Abstract:
A simple block coding arrangement is created with symbols transmitted over a plurality of transmit channels, in connection with coding that comprises only simple arithmetic operations, such as negation and conjugation. The diversity created by the transmitter utilizes space diversity and either time or frequency diversity. Space diversity is effected by redundantly transmitting over a plurality of antennas, time diversity is effected by redundantly transmitting at different times, and frequency diversity is effected by redundantly transmitting at different frequencies: Illustratively, using two transmit antennas and a single receive antenna, one of the disclosed embodiments provides the same diversity gain as the maximal-ratio receiver combining (MRRC) scheme with one transmit antenna and two receive antennas. The principles of this invention are applicable to arrangements with more than two antennas, and an illustrative embodiment is disclosed using the same space block code with two transmit and two receive antennas.

Description:
REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a continuation application of U.S. application Ser. No. 11/828,790, filed Jul. 26, 2007; which is a divisional application of U.S. application Ser. No. 11/536,474, filed Sep. 28, 2006 (now U.S. Pat. No. 7,386,077); which is a continuation of U.S. application Ser. No. 10/873,567, filed Jun. 22, 2004 (now U.S. Pat. No. 7,120,200); which is a continuation of U.S. application Ser. No. 09/730,151, filed Dec. 5, 2000 (now U.S. Pat. No. 6,775,329); which is a continuation of U.S. application Ser. No. 09/074,224, filed May 7, 1998 (now U.S. Pat. No. 6,185,258); which claims the benefit of U.S. Provisional Application No. 60/059,016, filed Sep. 16, 1997, U.S. Provisional Application No. 60/059,219, filed Sep. 18, 1997, and U.S. Provisional Application No. 60/063,780, filed Oct. 31, 1997; all of which applications are hereby incorporated by reference herein in their entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    This invention relates to wireless communication and, more particularly, to techniques for effective wireless communication in the presence of fading and other degradations. 
         [0003]    The most effective technique for mitigating multipath fading in a wireless radio channel is to cancel the effect of fading at the transmitter by controlling the transmitter&#39;s power. That is, if the channel conditions are known at the transmitter (on one side of the link), then the transmitter can pre-distort the signal to overcome the effect of the channel at the receiver (on the other side). However, there are two fundamental problems with this approach. The first problem is the transmitter&#39;s dynamic range. For the transmitter to overcome an x dB fade, it must increase its power by x dB which, in most cases, is not practical because of radiation power limitations, and the size and cost of amplifiers. The second problem is that the transmitter does not have any knowledge of the channel as seen by the receiver (except for time division duplex systems, where the transmitter receives power from a known other transmitter over the same channel). Therefore, if one wants to control a transmitter based on channel characteristics, channel information has to be sent from the receiver to the transmitter, which results in throughput degradation and added complexity to both the transmitter and the receiver. 
         [0004]    Other effective techniques are time and frequency diversity. Using time interleaving together with coding can provide diversity improvement. The same holds for frequency hopping and spread spectrum. However, time interleaving results in unnecessarily large delays when the channel is slowly varying. Equivalently, frequency diversity techniques are ineffective when the coherence bandwidth of the channel is large (small delay spread). 
         [0005]    It is well known that in most scattering environments antenna diversity is the most practical and effective technique for reducing the effect of multipath fading. The classical approach to antenna diversity is to use multiple antennas at the receiver and perform combining (or selection) to improve the quality of the received signal. 
         [0006]    The major problem with using the receiver diversity approach in current wireless communication systems, such as IS-136 and GSM, is the cost, size and power consumption constraints of the receivers. For obvious reasons, small size, weight and cost are paramount. The addition of multiple antennas and RF chains (or selection and switching circuits) in receivers is presently not feasible. As a result, diversity techniques have often been applied only to improve the up-link (receiver to base) transmission quality with multiple antennas (and receivers) at the base station. Since a base station often serves thousands of receivers, it is more economical to add equipment to base stations rather than the receivers. 
