# Patent

## Title
Channel estimation and spatial processing for TDD MIMO systems

## Abstract

Channel estimation and spatial processing for a TDD MIMO system. Calibration may be performed to account for differences in the responses of transmit/receive chains at the access point and user terminal. During normal operation, a MIMO pilot is transmitted on a first link and used to derive an estimate of the first link channel response, which is decomposed to obtain a diagonal matrix of singular values and a first unitary matrix containing both left eigenvectors of the first link and right eigenvectors of a second link. A steered reference is transmitted on the second link using the eigenvectors in the first unitary matrix, and is processed to obtain the diagonal matrix and a second unitary matrix containing both left eigenvectors of the second link and right eigenvectors of the first link. Each unitary matrix may be used to perform spatial processing for data transmission/reception via both links.

## Background
CLAIM OF PRIORITY UNDER 35 U.S.C. §119
This application claims the benefit of provisional U.S. Application Ser. No. 60/421,428, entitled “Channel Estimation and Spatial Processing for TDD MIMO Systems,” provisional U.S. Application Ser. No. 60/421,462, entitled “Channel Calibration for a Time Division Duplexed Communication System,” and provisional U.S. Application Ser. No. 60/421,309, entitled “MIMO WLAN System,” all of which are filed on Oct. 25, 2002, assigned to the assignee of the present application, and incorporated herein by reference.


BACKGROUND
1. Field
The present invention relates generally to data communication, and more specifically to techniques to perform channel estimation and spatial processing in time-division duplexed (TDD) multiple-input multiple-output (MIMO) communication systems.
2. Background
A MIMO system employs multiple (NT) transmit antennas and multiple (NR) receive antennas for data transmission. A MIMO channel formed by the NT transmit and NR receive antennas may be decomposed into NS independent channels, with NS≦min{NT, NR}. Each of the NS independent channels is also referred to as a spatial subchannel or an eigenmode of the MIMO channel and corresponds to a dimension. The MIMO system can provide improved performance (e.g., increased transmission capacity) if the additional dimensionalities created by the multiple transmit and receive antennas are utilized.
In order to transmit data on one or more of the NS eigenmodes of the MIMO channel, it is necessary to perform spatial processing at the receiver and typically also at the transmitter. The data streams transmitted from the NT transmit antennas interfere with each other at the receive antennas. The spatial processing attempts to separate out the data streams at the receiver so that they can be individually recovered.
To perform spatial processing, an accurate estimate of the channel response between the transmitter and receiver is typically required. For a TDD system, the downlink (i.e., forward link) and uplink (i.e., reverse link) between an access point and a user terminal both share the same frequency band. In this case, the downlink and uplink channel responses may be assumed to be reciprocal of one another, after calibration has been performed (as described below) to account for differences in the transmit and receive chains at the access point and user terminal. That is, if H represents the channel response matrix from antenna array A to antenna array B, then a reciprocal channel implies that the coupling from array B to array A is given by HT, where MT denotes the transpose of M.
The channel estimation and spatial processing for a MIMO system typically consume a large portion of the system resources. There is therefore a need in the art for techniques to efficiently perform channel estimation and spatial processing in a TDD MIMO system.
SUMMARY
Techniques are provided herein to perform channel estimation and spatial processing in an efficient manner in a TDD MIMO system. For the TDD MIMO system, the reciprocal channel characteristics can be exploited to simplify the channel estimation and spatial processing at both the transmitter and receiver. Initially, an access point and a user terminal in the system may perform calibration to determine differences in the responses of their transmit and receive chains and to obtain correction factors used to account for the differences. Calibration may be performed to ensure that the “calibrated” channel, with the correction factors applied, is reciprocal. In this way, a more accurate estimate of a second link may be obtained based on an estimate derived for a first link.
During normal operation, a MIMO pilot is transmitted (e.g., by the access point) on the first link (e.g., the downlink) and used to derive an estimate of the channel response for the first link. The channel response estimate may then be decomposed (e.g., by the user terminal, using singular value decomposition) to obtain a diagonal matrix of singular values and a first unitary matrix containing both the left eigenvectors of the first link and the right eigenvectors of the second link (e.g., the uplink). The first unitary matrix may thus be used to perform spatial processing for data transmission received on the first link as well as for data transmission to be sent on the second link.
A steered reference may be transmitted on the second link using the eigenvectors in the first unitary matrix. A steered reference (or steered pilot) is a pilot transmitted on specific eigenmodes using the eigenvectors used for data transmission. This steered reference may then be processed (e.g., by the access point) to obtain the diagonal matrix and a second unitary matrix containing both the left eigenvectors of the second link and the right eigenvectors of the first link. The second unitary matrix may thus be used to perform spatial processing for data transmission received on the second link as well as for data transmission to be sent on the first link.
Various aspects and embodiments of the invention are described in further detail below.



