Abstract:
In a wireless communication system using multiple antennas at the transmitter and multiple antennas at the receiver, with a sufficiently large number of antennas and/or diversity order, the same performance that is obtainable when employing instantaneous rate indication feedback can be attained without any such short-term feedback by adjusting the data rate of each transmit antenna according to a prescribed function. The prescribed function does not depend on the short-term state of the channel, but instead only depends on its long-term statistics, which may be fed back from the receiver to the transmitter at relatively lengthy intervals.

Description:
TECHNICAL FIELD 
   This invention relates to the art of wireless communications, and more particularly, to wireless communication systems using multiple antennas at the transmitter and multiple antennas at the receiver, so called multiple-input multiple-output (MIMO) systems. 
   BACKGROUND OF THE INVENTION 
   It is known in the art that multiple-input multiple-output (MIMO) systems can achieve dramatically improved capacity as compared to single antenna, i.e., single antenna to single antenna or multiple antenna to single antenna, systems. It is also known in the art that if information about the short-term state of the channel is fed back to the transmitter, then the throughput of the channel can be improved with respect to an identically configured system but without short-term feedback. However, because in MIMO systems the overall channel is actually made up of multiple channels, with one channel for each transmit antenna and receive antenna pairing, all of which are time-varying, such short-term feedback requires considerable bandwidth, and it is undesirable to dedicate so much bandwidth to feedback. Furthermore, each channel may span multiple coherence bandwidth intervals, where each coherence bandwidth interval is a swath of frequencies that experience the same effect due to the channel as they pass through the channel. The diversity order of a channel is the number of coherence bandwidth intervals spanned by the transmitted signal. 
   With some particular architectures, the amount of short-term feedback can be reduced with little loss in performance by replacing the information about the state of the channel with indications about the instantaneous data rate supported by each of the transmit antennas. See for example U.S. patent application Ser. No. 09/714,084. Nonetheless, there are instances in which even such feedback will be unacceptable, because it takes up to much of the available bandwidth of the reverse channel particularly when there is a large number of antennas. 
   SUMMARY OF THE INVENTION 
   In a MIMO system with a sufficiently large number of antennas and/or diversity order, the same performance that is obtainable when employing instantaneous rate indication feedback can be attained without any such short-term feedback, in accordance with the principles of the invention, by adjusting the data rate of each transmit antenna according to a prescribed function. In accordance with an aspect of the invention, such a function does not depend on the short-term state of the channel, but instead only depends on its long-term statistics, which may be fed back from the receiver to the transmitter at relatively lengthy intervals compared with the intervals required for short term feed back and requires considerably less bandwidth, e.g., 1,000 times less. Advantageously, the transmitter may employ only one-dimensional data coding for each of the transmit antennas. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
     In the drawing: 
       FIG. 1  shows an exemplary multiple-input multiple-output (MIMO) system arranged in accordance with the principles of the invention so as to achieve dramatically improved capacity as compared to single antenna systems; and 
       FIG. 2  shows an exemplary distribution of transmit data rates for a particular set of long-term conditions in accordance with an aspect of the invention. 
   

