator  44  outputs the calibration value calculated for each branch according to the reception signals. 
     Next, some embodiments of calculating a calibration value in the multi-antenna apparatus  10  will be described with reference to  FIGS. 2 to 4 . 
       FIG. 2  is a flowchart of a method of controlling transmission and reception of signals based on channel estimation in the multi-antenna apparatus  10 , according to some embodiments of the present disclosure. 
     Referring to  FIG. 2 , when calculating the calibration value, the multi-antenna apparatus  10  may use a transmission period of a pilot signal for downlink CSI for each antenna element. In operation S 1 , it is also possible to transmit a predetermined signal from each of the transmitters Tx 1  to TxN by time division and to receive a transmission signal by each of the receivers Rx 1  to RxN included in a signal receiver through the signal transferrer  3 . A method of using an antenna will be described in detail with reference to  FIG. 3 . 
       FIG. 3  is a view for explaining a method of using an antenna over time according to some embodiments of the present disclosure. Referring to  FIG. 3 , each of the transmitters Tx 1  to TxN in the multi-antenna apparatus  10  of  FIG. 2  may transmit a predetermined pilot signal by time division. 
     Meanwhile, referring to  FIG. 2 , in operation S 2 , the calculator  44  may calculate a predetermined comparison target value according to the signal transmitted from each of the transmitters Tx 1  to TxN and the signal received by each of the receivers Rx 1  to RxN, and may obtain a calibration value of each branch according to the comparison target value. Operation S 2  may be performed within a period T 2  of a data signal shown in  FIG. 4 . 
       FIG. 4  is a view for explaining a signal transmitted by a transmitter of a multi-antenna apparatus, according to some embodiments of the present disclosure. 
     Referring to  FIG. 4 , transmission periods T 1  and T 3  are periods during which a pilot signal Pilot is transmitted, and a transmission period T 2  is a period during which transmission data Data is transmitted. If the transmission of the pilot signal cannot be completed within the number of times N, which is equal to the number of antenna elements, within the transmission period T 1  of the pilot signal shown in  FIG. 4  by the TDD system, the transmission of the pilot signal may be performed using the transmission period T 3  of the pilot signal Pilot next to the transmission data of transmission period T 2  and may be divided into the period T 1  and the period T 3 . 
     Meanwhile, if a pilot signal transmitted from each of the transmitters Tx 1  to TxN in the multi-antenna apparatus  10  of  FIG. 2  is s(t), a reception signal x k1  which is received by the receiver Rxk from the transmitter Tx 1  . . . , a reception signal x kN  which is received by the receiver Rxk from the transmitter TxN may be represented by Equations (1-1) to (1-N) using the transfer functions T 1  to T N  and R k , as shown in Formula 5. Here, t denotes time. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     x 
                     
                       k 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       T 
                       1 
                     
                     ⁢ 
                     
                       R 
                       k 
                     
                     ⁢ 
                     
                       s 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     1 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     x 
                     
                       k 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       T 
                       2 
                     
                     ⁢ 
                     
                       R 
                       k 
                     
                     ⁢ 
                     
                       s 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     1 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 ⋮ 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     x 
                     kN 
                   
                   = 
                   
                     
                       T 
                       N 
                     
                     ⁢ 
                     
                       R 
                       k 
                     
                     ⁢ 
                     
                       s 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     1 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     N 
                   
                   ) 
                 
               
             
           
         
       
     
     Referring to Formula 5, a comparison target value may be T k /R k  according to a transfer function of each transceiver. Where T k  is a transfer function of the k th  transmitter Txk, and R k  is a transfer function of the k th  receiver Rxk. Where k=1 to N, and N denotes the number of elements of a multi-antenna. Furthermore, each of the transfer functions T k  and R k  is a complex amplitude, and is a complex number including a phase component and an amplitude component. The transfer function T k  of the transmitter Txk is a transfer function from the transmitter Txk to the divider  32 , and the transfer function R k  of the receiver Rxk is a transfer function from the divider  35  to the receiver Rxk. 
     If k=2 for Equation (1-1) and k=1 for Equation (1-2), Equations (1-1) and (1-2) are represented by Equations (2-1) and (2-2) as shown in Formula 6.
 