BRIEF DESCRIPTION OF THE DRAWINGS
The various aspects and features of the present invention are described below in conjunction with the following drawings, in which:
FIG. 1 is a block diagram of an access point and a user terminal in a TDD MIMO system, in accordance with one embodiment of the invention;
FIG. 2A shows a block diagram of the transmit and receive chains at the access point and user terminal, in accordance with one embodiment of the invention;
FIG. 2B shows application of correction matrices to account for differences in the transmit/receive chains at the access point and user terminal, in accordance with one embodiment of the invention;
FIG. 3 shows the spatial processing for the downlink and uplink for a spatial multiplexing mode, in accordance with one embodiment of the invention;
FIG. 4 shows the spatial processing for the downlink and uplink for a beam-steering mode, in accordance with one embodiment of the invention; and
FIG. 5 shows a process for performing channel estimation and spatial processing at the access point and user terminal, in accordance with one embodiment of the invention.



DETAILED DESCRIPTION
FIG. 1 is a block diagram of an embodiment of an access point 110 and a user terminal 150 in a TDD MIMO system 100. Access point 110 is equipped with Nap transmit/receive antennas for data transmission/reception, and user terminal 150 is equipped with Nut transmit/receive antennas.
On the downlink, at access point 110, a transmit (TX) data processor 114 receives traffic data (i.e., information bits) from a data source 112 and signaling and other data from a controller 130. TX data processor 114 formats, codes, interleaves, and modulates (i.e., symbol maps) the data to provide modulation symbols. A TX spatial processor 120 receives the modulation symbols from TX data processor 114 and performs spatial processing to provide Nap streams of transmit symbols, one stream for each antenna. TX spatial processor 120 also multiplexes in pilot symbols as appropriate (e.g., for calibration and normal operation).
Each modulator (MOD) 122 (which includes a transmit chain) receives and processes a respective transmit symbol stream to provide a corresponding downlink modulated signal. The Nap downlink modulated signals from modulators 122a through 122ap are then transmitted from Nap antennas 124a through 124ap, respectively.
At user terminal 150, Nut antennas 152a through 152ut receive the transmitted downlink modulated signals, and each antenna provides a received signal to a respective demodulator (DEMOD) 154. Each demodulator 154 (which includes a receive chain) performs processing complementary to that performed at modulator 122 and provides received symbols. A receive (RX) spatial processor 160 then performs spatial processing on the received symbols from all demodulators 154a through 154ut to provide recovered symbols, which are estimates of the modulation symbols sent by the access point. An RX data processor 170 further processes (e.g., symbol demaps, deinterleaves, and decodes) the recovered symbols to provide decoded data. The decoded data may include recovered traffic data, signaling, and so on, which may be provided to a data sink 172 for storage and/or a controller 180 for further processing.
The processing for the uplink may be the same or different from the processing for the downlink. Data and signaling are processed (e.g., coded, interleaved, and modulated) by a TX data processor 188 and further spatially processed by a TX spatial processor 190, which also multiplexes in pilot symbols as appropriate (e.g., for calibration and normal operation). The pilot and transmit symbols from TX spatial processor 190 are further processed by modulators 154a through 154ut to generate Nut uplink modulated signals, which are then transmitted via antennas 152a through 152ut to the access point.
At access point 110, the uplink modulated signals are received by antennas 124a through 124ap, demodulated by demodulators 122a through 122ap, and processed by an RX spatial processor 140 and an RX data processor 142 in a complementary manner to that performed at the user terminal. The decoded data for the uplink may be provided to a data sink 144 for storage and/or controller 130 for further processing.
Controllers 130 and 180 control the operation of various processing units at the access point and user terminal, respectively. Memory units 132 and 182 store data and program codes used by controllers 130 and 180, respectively.

