Abstract:
Wireless communications for frequency-selective fading channels is realized by employing a system including orthogonal frequency division multiplexing (OFDM) in combination with an at least two antenna transmit diversity arrangement. Specifically, OFDM converts a multipath channel into a plurality of narrowband subchannels each having flat fading. Then, the signals on the same frequency subchannels of the at least two antennas are grouped together. Considering a first frequency subchannel, during a first OFDM time interval, a first signal and a second signal are transmitted on the first frequency subchannel from a first antenna ( 0 ) and from a second antenna ( 1 ), respectively. During a second OFDM time interval, a reverse sign (−) complex conjugate of the second signal and a complex conjugate of the first signal are transmitted from the first antenna and the second antenna, respectively. In a specific embodiment of the invention, reduced complexity in the implementation is realized by a reverse order complex conjugate and a reverse order, reverse sign (−) complex conjugate and judicious selection of the processed data signals in order to transmit the appropriate ones of the signals during the first and second OFDM intervals. Again, if the channel remains constant over the two OFDM intervals, diversity combination is realized for each frequency subchannel. In another embodiment of the invention, antenna-group hopping is employed in conjunction with pairing in time of the OFDM frequency subchannel signals to realize increased transmit diversity without rate loss.

Description:
TECHNICAL FIELD 
   This invention relates to wireless communications and, more particularly, to orthogonal frequency division multiplexing (OFDM) transmission systems. 
   BACKGROUND OF THE INVENTION 
   Arrangements are know for realizing transmit diversity for flat-fading transmission channels in wireless communications systems. One such prior known system of particular interest is described in an article authored by S. M. Alamouti an entitled “A Simple Transmit Diversity Technique for Wireless Communications”,  IEEE Journal On Select Areas In Communications , Vol. 16, No. 8, pp. 1451–1458, October 1998. Also see PCT published patent application WO9914871A1 issued Mar. 25, 1999 to Alamouti et al. However, the Alamouti arrangement cannot be directly applied to frequency-selective fading channels. Moreover, the Alamouti arrangement leads to transmission rate loss when more than two (2) transmit antennas are employed. Additionally, other space-time block coding arrangements in the same spirit as the Alamouti arrangement can also result in rate loss when the number of transmit antennas is greater than two (2). See for example, an article authored by V. Tarokh et al. entitled “Space-time block codes from orthogonal designs”,  IEEE Transactions on Information Theory , Vol. 45, pp. 1456–1467, July 1999, for such space-time block coding. 
   SUMMARY OF THE INVENTION 
   Problems and/or limitations of transmit diversity arrangements for wireless communications are overcome for frequency-selective fading channels by employing a system including orthogonal frequency division multiplexing (OFDM) in combination with an at least two antenna transmit diversity arrangement. Specifically, OFDM converts a multipath channel into a plurality of narrowband subchannels each having flat fading. Then, the signals on the same subchannels of the at least two antennas are grouped together. Considering a first frequency subchannel, during a first OFDM time interval, a first signal and a second signal are transmitted on the first frequency subchannel from a first antenna ( 0 ) and from a second antenna ( 1 ), respectively. During a second OFDM time interval, a reverse sign (−) complex conjugate of the second signal and a complex conjugate of the first signal are transmitted from the first antenna and the second antenna, respectively. 
   In a specific embodiment of the invention, reduced complexity in the implementation is realized by employing a reverse order complex conjugate and a reverse order, reverse sign (−) complex conjugate and by judicious selection of the processed data signals in order to transmit the appropriate ones of the signals during the first and second OFDM intervals. Again, if the channel remains constant over the two OFDM intervals, diversity combination is realized for each frequency subchannel. 
   In another embodiment of the invention, antenna-group hopping is employed in conjunction with pairing in time of the OFDM frequency subchannel signals to realize increased transmit diversity without rate loss. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
       FIG. 1A  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a first antenna in an OFDM transmit diversity system; 
       FIG. 1B  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a second antenna in an OFDM transmit diversity system; 
       FIG. 2  shows, in simplified block diagram form, details of an embodiment of the invention; 
       FIG. 3  shows, in simplified block diagram form, details of a reduced complexity implement of an OFDM transmit diversity system in accordance with the invention; 
       FIG. 4A  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a first antenna in an antenna-group hopping OFDM transmit diversity system; 
       FIG. 4B  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a second antenna in an antenna-group hopping OFDM transmit diversity system; 
       FIG. 4C  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a third antenna in an antenna-group hopping OFDM transmit diversity system; 
       FIG. 4D  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a fourth antenna in an antenna-group hopping OFDM transmit diversity system; 
       FIG. 5  shows, in simplified block diagram form, details of an embodiment of the invention for use in effecting antenna-group hopping in an OFDM transmit diversity system; and 
       FIG. 6  is an example matrix of OFDM signals that may advantageously employed in the embodiment of the invention illustrated in  FIG. 5 . 
   