[Formula 6]
 
 x   21   =T   1   R   2   s ( t )  (2-1)
 
 x   12   =T   2   R   1   s ( t )  (2-2)
 
     Where dividing Equation (2-2) by Equation (2-1) yields Equation (3) as shown in Formula 7. Equation (3) represents a calibration value of the transceiver # 2  having the transceiver # 1  as a reference. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       12 
                     
                     
                       x 
                       21 
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           2 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           2 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           T 
                           2 
                         
                         / 
                         
                           R 
                           2 
                         
                       
                       
                         
                           T 
                           1 
                         
                         / 
                         
                           R 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Similarly, a calibration value of a transceiver #k having the transceiver # 1  as a reference may be represented as below. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         x 
                         
                           1 
                           ⁢ 
                           k 
                         
                       
                       
                         x 
                         
                           k 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             T 
                             k 
                           
                           ⁢ 
                           
                             R 
                             1 
                           
                           ⁢ 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             R 
                             k 
                           
                           ⁢ 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       = 
                       
                         
                           
                             T 
                             k 
                           
                           / 
                           
                             R 
                             k 
                           
                         
                         
                           
                             T 
                             1 
                           
                           / 
                           
                             R 
                             1 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       k 
                       = 
                       
                         2 
                         ~ 
                         N 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     That is, when the multi-antenna apparatus  10  of  FIG. 1  feeds back a transmission signal to a receiving side, the multi-antenna apparatus  10  may transmit the signal using the divider  32  without selecting a corresponding receiver by a switch. Furthermore, since the multi-antenna apparatus  10  may include the divider  35  in front of the receiving side, the multi-antenna apparatus  10  may simultaneously obtain transfer functions of all combinations of a transmitter and a receiver. 
     The multi-antenna apparatus  10  of  FIG. 1  may also include the variable attenuator  33  and the ON/OFF switch  34  between the dividers  32  and  35 . The variable attenuator  33  is provided for calibration between transceivers that operate at different powers. Therefore, even if a transmitter operates at relatively high power, it is possible to prevent the receiver Rxk from receiving a signal that becomes saturated by increasing attenuation of the variable attenuator  33 . 
     Furthermore, the ON/OFF switch  34  may be set to OFF when calibration is not necessary, so that the ON/OFF switch  34  may be used to ensure isolation between a transmitter and a receiver. 
       FIG. 5  is a view of a multi-antenna apparatus  10   a  of a frequency division system for controlling transmission and reception of signals based on channel estimation, according to another embodiment of the present disclosure. 
     The multi-antenna apparatus  10   a  of  FIG. 5  may perform communication using a frequency division duplex (FDD) system. That is, the multi-antenna apparatus  10   a  may simultaneously perform transmission and reception of signals using different frequencies. 
     The multi-antenna apparatus  10   a  shown in  FIG. 5  may include circulators  5 - 1  to  5 -N respectively corresponding to the antenna elements  1 - 1  to  1 -N instead of the TDD switches  2 - 1  to  2 -N included in the multi-antenna apparatus  10  shown in  FIG. 1 . 
     Furthermore, in the multi-antenna apparatus  10   a  of  FIG. 5 , a signal transferrer  3   a  (corresponding to the signal transferrer  3  of  FIG. 1 ) may further include a mixer  37  and an oscillator  38 . That is, the multi-antenna apparatus  10   a  of  FIG. 5  may include the mixer  37 , which mixes an output of a series circuit including the variable attenuator  33  and the ON/OFF switch  34  and an output of the oscillator  38 , between the ON/OFF switch  34  and the divider  35 . When a frequency of transmission signals of the transmitters Tx 1  to TxN is f 1  and a frequency of reception signals of the receivers Rx 1  to RxN is f 2 , oscillation frequencies of the oscillator  38  is f 1  to f 2 . Here, the mixer  37  may convert a frequency of an input signal of the frequency f 1  to the frequency f 2  and output the frequency f 2  to the divider  35 . 
     Meanwhile, an embodiment of obtaining a calibration value in the multi-antenna apparatus  10   a  will be described. A basic operation of the multi-antenna apparatus  10   a  is the same as that of the multi-antenna apparatus  10  described with reference to  FIG. 2 . 
     That is, in operation S 1  of  FIG. 2 , when calculating a calibration value, the multi-antenna apparatus  10   a  uses a transmission period of a pilot signal for downlink CSI for each antenna element, transmits a predetermined signal from each of the transmitters Tx 1  to TxN by time division, and receives a transmission signal by each of the receivers Rx 1  to RxN included in a signal receiver through the signal transferrer  3 . 
     Thereafter, in operation S 2  of  FIG. 2 , the calculator  44  calculates a predetermined comparison target value according to the signal transmitted from each of the transmitters Tx 1  to TxN and the signal received by each of the receivers Rx 1  to RxN, and obtains a calibration value of each branch according to the comparison target value. 
     If a pilot signal transmitted from each of the transmitters Tx 1  to TxN is s(t), a reception signal x k1  which is received by the receiver Rxk from the transmitter Tx 1  to a reception signal x kN  which is received by the receiver Rxk from the transmitter TxN may be represented by Equations (1-1) to (1-N) using the transfer functions T 1  to T N  and R k , as shown in Formula 5. 
     A comparison target value of the multi-antenna apparatus  10   a  according to Formula 5 may be, e.g., T k /T 1  according to a transfer function of each transmitter and R k /R 1  according to a transfer function of each receiver. Where T k  is a transfer function of a k th  transmitter Txk, and R k  is a transfer function of the k th  receiver Rxk. Where k=1 to N, and N denotes the number of elements of a multi-antenna. Furthermore, each of the transfer functions T k  and R k  is a complex amplitude and includes a phase component and an amplitude component. The transfer function T k  of the transmitter Txk is a transfer function from the transmitter Txk to the divider  32 , and the transfer function R k  of the receiver Rxk is a transfer function from the divider  35  to the receiver Rxk. 
     If k=1 and k=2 for Equation (1-1), Equation (1-1) is represented by Equations (5) and (6).
 