1. Calibration
For a TDD system, since the downlink and uplink share the same frequency band, a high degree of correlation normally exists between the downlink and uplink channel responses. Thus, the downlink and uplink channel response matrices may be assumed to be reciprocal (i.e., transpose) of each other. However, the responses of the transmit/receive chains at the access point are typically not equal to the responses of the transmit/receive chains at the user terminal. For improved performance, the differences may be determined and accounted for via calibration.
FIG. 2A shows a block diagram of the transmit and receive chains at access point 110 and user terminal 150, in accordance with one embodiment of the invention. For the downlink, at access point 110, symbols (denoted by a “transmit” vector xdn) are processed by a transmit chain 214 and transmitted from Nap antennas 124 over the MIMO channel. At user terminal 150, the downlink signals are received by Nut antennas 152 and processed by a receive chain 254 to provide received symbols (denoted by a “receive” vector rdn). For the uplink, at user terminal 150, symbols (denoted by a transmit vector xup) are processed by a transmit chain 264 and transmitted from Nut antennas 152 over the MIMO channel. At access point 110, the uplink signals are received by Nap antennas 124 and processed by a receive chain 224 to provide received symbols (denoted by a receive vector rup).
For the downlink, the receive vector rdn at the user terminal (in the absence of noise) may be expressed as:

rdn=RutHTapxdn,  Eq (1)

where xdn is the transmit vector with Nap entries for the downlink;

    
    
        rdn is the receive vector with Nut entries;
        Tap is an Nap×Nap diagonal matrix with entries for the complex gains associated with the transmit chain for the Nap antennas at the access point;
        Rut is an Nut×Nut diagonal matrix with entries for the complex gains associated with the receive chain for the Nut antennas at the user terminal; and
        H is an Nut×Nap channel response matrix for the downlink.

The responses of the transmit/receive chains and the MIMO channel are typically a function of frequency. For simplicity, a flat-fading channel (i.e., with a flat frequency response) is assumed for the following derivation.

    
    


For the uplink, the receive vector rup at the access point (in the absence of noise) may be expressed as:

rup=RapHTTutxup,  Eq (2)

where xup is the transmit vector with Nut entries for the uplink;

    
    
        rup is the receive vector with Nap entries;
        Tut is an Nut×Nut diagonal matrix with entries for the complex gains associated with the transmit chain for the Nut antennas at the user terminal;
        Rap is an Nap×Nap diagonal matrix with entries for the complex gains associated with the receive chain for the Nap antennas at the access point; and
        HT is an Nap×Nut channel response matrix for the uplink.
    
    


From equations (1) and (2), the “effective” downlink and uplink channel responses, Hdn and Hup, which include the responses of the applicable transmit and receive chains, may be expressed as:

Hdn=RutHTap and Hup=RapHTTut.  Eq (3)

As shown in equation (3), if the responses of the transmit/receive chains at the access point are not equal to the responses of the transmit/receive chains at the user terminal, then the effective downlink and uplink channel responses are not reciprocal of one another, i.e., RutHTap≠(RapHTTut)T.

Combining the two equations in equation set (3), the following relationship may be obtained:

H=Rut−1HdnTap−1=(Rap−1HupTut−1)T=Tut−1HupTRap−1.  Eq (4)

Rearranging equation (4), the following is obtained:

Hup=TutRut−1HdnTap−1Rap=Kut−1HdnKap 

or

HupT=(Kut−1HdnKap)T,  Eq (5)

where Kut=Tut−1Rut and Kap=Tap−1Rap. Because Tut, Rut, Tap, and Rap are diagonal matrices, Kap and Kut are also diagonal matrices. Equation (5) may also be expressed as:

HupKut=(HdnKap)T.  Eq (6)

The matrices Kap and Kut may be viewed as including “correction factors” that can account for differences in the transmit/receive chains at the access point and user terminal. This would then allow the channel response for one link to be expressed by the channel response for the other link, as shown in equation (5).
Calibration may be performed to determine the matrices Kap and Kut. Typically, the true channel response H and the transmit/receive chain responses are not known nor can they be exactly or easily ascertained. Instead, the effective downlink and uplink channel responses, Hdn and Hup, may be estimated based on MIMO pilots sent on the downlink and uplink, respectively. The generation and use of MIMO pilot are described in detail in the aforementioned U.S. patent application Ser. No. 60/421,309.
Estimates of the matrices Kap and Kut, which are referred to as correction matrices, {circumflex over (K)}ap and {circumflex over (K)}ut, may be derived based on the downlink and uplink channel response estimates, Ĥdn and Ĥup, in various manners, including by a matrix-ratio computation and a minimum mean square error (MMSE) computation. For the matrix-ratio computation, an (Nut×Nap) matrix C is first computed as a ratio of the uplink and downlink channel response estimates, as follows:




  
    
      
        
          
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        Eq
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where the ratio is taken element-by-element. Each element of C may thus be computed as:





  
    
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    =
    
      
        
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  ,




where ĥup i,j and ĥdn i,j are the (i,j)-th (row, column) element of ĤupT and Ĥdn, respectively, and ci,j is the (i,j)-th element of C.

