Patent Publication Number: US-7916745-B2

Title: Apparatus and method for automatic repeat request in multi input multi output system

Description:
PRIORITY 
     This application claims priority under 35 U.S.C. §119(a) to a Korean patent application filed in the Korean Intellectual Property Office on Sep. 13, 2006 and assigned Serial No. 2006-88476, the disclosure of which is hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention generally relates to a Multi Input Multi Output (MIMO) system. More particularly, the present invention relates to an apparatus and method for Automatic Repeat reQuest (ARQ) in a MIMO system. 
     2. Description of the Related Art 
     In MIMO systems, data is transmitted by using either spatial multiplexing or space-time coding. When using the spatial multiplexing, two or more data streams are simultaneously transmitted through a plurality of antennas included in a transmitting end and a receiving end. When using the space-time coding, a suitable code is combined with a data stream, and the resultant data stream is transmitted through the plurality of antennas over certain time periods. For example, in a 2×2 MIMO system, a transmitting end has two transmitting antennas and signals are transmitted through the two transmitting antennas. Then, a receiving end receives the signals so two data streams can be transmitted and received within one time period. When using an Alamouti code, the transmitting end transmits two data streams within two time periods through the two transmitting antennas, and thus a diversity gain can be obtained, thereby reducing an error rate. 
     According to an ARQ scheme, a transmitting end retransmits data when an error is detected from the data while the data is received by a receiving end. In particular, a Hybrid ARQ (HARQ) scheme combines an ARQ scheme and a coding scheme. With a HARQ scheme, when an error is detected from data transmitted in a previous time period, the erroneous data is stored rather than discarded, and when retransmitted, the data is combined with the previously transmitted data. This can increase probability of successful data reception. To detect errors, data packets are transmitted using a Cyclic Redundancy Check (CRC) code. 
     The receiving end detects errors by using a CRC code from a received packet and feeds back an acknowledgement/non-acknowledgement (ACK/NACK) signal to the transmitting end. Specifically, if no error is detected from the received packet, the ACK signal is fed back. Otherwise, the NACK signal is fed back. The transmitting end transmits a new packet to the receiving end in response to the ACK signal, and transmits the error detected signal to the receiving end in response to the NACK signal. 
     Unlike a Single Input Single Output (SISO) system, a MIMO system transmits two or more data streams at the same time. Therefore, in addition to an ACK/NACK signal, a stream identifier bit is also fed back to distinguish an error detected data stream. In the receiving end, a receiving filter is configured by using a pilot signal according to an antenna. When a signal is transmitted from an antenna, an output unit of the receiving filter can recognize the antenna from which the signal is transmitted. Therefore, the receiving end can recognize an error status of data streams. 
     In a conventional MIMO system employing an ARQ scheme, when an error is detected from a packet, the packet is retransmitted through the previously used antenna without having to select another antenna. Alternatively, all packets are retransmitted including the error detected packet by using another antenna. Since there is no method for selecting a specific antenna assigned to an error detected packet, a need exists for a method in which the error detected packet is retransmitted by selecting an antenna assigned for that packet. 
     SUMMARY OF THE INVENTION 
     The present invention addresses at least the above-mentioned problems and/or disadvantages and provides at least the advantages described below. Accordingly, an aspect of the present invention is to provide an apparatus and method for ARQ in a MIMO system. 
     According to an aspect of the present invention, a method of selecting a retransmission antenna in a MIMO system is provided. The method includes computing weights of erroneous packets and weights of transmitting antennas by using channel information; sorting the weights of the erroneous packets in descending order; sorting the weights of the transmitting antennas in ascending order; and assigning the transmitting antennas to the erroneous packets according to sorting results. 
     According to another aspect of the present invention, an apparatus for selecting a retransmission antenna in a MIMO system is provided. The apparatus includes a CRC detector for detecting an error from an input packet; and an ARQ transmitter for computing weights of erroneous packets and weights of transmitting antennas by using channel information, for sorting the weights of the erroneous packets in descending order, for sorting the weights of the transmitting antennas in ascending order, for assigning the transmitting antennas to the erroneous packets according to sorting results, and for transmitting information on the antenna assignment to a transmitting end. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, features and advantages of certain exemplary embodiments of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which: 
         FIG. 1  illustrates a concept of data communication in an N A ×N A  MIMO system according to the present invention; 
         FIGS. 2A and 2B  are block diagrams illustrating a transmitting end and a receiving end in a MIMO system according to the present invention; 
         FIG. 3  is a flowchart illustrating an ARQ method in a MIMO system according to the present invention; 
         FIGS. 4A to 4C  illustrate examples of a method of selecting a retransmission antenna according to the present invention; and 
         FIG. 5  and  FIG. 6  are graphs for comparing throughput between the prior art and the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention are described below with reference to the accompanying drawings. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail. 
     An apparatus and method for Automatic Repeat reQuest (ARQ) in a Multi Input Multi Output (MIMO) system of the present invention will now be described. It will be assumed hereinafter that an N A ×N A  MIMO system is used, a communication channel does not change within a maximum retransmission time period of ARQ, and a maximum retransmission number of ARQ is limited to 4. 
       FIG. 1  illustrates a concept of data communication in an N A ×N A  MIMO system according to the present invention. 
     Referring to  FIG. 1 , in the N A ×N A  MIMO system, a transmitting end transmits N A  signals to a receiving end through N A  transmitting antennas at time t. The signals are transmitted to the receiving end through a channel H. The signals are then received by the receiving end through receiving antennas and are decoded to detect original signals. 
     Such data communication carried out in the N A ×N A  MIMO system can be expressed by Equation (1) below. 
     