[Formula 9]
 
 x   11   =T   1   R   1   s ( t )  (5)
 
 x   21   =T   1   R   2   s ( t )  (6)
 
     Where dividing Equation (6) by Equation (5) yields Equation (7). Equation (7) represents a calibration value of a receiver # 2  having a receiver # 1  as a reference. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       21 
                     
                     
                       x 
                       11 
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           2 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         R 
                         2 
                       
                       
                         R 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Similarly, if k=1 and k=3 to N for Equation (1-1), Equation (1-1) is represented by Equations (8) and (9).
 
[Formula 11]
 
 x   11   =T   1   R   1   s ( t )  (8)
 
 x   k1   =T   1   R   k   s ( t )  (9)
 
     Accordingly, a calibration value of a receiver #k having the receiver # 1  as a reference may be represented as below. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     
                       x 
                       11 
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           k 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         R 
                         k 
                       
                       
                         R 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Furthermore, if k=1 for Equations (1-1) and (1-2), the following Equations 11 and 12 are obtained.
 
[Formula 13]
 
 x   11   =T   1   R   1   s ( t )  (11)
 
 x   12   =T   2   R   1   s ( t )  (12)
 
     Where dividing Equation (12) by Equation (11) yields Equation (13). Equation (13) represents a calibration value of a transmitter # 2  having a transmitter # 1  as a reference. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       12 
                     
                     
                       x 
                       11 
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           2 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         T 
                         2 
                       
                       
                         T 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Similarly, if k=1 for Equations (1-1) to (1-N), Equations (1-1) to (1-N) is represented by Equations 14 and 15.
 
[Formula 15]
 
 x   11   =T   1   R   1   s ( t )  (14)
 
 x   1k   =T   k   R   1   s ( t )  (15)
 
     Accordingly, a calibration value of a transmitter #k having the transmitter # 1  as a reference may be represented as below. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       
                         1 
                         ⁢ 
                         k 
                       
                     
                     
                       x 
                       11 
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           k 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         T 
                         k 
                       