   DETAILED DESCRIPTION 
     FIG. 1A  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a first antenna, antenna  0 , in an OFDM transmit diversity system. Specifically, shown are signal components x 0  ( 0 ) and −x 1   * ( 0 ) along the vertical time axis prior to their inverse fast Fourier transform (IFFT) and where the * denotes the complex conjugate. 
   Similarly,  FIG. 1B  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a second antenna, antenna  1 , in an OFDM transmit diversity system. Specifically, shown are signal components x 1  ( 0 ) and x 0   * ( 0 ) along the vertical time axis prior to their inverse fast Fourier transform (IFFT and where the * denotes the complex conjugate. 
   Thus, in a first OFDM interval, the signal pairing is such that signal component x 0 ( 0 ) is transmitted from antenna  0  and signal x 1 ( 0 ) is transmitted from antenna  1 , and in a second OFDM interval, the signal pairing is such that signal component −x 1   * ( 0 ) is transmitted from antenna  0  and signal component x 0   * ( 0 ) is transmitted from antenna  1 . Again, the * denotes the complex conjugate of the signal. 
     FIG. 2  shows, in simplified block diagram form, details of an embodiment of the invention. Specifically, N length signal vector X 0 =[x 0 ( 0 ),x 0  ( 1 ), . . . , x 0  (N−1)] to be transmitted is supplied to inverse fast Fourier transform (IFFT) unit  201 , and to complex conjugate unit  202 . Note that signal X 0  is a digital signal that has already been encoded and modulated, e.g., using phase shift keying (PSK), quadrature amplitude modulation (QAM) or the like. IFFT unit  201  obtains the inverse fast Fourier transform of signal X 0 , in well known fashion, and yields Y 0 . In this example, Y 0 =[y 0 ( 0 ),y 0 ( 1 ), . . . , (N−1)]=F −1 (X 0 ), which is the N-point IFFT of X 0  and where 
             y   0     ⁡     (   n   )       =       1     N       ⁢         ∑     N   -   1         m   =   0       ⁢         x   0     ⁡     (   m   )       ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N               ,         
for n=0, . . . , N−1. In turn, Y 0  is supplied to a first input of controllable selector  205 .
 
   Similarly, N length signal vector X 1 =[x 1 ( 0 ),x 1 ( 1 ), . . . ,x 1 (N−1)] also to be transmitted is supplied to inverse fast Fourier transform (IFFT) unit  203 , and to reverse sign (−) complex conjugate unit  204 . Note that signal X 1  is also a digital signal that has already been encoded and modulated, e.g., using PSK, QAM or the like. IFFT unit  203  obtains the inverse fast Fourier transform of signal X 1 , in well known fashion, and yields Y 1 . In this example, Y 1 =[y 1 ( 0 ), y 1 ( 1 ), . . . ,y 1 (N−1)]=F −1 (X 1 ), which is the N-point IFFT of X 1  and where 
             y   1     ⁡     (   n   )       =       1     N       ⁢         ∑     N   -   1         m   =   0       ⁢         x   1     ⁡     (   m   )       ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N               ,       
 
for n=0, . . . , N−1. In turn, Y 1  is supplied to a first input of controllable selector  206 .
 
