Abstract:
In a MIMO system the signals transmitted from the various antennas are processed so as to improve the ability of the receiver to extract them from the received signal even in the face of some correlation. More specifically the number of bit streams that is transmitted simultaneously is adjusted, e.g., reduced, depending on the level of correlation, while multiple versions of each bit stream, variously weighted, are transmitted simultaneously. The variously weighted versions are combined to produced one combined weighted signal. The receiver processes the received signals in the same manner as it would have had all the signals reaching the receive antennas been uncorrelated. The weight vectors may be determined by the forward channel transmitter using the channel properties of the forward link which are made known to the transmitter of the forward link by being transmitted from the receiver of the forward link by the transmitter of the reverse link or the weight vectors may be determined by the forward channel transmitter using the channel properties of the forward link and the determined weight vectors are made known to the transmitter of the forward link by being transmitted from the receiver of the forward link by the transmitter of the reverse link. The channel properties used to determine the weight vectors may include the channel response from the transmitter to the receiver and the covariance matrix of noise and interference measured at the receiver.

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 receivers, so called multiple-input, multiple-output (MIMO) systems. 
   BACKGROUND OF THE INVENTION 
   It is well 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. However, to achieve this improvement, it is preferable that there be a rich scattering environments, so that the various signals reaching the multiple receive antennas be largely uncorrelated. If the signals have some degree of correlation, and such correlation is ignored, performance degrades and capacity is reduced. 
   SUMMARY OF THE INVENTION 
   We have invented a way of developing signals in a MIMO system such that even in the face of some correlation so as to obtain the most performance and capacity that can be achieved with a channel of that level of correlation. In accordance with the principles of the invention, the signals transmitted from the various antennas are processed so as to improve the ability of the receiver to extract them from the received signal. More specifically the number of bit streams that is transmitted simultaneously is adjusted, e.g., reduced, depending on the level of correlation, while multiple versions of each bit stream, variously weighted, are transmitted simultaneously. The variously weighted versions are combined to produced one combined weighted signal, a so-called “transmit vector”, for each antenna. The receiver processes the received signals in the same manner as it would have had all the signals reaching the receive antennas been uncorrelated. 
   In one embodiment of the invention, the weight vectors are determined by the forward channel transmitter using the channel properties of the forward link which are made known to the transmitter of the forward link by being transmitted from the receiver of the forward link by the transmitter of the reverse link. In another embodiment of the invention the weight vectors are determined by the forward channel receiver using the channel properties of the forward link and the determined weight vectors are made known to the transmitter of the forward link by being transmitted from the receiver of the forward link by the transmitter of the reverse link. 
   The channel properties used to determine the weight vectors may include the channel response from the transmitter to the receiver and the covariance matrix of noise and interference measured at the receiver. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
     In the drawing: 
       FIG. 1  shows an exemplary portion of a transmitter for developing signals to transmit in a MIMO system such that even in the face of some correlation the most performance and capacity that can be achieved with a channel of that level of correlation is obtained, in accordance with the principles of the invention; 
       FIG. 2  shows an exemplary portion of a receiver for a MIMO system arranged in accordance with the principles of the invention; and 
       FIG. 3  shows an exemplary process, in flow chart form, for developing signals to transmit in a MIMO system such that even in the face of some correlation the most performance and capacity that can be achieved with a channel of that level of correlation is obtained, in accordance with the principles of the invention; 
       FIG. 4  shows another exemplary process, in flow chart form, for developing signals to transmit in a MIMO system such that even in the face of some correlation the most performance and capacity that can be achieved with a channel of that level of correlation is obtained, in accordance with the principles 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 portion of a transmitter for developing signals to transmit in a MIMO system having a transmitter with N transmit antennas transmitting over a forward channel to a receiver having L receiver antennas and a reverse channel for communicating from said receiver to said transmitter, such that even in the face of some correlation the most performance and capacity that can be achieved with a channel of that level of correlation is obtained, in accordance with the principles of the invention. Shown in  FIG. 1  are a) demultiplexer (demux)  101 ; b) antenna signal developers  103 , including antenna signal developers  103 - 1  through  103 -N; c) weight supplier  105 ; d) N antennas  107 , including antennas  107 - 1  through  107 -N; e) digital-to-analog converters (DAC)  115 , including  115 - 1  through  115 -N; and f) upconverters  117 , including upconverters  117 - 1  through  117 -N. 
   Demultiplexer  101  takes a data stream as an input and supplies as an output data substreams by supplying various bits from the input data stream to each of the data substreams. One data substream may be supplied by demultiplexer  101  to one of N outputs. However, when the number of uncorrelated signals that can be transmitted is reduced, the number of bit streams that are transmitted simultaneously is reduced to match the number of uncorrelated signals that can be transmitted. In such a case, the particular outputs utilized is at the discretion of the implementor. For example, only the first Y outputs, where Y is the number of uncorrelated signals that can be transmitted, are employed. 