                       
                         T 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     That is, when the multi-antenna apparatus  10   a  of  FIG. 5  feeds back a transmission signal to a receiving side, the multi-antenna apparatus  10   a  may transmit the signal using the divider  32  without selecting a corresponding receiver by a switch. Furthermore, since the multi-antenna apparatus  10   a  of  FIG. 5  includes the divider  35  in front of the receiving side, the multi-antenna apparatus  10   a  may simultaneously obtain transfer functions of all combinations of a transmitter and a receiver. Therefore, all correction values may be obtained by one process. 
     Furthermore, since the signal transferrer  3   a  included in the multi-antenna apparatus of  FIG. 5  further includes the mixer  37  and the oscillator  38  as compared to the signal transmitter  3  included in the multi-antenna apparatus of  FIG. 1 , calibration may be realized in signal transmission/reception according to TDD/FDD systems. 
     Furthermore, it is possible to correct a calibration value when levels of the transmitter and the receiver are different from each other by using a variable attenuator and transmission/reception isolation may be ensured by an ON/OFF switch. The level difference indicates a difference between a voltage range of an amplitude level of a transmission signal of the transmitter and a voltage range of an amplitude level receivable by the receiver. Therefore, when the voltage range of the amplitude level receivable by the receiver is limited to a voltage lower than the voltage range of the amplitude level of the transmission signal of the transmitter, the variable attenuator is used to lower the amplitude level of the transmission signal to within the voltage range of the amplitude level receivable by the receiver. 
     Furthermore, a comparison target value of the multi-antenna apparatus of  FIG. 5  may be, e.g., T k /T 1  according to a transfer function of each transmitter and R k /R 1  according to a transfer function of each receiver. 
       FIG. 6  is a view of radiation patterns of a multi-antenna where a horizontal axis represents an angle and a vertical axis represents relative power. 
       FIG. 6  is a graph of experimental results assuming a linear antenna apparatus whose number of antenna elements N is 16 in a multi-antenna apparatus. Referring to  FIG. 6 , a dashed line indicates a relative power when there is no error in a transmitter. A solid line indicates a relative power when a transmission signal is calibrated according to an embodiment of the present disclosure when there is an error in a transmitter. Furthermore, a broken line indicates a state power when a transmission signal is calibrated and there is an error in a transmitter. According to an embodiment of the present disclosure, it can be seen that a transmission signal is calibrated with relative accuracy, since a solid line is close to the dashed line. 
     According to some embodiments of the present disclosure, after a predetermined transmission signal s(t) is transmitted from the transmitters Tx 1  to TxN, a calibration value is calculated according to a reception signal which is obtained by receiving the transmission signal s(t) by the receivers Rx 1  to RxN via the dividers  32  and  35  or the like. 
     Meanwhile, according to another embodiment of the present disclosure, a calibration value may be obtained using not only a predetermined signal (that is, a transmission signal) but also an arbitrary signal. Therefore, since a calibration value may be obtained by using an arbitrary signal, a calibration value may be obtained even when all transmitters and receivers perform general signal transmission/reception operations. 
     A multi-antenna apparatus for obtaining a calibration value using an arbitrary signal may be the same as the multi-antenna apparatus  10  of  FIG. 1  or the multi-antenna apparatus  10   a  of  FIG. 5 . However, processing content of the calculator  44  may be different from that of the multi-antenna apparatuses of  FIG. 1  and  FIG. 5 . Hereinafter, operations of the calculator  44  will be described with reference to  FIG. 7 . 
       FIG. 7  is a flowchart of a method of controlling transmission and reception of signals based on channel estimation in a multi-antenna apparatus, according to another embodiment of the present disclosure. 
     Referring to  FIG. 7 , a variable N is the number of antenna elements (i.e., the number of branches) of the multi-antenna  1 , and the number of antenna elements is equal to the number of samples of data (the number of sampled data). Furthermore, T k  is a transfer function (complex amplitude) of the k th  transmitter Txk. R k  is a transfer function (complex amplitude) of the k th  receiver Rxk. S k (n) is an n th  sample of a transmission signal of the k th  transmitter Txk, and x k (n) is an n th  sample of a reception signal of the k th  receiver Rxk. Furthermore, T k /T 1  is a calibration value of the k th  transmitter Txk having a transmitter # 1  as a reference, and R k /R 1  is a calibration value of the k th  receiver Rxk having the receiver # 1  as a reference. 
       FIG. 7  relates to an embodiment in which the calculator  44  calculates a pair of (i.e., one-time) branch calibration values. Referring to  FIG. 7 , a calibration value may be calculated using sampled data of a transmission signal and a reception signal transmitted in time series from the number of branches N. In operations S 11  to S 14 , the calculator  44  may sample a reception signal x k (n) while storing a transmission signal s k (n) until the number of samples n reaches the number of branches N. 
     Next, in operation S 15 , the calculator  44  calculates a calibration value of each branch according to the transmission signal s k (n) and the reception signal x k (n) of the number of samples n (operation S 15 ). 
     According to some embodiments of the present disclosure, it is not necessary to newly obtain data sampled N times every n times when calculating a calibration value. If data is continuously sampled, a calibration value may be calculated using the sampled data of N times in the past. 
     Hereinafter, an embodiment related to a method of calculating a calibration value will be described. 
     (A) When the number of antenna elements is two, a reception signal may be represented as follows.
 
[Formula 17]
 
 x   1 (1)=( T   1   s   1 (1)+ T   2   s   2 (1)) R   1   (17)
 
 x   2 (1)=( T   1   s   1 (1)+ T   2   s   2 (1)) R   2   (18)
 
 x   1 (2)=( T   1   s   1 (2)+ T   2   s   2 (2)) R   1   (19)
 
 x   2 (2)=( T   1   s   1 (2)+ T   2   s   2 (2)) R   2   (20)
 
     Where Equations (17) and (18) are for n=1 (i.e., first sampled data), and Equations (19) and (20) are for n=2 (i.e., second sampled data). 
     Equation (21) is obtained by representing each of Equations (17) and (19) (or Equations (18) and (20)) using a matrix. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   s 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   s 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   2 
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   2 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   R 
                                   k 
                                 
                                 ⁢ 
                                 
                                   T 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   R 
                                   k 
                                 