   An output from complex conjugate unit  203  is X 0   * =[x 0   * ( 0 ),x 0   * ( 1 ), . . . ,x 0   * (N−1)]. Again, where “*” indicates complex conjugate. Then, signal X 0   *  to be transmitted is supplied to inverse fast Fourier transform (IFFT) unit  207 . IFFT unit  207  generates an inverse fast Fourier transform of X 0   * , in well known fashion, namely, Y 0   ′ =[y 0   ′ ( 0 ), y 0   ′ ( 1 ), . . . , y 0   ′ (N−1)]=F −1 (X 0   * ), where 
             y   0   ′     ⁡     (   n   )       =       1     N       ⁢         ∑     N   -   1         m   =   0       ⁢         x   0   *     ⁡     (   m   )       ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N               ,       
 
for n=0, . . . , N−1. In turn, Y 0   ′  is supplied to a second input of controllable selector  206 .
 
   An output from reverse sign (−) complex conjugate unit  205  is −X 1   * =[−x 1   * ( 0 ),−x 1   * ( 1 ), . . . ,−x 1   * (N−1)]. Then, signal −X 1   *  to be transmitted is supplied to inverse fast Fourier transform (IFFT) unit  208 . IFFT unit  208  generates an inverse fast Fourier transform of −X 1   * , in well know fashion, namely, Y 1   ′ =[y 1   ′ ( 0 ),y 1   ′ ( 1 ), . . . , y 1   ′ (N− 1 )]=F −1 (X 1   * ), where 
             y   1   ′     ⁡     (   n   )       =       1     N       ⁢         ∑     N   -   1         m   =   0       ⁢       -       x   1   *     ⁡     (   m   )         ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N               ,       
 
for n=0, . . . , N−1. In turn, Y 1   ′  is supplied to a second input of controllable selector  205 .
 
   It is noted that signals X 0 , X 1 , X 0   * , and −X 1   *  are frequency domain signals, and that Y 0 , Y 1 , Y 0   ′ , and Y 1   ′  are time domain signals. 
   Controllable selector  205 , under control of select input  217 , supplies Y 0  during a first, e.g., an even, OFDM interval and Y 1   ′  during a second, e.g., an odd, OFDM interval, as an output which is supplied to cyclic prefix unit  209 . In turn, cyclic prefix unit  209  prepends a cyclic prefix to each OFDM interval, i.e., each symbol period. The cyclic prefix is used to compensate for the dispersion introduced by the channel response and by a pulse shaping filter (not shown) used in the transmitter. Note that the cyclic prefix is added only for those tones used in an OFDM transmitter. Since the instant transmitter is primarily intended for use in a base station, a cyclic prefix is added for all of the available orthogonal tones. However, if the transmitter were to be used in a mobile unit using only a single OFDM tone, then the cyclic prefix uses only the particular single tone being used by the mobile unit. Then, the prepended Y 0  or Y 1   ′  signal is converted to analog form via digital-to-analog (D/A) converter  210  and supplied to RF transmitter  211  for transmission via antenna  212 , i.e., antenna  0 . Note that RF transmitter  211  performs a conventional baseband-to-passband conversion of the OFDM signal for transmission. 
   Similarly, controllable selector  206 , under control of select input  218 , supplies Y 1  during a first, e.g., an even, OFDM interval and Y 0   ′  during a second, e.g., an odd, OFDM interval, as an output to cyclic prefix unit  213 . In turn, cyclic prefix unit  213  prepends a cyclic prefix to each OFDM interval, i.e., each symbol period. The cyclic prefix is used to compensate for the dispersion introduced by the channel response and by a pulse shaping filter (not shown) used in the transmitter. Note that the cyclic prefix is added only for those tones used in an OFDM transmitter. Since the instant transmitter is primarily intended for use in a base station, a cyclic prefix is added for all of the available orthogonal tones. However, if the transmitter were to be used in a mobile unit using only a single OFDM tone, then the cyclic prefix uses only the particular single tone being used by the mobile unit. Then, the prepended Y 1  or Y 0   ′  signal is converted to analog form via digital-to-analog (D/A) converter  214  and supplied to RF transmitter  215  for transmission via antenna  216 , i.e., antenna  1 . 
     FIG. 3  shows, in simplified block diagram form, details of a reduced complexity implement of an OFDM transmit diversity system in accordance with the invention. Specifically, N length signal vector X 0 =[x 0 ( 0 ),x 0 ( 1 ), . . . , x 0  (N−1)] to be transmitted is supplied to inverse fast Fourier transform (IFFT) unit  301  which obtains the inverse fast Fourier transform of signal X 0 , in well known fashion, and yields Y 0 . In this example, Y 0 =[y 0 ( 0 ), y 0 ( 1 ), . . . , (N−1)]=F −1 (X 0 ), which is the N-point IFFT of X 0  and where 
             y   0     ⁡     (   n   )       =       1     N       ⁢         ∑     N   -   1         m   =   0       ⁢         x   0     ⁡     (   m   )       ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N               ,         
for n=0, . . . , N−1. In turn, Y 0  is supplied to a first input of controllable selector  302  and to reverse order complex conjugate unit  303 . Note that signal vector X 0  is a digital signal that has already been encoded and modulated, e.g., using PSK, QAM or the like.
 