         [0007]    Recently, some interesting approaches for transmitter diversity have been suggested. A delay diversity scheme was proposed by A. Wittneben in “Base Station Modulation Diversity for Digital SIMULCAST,”  Proceedings of the  1991  IEEE Vehicular Technology Conference  ( VTC  41  st ), pp. 848-853, May 1991, and in “A New Bandwidth Efficient Transmit Antenna Modulation Diversity Scheme For Linear Digital Modulation,” in  Proceedings of the  1993  IEEE International Conference on Communications  ( IICC &#39; 93), pp. 1630-1634, May 1993. The proposal is for a base station to transmit a sequence of symbols through one antenna, and the same sequence of symbols—but delayed—through another antenna. 
         [0008]    U.S. Pat. No. 5,479,448, issued to Nambirajan Seshadri on Dec. 26, 1995, discloses a similar arrangement where a sequence of codes is transmitted through two antennas. The sequence of codes is routed through a cycling switch that directs each code to the various antennas, in succession. Since copies of the same symbol are transmitted through multiple antennas at different times, both space and time diversity are achieved. A maximum likelihood sequence estimator (MLSE) or a minimum mean squared error (MMSE) equalizer is then used to resolve multipath distortion and provide diversity gain. See also N. Seshadri, J. H. Winters, “Two Signaling Schemes for Improving the Error Performance of FDD Transmission Systems Using Transmitter Antenna Diversity,”  Proceedings of the  1993  IEEE Vehicular Technology Conference  (VTC 43rd), pp. 508-511, May 1993; and J. H. Winters, “The Diversity Gain of Transmit Diversity in Wireless Systems with Rayleigh Fading,”  Proceedings of the  1994  ICC/SUPERCOMM , New Orleans, Vol. 2, pp. 1121-1125, May 1994. 
         [0009]    Still another interesting approach is disclosed by Tarokh, Seshadri, Calderbank and Naguib in U.S. application Ser. No. 08/847,635, filed Apr. 25, 1997 (based on a provisional application filed Nov. 7, 1996), where symbols are encoded according to the antennas through which they are simultaneously transmitted, and are decoded using a maximum likelihood decoder. More specifically, the process at the transmitter handles the information in blocks of M1 bits, where M1 is a multiple of M2, i.e., M1=k*M2. It converts each successive group of M2 bits into information symbols (generating thereby k information symbols), encodes each sequence of k information symbols into n channel codes (developing thereby a group of n channel codes for each sequence of k information symbols), and applies each code of a group of codes to a different antenna. 
       SUMMARY 
       [0010]    The problems of prior art systems are overcome, and an advance in the art is realized with a simple block coding arrangement where symbols are transmitted over a plurality of transmit channels and the coding comprises only simple arithmetic operations, such as negation and conjugation. The diversity created by the transmitter utilizes space diversity and either time diversity or frequency diversity. Space diversity is effected by redundantly transmitting over a plurality of antennas; time diversity is effected by redundantly transmitting at different times; and frequency diversity is effected by redundantly transmitting at different frequencies. Illustratively, using two transmit antennas and a single receive antenna, one of the disclosed embodiments provides the same diversity gain as the maximal-ratio receiver combining (MRRC) scheme with one transmit antenna and two receive antennas. The novel approach does not require any bandwidth expansion or feedback from the receiver to the transmitter, and has the same decoding complexity as the MRRC. The diversity improvement is equal to applying maximal-ratio receiver combining (MRRC) at the receiver with the same number of antennas. The principles of this invention are applicable to arrangements with more than two antennas, and an illustrative embodiment is disclosed using the same space block code with two transmit and two receive antennas. This scheme provides the same diversity gain as four-branch MRRC. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  is a block diagram of a first embodiment in accordance with the principles of this invention; 
           [0012]      FIG. 2  presents a block diagram of a second embodiment, where channel estimates are not employed; 
           [0013]      FIG. 3  shows a block diagram of a third embodiment, where channel estimates are derived from recovered signals; and 
           [0014]      FIG. 4  illustrates an embodiment where two transmitter antennas and two receiver antennas are employed. 
       