       
         
           
             
               
                 
                   
                     
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     In Equation (1), t denotes a packet index in the time axis, and N A  denotes the number of transmitting antennas (or receiving antennas). X i (t) denotes a packet transmission signal transmitted using an i th  transmitting antenna at time t. Y j (t) denotes a packet reception signal received using a j th  receiving antenna at time t. H denotes an N A ×N A  MIMO channel. N j (t) denotes a white noise of a j th  receiving antenna at time t. X i (t) can be expressed by X i (t)=[x 1   (i) (t) . . . x N     A     (i) (t)], where x k   (i) (t) denotes a transmission symbol. A dispersion of the transmission symbol can be represented by σ x   2 . N j (t) can be expressed by N j (t)=[n 1   (j) (t) . . . n N     A     (j) (t)], where n k   (j) (t) denotes a noise sample of the dispersion σ x   2 . H can be expressed by H=└H 1  . . . H N     A   ┘. A channel H k  from a j th  transmitting antenna to a plurality of receiving antennas  1 , . . . , and N A  can be expressed by 
                 H   k     =     [           h     1   ⁢           ⁢   k               ⋮             h       N   A     ⁢   K             ]       ,         
where h ji  denotes a channel coefficient from an i th  transmitting antenna to a j th  receiving antenna. In  FIG. 1 , {circumflex over (X)} i (t) denotes a signal obtained by decoding the signal X i (t) at time t.
 