   Similarly, N length signal vector X 1 =[x 1 ( 0 ),x 1 ( 1 ), . . . ,x 1 (N−1)] to be transmitted is supplied to inverse fast Fourier transform (IFFT) unit  304  which obtains the inverse fast Fourier transform of signal X 1 , in well known fashion, and yields Y 1 . In this example, Y 1 =[y 1 ( 0 ),y 1 ( 1 ), . . . , y 1 (N−1)]=F −1 (X 1 ), which is the N-point IFFT of X 1  and where 
             y   1     ⁡     (   n   )       =       1     N       ⁢         ∑     N   -   1         m   =   0       ⁢         x   1     ⁡     (   m   )       ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N               ,       
 
for n=0, . . . , N−1. In turn, Y 1  is supplied to a first input of controllable selector  305  and to reverse order, reverse sign (−) complex conjugate unit  306 . Note that signal vector X 1  is also a digital signal that has already been encoded and modulated, e.g., using PSK, QAM or the like.
 
   Reverse order complex conjugate unit  303  generates the inverse Fourier transform of X 0   *  from Y 0 , namely, Y 0   ′ =[y 0   ′ ( 0 ), y 0   ′ ( 1 ), . . . , y 0   ′ (N−0)]=F −1 (X 0   * ), where 
             y   0   ′     ⁡     (   n   )       =         1     N       ⁢         ∑     N   -   1         m   =   0       ⁢         x   0   *     ⁡     (   m   )       ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N             =       y   0   *     ⁡     (     N   -   n     )           ,       
 
for n=0, . . . , N−1 and where * denotes the complex conjugate. Note with reverse order, y 0   ′ ( 0 )=y 0   * (N)=y 0   * ( 0 ), y 0   ′ ( 1 )=y 0   * (N−1), . . . y 0   ′ (N−1)=y 0   * ( 1 ). In turn, Y 0   ′  is supplied to a second input of controllable selector  305 . Note that controllable selector  305  is controlled via a signal supplied to control input  314  to select as an output, either a signal supplied to its first input or a signal supplied to its second input, namely, either Y 1  or Y 0   ′ , respectively.
 