                                 ⁢ 
                                 
                                   T 
                                   2 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 x 
                                 k 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 x 
                                 k 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       k 
                       = 
                       
                         1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         or 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     If both sides are multiplied by an inverse matrix of the matrix with s as an element, then Equation (21) becomes Equation (22). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 2 
                               
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     s 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     s 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     2 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     2 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   x 
                                   k 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   x 
                                   k 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   2 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ( 
                     
                       k 
                       = 
                       
                         1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         or 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     s, x are each a transmission signal and a reception signal, and values of respective elements of a matrix of the transmission signal s are different from each other, so that Equation (20) may be derived from Equation (22). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         R 
                         k 
                       
                       ⁢ 
                       
                         T 
                         2 
                       
                     
                     
                       
                         R 
                         k 
                       
                       ⁢ 
                       
                         T 
                         1 
                       
                     
                   
                   = 
                   
                     
                       T 
                       2 
                     
                     
                       T 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     That is, a calibration value of a transmitter # 2  for the transmitter # 1  is obtained according to Equation (20). Meanwhile, there are two methods for a receiver. 
     Method A1: It can be calculated by Equation (20)/Equation (19), that is, by dividing Equation (18) by Equation (17), or by Equation (20)/Equation (19), that is, by dividing Equation (20) by Equation (19). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         x 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     
                       
                         x 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 T 
                                 1 
                               
                               ⁢ 
                               
                                 
                                   s 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 T 
                                 2 
                               
                               ⁢ 
                               
                                 
                                   s 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           R 
                           2 
                         
                       
                       
                         
                           ( 
                           
                             
                               
                                 T 
                                 1 
                               
                               ⁢ 
                               
                                 
                                   s 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 T 
                                 2 
                               
                               ⁢ 
                               
                                 
                                   s 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                       
                     
                     = 
                     
                       
                         
                           R 
                           2 
                         
                         
                           R 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           k 
                           = 
                           
                             1 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             or 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     That is, a calibration value of the receiver # 2  for the receiver # 1  is obtained according to Equation (24). 
     Method A2: in method A1, as a value of N increases, much information needs to be stored in a memory at a time. However, according to this method, a calibration value between receivers may be obtained from a reception signal of another time. 
     Equations (25) and (26) are obtained by deforming Equations (17) and (20), respectively. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       1 
                       ) 
                     
                   
                   = 
                   
                     
                       T 
                       1 
                     
                     ⁢ 
                     
                       
                         R 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                           + 
                           
                             
                               
                                 T 
                                 2 
                               
                               
                                 T 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       x 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       2 
                       ) 
                     
                   
                   = 
                   
                     
                       T 
                       1 
                     
                     ⁢ 
                     
                       
                         R 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               2 
                               ) 
                             
                           
                           + 
                           
                             
                               
                                 T 
                                 2 
                               
                               
                                 T 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     In a case where T 2 /T 1 , which is a calibration value of a transmitter, has already been calculated, Equation (27) may be obtained from Equations (25) and (26) by calculation. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     P 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         s 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         
                           T 
                           2 
                         
                         
                           T 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           s 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           2 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     That is, Equation (28) is obtained by calculating Equation (26)/Equation (25). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     24 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         x 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         2 
                         ) 
                       
                     
                     
                       
                         x 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         1 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           2 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             2 
                             ) 
                           
                         
                       
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           R 
                           2 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             2 
                             ) 
                           
                         
                       
                       
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     Equation (29) is obtained by deforming Equation (28). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     25 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       R 
                       2 
                     
                     
                       R 
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           x 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           2 
                           ) 
                         
                       
                       
                         
                           x 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           1 
                           ) 
                         
                       
                     
                     · 
                     
                       
                         P 
                         ⁡ 
                         
                           ( 
                           1 
                           ) 
                         
                       
                       
                         P 
                         ⁡ 
                         
                           ( 
                           2 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     Where x is a reception signal and P can be calculated, so that a value of Equation (29) may be obtained. 
     (B) When the Number of Antenna Elements is N 
     B1) Calibration of a Transmitter 
     In a case of the N element, the reception signal in a k th  receiver is as Formula 26. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     26 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       1 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             T 
                             2 
                           
                           ⁢ 
                           
                             
                               s 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             T 
                             N 
                           
                           ⁢ 
                           
                             
                               s 
                               N 
                             
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       R 
                       k 
                     
                   
                 
               
               
                 
                   ( 
                   
                     30 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       x 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       2 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             T 
                             2 
                           
                           ⁢ 
                           
                             
                               s 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             T 
                             N 
                           
                           ⁢ 
                           
                             
                               s 
                               N 
                             
                             ⁡ 
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       R 
                       k 
                     