A correction vector for the access point, {circumflex over (k)}ap, which includes only the Nap diagonal elements of {circumflex over (K)}ap, may be defined to be equal to the mean of the normalized rows of C. Each row of C, ci, is first normalized by dividing each element of the row with the first element of the row to obtain a corresponding normalized row, {tilde over (c)}i. Thus, if ci(k)=[ci,1 . . . ci,Nap] is the i-th row of C, then the normalized row {tilde over (c)}i may be expressed as:

{tilde over (c)}i(k)=[ci,1(k)/ci,1(k) . . . ci,j(k)/ci,1(k) . . . ci,Nap(k)/ci,1(k)].

The correction vector {circumflex over (k)}ap(k) is then set equal to the mean of the Nut normalized rows of C and may be expressed as:





  
    
      
        
          
            
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Because of the normalization, the first element of {circumflex over (k)}ap(k) is unity.

A correction vector {circumflex over (k)}ut(k) for the user terminal, {circumflex over (k)}ut(k), which includes only the Nut diagonal elements of {circumflex over (K)}ut(k), may be defined to be equal to the mean of the inverses of the normalized columns of C. Each column of C, cj, is first normalized by scaling each element in the column with the j-th element of the vector {circumflex over (k)}ap, which is denoted as Kapj,j to obtain a corresponding normalized column, {hacek over (c)}j. Thus, if cj(k)=[c1,j . . . cNut,j]T is the j-th column of C, then the normalized column {hacek over (c)}j may be expressed as:

{hacek over (c)}j=[c1,j/Kap,j,j . . . ci,j/Kap,j,j . . . cNut,j/K ap,j,j]T.

The correction vector {circumflex over (k)}ap is then set equal to the mean of the inverses of the Nap normalized columns of C and may be expressed as:





  
    
      
        
          
            
              
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where the inversion of the normalized columns, {hacek over (c)}j(k), is performed element-wise. The calibration provides the correction vectors, {circumflex over (k)}ap and {circumflex over (k)}ut, or the corresponding correction matrices {circumflex over (K)}ap and {circumflex over (K)}ut, for the access point and user terminal, respectively.

The MMSE computation for the correction matrices {circumflex over (K)}ap and {circumflex over (K)}ut is described in detail in aforementioned U.S. patent application Ser. No. 60/421,462.
FIG. 2B illustrates the application of the correction matrices to account for differences in the transmit/receive chains at the access point and user terminal, in accordance with one embodiment of the invention. On the downlink, the transmit vector xdn is first multiplied with the matrix {circumflex over (K)}ap by a unit 212. The subsequent processing by transmit chain 214 and receive chain 254 for the downlink is the same as shown in FIG. 2A. Similarly, on the uplink, the transmit vector xup is first multiplied with the matrix {circumflex over (K)}ut by a unit 262. Again, the subsequent processing by transmit chain 264 and receive chain 224 for the uplink is the same as shown in FIG. 2A.
The “calibrated” downlink and uplink channel responses observed by the user terminal and access point, respectively, may be expressed as:

Hcdn=Hdn{circumflex over (K)}ap and Hcup=Hup{circumflex over (K)}ut,  Eq (10)

where HcdnT and Hcup are estimates of the “true” calibrated channel response expressions in equation (6). From equations (6) and (10), it can be seen that Hcup≈HcdnT. The accuracy of the relationship Hcup≈HcdnT is dependent on the accuracy of the estimates {circumflex over (K)}ap and {circumflex over (K)}ut, which in turn is dependent on the quality of the downlink and uplink channel response estimates, Ĥdn and Ĥup. As shown above, once the transmit/receive chains have been calibrated, a calibrated channel response estimate obtained for one link (e.g., Ĥcdn) may be used as an estimate of the calibrated channel response for the other link (e.g., Ĥcup)