    
    
     DETAILED DESCRIPTION 
       [0015]    In accordance with the principles of this invention, effective communication is achieved with encoding of symbols that comprises merely negations and conjugations of symbols (which really is merely negation of the imaginary part) in combination with a transmitter created diversity. Space diversity and either frequency diversity or time diversity are employed. 
         [0016]      FIG. 1  presents a block diagram of an arrangement where the two controllable aspects of the transmitter that are used are space and time. That is, the  FIG. 1  arrangement includes multiple transmitter antennas (providing space diversity) and employs multiple time intervals. Specifically, transmitter  10  illustratively comprises antennas  11  and  12 , and it handles incoming data in blocks of n symbols, where n is the number of transmitter antennas, and in the illustrative embodiment of  FIG. 1 , it equals 2, and each block takes n symbol intervals to transmit. Also illustratively, the  FIG. 1  arrangement includes a receiver  20  that comprises a single antenna  21 . 
         [0017]    At any given time, a signal sent by a transmitter antenna experiences interference effects of the traversed channel, which consists of the transmit chain, the air-link, and the receive chain. The channel may be modeled by a complex multiplicative distortion factor composed of a magnitude response and a phase response. In the exposition that follows therefore, the channel transfer function from transmit antenna  11  to receive antenna  21  is denoted by h 0 , and from transmit antenna  12  to receive antenna  21  is denoted by h 1  where: 
         [0000]      h 0 =α 0 e jθ     0    
 
         [0000]      h i =α 1 e jθ     1     (1)
 
         [0000]    Noise from interference and other sources is added at the two received signals and, therefore, the resulting baseband signal received at any time and outputted by reception and amplification section  25  is 
         [0000]        r ( t )=α 0   e   jθ     0     s   i +α 1   e   jθ     1     s   j   +n ( t ),  (2)
 
         [0000]    where s i  and s i  are the signals being sent by transmit antenna  11  and  12 , respectively. 
         [0018]    As indicated above, in the two-antenna embodiment of  FIG. 1  each block comprises two symbols and it takes two symbol intervals to transmit those two symbols. More specifically, when symbols s i  and s j  need to be transmitted, at a first time interval the transmitter applies signal s i  to antenna  11  and signal s j  to antenna  12 , and at the next time interval the transmitter applies signal −s* 1  to antenna  11  and signal s 0 * to antenna  12 . This is clearly a very simple encoding process where only negations and conjugations are employed. As demonstrated below, it is as effective as it is simple. Corresponding to the above-described transmissions, in the first time interval the received signal is 
         [0000]        r ( t )= h   0   s   i   +h   i   s   j   +n ( t ),  (3)
 
         [0000]    and in the next time interval the received signal is 
         [0000]        r ( t+T )=− h   0   s   j   *+h   1   s   i   *+n ( t+T ).  (4)
 
         [0019]    Table 1 illustrates the transmission pattern over the two antennas of the  FIG. 1  arrangement for a sequence of signals {s 0 , s 1 , s 2 , s 3 , s 4 , s 5  . . . }. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Time: 
                 t 
                 t + T 
                 t + 2T 
                 t + 3T 
                 t + 4T 
                 t + 5T 
               
               
                   
               
             
             
               
                 Antenna 11 
                 s 0   
                 −s 1 * 
                 s 2   
                 −s 3 * 
                 s 4   
                 −s 5 * 
                 . . . 
               
               
                 Antenna 12 
                 s 1   
                  s 0 * 
                 s 3   
                  s 2 * 
                 s 5   
                  s 4 * 
                 . . . 
               
               
                   
               
             
          
         
       
     
         [0020]    The received signal is applied to channel estimator  22 , which provides signals representing the channel characteristics or, rather, the best estimates thereof. Those signals are applied to combiner  23  and to maximum likelihood detector  24 . The estimates developed by channel estimator  22  can be obtained by sending a known training signal that channel estimator  22  recovers, and based on the recovered signal the channel estimates are computed. This is a well known approach. 
         [0021]    Combiner  23  receives the signal in the first time interval, buffers it, receives the signal in the next time interval, and combines the two received signals to develop signals 
         [0000]        {tilde over (s)}   i   ={tilde over (h)}   0   *r ( t ) +{tilde over (h)}   1   r *( t+T ) 
         [0000]        {tilde over (s)}   j   ={tilde over (h)}   1   *r ( t ) −{tilde over (h)}   0   r *( t+T )  (5)
 