   Each data substream is supplied to a corresponding one of antenna signal developers  103 . Each one of antenna signal developers  103  includes one of weight blocks  109 - 1  through  109 -N and one of adders  111 - 1  through  111 -N. Within each of antenna signal developers  103  the data substream is supplied to each of multipliers  113  within the one of weight blocks  109  therein. 
   Weight supplier  105  supplies weight values to each of multipliers  113 . In one embodiment of the invention weight supplier  105  actually develops the weight values in response to information received via the reverse channel from the receiver (not shown). In another embodiment of the invention the weight values are developed in the receiver, then supplied via the reverse channel to the transmitter, in which they are stored in weight supplier  105  until such time as they are required. A process for developing the weights in accordance with an aspect of the invention will be described hereinbelow. 
   Each of multipliers  113  multiplies the substream it receives by the weight it receives. The resulting product is supplied to a respective one of adders  111 . More specifically, the product supplied by the Rth multiplier of each weight block  109 , where R is from 1 to N, is supplied to the Rth one of adders  111 . For those multipliers that are not supplied with a substream, their output is insured to be zero (0), by any technique desired by the implementor. 
   Each of adders  111  adds the signals input to it and supplies the resulting sum as an output to its associated respective one of DACs  115 . Each of DACs  115  takes the digital signal it receives from one of adders  111  and converts it to an analog baseband signal. The analog baseband signal produced by each of DACs  115  is supplied to a respective one of upconverters  117 , which upconverts the baseband analog signal to a radio frequency signal. The radio frequency signals produced by upconverters  117  are supplied to respective ones of antennas  107  for broadcast to a receiver. 
     FIG. 2  shows an exemplary portion of a receiver for a MIMO system arranged in accordance with the principles of the invention.  FIG. 2  shows a) L antennas  201 , including antennas  201 - 1  through  201 -L; b) downconverters  203 , including downconverters  203 - 1  through  203 -L; c) analog-to-digital converters (ADCs)  205 , including analog-to-digital converters  205 - 1  through  205 -L; d) estimate interference covariance matrix and channel response unit  207 ; e) optional weight calculator  209 ; and f) optional switch  211 . 
   Each of antennas  201  receives radio signals and supplies an electrical version thereof to its respective, associated one of downconverters  203 . Each of downconverters  203  downconverts the signal it receives to baseband, and supplies the resulting baseband signal to its associated one of ADCs  205 . Each of ADCs  205  converts the baseband analog signal it received to a digital representation and supplies the digital representation to estimate interference covariance matrix and channel response unit  207 . 
   Estimate interference covariance matrix and channel response unit  207  develops an estimate of the interference covariance matrix and an estimate of the forward matrix channel response in the conventional manner. Note that matrices are required because there are multiple transmit antennas and multiple receive antennas. 
   The estimate of the interference covariance matrix and an estimate of the forward matrix channel response are supplied either to optional weight calculator  209  or they are supplied for via the reverse channel to the transmitter (FIG.  1 ). If the estimate of the interference covariance matrix and an estimate of the forward matrix channel response is supplied to weight calculator  209 , weight calculator determines the weight values that are to be used, in accordance with an aspect of the invention and as described hereinbelow, and supplies the resulting weight values to the transmitter ( FIG. 1 ) via the reverse channel. 
     FIG. 3  shows an exemplary process, in flow chart form, for developing signals to transmit in a MIMO system having a transmitter with N transmit antennas transmitting over a forward channel to a receiver having L receiver antennas and a reverse channel for communicating from said receiver to said transmitter, such that even in the face of some correlation the most performance and capacity that can be achieved with a channel of that level of correlation is obtained, in accordance with the principles of the invention. The process of  FIG. 3  may be employed in an embodiment of the invention that uses the hardware of  FIGS. 1 and 2 , with switch  211  being connected to estimate interference covariance matrix and channel response unit  207  and with a communication protocol as follows. First it is necessary to determine the length of time during which the channel characteristics are stable. This is typically performed at the system engineering phase of developing the system, using measurements of the environment into which the system is to be deployed, as is well known by those of ordinary skill in the art. Once the length of time for which the channel characteristics are stable is known, that time is considered as a frame, and the frame is divided into time slots. Each frame has a preamble, which may occupy one or more of the time slots. The frames, and accordingly the time slots, are repeating in nature. 
   The process of  FIG. 3  is entered in step  301  at the beginning of each frame. Next, in step  303 , the interference covariance matrix K N  and channel response  11  at the receiver are determined, e.g., in the receiver of the forward link, such as in interference covariance matrix and channel response unit  207  (FIG.  2 ). Thereafter, in step  305 , ( FIG. 3 ) interference covariance matrix K N  and channel response matrix H are supplied by the receiver of the forward link to the transmitter of forward link, e.g., via the reverse channel. 
   In step  307  weights w i =[w i1 , . . . , w iN ] are calculated, e.g., by weight supplier  105  (FIG.  1 ), where i is an integer ranging from 1 to N. More specifically, the weights are calculated as follows. First the matrix equation H † (K N )H=U † Λ 2 U is solved, where:
         a) H is the channel response matrix;   b) H †  is the conjugate transpose of channel response matrix H, † being the well known symbol for conjugate transpose;   c) K N  is the interference covariance matrix;   d) U is a unitary matrix, each column of which is an eigenvector of H † (K N )H;   e) Λ is a diagonal matrix defined as Λ=diag(λ 1 , . . . , λ M ), where λ 1 , . . . , λ M  are each eignevalues of H † (K N )H, M being the maximum number of nonzero eigenvalues, which corresponds to the number of substreams that actually can be used; and   f) U †  is the conjugate transpose of matrix U.       