       FIGS. 2A and 2B  show a transmitting end and a receiving end, respectively, in a MIMO system according to the present invention. The transmitting end of  FIG. 2A  includes a packet data block generator  201 , first to n th  Cyclic Redundancy Check (CRC) adders  202 - 1  to  202 -N, first to n th  channel encoders  203 - 1  to  203 -N, first to n th  interleavers  204 - 1  to  204 -N, first to n th  data modulators  205 - 1  to  205 -N, a Space-Time Block Code (STBC) modulator  206 , an ARQ &amp; feedback receiver  207 , and an STBC determining unit  208 . In the ARQ &amp; feedback receiver  207 , “ARQ” refers to ARQ information which is either acknowledgement or non-acknowledgement, e.g. “ACK” or “NACK”, and “feedback” refers to feedback information which is either “retransmission antenna information” or “STBC period sequence information”. The receiving end of  FIG. 2B  includes an STBC demodulator  210 , an equalizer  211 , first to n th  de-interleavers  212 - 1  to  212 -N, first to n th  packet synthesizers  213 - 1  to  213 -N, first to n th  channel decoders  214 - 1  to  214 -N, first to n th  CRC detectors  215 - 1  to  215 -N, an ARQ &amp; feedback transmitter  216 , a buffer  217 , and a channel estimator  218 . In the ARQ &amp; feedback transmitter  216 , “ARQ” refers to ARQ information which is either “ACK” or “NACK”, and “feedback” refers to feedback information which is either “retransmission antenna information” or “STBC period sequence information”. 
     In  FIG. 2A , the packet data block generator  201  receives the ARQ (ACK/NACK) information and the retransmission antenna information (or the STBC period sequence information) from the ARQ &amp; feedback receiver  207 , and thus generates 1 to N packet data blocks to be transmitted at a current frame. The generated packet data blocks are respectively output to the CRC adders  202 - 1  to  202 -N. The generated packet data block may include a new packet or a retransmission packet which is retransmitted when packet transmission has been failed in a previous time period. By the use of the aforementioned information (i.e., the ARQ (ACK/NACK) information and the retransmission antenna information (or the STBC period sequence information)), the packet data block generator  201  selects a retransmission antenna through which the packet is retransmitted. Specifically, when an ACK signal is received after a packet is transmitted in a previous time period, a new packet is transmitted in a current time period. In contrast, when an NACK signal is received after a packet is transmitted in a previous time period, the receiving end selects an antenna by using retransmission antenna information and retransmits the packet through the selected antenna. If STBC period sequence information is used, the packet is retransmitted in the same manner as it is previously transmitted. 
     The CRC adders  202 - 1  to  202 -N add CRC bits to the input packet data blocks, and transmit the packet data added with the CRC bit to the channel encoders  203 - 1  to  203 -N. 
     The channel encoders  203 - 1  to  203 -N perform channel coding on the input packet data at a particular coding rate, and transmit the encoded data (bits or symbols) to the interleavers  204 - 1  to  204 -N. If k pieces of input data are received at a coding rate R, then a total number of output symbols is k/R. The channel encoders  203 - 1  to  203 -N may be convolutional encoders, turbo encoders, Low Density Parity Check (LDPC) encoders, and so on. 
     The interleavers  204 - 1  to  204 -N interleave the data encoded by the channel encoders  203 - 1  to  203 -N so that the data is not affected by burst errors, and transmit the interleaved data to the data modulators  205 - 1  to  205 -N. That is, in order to improve channel throughput, the interleavers  204 - 1  to  204 -N change the order of bits included in a packet. 
     The data modulators  205 - 1  to  205 -N modulate the interleaved symbols according to a particular modulation scheme (modulation order), and transmit the modulated symbols to the STBC modulator  206 . In this case, complex symbols are output by performing signal point mapping on a constellation based on a particular mapping scheme. Some examples of the modulation scheme include a Binary Phase Shift Keying (BPSK) method in which one bit (s=1) is mapped to one complex signal, a Quadrature Phase Shift keying (QPSK) method in which two bits (s=2) are mapped to one complex signal, an 8ary Quadrature Amplitude Modulation (8 QAM) method in which three bits (s=3) are mapped to one complex signal, and a 16 QAM method in which four bits (s=4) are mapped to one complex signal. 
     The STBC modulator  206  modulates the received symbols according to STBC information. If the STBC information is not received from the STBC determining unit  208 , the STBC modulator  206  outputs the received symbols without performing modulation. The modulated symbols are subject to an Inverse Fast Fourier Transform (IFFT) process and a Radio Frequency (RF) process, and then are transmitted over the air through a corresponding antenna. 
     The ARQ &amp; feedback receiver  207  receives from the receiving end the ARQ (ACK/NACK) information and the retransmission antenna information (or STBC period sequence information). The received information is output to the packet data block generator  201 . Furthermore, the ARQ &amp; feedback receiver  207  outputs the received STBC period sequence information to the STBC determining unit  208 . 
     According to the received STBC period sequence information, the STBC determining unit  20  determines an STBC, and outputs information on the determined STBC to the STBC modulator  206 . 
     Now, the receiving end of  FIG. 2B  will be described. The STBC demodulator  210  receives first to n th  signals  1  to N through corresponding antennas, wherein the N signals have been demodulated according to a particular demodulation scheme. Then, the STBC demodulator  210  performs STBC demodulation on the received signals  1  to N. The STBC demodulation may be performed according to STBC demodulation information which uses the STBC period sequence information transmitted to the transmitting end when packet retransmission is necessary due to errors occurring in previous transmission. 
     The equalizer  211  performs channel compensation on the input signals  1  to N by using a channel estimation value received from the channel estimator  218 . The channel-compensated signals are respectively transmitted to the de-interleavers  212 - 1  to  212 -N. As a result, various noises generated from a communication channel can be compensated for. Throughput information (i.e., channel information) of the equalizer  211  is output to the ARQ &amp; feedback transmitter  216 . 
     It will be assumed herein that, among N signals to be received, if the equalizer  211  successfully receives one signal by using a Successive Interference Cancellation (SIC) scheme, probability of receiving the remaining signals increases. The SIC scheme uses a fact that a signal detection probability increases by canceling interference of a signal received from another antenna when the signal is known. This is possible because interference of the signal received from another antenna is a major cause of error occurrence in the MIMO system. Generally, in the MIMO system, an Ordered Successive Interference Cancellation (OSIC) scheme is used in which, when N signals are simultaneously received, these signals are sorted in descending order of a Signal to Noise ratio (SNR), a signal having a high probability of successful detection is first detected, and the detected signal component is removed from a next signal, thereby enhancing a signal detection success probability. 