   Similarly, reverse order, reverse sign (−) complex conjugate unit  306  generates the inverse sign (−), reverse order Fourier transform of X 1   *  of Y 1 , namely, Y 1   ′ =[y 1   ′ ( 0 ),y 1   ′ ( 1 ), . . . , y 1   ′ (N−1)]=F −1 (X 1   * ), where 
             y   1   ′     ⁡     (   n   )       =         1     N       ⁢         ∑     N   -   1         m   =   0       ⁢       -       x   1   *     ⁡     (   m   )         ⁢     ⅇ     j2   ⁢           ⁢   π   ⁢           ⁢   mn   ⁢     /     ⁢   N             =     -       y   1   *     ⁡     (     N   -   n     )             ,       
 
for n=0, . . . , N−1 and where * denotes the complex conjugate. Note with reverse order, y 1   ′ ( 0 )=−y 1   * (N)=−y 1   * ( 0 ), y 1   ′ ( 1 )=−y 1   * (N−1), . . . , y 1   ′ (N−1)=−y 1   * ( 1 ). In turn, Y 1   ′  is supplied to a second input of controllable selector  302 . Note that controllable selector  302  is also controlled via a signal supplied to control input  313  to select as an output, either a signal supplied to its first input or a signal supplied to its second input, namely, either Y 0  or Y 1   ′ , respectively.
 