                   
                 
               
               
                 
                   ( 
                   
                     30 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ⋮ 
                     ⁢ 
                     
                         
                     
                     = 
                     
                         
                     
                     ⁢ 
                     ⋮ 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       N 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               N 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             T 
                             2 
                           
                           ⁢ 
                           
                             
                               s 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               N 
                               ) 
                             
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             T 
                             N 
                           
                           ⁢ 
                           
                             
                               s 
                               N 
                             
                             ⁡ 
                             
                               ( 
                               N 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       R 
                       k 
                     
                   
                 
               
               
                 
                   ( 
                   
                     30 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     N 
                   
                   ) 
                 
               
             
           
         
       
     
     Where Equation (30-1) is for n=1, Equation (30-1) is for n=2, and the Equations (30-1) is for n=N. 
     When the above Equation is written in matrix form, Equation (31) is obtained. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     27 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 s 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                           
                             … 
                           
                           
                             
                               
                                 s 
                                 N 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 s 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                           
                             … 
                           
                           
                             
                               
                                 s 
                                 N 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋱ 
                           
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 s 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                           
                           
                             … 
                           
                           
                             
                               
                                 s 
                                 N 
                               
                               ⁡ 
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 2 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 N 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               x 
                               k 
                             
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               x 
                               k 
                             
                             ⁡ 
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             
                               x 
                               k 
                             
                             ⁡ 
                             
                               ( 
                               N 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
     
     Where, if 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     28 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     S 
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 s 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                           
                             … 
                           
                           
                             
                               
                                 s 
                                 N 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 s 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                           
                             … 
                           
                           
                             
                               
                                 s 
                                 N 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋱ 
                           
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 s 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                           
                           
                             … 
                           
                           
                             
                               
                                 s 
                                 N 
                               
                               ⁡ 
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       t 
                       
                         R 
                         k 
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 2 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 R 
                                 k 
                               
                               ⁢ 
                               
                                 T 
                                 N 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       x 
                       k 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 x 
                                 k 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 x 
                                 k 
                               
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 x 
                                 k 
                               
                               ⁡ 
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
     Equation (33) may be calculated.
 
[Formula 29]
 
 St   R     k     =x   k   ⇒t   R     k     =S   −1 x k   (33)
 
     Equation (34) may be obtained by using an element of t Rk . 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     30 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         R 
                         k 
                       
                       ⁢ 
                       
                         T 
                         j 
                       
                     
                     
                       
                         R 
                         k 
                       
                       ⁢ 
                       
                         T 
                         1 
                       
                     
                   
                   = 
                   
                     
                       
                         T 
                         j 
                       
                       
                         T 
                         1 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         j 
                         = 
                         
                           2 
                           ⁢ 
                           
                             ~ 
                           
                           ⁢ 
                           N 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
     B2) Calibration of a Receiver (Method 1) 
     In a case of an N element, a reception signal at each receiver in an n th  sample is as Formula 31. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     31 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             T 
                             2 
                           
                           ⁢ 
                           
                             
                               s 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             T 
                             N 
                           
                           ⁢ 
                           
                             
                               s 
                               N 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       R 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   
                     35 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       x 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             T 
                             2 
                           
                           ⁢ 
                           
                             
                               s 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             T 
                             N 
                           
                           ⁢ 
                           
                             
                               s 
                               N 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       R 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     35 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     ⋮ 
                     ⁢ 
                     
                         
                     
                     = 
                     
                         
                     
                     ⁢ 
                     ⋮ 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       N 
                     
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             
                               s 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             T 
                             2 
                           
                           ⁢ 
                           
                             
                               s 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         + 
                         … 
                         + 
                         
                           
                             T 
                             N 
                           
                           ⁢ 
                           
                             
                               s 
                               N 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       R 
                       N 
                     
                   
                 
               
               
                 
                   ( 
                   
                     35 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     N 
                   
                   ) 
                 
               
             
           
         
       
     
     Where terms of (T 1 s 1 (n)+T 2 s 2 (n)+ . . . +T N s N (n)) are identical. A calibration value of the receiver may be obtained from the following calculation. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     32 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               x 
                               k 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                           
                             
                               x 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     T 
                                     1 
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       1 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     T 
                                     2 
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 … 
                                 + 
                                 
                                   
                                     T 
                                     N 
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       N 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               R 
                               k 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     T 
                                     1 
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       1 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     T 
                                     2 
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 … 
                                 + 
                                 
                                   
                                     T 
                                     N 
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       N 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               R 
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               R 
                               k 
                             
                             
                               R 
                               1 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               k 
                               = 
                               