     The de-interleavers  212 - 1  to  212 -N de-interleave the signals input from the equalizer  211  according to a particular rule, so that the order of bits included in the modulated signals change into the original order. The resultant signals are output to the packet synthesizers  213 - 1  to  213 -N. 
     The packet synthesizers  213 - 1  to  213 -N combine the de-interleaved signals with packets which have been failed to be transmitted in the previous time period. The de-interleaved signals are output to the channel decoders  214 - 1  to  214 -N. If the de-interleaved signals correspond to new packets rather than retransmission packets when retransmission is necessary due to the erroneous packets, the input signals are output without alteration. 
     The channel decoders  214 - 1  to  214 -N decode the encoded data, thereby restoring the data as it was before encoding. That is, according to a decoding scheme corresponding to the encoding scheme used in the transmitting end, the data is subject to channel decoding, thereby being restored as original packet data. The restored packet data is output to the CRC detectors  215 - 1  to  215 -N. 
     The CRC detectors  215 - 1  to  215 -N detect errors from input packet data. The error detection result is transmitted to the ARQ &amp; feedback transmitter  216 . Erroneous packets are transmitted to the buffer  217 . 
     According to the error detection result, the ARQ &amp; feedback transmitter  216  feeds back an ACK/NACK signal to the transmitting end. That is, if no error is detected from the packet data, the ACK signal is fed back to the transmitting end. Otherwise, the NACK signal is transmitted to the transmitting end. Furthermore, the ARQ &amp; feedback transmitter  216  computes weights of transmitting antennas and weights of erroneous packets by using the throughput information (i.e., channel information) of the equalizer  211 . According to the computation result, transmission antenna information for the erroneous packets is generated. The generated information is combined with the NACK signal and is then fed back to the transmitting end. It will be assumed herein that the ACK/NACK signal is fed back without error. If all transmitting antennas have the same weight, the ARQ &amp; feedback transmitter  216  combines an STBC period sequence information depending on an STBC structure with the NACK signal, and then feeds back the resultant signal to the transmitting end. 
     The buffer  217  buffers the erroneous packets received from the CRC detectors  215 - 1  to  215 -N so that the erroneous packets are combined with retransmission packets. Upon receiving the retransmission packets, the erroneous packets are transmitted to the packet synthesizers  213 - 1  to  213 -N. 
     The channel estimator  218  estimates a channel by using preambles of the signals  1  to N output from the STBC demodulator  210 . The estimated channel is transmitted to the equalizer  211 . 
       FIG. 3  shows an ARQ method in a MIMO system according to the present invention. 
     It will be assumed that a transmitting end transmits packets X 1 , X 2 , and X 3  to a receiving end at time t−1 through antennas  1 ,  2 , and  3 , respectively, and transmits a retransmission packet for the packet X 2  and new packets X 4  and X 5  to the receiving end at time t through the antennas  1 ,  2 , and  3 , respectively. Further, retransmission packets for the packets X 2  and X 5  and a new packet X 6  are transmitted to the receiving end at time t+1 through the antennas  1 ,  2 , and  3 , respectively. 
     Signals finally received by the receiving end at time t+1 are obtained by combining retransmission packets with previously received packets, and can be expressed by Equation (2) below. It will be assumed herein that a channel does not change for a certain time period. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     Equation (2) shows that the packet X 2  is transmitted to the receiving end at time t−1 through the antenna  2 , is retransmitted at time t through the antenna  1 , and is retransmitted at time t+1 through an antenna P 1  selected from the antennas  1 ,  2 , and  3 . Further, the packet X 5  is transmitted through the antenna  3  at time t, and is retransmitted through an antenna P 2  selected from the antennas  1 ,  2 , and  3  at time t+1. Furthermore, the packet X 6  is transmitted through an antenna P 3  selected from the antennas  1 ,  2 , and  3  at time t+1. 
     Packet retransmission can be made in the most effective way when the transmitting end retransmits erroneous packets through N A  antennas such that the average of estimated error dispersion of streams is minimized. According to the present invention, a water filling process is used to minimize an estimated error of streams, and thus the average of estimated error dispersion of streams will be minimized. The water filling process is derived from a concept that a certain amount of water is poured into a vessel having an uneven bottom surface. In order for the estimated errors of streams to have a constant value, the present invention provides a method in which weights of erroneous packets are sorted in descending order, weights of antennas are sorted in ascending order, and antenna retransmission information is transmitted to the transmitting end according to the sorting results. The antenna retransmission information indicates antennas to which erroneous packet are assigned. With this method, when an error is detected in a packet previously transmitted through a poor antenna, a good antenna is selected so the packet is transmitted through the good antenna in the next transmission. 
     Referring to  FIG. 3 , in step  301 , the receiving end evaluates input packets to determine whether errors are detected from the input packets. The input packet may either be an initially transmitted packet or a retransmitted packet. The retransmitted packet is received when packet transmission has been failed in a previous time period. When the retransmission packet is input, the retransmission packet is combined with the previously transmitted packet which has been failed to be transmitted, and the combined packet is evaluated to detect errors. The subsequence steps described below will be performed under the assumption that an error has been detected from the input packet. 
     In step  303 , weights of all transmitting antennas are determined to know whether the transmitting antennas have the same weight. A weight of an i th  transmitting antenna may be determined using channel information for a packet to be retransmitted at a next time period. Under the assumption that a channel does not change for a certain time period, the weight of the transmitting antenna can be expressed by Equation (3) below by using the current channel information.
 