   An output from controllable selector  302  is supplied to cyclic prefix unit  307 , which prepends a cyclic prefix to each OFDM interval, i.e., each symbol period. The cyclic prefix is used to compensate for the dispersion introduced by the channel response and by a pulse shaping filter (not shown) used in the transmitter. Note that the cyclic prefix is added only for those tones used in an OFDM transmitter. Since the instant transmitter is primarily intended for use in a base station, a cyclic prefix is added for all of the available orthogonal tones. However, if the transmitter were to be used in a mobile unit using only a single OFDM tone, then the cyclic prefix uses only the particular single tone being used by the mobile unit. Then, the prepended Y 0  or Y 1   ′  signal is converted to analog form via digital-to-analog (D/A) converter  308  and supplied to RF transmitter  309  for transmission via antenna  310 , i.e., antenna  0 . 
   Similarly, an output from controllable selector  305  is supplied to cyclic prefix unit  311 , which prepends a cyclic prefix to each OFDM interval, i.e., each symbol period. Again, the cyclic prefix is used to compensate for the dispersion introduced by the channel response and by a pulse shaping filter (not shown) used in the transmitter. Note that the cyclic prefix is added only for those tones used in an OFDM transmitter. Since the instant transmitter is primarily intended for use in a base station, a cyclic prefix is added for all of the available orthogonal tones. However, if the transmitter were to be used in a mobile unit using only a single OFDM tone, then the cyclic prefix uses only the particular single tone being used by the mobile unit. Then, the prepended Y 1  or Y 0   ′  signal is converted to analog form via digital-to-analog (D/A) converter  312  and supplied to RF transmitter  313  for transmission via antenna  314 , i.e., antenna  1 . 
   Thus, in first, e.g., even, OFDM intervals controllable selectors  302  and  305  select signal vectors Y 0  and Y 1 , respectively, and in second, e.g., odd, OFDM intervals controllable selectors select signal vectors Y 1   ′  and Y 0   ′ , respectively. Therefore, in the first OFDM intervals, a signal vector version of Y 0  after the cyclic prefix is prepended and then D/A converted is supplied for transmission to antenna ( 0 )  310  and a signal vector version of Y 1  after the cyclic prefix is prepended and then D/A converted is supplied for transmission to antenna ( 1 )  314 . In second, e.g., odd, OFDM intervals, a signal vector version of Y 1   ′  after the cyclic prefix is prepended and then D/A converted is supplied for transmission to antenna ( 0 )  310  and a signal vector version of Y 0   ′  after the cyclic prefix is prepended and then D/A converted is supplied for transmission to antenna ( 1 )  314 . 
   Therefore, it is seen that the transmit diversity is realized in OFDM by employing a significantly less complex implement than that shown in  FIG. 2 . 
   In another embodiment of the invention, more than two transmit antennas are advantageously employed to realize the transmit diversity. In each frequency subchannel two of the antennas are grouped together and use the signal pattern shown in  FIGS. 1A and 1B . It is noted that the grouping pattern, i.e., the selection of antennas for each frequency subchannel may vary. 
   Further note that although the following example employs four antennas any number greater than two may be employed. Additionally, hereinafter “frequency subchannel” is referred to as just “subchannel”. 
     FIG. 4A  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a first antenna, in this example, antenna  0 , in an antenna-group hopping OFDM transmit diversity system. Thus, as shown, in a first OFDM time interval: a first subchannel includes signal component x 0 ( 0 ); a second subchannel includes a zero ( 0 ); a third subchannel includes signal component x 0 ( 2 ); a fourth subchannel includes a zero ( 0 ); etc., and in a second OFDM time interval: the first subchannel includes signal component −x 1   * ( 0 ); the second subchannel includes a zero ( 0 ); the third subchannel includes signal component −x 1   * ( 2 ); a fourth subchannel includes a zero ( 0 ); etc. 