         [0000]    Substituting equation (1) into (5) yields 
         [0000]        {tilde over (s)}   i =({tilde over (α)} 0   2 +{tilde over (α)} 1   2 ) s   i   +{tilde over (h)}   0   *n ( t ) +{tilde over (h)}   1   n *( t+T )
 
         [0000]        {tilde over (s)}   j =({tilde over (α)} 0   2 +{tilde over (α)} 1   2 ) s   j   +{tilde over (h)}   0   n *( t+T ) +{tilde over (h)}   1   *n ( t ),  (6)
 
         [0000]    where {tilde over (α)} 0   2 ={tilde over (h)} 0 {tilde over (h)} 0 * and {tilde over (α)} 1   2 ={tilde over (h)} 1 {tilde over (h)} 1 *, demonstrating that the signals of equation (6) are, indeed, estimates of the transmitted signals (within a multiplicative factor). Accordingly, the signals of equation (6) are sent to maximum likelihood detector  24 . 
         [0022]    In attempting to recover s i , two kinds of signals are considered: the signals actually received at time t and t+T, and the signals that should have been received if s i  were the signal that was sent. As demonstrated below, no assumption is made regarding the value of s j . That is, a decision is made that s i =s x  for that value of x for which 
         [0000]      d 2 [r(t),(h 0 s x +h 1 s j )]+d 2 [r(t+T),(−h 1 s j *+h 0 s x *)]
 
         [0000]      is less than 
         [0000]      d 2 [r(t),(h 0 s k +h 1 s j )]+d 2 [r(t+T),(−h 1 s j *+h 0 s k *)]  (7)
 
         [0000]    where d 2  (x,y) is the squared Euclidean distance between signals x and y, i.e., d 2  (x,y)=|x−y| 2 . 
         [0023]    Recognizing that {tilde over (h)} 0 =h 0 +noise that is independent of the transmitted symbol, and that {tilde over (h)} 1 =h 1 +noise that is independent of the transmitted symbol, equation (7) can be rewritten to yield 
         [0000]      (α 0   2 +α 1   2 )| s   x | 2   −{tilde over (s)}   i   s   x   *−{tilde over (s)}   i *≦(α 0   2 +α 1   2 )| s   k | 2   −{tilde over (s)}   i   s   k   *−{tilde over (s)}   i   *s   k   (8)
 
         [0000]    where α 0   2 =h 0 h 0 * and α 1   2 =h 1 h 1 *; or equivalently 
         [0000]      ( a   0   2   +a   1   2 −1)| s   x | 2   +d   2 ( {tilde over (s)}   i   ,s   x )≦( a   0   2   +a   1   2 −1)| s   k | 2   +d   2 ( {tilde over (s)}   i   ,s   k )  (9)
 
         [0024]    In Phase Shift Keying modulation, all symbols carry the same energy, which means that |s x | 2 =|s k | 2  and, therefore, the decision rule of equation (9) may be simplified to choose signal 
         [0000]        ŝ   i   =s   x   iffd   2 ( {tilde over (s)}   i   ,s   x )≦ d   2 ( {tilde over (s)}   i   ,s   k ).  (10)
 
         [0000]    Thus, maximum likelihood detector  24  develops the signals s k  for all values of k, with the aid of {tilde over (h)} 0  and {tilde over (h)} 1  from estimator  22 , develops the distances d 2 ({tilde over (s)} i , s k ), identifies x for which equation (10) holds and concludes that ŝ i =s x . A similar process is applied for recovering ŝ j . 
         [0025]    In the above-described embodiment each block of symbols is recovered as a block with the aid of channel estimates {tilde over (h)} 0  and {tilde over (h)} 1 . However, other approaches to recovering the transmitted signals can also be employed. Indeed, an embodiment for recovering the transmitted symbols exists where the channel transfer functions need not be estimated at all, provided an initial pair of transmitted signals is known to the receiver (for example, when the initial pair of transmitted signals is prearranged). Such an embodiment is shown in  FIG. 2 , where maximum likelihood detector  27  is responsive solely to combiner  26 . (Elements in  FIG. 3  that are referenced by numbers that are the same as reference numbers in  FIG. 1  are like elements.) Combiner  26  of receiver  30  develops the signals 
         [0000]        r   0   =r ( t )= h   0   s   0   +h   1   s   1   +n   0    
         [0000]        r   1   =r ( t+T )= h   1   s   0   *−h   0   s   1   *+n   1    
         [0000]        r   2   =r ( t+ 2 T )= h   0   s   2   +h   1   s   3   +n   2    
         [0000]        r   3   =r ( t+ 3 T )= h   1   s   2   *−h   0   s   3   *+n   3 ,  (11)
 