   Then well known, so-called “waterfilling” is performed on the eigenvalues λ by solving the simultaneous equations 
             λ   ~     k     =           (     v   -     1       (     λ   k     )     2         )     +     ⁢           ⁢   and   ⁢           ⁢       ∑   k     ⁢           ⁢       λ   ~     k         =   P       ,       
 
for ν, where:
         k is an integer index that ranges from 1 to M;   P is the transmitted power;   + is an operator that returns zero (0) when its argument is negative, and returns the argument itself when it is positive; and   each {tilde over (λ)} is an intermediate variable representative of a power for each weight vector.       

   A new matrix Φ is defined as Φ=U † diag({tilde over (λ)} 1 , . . . , {tilde over (λ)} M )U, where diag indicates that the various {tilde over (λ)} are arranged as the elements of the main diagonal of the matrix, all other entries being zero (0). Each column of matrix Φ is used as a normalized, i.e., based on unit power, weight vector as indicated by Φ=[z 1 , . . . , z N ] and the weight vectors are made up of individual weights z, z i =[z i1 , . . . , z iN ]. The weight vector w i =[w i1 , . . . , w iN ] is then determined by unnormalizing, based on the power to be assigned to the weight vector, the various weights therein, being √{square root over({tilde over (λ)})} i z ij , where j is an integer ranging from 1 to N. 
   In step  309  the input data stream, S(t) (FIG.  1 ), is divided into N substreams S 1  . . . S N , e.g., by demultiplexer  101 . Each of the data streams is then multiplied by a respective one of weight vectors w i1 , . . . , w iN , in step  311  (FIG.  3 ). In other words, each bit of each of each particular data stream is multiplied by each of the weights in its respective weight vector to produce N weighted bits for each data stream. 
   In step  313  the weighted bits for each of the substreams is combined by each antenna adder, e.g., adders  111 . In this regard, the weighted bit produced for each substream from the first weight is added at the adder of the first antenna, the weighted bit produced for each substream from the second weight is added at the adder of the second antenna, and so forth, as indicated in FIG.  1 . As will be readily apparent from the foregoing, any substream greater in number than M will be zero, since M corresponds to the number of substreams that actually can be used. Such zero substreams do not contribute to the sum produced by adders  111 . 
   The process then exits in step  315 . 
     FIG. 4  shows another exemplary process, in flow chart form, for developing signals to transmit in a MIMO system having a transmitter with N transmit antennas transmitting over a forward channel to a receiver having L receiver antennas and a reverse channel for communicating from said receiver to said transmitter, such that even in the face of some correlation the most performance and capacity that can be achieved with a channel of that level of correlation is obtained, in accordance with the principles of the invention. The process of  FIG. 4  may be employed in an embodiment of the invention that uses the hardware of  FIGS. 1 and 2 , with switch  211  being connected to weight calculator  209  and with a communication protocol as described in connection with FIG.  3 . Note that for the process of  FIG. 4 , weight supplier  105  of  FIG. 1  will not compute the various weights, but will instead merely store the weights received from weight calculator  209  and supply them to the various ones of multipliers  113  as is necessary. 
   The process of  FIG. 4  is entered in step  401  at the beginning of each frame. Next, in step  403 , the interference covariance matrix K N  and channel response H at the receiver are determined, e.g., in the receiver of the forward link, such as in interference covariance matrix and channel response unit  207  (FIG.  2 ). In step  405  weights w i =[w i1 , . . . , w iN ] are calculated, e.g., by weight supplier  105  (FIG.  1 ). More specifically, the weights are calculated as follows. 
   First the matrix equation H † (K N )H=U † Λ 2 U is solved, where:
         a) H is the channel response matrix;   b) H †  is the conjugate transpose of channel response matrix H, † being the well known symbol for conjugate transpose;   c) K N  is the interference covariance matrix;   d) U is a unitary matrix, each column of which is an eigenvector of H † (K N )H;   e) Λ is a diagonal matrix defined as Λ=diag(λ 1 , . . . , λ M ), where λ 1 , . . . , λ M  are each eignevalues of H † (K N )H, M being the maximum number of nonzero eigenvalues, which corresponds to the number of substreams that actually can be used; and   f) U †  is the conjugate transpose of matrix U.       