 W ( A   i )=∥ H   P     i   ∥ 2   (3)
 
     If the weights of all transmitting antennas are different from one another, the weights of the transmitting antennas are sorted in ascending order, and the weights of the erroneous packets are sorted in descending order in step  305 . The weights of the erroneous packets may be determined by using channel information from a pervious time period to a current time period, and can be expressed by Equation (4) below.
 
 W ( E   i )=∥ H   i ∥ 2   (4)
 
     If the same assumption as in Equation (2) above is applied to Equation (4), a weight of each erroneous packet can be expressed by Equation (5) below. 
       W ( E   2 )=∥ H   2 ∥ 2   =∥H   2 ∥ 2   +∥H   1 ∥ 2  
 
 W ( E   5 )=∥ H   5 ∥ 2   =∥H   3 ∥ 2   (5)
 
     In step  307 , the antennas are assigned to the erroneous packets according to the above sorting results. In  FIGS. 4A to 4C , the erroneous packets are sorted in descending order of weights, as shown in  FIG. 4A . The transmitting antennas are sorted in ascending order of weights, as shown in  FIG. 4B . According to the sorting results, the transmitting antennas are assigned to the erroneous packets, as shown in  FIG. 4C  so the sum of weights of the erroneous packets and the transmitting antennas are constant. 
     In step  309 , information on a retransmission antenna assigned to the erroneous packet is transmitted to the transmitting end. The retransmission antenna information includes an identifier for the erroneous packet and information on a retransmission antenna through which the erroneous packet is retransmitted. Then, the procedure returns to step  301 . 
     If the result of step  303  show that the weights of all transmitting antennas are equal to one another, the procedure proceeds to step  311 . In step  311 , according to a N A ×N A  STBC structure, retransmission information (i.e., an identifier for the erroneous packet and an STBC time period sequence) is transmitted to the transmitting end. The procedure is then returned to step  301 . 
     The STBC may be a full rate quasi-orthogonal code which can be expressed by Equation (6) below. 
     