The calibration for TDD MIMO systems is described in detail in the aforementioned U.S. patent application Ser. No. 60/421,309 and U.S. patent application Ser. No. 60/421,462.
2. Spatial Processing
For a MIMO system, data may be transmitted on one or more eigenmodes of the MIMO channel. A spatial multiplexing mode may be defined to cover data transmission on multiple eigenmodes, and a beam-steering mode may be defined to cover data transmission on a single eigenmode. Both operating modes require spatial processing at the transmitter and receiver.
The channel estimation and spatial processing techniques described herein may be used for MIMO systems with and without OFDM. OFDM effectively partitions the overall system bandwidth into a number of (NF) orthogonal subbands, which are also referred to as frequency bins or subchannels. With OFDM, each subband is associated with a respective subcarrier upon which data may be modulated. For a MIMO system that utilizes OFDM (i.e., a MIMO-OFDM system), each eigenmode of each subband may be viewed as an independent transmission channel. For clarity, the channel estimation and spatial processing techniques are described below for a TDD MIMO-OFDM system. For this system, each subband of the wireless channel may be assumed to be reciprocal.
The correlation between the downlink and uplink channel responses may be exploited to simplify the channel estimation and spatial processing at the access point and user terminal for a TDD system. This simplification is effective after calibration has been performed to account for differences in the transmit/receive chains. The calibrated channel responses may be expressed as a function of frequency, as follows:

Hcdn(k)=Hdn(k){circumflex over (K)}ap(k), for k∈K, and

Hcup(k)=Hup(k){circumflex over (K)}ut(k)≈(Hdn(k){circumflex over (K)}ap(k))T, for k K,   Eq(11)

where K represents a set of all subbands that may be used for data transmission (i.e., the “data subbands”). The calibration may be performed such that the matrices {circumflex over (K)}ap(k) and {circumflex over (K)}ut(k) are obtained for each of the data subbands. Alternatively, the calibration may be performed for only a subset of all data subbands, in which case the matrices {circumflex over (K)}ap(k) and {circumflex over (K)}ut(k) for the “uncalibrated” subbands may be obtained by interpolating the matrices for the “calibrated” subbands, as described in the aforementioned U.S. patent application Ser. No. 60/421,462.

The channel response matrix H(k) for each subband may be “diagonalized” to obtain the NS eigenmodes for that subband. This may be achieved by performing either singular value decomposition on the channel response matrix H(k) or eigenvalue decomposition on the correlation matrix of H(k), which is R(k)=HH(k)H(k). For clarity, singular value decomposition is used for the following description.
The singular value decomposition of the calibrated uplink channel response matrix, Hcup(k), may be expressed as:

Hcup(k)=Uap(k)Σ(k)VutH(k), for k K,  Eq (12)

where Uap(k) is an (Nap×Nap) unitary matrix of left eigenvectors of Hcup(k);

Σ(k) is an (Nap×Nut) diagonal matrix of singular values of Hcup(k); and
Vut(k) is an (Nut×Nut) unitary matrix of right eigenvectors of Hcup(k).
A unitary matrix is characterized by the property MHM=I, where I is the identity matrix.
Correspondingly, the singular value decomposition of the calibrated downlink channel response matrix, Hcdn(k), may be expressed as:

Hcdn(k)=Vut*(k)Σ(k)UapT(k), for k∈ K,  Eq (13)

where the matrices Vut*(k) and Uap*(k) are unitary matrices of left and right eigenvectors, respectively, of Hcdn(k). As shown in equations (12) and (13) and based on the above description, the matrices of left and right eigenvectors for one link are the complex conjugate of the matrices of right and left eigenvectors, respectively, for the other link. The matrices Vut(k), Vut*(k), VutT(k), and VutH(k) are different forms of the matrix Vut(k), and the matrices Uap(k), Uap*(k), UapT(k), and UapH(k) are also different forms of the matrix Uap(k). For simplicity, reference to the matrices Uap(k) and Vut(k) in the following description may also refer to their various other forms. The matrices Uap(k) and Vut(k) are used by the access point and user terminal, respectively, for spatial processing and are denoted as such by their subscripts. The eigenvectors are also often referred to as “steering” vectors.