     FIG. 4B  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a second antenna in an antenna-group hopping OFDM transmit diversity system. Thus, as shown, in a first OFDM time interval: a first subchannel includes signal component x 1 ( 0 ); a second subchannel includes a zero ( 0 ); a third subchannel includes a zero ( 0 ); a fourth subchannel includes signal component x 0   * ( 3 ); etc., and in a second OFDM time interval: the first subchannel includes signal component x 0   * ( 0 ); the second subchannel includes a zero ( 0 ); the third subchannel includes a zero ( 0 ); a fourth subchannel includes signal component −x 1   * ( 3 ); etc. 
     FIG. 4C  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a third antenna in an antenna-group hopping OFDM transmit diversity system. Thus, as shown, in a first OFDM time interval: a first subchannel includes a zero ( 0 ); a second subchannel includes signal component x 0  ( 1 ); a third subchannel includes signal component x 1  ( 2 ); a fourth subchannel includes a zero ( 0 ); etc., and in a second OFDM time interval: the first subchannel includes a zero ( 0 ); the second subchannel includes signal component −x 1   * ( 1 ); the third subchannel includes signal component x 0   * ( 2 ); a fourth subchannel includes a zero ( 0 ); etc. 
     FIG. 4D  graphically illustrates the pairing of signals in time for use in an embodiment of the invention in transmitting from a fourth antenna in an antenna-group hopping OFDM transmit diversity system. Thus, as shown, in a first OFDM time interval: a first subchannel includes a zero ( 0 ); a second subchannel includes signal component x 1 ( 1 ); a third subchannel includes a zero ( 0 ); a fourth subchannel includes signal component x 1 ( 3 ); etc., and in a second OFDM time interval: the first subchannel includes a zero ( 0 ); the second subchannel includes signal component x 0   * ( 1 ); the third subchannel includes a zero ( 0 ); a fourth subchannel includes signal component x 0   * ( 3 ); etc. 
   As shown, in each group of two (2) antennas, the signal components are paired in time on each subchannel. In this example, the grouping of the antennas varies from subchannel to subchannel. On a first subchannel antennas  0  and  1  are grouped together; on a second subchannel, antennas  2  and  3  are grouped together; on a third subchannel antennas  0  and  2  are grouped together; on a fourth subchannel antennas  1  and  3  are grouped together; and so on. 
     FIG. 5  shows, in simplified block diagram form, details of an embodiment of the invention for use in effecting antenna-group hopping in an OFDM transmit diversity system. Specifically, N length signal vector X 0 =[x 0  ( 0 ), x 0  ( 1 ), . . . , x 0  (N−1)] to be transmitted is supplied to “signal and select processor, and distributor”  501 . Similarly, N length signal vector X 1 =[x 1 ( 0 ),x 1 ( 1 ), . . . , x 1 (N−1)] also to be transmitted is also supplied to signal and select processor, and distributor  501 . As shown above in relationship to the embodiment of the invention of  FIG. 2 , signal and select processor, and distributor  501  is operative to generate the complex conjugate of signal vector X 0 , namely, X 0   * =[x 0   * ( 0 ),x 0   * ( 1 ), . . . ,x 0   * (N−1)], and the reverse sign (−) complex conjugate of signal vector X 1 , namely, −X 1   * =[−x 1   * ( 0 ), −x 1   * ( 1 ), . . . ,−x 1   * (N−1)]. From the signal components of X 0 , X 1 , X 0    *  and −X 1   *  signal and select processor, and distributor  501  generates, in this example, the matrix of signal as shown in  FIG. 6 . Specifically, signals are generated as represented by X 0   ′ , X 1   ′ , X 2   ′ , X 3   ′ , X 4   ′ , X 5   ′ , X 6    ′  and X 7   ′ . As shown in  FIG. 6 :
   X   0   ′=[x   0 ( 0 ), 0 , x 0 ( 2 ),0,x 0  ( 4 ),0, x 0 ( 6 ),0, . . . ];   X   1   ′=[−x   1   * ( 0 ), 0 ,−x 1   * ( 2 ), 0 ,−x 1   * ( 4 ), 0 ,−x 1   * ( 6 ), 0 , . . . ];   X   2   ′=[x   1 ( 0 ), 0 , 0 ,x 0 ( 3 ), x 1 ( 4 ), 0 , 0 , x 0 ( 7 ), . . . ];   X   3   ′=[x   0   * ( 0 ), 0 , 0 ,−x 0   * ( 3 ),x 0    * ( 4 ), 0 , 0 ,−x 1   * ( 7 ), . . . ];   X   4   ′=[0,x   0 ( 1 ), x 1 ( 2 ), 0 , 0 ,x 0  ( 5 ),x 1 ( 6 ), 0 , . . . ];   X   5   ′=[0,− x 1   * ( 1 ), x 0   * ( 2 ), 0 , 0 ,−x 1   * ( 5 ), x 0   * ( 6 ), 0 , . . . ];   X   6   ′=[0,x   1 ( 1 ), 0 ,x 1 ( 3 ), 0 , x 1 ( 5 ), 0 , x 1 ( 7 ), . . . ]; and   X   7   ′=[0, x   0   * ( 1 ), 0 , x 0   * ( 3 ), 0 , x 0   * ( 5 ), 0 , x 0    * ( 7 ), . . . ], 
where “*” denotes complex conjugate.
 