       
         
           
             
               
                 
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                           * 
                         
                       
                       
                         
                           x 
                           4 
                         
                       
                       
                         
                           x 
                           3 
                           * 
                         
                       
                     
                     
                       
                         
                           x 
                           3 
                         
                       
                       
                         
                           - 
                           
                             x 
                             4 
                             * 
                           
                         
                       
                       
                         
                           x 
                           1 
                         
                       
                       
                         
                           - 
                           
                             x 
                             2 
                             * 
                           
                         
                       
                     
                     
                       
                         
                           x 
                           4 
                         
                       
                       
                         
                           x 
                           3 
                           * 
                         
                       
                       
                         
                           - 
                           
                             x 
                             2 
                           
                         
                       
                       
                         
                           - 
                           
                             x 
                             1 
                             * 
                           
                         
                       
                     
                   
                   ] 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     The full rate quasi-orthogonal code represents a coding matrix of packets transmitted through four transmitting antennas. x 1 , x 2 , x 3 , and x 4  denote four input packets to be transmitted. In the matrix of Equation (6), the number of rows corresponds to the number of transmitting antennas, and the number of columns corresponds to a time period for transmitting the four packets. For example, the input packet x 1  may be transmitted through a first receiving antenna at time t, be retransmitted through a second transmitting antenna at time t+1 in the format of x 1 *, be retransmitted through a third transmitting antenna at time t+2 in the format of x 1 , and be retransmitted through a fourth transmitting antenna at time t+3 in the format of −x 1 *. 
     The time period sequence is used to represent the STBC by using a symbol as expressed by Equation (7) below.
 
(b,ρ i ,s i )  (7)
 
     b denotes whether packet conjugation is needed when a packet is retransmitted. b is set to 1 when packet conjugation is needed, otherwise b is set to 0. ρ i  denotes a permutation method that is either ρ 1 (1,2,3,4)=(2,1,4,3) or ρ 2 (1,2,3,4)=(4,3,2,1). When using the permutation method ρ 1 (1,2,3,4)=(2,1,4,3), first and second packets respectively transmitted through first and second antennas are transmitted in a next time period by switching the antennas, that is, respectively through the second and first antennas. Likewise, third and fourth packets respectively transmitted through third and fourth antennas are transmitted in a next period by switching the antennas, that is, respectively through the fourth and third antennas. When using the permutation method ρ 2  (1,2,3,4)=(4,3,2,1), first, second, third, and fourth packets respectively transmitted through first, second, third, and fourth antennas are transmitted in a next time period by reversing the order of the antennas, that is, respectively through the fourth, third, second, and first antennas. s i  denotes a sign (i.e., plus or minus) applied to the retransmission packet. For example, the signal may be s 1 =(−1, 1, −1, 1) or s 2 =(1, 1, −1, −1). 1 indicates that a sign used in a previously transmitted packet is also applied to a current transmitted packet. −1 indicates that a sign used in a previously transmitted packet is inversely applied to a current transmitted packet. Thus, the time period sequences for indicating the full rate quasi-orthogonal code of Equation (7) above are (1,ρ 1 ,s 1 ), (1,ρ 2 ,s 2 ), (0,ρ 1 ,s 1 )), and (0,ρ 2 ,s 2 ). According to the STBC structure, the receiving end transmits one of the four time period sequences to the transmitting end. 
     In this case, by using the time period sequence, the transmitting end encodes an initially transmitted packet and a retransmission packet which is retransmitted when packet transmission has been failed in a previous time period, and transmits the packets to the receiving end. This can be expressed by Equation (8) below. 
     