   Then well known, so-called “waterfilling” is performed on the eigenvalues λ by solving the simultaneous equations 
           λ   ~     k     =           (     v   -     1       (     λ   k     )     2         )     +     ⁢           ⁢   and   ⁢           ⁢       ∑   k     ⁢           ⁢       λ   ~     k         =     P   .           
 
for ν, where:
         k is an integer index that ranges from 1 to M;   P is the transmitted power;   + is an operator that returns zero (0) when its argument is negative, and returns the argument itself when it is positive; and   each {tilde over (λ)} is an intermediate variable representative of a power for each weight vector.       

   A new matrix Φ is defined as Φ=U † diag({tilde over (λ)} 1 , . . . , {tilde over (λ)} M )U, where diag indicates that the various {tilde over (λ)} are arranged as the elements of the main diagonal of the matrix, all other entries being zero (0). Each column of matrix Φ is used as a normalized, i.e., based on unit power, weight vector as indicated by Φ=[z 1 , . . . z N ] and the weight vectors are made up of individual weights z, z i =[z i1 , . . . , z iN ]. The weight vector w i =[w i1 , . . . , w iN ] is then determined by unnormalizing, based on the power to be assigned to the weight vector, the various weights therein being √{square root over({tilde over (λ)})} i z ij , where j is an integer ranging from 1 to N. 
   Thereafter, in step  407 , the determined weight values are supplied by the receiver of the forward link to the transmitter of forward link, e.g., via the reverse channel. The weights are stored in weight supplier  105  (FIG.  1 ). 
   In step  409  ( FIG. 4 ) the input data stream. S(t) (FIG.  1 ), is divided into N substreams S 1  . . . S N , e.g., by demultiplexer  101 . Each of the data streams is then multiplied by a respective one of weight vectors w i1 , . . . , w iN , in step  411  (FIG.  4 ), where i is an integer ranging from 1 to N. In other words, each bit of each of each particular data stream is multiplied by each of the weights in its respective weight vector to produce N weighted bits for each data stream. 
   In step  413  the weighted bits for each of the substreams is combined by each antenna adder, e.g., adders  111 . In this regard, the weighted bit produced for each substream from the first weight is added at the adder of the first antenna, the weighted bit produced for each substream from the second weight is added at the adder of the second antenna, and so forth, as indicated in FIG.  1 . As will be readily apparent from the foregoing, any substream greater in number than M will be zero, since M corresponds to the number of substreams that actually can be used. Such zero substreams do not contribute to the sum produced by adders  111 . 
   The process then exits in step  415 . 
   In another embodiment of the invention, for use with so-called “time division duplex” (TDD) systems, which share a single channel for both the forward and reverse channels, the estimation of the channel response may be performed at either end of the wireless link. This is because since the forward and reverse channels share the same frequency channel, alternating between which is using the channel at any one time, then provided the time split between the forward and reverse channel is small, the channel response for the forward and reverse channels will be the same. Therefore, the receiver of the reverse channel will experience the same channel response as the receiver of the forward channel, and so the receiver of the reverse link can perform all the channel estimations that were previously performed by the receiver of the forward link. Likewise, the receiver of the forward channel will experience the same channel response as the receiver of the reverse channel, and so the receiver of the forward link can perform all the channel estimations that were previously performed by the receiver of the reverse link.