   Then, X 0   ′  is supplied to IFFT unit  502  that generates the inverse fast Fourier transform thereof, namely, Z 0   ′ =F −1 X 0   ′ , in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 0   ′  is supplied to a first input of controllable selector  503 . 
   Similarly, X 1   ′  is supplied to IFFT unit  504  that generates the inverse fast Fourier transform thereof, namely, Z 1   ′ =F −1 X 1   ′ , also in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 1   ′  is supplied to a second input of controllable selector  503 . Controllable selector  503  is responsive to control signals supplied to terminal  515 , from select bus  514  generated by signal and select processor, and distributor  501 , to realize selection of the signal components during alternate OFDM time intervals, e.g., during even and odd intervals. 
   The output from controllable selector  503  is supplied to cyclic prefix unit  516  that prepends a cyclic prefix to each OFDM interval, i.e., each symbol period, as described above. Then, the prepended Z 0   ′  or Z 1   ′  signal is converted to analog form via digital-to-analog (D/A) converter  517  and supplied to RF transmitter  518  for transmission via antenna  519 , i.e., antenna  0 . 
   X 2   ′  is supplied to IFFT unit  505  that generates the inverse fast Fourier transform thereof, namely, Z 2   ′ =F −1 X 2   ′ , in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 2   ′  is supplied to a first input of controllable selector  506 . 
   Similarly, X 3   ′  is supplied to IFFT unit  507  that generates the inverse fast Fourier transform thereof, namely, Z 3   ′ =F −1 X 3   ′ , also in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 3   ′  is supplied to a second input of controllable selector  506 . Controllable selector  506  is responsive to control signals supplied to terminal  520 , from select bus  514  generated by signal and select processor, and distributor  501 , to realize selection of the signal components during alternate OFDM time intervals, e.g., during even and odd intervals. 
   The output from controllable selector  506  is supplied to cyclic prefix unit  521  that prepends a cyclic prefix to each OFDM interval, i.e., each symbol period, as described above. Then, the prepended Z 2   ′  or Z 3   ′  signal is converted to analog form via digital-to-analog (D/A) converter  522  and supplied to RF transmitter  523  for transmission via antenna  524 , i.e., antenna  1 . 
   X 4   ′  is supplied to IFFT unit  508  that generates the inverse fast Fourier transform thereof, namely, Z 4   ′ =F −1 X 4   ′ , in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 4   ′  is supplied to a first input of controllable selector  509 . 
   Similarly, X 5   ′  is supplied to IFFT unit  510  that generates the inverse fast Fourier transform thereof, namely, Z 5   ′ =F −1 X 5   ′ , also in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 5   ′  is supplied to a second input of controllable selector  509 . Controllable selector  509  is responsive to control signals supplied to terminal  525 , from select bus  514  generated by signal and select processor, and distributor  501 , to realize selection of the signal components during alternate OFDM time intervals, e.g., during even and odd intervals. 
   The output from controllable selector  509  is supplied to cyclic prefix unit  526  that prepends a cyclic prefix to each OFDM interval, i.e., each symbol period, as described above. Then, the prepended Z 4   ′  or Z 5   ′  signal is converted to analog form via digital-to-analog (D/A) converter  527  and supplied to RF transmitter  528  for transmission via antenna  529 , i.e., antenna  2 . 
   X 6   ′  is supplied to IFFT unit  511  that generates the inverse fast Fourier transform thereof, namely, Z 6   ′ =F −1 X 6   ′ , in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 6   ′  is supplied to a first input of controllable selector  512 . 
   Similarly, X 7   ′  is supplied to IFFT unit  513  that generates the inverse fast Fourier transform thereof, namely, Z 7   ′ =F −1 X 7   ′ , also in a manner similar to that described above in relationship to the embodiment of the invention of  FIG. 2 . Z 7   ′  is supplied to a second input of controllable selector  512 . Controllable selector  512  is responsive to control signals supplied to terminal  530 , from select bus  514  generated by signal and select processor, and distributor  501 , to realize selection of the signal components during alternate OFDM time intervals, e.g., during even and odd intervals. 
   The output from controllable selector  512  is supplied to cyclic prefix unit  531  that prepends a cyclic prefix to each OFDM interval, i.e., each symbol period, as described above. Then, the prepended Z 6   ′  or Z 7   ′  signal is converted to analog form via digital-to-analog (D/A) converter  532  and supplied to RF transmitter  533  for transmission via antenna  534 , i.e., antenna  3 . 
   It is further noted that the antenna grouping can be in clusters of tones, instead of tone-by-tone. Indeed, other special antenna grouping patterns are also readily realizable without departing from the spirit and scope of the invention. For one clustered OFDM communication system, see U.S. Pat. No. 5,914,933, issued Jun. 22, 1999. 
   The above-described embodiments are, of course, merely illustrative of the principles of the invention. Indeed, numerous other methods or apparatus may be devised by those skilled in the art without departing from the spirit and scope of the invention. Specifically, it is noted that although the invention was described in terms of pairing signal in time, they could equally be paired in frequency or paired both in time and frequency. Additionally, over sampled signals may be utilized.