       
         
           
             
               
                 
                   [ 
                   
                     
                       
                         
                           x 
                           1 
                         
                       
                       
                         
                           - 
                           
                             x 
                             5 
                             * 
                           
                         
                       
                       
                         
                           - 
                           
                             x 
                             3 
                           
                         
                       
                       
                         
                           x 
                           6 
                           * 
                         
                       
                     
                     
                       
                         
                           x 
                           2 
                         
                       
                       
                         
                           x 
                           1 
                           * 
                         
                       
                       
                         
                           x 
                           6 
                         
                       
                       
                         
                           x 
                           3 
                           * 
                         
                       
                     
                     
                       
                         
                           x 
                           3 
                         
                       
                       
                         
                           - 
                           
                             x 
                             6 
                             * 
                           
                         
                       
                       
                         
                           x 
                           1 
                         
                       
                       
                         
                           - 
                           
                             x 
                             5 
                             * 
                           
                         
                       
                     
                     
                       
                         
                           x 
                           4 
                         
                       
                       
                         
                           x 
                           3 
                           * 
                         
                       
                       
                         
                           - 
                           
                             x 
                             5 
                           
                         
                       
                       
                         
                           - 
                           
                             x 
                             7 
                             * 
                           
                         
                       
                     
                   
                   ] 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     It is assumed herein that the transmitting end transmits the packets x 1 , x 2 , x 3 , and x 4  respectively through first, second, third, and fourth antennas in a first time period, and thereafter the receiving end requests the transmitting end to retransmit the packets x 1  and x 2 . In this case, the transmitting end encodes new packets x 5  and x 6  and the packets x 1  and x 2  in a second time period by using time period sequence information for retransmission, and transmits the encoded packets to the receiving end. If the receiving end requests the transmitting end to retransmit all packets that have been transmitted in the second time period, the transmitting end encodes the packets in a third time period by using the time period sequence information for retransmission and transmits the encoded packets to the receiving end. Thereafter, if the receiving end requests the transmitting end to retransmit the packets x 3 , x 5 , and x 6 , the transmitting end encodes the packets and a new packet x 7  in a fourth time period by using the time period sequence information for retransmission, and transmits the encoded packets to the receiving end. 
       FIG. 5  and  FIG. 6  are graphs for comparing throughput between the prior art and the present invention. A 4×4 MIMO system is used to obtain this comparison result, and a channel coefficient of a 4×4 matrix conforms to a normal distribution. In  FIG. 5 , four streams have the same weight. In  FIG. 6 , four streams have different weights from one another. 
     In the graphs of  FIG. 5  and  FIG. 6 , “weight” indicates throughput in a case where a packet is retransmitted in consideration of weights of antennas and weights of erroneous packets according to an embodiment of the present invention. “STBC like” indicates throughput in a case where a packet is retransmitted according to a 4×4 quasi orthogonal STBC. “Selective Rtx Same Ant” indicates throughput in a case where an erroneous packet is retransmitted to an antenna through which the packet has previously been transmitted according to the prior art. “Rtx All Packets” indicates throughput in a case where all packets are retransmitted through the same antenna. The graphs of  FIG. 5  and  FIG. 6  show that the present invention can provide better throughput than the prior art in terms of “weight” and “STBC like”. 
     Although it has been described that the receiving end selects an antenna used for packet retransmission, the antenna may be selected by the transmitting end if a channel state does not frequently change and Channel State Information (CSI) can be fed back. 
     According to the present invention, in a receiving end of a MIMO system, erroneous packets are sorted in descending order of weights and transmitting antennas are sorted in ascending order of weights. Then, the antennas are assigned to the erroneous packets in consideration of the sorting result. Information on the antenna assignment is transmitted to the transmitting end, and by the use of the information, an antenna used for packet retransmission is selected. Therefore, an error rate of retransmitted data can be minimized by using an ARQ method. Furthermore, the number of times of performing retransmission is reduced, thereby increasing overall data throughput. 
     While the invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims and their equivalents. Therefore, the scope of the invention is defined not by the detailed description of the invention but by the appended claims and their equivalents, and all differences within the scope will be construed as being included in the present invention.