         [0000]    then develops intermediate signals A and B 
         [0000]        A=r   0   r   3   *−r   2   r   1 * 
         [0000]        B=r   2   r   0   *−r   1   r   3 *,  (12)
 
         [0000]      and finally develops signals 
         [0000]    
       
      
       {tilde over (s)} 
       2 
       =As 
       1 
       *+Bs 
       0  
      
     
         [0000]        {tilde over (s)}   3   =−As   0   *+Bs   1 ,  (13)
 
         [0000]    where N 3  and N 4  are noise terms. It may be noted that signal r 2  is actually r 2 =h 0 ŝ 2 +h 1 ŝ 3 =h 0 s 2 +h 1 s 3 +n 2 , and similarly for signal r 3 . Since the makeup of signals A and B makes them also equal to 
         [0000]        A =(α 0   2 +α 1   2 )( s   2   s   1   −s   3   s   0 )+ N   1  
 
         [0000]        B =(α 0   2 +α 1   2 )( s   2   s   0   *+s   3   s   1 *)+ N   2 ,  (14)
 
         [0000]    where N 1  and N 2  are noise terms, it follows that signals {tilde over (s)} 2  and {tilde over (s)} 3  are equal to 
         [0000]        {tilde over (s)}   2 =(α 0   2 +α 1   2 )(| s   0 | 2   +|s   1 | 2 ) s   2   +N   3  
 
         [0000]        {tilde over (s)}   3 =(α 0   2 +α 1   2 )(| s   0 | 2   +|s   1 | 2 ) s   3   +N   4 .  (15)
 
         [0026]    When the power of all signals is constant (and normalized to 1) equation (15) reduces to 
         [0000]        {tilde over (s)}   2 =(α 0   2 +α 1   2 ) s   2   +N   3  
 
         [0000]        {tilde over (s)}   3 =(α 0   2 +α 1   2 ) s   3   +N   4 .  (16)
 
         [0027]    Hence, signals {tilde over (s)} 2  and {tilde over (s)} 3  are, indeed, estimates of the signals s 2  and s 3  (within a multiplicative factor). Lines  28  and  29  demonstrate the recursive aspect of equation (13), where signal estimates {tilde over (s)} 2  and {tilde over (s)} 3  are evaluated with the aid of recovered signals s 0  and s 1  that are fed back from the output of the maximum likelihood detector. 
         [0028]    Signals {tilde over (s)} 2  and {tilde over (s)} 3  are applied to maximum likelihood detector  24  where recovery is effected with the metric expressed by equation (10) above. As shown in  FIG. 2 , once signals s 2  and s 3  are recovered, they are used together with received signals r 2 , r 3 , r 4 , and r 5  to recover signals s 4  and s 5 , and the process repeats. 
         [0029]      FIG. 3  depicts an embodiment that does not require the constellation of the transmitted signals to comprise symbols of equal power. (Elements in  FIG. 3  that are referenced by numbers that are the same as reference numbers in  FIG. 1  are like elements.) In  FIG. 3 , channel estimator  43  of receiver  40  is responsive to the output signals of maximum likelihood detector  42 . Having access to the recovered signals s 0  and s 1 , channel estimator  43  forms the estimates 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
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                                 1 
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                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0030]    and applies those estimates to combiner  23  and to detector  42 . Detector  24  recovers signals s 2  and s 3  by employing the approach used by detector  24  of  FIG. 1 , except that it does not employ the simplification of equation (9). The recovered signals of detector  42  are fed back to channel estimator  43 , which updates the channel estimates in preparation for the next cycle. 
         [0000]    The  FIGS. 1-3  embodiments illustrate the principles of this invention for arrangements having two transmit antennas and one receive antenna. However, those principles are broad enough to encompass a plurality of transmit antennas and a plurality of receive antennas. To illustrate,  FIG. 4  presents an embodiment where two transmit antennas and two receive antennas are used; to wit, transmit antennas  31  and  32 , and receive antennas  51  and  52 . The signal received by antenna  51  is applied to channel estimator  53  and to combiner  55 , and the signal received by antenna  52  is applied to channel estimator  54  and to combiner  55 . Estimates of the channel transfer functions h 0  and h 1  are applied by channel estimator  53  to combiner  55  and to maximum likelihood detector  56 . Similarly, estimates of the channel transfer functions h 2  and h 3  are applied by channel estimator  54  to combiner  55  and to maximum likelihood detector  56 . Table 2 defines the channels between the transmit antennas and the receive antennas, and table 3 defines the notion for the received signals at the two receive antennas. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Antenna 51 
                 Antenna 52 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Antenna 31 
                 h 0   
                 h 2   
               