Singular value decomposition is described in further detail by Gilbert Strang in a book entitled “Linear Algebra and Its Applications,” Second Edition, Academic Press, 1980.
The user terminal can estimate the calibrated downlink channel response based on a MIMO pilot sent by the access point. The user terminal may then perform singular value decomposition for the calibrated downlink channel response estimate Ĥcdn(k), for k∈ K, to obtain the diagonal matrix {circumflex over (Σ)}(k) and the matrix Vut*(k) of left eigenvectors of Ĥcdn(k). This singular value decomposition may be given as Ĥcdn(k)={circumflex over (V)}ut*(k){circumflex over (Σ)}(k)ÛapT(k), where the hat (“^”) above each matrix indicates that it is an estimate of the actual matrix.
Similarly, the access point can estimate the calibrated uplink channel response based on a MIMO pilot sent by the user terminal. The access point may then perform singular value decomposition for the calibrated uplink channel response estimate Ĥcup(k), for k∈ K, to obtain the diagonal matrix {circumflex over (Σ)}(k) and the matrix Ûap(k) of left eigenvectors of Ĥcup(k). This singular value decomposition may be given as Ĥcup(k)=Ûap(k){circumflex over (Σ)}(k){circumflex over (V)}utH(k).
However, because of the reciprocal channel and the calibration, the singular value decomposition only needs to be performed by either the user terminal or the access point. If performed by the user terminal, then the matrix {circumflex over (V)}ut(k), for k∈ K, are used for spatial processing at the user terminal and the matrix Ûap(k), for k∈ K, may be provided to the access point in either a direct form (i.e., by sending entries of the matrices Ûap(k)) or an indirect form (e.g., via a steered reference, as described below).
The singular values in each matrix {circumflex over (Σ)}(k), for k∈ K, may be ordered such that the first column contains the largest singular value, the second column contains the next largest singular value, and so on (i.e., σ1≧σ2≧ . . . ≧σNS, where σi is the eigenvalue in the i-th column of {circumflex over (Σ)}(k) after the ordering). When the singular values for each matrix {circumflex over (Σ)}(k) are ordered, the eigenvectors (or columns) of the associated unitary matrices {circumflex over (V)}ut(k) and Ûap(k) for that subband are also ordered correspondingly. A “wideband”eigenmode may be defined as the set of same-order eigenmode of all subbands after the ordering (i.e., the m-th wideband eigenmode includes the m-th eigenmode of all subbands). Each wideband eigenmode is associated with a respective set of eigenvectors for all of the subbands. The principle wideband eigenmode is the one associated with the largest singular value in each matrix {circumflex over (Σ)}(k) after the ordering.
A. Uplink Spatial Processing
The spatial processing by the user terminal for an uplink transmission may be expressed as:

xup(k)={circumflex over (K)}ut(k){circumflex over (V)}ut(k)sup(k), for k0 K,  Eq (14)

where xup(k) is the transmit vector for the uplink for the k-th subband; and

    
    
        sup(k) is a “data” vector with up to NS non-zero entries for the modulation symbols to be transmitted on the NS eigenmodes of the k-th subband.
    
    


The received uplink transmission at the access point may be expressed as:




  
    
      
        
          
            
              
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                    k
                    )
                  
                
              
              ⁢
              
                

              
              ⁢
              
                
              
              ≈
              
                
                  
                    
                      
                        
                          H
                          _
                        
                        ^
                      
                      cup
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                  ⁢
                  
                    
                      
                        
                          V
                          _
                        
                        ^
                      
                      ut
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                  ⁢
                  
                    
                      
                        s
                        _
                      
                      up
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                
                +
                
                  
                    
                      n
                      _
                    
                    up
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
              
            
            ⁢
            
              

            
            ⁢
            
              
            
            =
            
              
                
                  
                    
                      
                        
                          U
                          _
                        
                        ^
                      
                      ap
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                  ⁢
                  
                    
                      
                        ∑
                        _
                      
                      ^
                    
                    ⁢
                    
                      
                        (
                        k
                        )
                      
                      ⁢
                      
                        
                          
                            
                              V
                              _
                            
                            ^
                          
                          ut
                          H
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                      ⁢
                      
                        
                          
                            
                              V
                              _
                            
                            ^
                          
                          ut
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                      ⁢
                      
                        
                          
                            s
                            _
                          
                          up
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                    
                  
                
                +
                
                  
                    
                      n
                      _
                    
                    up
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
              
              ⁢
              
                

              
              ⁢
              
                
              
              =
              
                
                  
                    
                      
                        
                          U
                          _
                        
                        ^
                      
                      ap
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                  ⁢
                  
                    
                      
                        ∑
                        _
                      
                      ^
                    
                    ⁢
                    
                      
                        (
                        k
                        )
                      
                      ⁢
                      
                        
                          
                            s
                            _
                          
                          up
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                    
                  
                
                +
                
                  
                    
                      n
                      _
                    
                    up
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
              
            
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          15
          )
        
      
    
  




where rup(k) is the received vector for the uplink for the k-th subband; and

    
    
        nup(k) is additive white Gaussian noise (AWGN) for the k-th subband.