   DETAILED DESCRIPTION 
   The following merely illustrates the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples and conditional language recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure. 
   Thus, for example, it will be appreciated by those skilled in the art that the block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the invention. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudocode, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown. 
   The functions of the various elements shown in the FIGS., including functional blocks labeled as “processors” may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term “processor” or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, read-only memory (ROM) for storing software, random access memory (RAM), and non-volatile storage. Other hardware, conventional and/or custom, may also be included. Similarly, any switches shown in the FIGS. are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementor as more specifically understood from the context. 
   In the claims hereof any element expressed as a means for performing a specified function is intended to encompass any way of performing that function including, for example, a) a combination of circuit elements which performs that function or b) software in any form, including, therefore, firmware, microcode or the like, combined with appropriate circuitry for executing that software to perform the function. The invention as defined by such claims resides in the fact that the functionalities provided by the various recited means are combined and brought together in the manner which the claims call for. Applicant thus regards any means which can provide those functionalities as equivalent as those shown herein. 
     FIG. 1  shows an exemplary multiple-input multiple-output (MIMO) system arranged in accordance with the principles of the invention so as to achieve dramatically improved capacity as compared to single antenna systems. In particular,  FIG. 1  shows transmitter (TX)  101  and receiver (RX)  103 . Transmitter  101  includes a) demultiplexer (demux)  105 ; b) encoders  107 , including encoders  107 - 1  through  107 -N; c) interleavers  109 , including interleavers  109 - 1  through  109 -N; d) symbol mappers  111 , including symbol mappers  111 - 1  through  111 -N; e) optional upconverters  115 , including optional upconverters  115 - 1  through  115 -N; f) optional transmit antennas  117 , including optional transmit antennas  117 - 1  through  117 -N; and g) rate controller  119 . Receiver  103  includes a) optional receive antennas  131 , including optional receive antennas  131 - 1  through  131 -M; b) optional downconverters  133 , including optional downconverters  133 - 1  through  133 -M; c) channel estimator  135 ; d) Mimimum-Mean Square Error (MMSE) filter with successive decoding and cancellation  137 ; and e) multiplexer (mux)  139 . 
   Demultiplexer  105  receives as an input an original data stream, which is the data to be transmitted, and divides it into N data substreams, each to be processed along an independent transmit path and then transmitted. 
   Each of encoders  107  applies channel coding to the respective data substream it receives so as to increase the redundancy of the data substream. This facilitates error recovery at the receiver should errors occur. The type of channel coding used is a function of the rate as determined by the rate controller  119 . The type of channel coding employed determines the particular amount of redundancy in the encoded data substream, and it is noted that the amount of redundancy is known as the code rate. Each of encoders  107  may use a channel coding that is independent of the channel coding used by any other of encoders  107 , and each may receive an independently specified rate from the rate controller. 
   Interleavers  109  are conventional in nature and each rearranges the bits of the encoded data substream it receives to provide additional protection against errors. 
   Each of symbol mappers  111  maps the bits of the interleaved encoded channel substream that it receives to a point in a constellation. The particular constellation employed is selected as a function of the rate determined by the rate controller. Typically, the lower the rate of data transmission the lower the number of symbols in the constellation for transmitting data at that rate. 
   Each of optional upconverters  115  performs conventional upconverting functionality. In the case of a radio-based system each of upconverters  115  generates a radio frequency signal by modulating a carrier waveform using the gain regulated mapped data substream it receives as an input. Each resulting modulated signal may be supplied to the respective one of optional transmit antennas  117  that may be coupled to each of upconverters  115 . 
   Rate controller  119  determines the code rate and the constellation size for each substream. Each code rate or an indicator thereof, is then supplied to the appropriate encoder and the constellation to employ, or an indicator thereof, is supplied to each symbol mapper. 
   Each of optional receive antennas  131  receives a signal from each of optional transmit antennas  117 . The signals received at each antenna are converted to baseband by the one of optional downconverters  133  to which it is coupled. The resulting baseband signals each of which may be referred to as a receive branch, are fed into channel estimator  135  and MMSE filter with successive decoding and cancellation  137 . 
   Channel estimator  135  develops an estimate of the channels for each transmit and receive pair. Thus, for N transmit antennas and M receive antennas there are M×N channels. The estimates for each of the channels are collectively arranged into an M×N matrix of the overall channel estimate Ĥ. Additionally, channel estimator  135  develops an estimate of the noise power in the channel, {circumflex over (σ)} 2 . 
   MMSE filter with successive decoding and cancellation  137  receives Ĥ and {circumflex over (σ)} 2  from channel estimator  135 . Then, using well-established techniques, MMSE filter with successive decoding and cancellation  137  successively decodes each of the constituent substreams and then re-encodes, reconstructs, and cancels its interference contribution in order to facilitate the decoding of the remaining substreams. This process is fully set forth in “Approaching eigenmode BLAST channel capacity using V-BLAST with rate and power feedback”, Vehicular Technology Conference (VTC&#39;01 Fall), Atlantic City, N.J., October 2001 by S. T. Chung, A. Lozano and H. C. Huang, which is incorporated by reference as if fully set forth herein. The order with which the substreams are decoded is arbitrary, but known to the transmitter and, more specifically, to the rate controller  119  therein. Such order may be set by the implementor. 
   The decoded substreams are supplied by the MMSE filter with successive decoding and cancellation to multiplexer (mux)  139 , which multiplexes them as in the original data stream. 
   Note that receiver  103  does not explicitly show a decoder and a deinterleaver, which are necessary so as to reverse the complementary functions performed in the transmitter, because these functions are part of the MMSE filter with successive decoding and cancellation. More specifically, each of the constituent substreams is therein deinterleaved, by a corresponding deinterleaver, and then decoded by a corresponding decoder. The output of each decoder is supplied to multiplexer  139  and also re-encoded and used within MMSE filter with successive decoding and cancellation  137  for interference cancellation. 
   It was shown by S. T. Chung, A. Lozano and H. C. Huang in “Approaching eigenmode BLAST channel capacity using V-BLAST with rate and power feedback”, Vehicular Technology Conference (VTC&#39;01 Fall), Atlantic City, N.J., October 2001, that the transmitter and receiver architectures described therein can approach the capacity of the channel if the rate of each transmit antenna is optimally adjusted. Such optimality, however, comes typically at the expense of requiring short-term feedback. Furthermore, this optimality is maintained regardless of the particular decoding order employed. However, it should be noted that although the rate of each individual antenna depends on the decoding order, the aggregate rate does not. Thus, regardless of the decoding order employed, the same aggregate rate is attained. Hence, it may be taken, without loss of generality, that the antennas are decoded in accordance with their index n. 
   It has been shown in U.S. patent application Ser. No. 09/714,084 that the optimal rate for antenna n is given by 
   