               
                   
                 Antenna 32 
                 h 1   
                 h 3   
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Antenna 51 
                 Antenna 52 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Time t 
                 r 0   
                 r 2   
               
               
                   
                 Time t + T 
                 r 1   
                 r 3   
               
               
                   
                   
               
             
          
         
       
     
         [0031]    Based on the above, it can be shown that the received signals are 
         [0000]    
       
      
       r 
       0 
       =h 
       0 
       s 
       0 
       +h 
       1 
       s 
       1 
       +n 
       0  
      
     
         [0000]    
       
      
       r 
       1 
       =−h 
       0 
       s 
       1 
       +h 
       1 
       s 
       0 
       +n 
       1  
      
     
         [0000]    
       
      
       r 
       2 
       =h 
       2 
       s 
       0 
       +h 
       3 
       s 
       1 
       +n 
       2  
      
     
         [0000]        r   3   =−h   2   s   1   +h   3   s   0   +n   3   (18)
 
         [0000]    where n 0 , n 1 , n 2 , and n 3  are complex random variables representing receiver thermal noise, interferences, etc. 
         [0032]    In the  FIG. 4  arrangement, combiner  55  develops the following two signals that are sent to the maximum likelihood detector: 
         [0000]        {tilde over (s)}   0   =h   0   *r   0   +h   1   r   1   *+h   2   *r   2   +h   3   r   3 * 
         [0000]        {tilde over (s)}   1   =h   1   *r   0   −h   0   r   1   *+h   3   *r   2   −h   2   r   3 *.  (19)
 
         [0033]    Substituting the appropriate equations results in 
         [0000]        {tilde over (s)}   0 =( a   0   2   +a   1   2   +a   2   2   +a   3   2 ) s   0   +h   0   *n   0   +h   1   n   1   *+h   2   *n   2   +h   3   n   3 * 
         [0000]        {tilde over (s)}   1 =( a   0   2   +a   1   2   +a   2   2   +a   3   2 ) s   1   +h   1   *n   0   −h   0   n   1   *+h   3   *n   2   −h   2   n   3   (20)
 
         [0000]    which demonstrates that the signal {tilde over (s)} 0  and {tilde over (s)} 1  are indeed estimates of the signals s 0  and s 1 . Accordingly, signals {tilde over (s)} 0  and {tilde over (s)} 1  are sent to maximum likelihood decoder  56 , which uses the decision rule of equation (10) to recover the signals ŝ 0  and ŝ 1 . 
         [0034]    As disclosed above, the principles of this invention rely on the transmitter to force a diversity in the signals received by a receiver, and that diversity can be effected in a number of ways. The illustrated embodiments rely on space diversity—effected through a multiplicity of transmitter antennas, and time diversity—effected through use of two time intervals for transmitting the encoded symbols. It should be realized that two different transmission frequencies could be used instead of two time intervals. Such an embodiment would double the transmission speed, but it would also increase the hardware in the receiver, because two different frequencies need to be received and processed simultaneously. 
         [0035]    The above illustrated embodiments are, obviously, merely illustrative implementations of the principles of the invention, and various modifications and enhancements can be introduced by artisans without departing from the spirit and scope of this invention, which is embodied in the following claims. For example, all of the disclosed embodiments are illustrated for a space-time diversity choice, but as explained above, one could choose the space-frequency pair. Such a choice would have a direct effect on the construction of the receivers.