                                 1 
                                 ~ 
                                 N 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     B3) Calibration of a Receiver (Method 2) 
     A reception signal at a k th  sample of a k th  receiver is as Formula 33. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     33 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             x 
                             k 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             
                               R 
                               k 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     s 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       T 
                                       2 
                                     
                                     
                                       T 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 … 
                                 + 
                                 
                                   
                                     
                                       T 
                                       N 
                                     
                                     
                                       T 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       s 
                                       N 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             1 
                           
                           ⁢ 
                           
                             R 
                             k 
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               N 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     T 
                                     j 
                                   
                                   
                                     T 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     s 
                                     j 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
     Where P(k) in Equation (38) may be calculated if a calibration value of a transmitter is obtained. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     34 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     P 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       N 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             T 
                             j 
                           
                           
                             T 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             j 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
     Furthermore, a calibration value of the receiver may be obtained by Equation (40) from calculation of Equation (39). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     35 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         x 
                         k 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     
                       
                         x 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         1 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           k 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       
                         
                           T 
                           1 
                         
                         ⁢ 
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           R 
                           k 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       
                         
                           R 
                           1 
                         
                         ⁢ 
                         
                           P 
                           ⁡ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     36 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       R 
                       k 
                     
                     
                       R 
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           x 
                           k 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       
                         
                           x 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           1 
                           ) 
                         
                       
                     
                     · 
                     
                       
                         P 
                         ⁡ 
                         
                           ( 
                           1 
                           ) 
                         
                       
                       