     
       
         
           
             
               
                 
                   R 
                   n 
                 
                 = 
                 
                   
                     log 
                     2 
                   
                   ( 
                   
                     1 
                     + 
                     
                       
                         
                           
                             h 
                             n 
                             H 
                           
                           ( 
                           
                             
                               
                                 H 
                                 n 
                               
                               ⁢ 
                               
                                 H 
                                 n 
                                 H 
                               
                             
                             + 
                             
                               
                                 
                                   N 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     σ 
                                     2 
                                   
                                 
                                 P 
                               
                               ⁢ 
                               I 
                             
                           
                           ) 
                         
                         
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         h 
                         n 
                       
                     
                   
                   ) 
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
   where 
   h n =[h I,n  . . . h M,n ] T  is the complex M-dimensional channel vector for transmit antenna n, with h m,n  being the channel transfer coefficient between transmit antenna n and receive antenna m; 
   X T  indicates the matrix transpose operation for matrix X; 
   H n =[h n+1  h n+2  . . . h N ], an M-by-(N-n) matrix; 
   P represents the total radiated power; 
   X H  indicates the Hermitian transpose operation for matrix X; 
   I the M-by-M identity matrix; and 
   σ 2  is the noise variance. 
   These optimal rates are fed back on a short-term basis to the transmitter in U.S. patent application Ser. No. 09/714,084. Eq. (1) can be rewritten as 
                   R   n     =         log   2     ⁡     (     I   +       P     N   ⁢           ⁢     σ   2         ⁢     H     n   -   1       ⁢     H     n   -   1     H         )       -       log   2     ⁡     (     I   +       P     N   ⁢           ⁢     σ   2         ⁢     H   n     ⁢     H   n   H         )                 (   2   )               
which indicates that the rate supported by the n-th transmit antenna is given by the difference between the aggregate rate of transmit antennas n to N and the aggregate rate of transmit antennas n+1 to N.
 
   As the number of antennas increases, the capacity hardens, i.e., its short-term randomness vanishes. This can be seen from the matrix analysis taught by S. Verdu and S. Shamai, in “Spectral efficiency of CDMA with random spreading”, IEEE Transactions on Information Theory, Vol. 45, March 1999, pp. 622–640, which is incorporated by reference as if fully set forth herein. Mathematically, this hardening process stems from the so-called “almost-sure” convergence of the singular values of H=[h 1  h 2  . . . h N ]. Defining the ratio of transmit and receive antennas as 
           β   =     N   M           
and the capacity per receive antenna as
 
           ??   =     C   M           
with C being the total capacity, then, as the number of antennas, i.e., either M, N or both M and N, is driven to infinity, C converges to a function that is deterministic in the short-term, that is, the function depends only on long-term parameters such as the signal-to-noise ratio and fixed parameters such as β, i.e.,
 C→f(β,long-term parameters) 
Furthermore, in accordance with an aspect of the invention, we have recognized that although such a function is actually asymptotic, it yields an extremely accurate approximation of the short-term average capacity even when the number of antennas is finite, and even a small finite number, e.g., 4 antennas.
 
   Defining a normalized version of the decoding index, which is the index of the transmit antennas divided by the total number of receive antennas, i.e., 
           b   =     n   M           
then, as the number of antennas is driven to infinity, b becomes a continuous function between 0 and β and the difference in Eq. (2) converges in the limit to a derivative. The set of optimal rates, i.e., as computed from Eq. (1), becomes, in the limit, i.e., as the number of antennas becomes infinite, a continuous rate distribution function. This continuous rate distribution function can be expressed as
 
                   R   ⁡     (   b   )       =         ⅆ     ⅆ   x       ⁢     ??   ⁡     (     x   ,     long   ⁢     -     ⁢   term   ⁢           ⁢   parameters       )         ⁢     ❘     x   =     β   -   b                   (   3   )               
which, again, yields an extremely accurate approximation of the short-term average of the rates given by Eq. (1). Note that the capacity per receive antenna C is the integral of the rates R(b) as b goes from 0 to β.
 
   Thus, the set of rates to be employed is given by the derivative of the asymptotic capacity. Therefore, in accordance with the principles of the invention, rate controller  119  adjusts the rates of the various transmit antennas according to Eq. (3), the computation of which requires the use of only long-term parameters. Advantageously, having rate controller  119  use such a rate distribution yields quasi-optimal performance, without requiring any short-term feedback, so long as the number of antennas and/or the diversity order is sufficiently large. 
   Further note that the capacity that is available depends on the type of noise present on the channel. Thus, for example, in the presence of additive white Gaussian noise (AWGN), which is the most common type of noise, the asymptotic capacity per receive antenna is given by 
   
     
       
         
           
             
               
                 
                   
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                         β 
                         , 
                         SNR 
                       
                       ) 
                     
                   
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                       ⁡ 
                       
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                           1 
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                           - 
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                       ⁢ 
                       
                         
                           log 
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                         ⁡ 
                         
                           ( 
                           
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                       ⁢ 
                       
                         
                           
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                           ⁢ 
                           e 
                         
                         SNR 
                       
                       ⁢ 
                       ℱ 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 where 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ℱ 
                   = 
                   
                     
                       1 
                       4 
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             
                               1 
                               + 
                               
                                 
                                   SNR 
                                   β 
                                 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       
                                         β 
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                           
                           - 
                           
                             
                               1 
                               + 
                               
                                 
                                   SNR 
                                   β 
                                 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
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                                   2 
                                 
                               
                             
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   SNR is the long-term average signal-to-noise ratio per receive antenna (SNR) given by 
             SNR   =       P   ·   g       σ   2         ,         
where P is the total transmit power and g is the variance of the entries of H. Note that the SNR may be obtained by determining it either at the transmitter itself, e.g., employing the SNR of the reverse channel, or by having it periodically fed back from the receiver, at which it is determined. Note that feeding back of the SNR from the receiver is not shown in  FIG. 1  to avoid confusion with prior art feed back arrangements which had to feed back short term parameters quite frequently. By contrast, the SNR is a long term parameter that would need to be fed back relatively infrequently.
 
Thus, for AWGN, in accordance with an aspect of the invention, the asymptotic capacity is solely a function of the SNR and β, and the derivative of the asymptotic capacity, Eq. (4) can be calculated to yield
 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         R 
                         ⁡ 
                         
                           ( 
                           b 
                           ) 
                         
                       
                       = 
                         
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                         ( 
                         
                           1 
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                             SNR 
                             β 
                           
                           - 
                           
                             
                               1 
                               4 
                             
                             [ 
                             
                               
                                 
                                   1 
                                   + 
                                   
                                     
                                       SNR 
                                       β 
                                     
                                     ⁢ 
                                     
                                       
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                                           1 
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                                   ⁢ 
                                   
                                     
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                 ( 
                 5 
                 ) 
               
             
           
         
       
     
   
     FIG. 2 , shows an exemplary distribution, for an architecture with β=1 and with the long-term SNR parameter set to 10 dB for the distribution given in Eq. (5). Overlaid on curve  201  corresponding to Eq. (5), which is for an infinite number of antennas, are dots  203  that indicate the short-term average of the optimal rates in Eq. (1) for the case of 4 transmit and 4 receive antennas at the same long-term SNR. The dots have been positioned on the b axis to be in the middle of the steps when the entire range from 0 to β is divided by the number of transmit antennas N, i.e., the dot for each antenna n is located at 
               n   -   0.5     M     .         
In  FIG. 2 , because the short-term average is employed, it is as if there is diversity order of infinity.
 
   Note that wherever a signal that originates at a receive antenna is referred to, in systems without antennas a receive branch may be referred to. Similarly, the number of antennas may be substituted by the number of receive branches.