                         P 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
     That is, since a calibration value may be obtained from an arbitrary signal in addition to a predetermined signal, the calibration value may be obtained even when all transceivers operate. 
     Furthermore, when a multi-antenna apparatus performs transmission and reception of signals simultaneously with the FDD system according to some embodiments of the present disclosure and when a signal other than a transmission signal through the signal transferrer  3  or  3   a  is included in a reception signal, the above-mentioned calibration value may be calculated after removing the signal other than the transmission signal by removing general interference. For example, a signal having a high degree of correlation with an existing transmission signal may be extracted using an adaptive filter, thereby extracting a transmission signal through the signal transferrer  3  or  3   a . In addition, when the transmission signal is fed back through the signal transferrer  3  or  3   a  during data communication, data signal may be extracted from a reception signal by removing a signal having a high degree of correlation with the transmission signal. 
     Meanwhile, according to some embodiments of the present disclosure, the variable attenuator  33  or the ON/OFF switch  34  may be omitted, or it is possible to configure the divider  32  or  35  of 1 to N by combining a plurality of dividers of M to 1 (where M is smaller than N) or to change to integrate or divide each block in the controller  4 . 
       FIG. 12  is a flowchart for explaining a method of controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
     In operation S 1210 , a signal transmitter of a multi-antenna apparatus may transmit a first signal. 
     In operation S 1220 , a third signal received from a signal transmitter may be transferred to a signal receiver. That is, the first signal and the third signal are signals input to a multi-antenna and a signal transferrer by the signal transmitter, respectively, and signal content may be identical. Here, the signal transmitter may correct a power intensity of the multi-antenna using different power intensities for different antennas when transmitting and receiving the third signal. Also, the first signal may be a downlink pilot signal, but is not limited thereto. 
     In operation S 1230 , the signal receiver may receive a second signal using the multi-antenna based on the transmitted first signal. The second signal may be a signal that has received the first signal transmitted by the signal transmitter. 
     In operation S 1240 , a calculator may estimate a channel state of the multi-antenna based on the received second signal and the transferred third signal, and the multi-antenna apparatus may control transmission and reception of signals through the multi-antenna according to the estimated channel state. 
     Furthermore, the multi-antenna apparatus may further include calculating a calibration value of the multi-antenna based on the estimated channel state of the multi-antenna. In more detail, the calibration value is defined as a ratio of a comparison target value determined based on respective transfer functions of the third signal and a second signal of a first antenna among the multi-antenna to a comparison target value of a second antenna among the multi-antenna. Here, the number of times the second signal is sampled may be equal to the number of antennas of the multi-antenna and the calibration value of the multi-antenna may be calculated by storing the third signal by the number of times of sampling. Furthermore, when a calibration value of the first signal is calculated, a calibration value of the second signal may be calculated by using the second signal received at an arbitrary time. 
     Meanwhile, the comparison target value may be a ratio of a transfer function of the second signal of the first antenna to a transfer function of the third signal of the first antenna. Also, the comparison target value may be a ratio of the transfer function of the third signal or the second signal of the first antenna to a transfer function of a third signal or a second signal of the second antenna, but is not limited thereto. 
     On the other hand, the multi-antenna apparatus may further control amplitude and phase of the first signal based on the estimated channel state. 
       FIG. 13  is a block diagram for explaining the multi-antenna apparatus  10  for controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
     Referring to  FIG. 13 , the multi-antenna apparatus  10  may include a signal transmitter  1310 , a signal receiver  1320 , a signal transferrer  1330 , a controller  1340 , and a multi-antenna  1350 . Only components related to embodiments are shown in the multi-antenna apparatus  10  of  FIG. 13 . Accordingly, it will be understood by those skilled in the art that other general-purpose elements may be further included in addition to the elements shown in  FIG. 13 . 
     The signal transmitter  1310  may transmit a first signal using the multi-antenna  1350 . The first signal may be a downlink pilot signal, but is not limited thereto. 
     The signal receiver  1320  may receive a second signal using the multi-antenna  1350  based on the transmitted first signal. 
     The signal transferrer  1330  may receive a third signal input to the signal transmitter  1310  and provide a third signal to the signal receiver. 
     The controller  1340  may estimate a channel state of the multi-antenna  1350  based on the second signal and the third signal obtained from the signal receiver and may control transmission and reception of signals through the multi-antenna  1350  according to the estimated channel state. 
     The multi-antenna  1350 , which includes a plurality of transmitting antennas and receiving antennas, may include, but is not limited to, linear or non-linear antennas. 
       FIG. 14  is a detailed block diagram for explaining the multi-antenna apparatus  10  for controlling transmission and reception of signals based on channel estimation, according to some embodiments of the present disclosure. 
     A controller  1440  may include a transmission signal controller  1441 , a reception signal controller  1442 , a transmission signal processor  1444 , and a calculator  1443 . Only components related to embodiments are shown in the multi-antenna apparatus  10  of  FIG. 14 . Accordingly, it will be understood by those skilled in the art that other general-purpose elements may be further included in addition to the elements shown in  FIG. 14 . 
     The transmission signal controller  1441  may distribute a transmission signal to a plurality of transmission signals, adjust an intensity of the plurality of transmission signals, and transmit the transmission signals to a signal transmitter  1430  for transmitting the transmission signal through a multi-antenna  1450 . 
     The reception signal controller  1442  may adjust intensities of a plurality of reception signals received through the multi-antenna  1450  and may synthesize the plurality of reception signals into one reception signal. 
     The calculator  1443  may calculate a calibration value of the multi-antenna based on a channel state. Here, the calibration value may be calculated based on a ratio of a comparison target value determined based on respective transfer functions of a second signal and third signal of a first antenna among the multi-antenna to a comparison target value of a second antenna among the multi-antenna  1450 . Meanwhile, the comparison target value may be a ratio of the transfer function of the second signal of the first antenna to the transfer function of the third signal of the first antenna. Furthermore, the comparison target value may be determined by, but is not limited to, the ratio of the transfer function of the second signal of the first antenna to the transfer function of the third signal of the first antenna. 
     Meanwhile, the calculator  1443  may sample the second signal equal to the number of antennas of the multi-antenna  1450  and may calculate the calibration value of the multi-antenna  1450  by storing the third signal by the number of times the second signal is sampled. Furthermore, when a calibration value of the first signal is calculated, the calculator  1443  may calculate a calibration value of the second signal by using the second signal received at an arbitrary time. 
     The transmission signal processor  1444  may control amplitude and phase of the first signal input to a signal transmitter  1410  based on a channel state. 
     The signal transmitter  1430  may include a variable attenuator (not shown) that corrects a power intensity of the multi-antenna  1450  using different power intensities for different antennas when transmitting and receiving signals. Furthermore, the signal transmitter  1430  may include an oscillator (not shown) for generating an electrical vibration and a mixer (not shown) for mixing an output signal of the variable attenuator and an output signal of the oscillator. 
     The present disclosure may be embodied as computer readable code/instructions on a recording medium, e.g., a program module to be executed in computers, the program module including computer-readable commands. The computer readable medium may be any usable medium that may be accessed by a computer, and may include any usable medium, such as, a volatile and non-volatile medium and a discrete type and non-discrete type medium. Also, the computer readable medium may include all computer storing media and communication media. The computer storing medium may include any medium, such as, a volatile and non-volatile medium and a discrete type and non-discrete type medium that is realized by a method or technique for storing information, such as, a computer readable command, a data structure, a program module, or other data. The communication medium may include other data of modulated signal, such as, a computer readable command, a data structure, a program module, or a carrier signal, or other transmission mechanism, and an arbitrary information medium. 
     Therefore, the scopes of the present embodiments are defined not by the detailed description but by the appended claims, and all differences within the scope will be construed as being included in the present embodiments.