Equation (15) uses the following relationships: Hup(k){circumflex over (K)}up(k)=Hcup(k)≈Ĥcup(k) and Ĥcup(k)=Ûap(k){circumflex over (Σ)}(k){circumflex over (V)}utH(k).

    
    


A weighted matched filter matrix Map(k) for the uplink transmission from the user terminal may be expressed as:

Map(k)={circumflex over (Σ)}−1(k)ÛapH(k), for k∈ K.  Eq (16)

The spatial processing (or matched filtering) at the access point for the received uplink transmission may be expressed as:





  
    
      
        
          
            
              
                
                  s
                  _
                
                ^
              
              up
            
            ⁡
            
              (
              k
              )
            
          
          =
          
            
              
                
                  
                    ∑
                    _
                  
                  ^
                
                
                  -
                  1
                
              
              ⁢
              
                
                  (
                  k
                  )
                
                ⁢
                
                  
                    
                      
                        U
                        _
                      
                      ^
                    
                    ap
                    H
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    
                      r
                      _
                    
                    up
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
              
            
            ⁢
            
              

            
            ⁢
            
              
            
            =
            
              
                
                  
                    ∑
                    _
                  
                  ^
                
                
                  -
                  1
                
              
              ⁢
              
                
                  (
                  k
                  )
                
                ⁢
                
                  
                    
                      
                        U
                        _
                      
                      ^
                    
                    ap
                    H
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  (
                  
                    
                      
                        
                          
                            
                              U
                              _
                            
                            ^
                          
                          ap
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                      ⁢
                      
                        
                          
                            ∑
                            _
                          
                          ^
                        
                        ⁢
                        
                          
                            (
                            k
                            )
                          
                          ⁢
                          
                            
                              
                                s
                                _
                              
                              up
                            
                            ⁡
                            
                              (
                              k
                              )
                            
                          
                        
                      
                    
                    +
                    
                      
                        
                          n
                          _
                        
                        up
                      
                      ⁡
                      
                        (
                        k
                        )
                      
                    
                  
                  )
                
              
            
          
        
        ,
        
          
            for
            ⁢
            
              
            
            ⁢
            k
          
          ∈
          K
        
        ,
        
          
        
        ⁢
        
          

        
        ⁢
        
          
        
        ⁢
        
          =
          
            
              
                
                  s
                  _
                
                up
              
              ⁡
              
                (
                k
                )
              
            
            +
            
              
                
                  
                    n
                    ~
                  
                  _
                
                up
              
              ⁡
              
                (
                k
                )
              
            
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          17
          )
        
      
    
  




where ŝup(k) is an estimate of the data vector sup(k) transmitted by the user terminal on the uplink, and ñup(k) is the post-processed noise.

B. Downlink Spatial Processing
The spatial processing by the access point for a downlink transmission may be expressed as:

xdn(k)={circumflex over (K)}ap(k)Ûap*(k)sdn(k), for k∈ K,  Eq (18)

where xdn(k) is the transmit vector and sdn(k) is the data vector for the downlink.

The received downlink transmission at the user terminal may be expressed as:




  
    
      
        
          
            
              
                
                  
                    r
                    _
                  
                  dn
                
                ⁡
                
                  (
                  k
                  )
                
              
              =
              
                
                  
                    
                      
                        
                          H
                          _
                        
                        dn
                      
                      ⁡
                      
                        (
                        k
                        )
                      
                    
                    ⁢
                    
                      
                        
                          x
                          _
                        
                        dn
                      
                      ⁡
                      
                        (
                        k
                        )
                      
                    
                  
                  +
                  
                    
                      
                        n
                        _
                      
                      dn
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                
                ⁢
                
                  

                
                ⁢
                
                  
                
                =
                
                  
                    
                      
                        
                          
                            
                              H
                              _
                            
                            dn
                          
                          ⁡
                          
                            (
                            k
                            )
                          
                        
                        ⁢
                        
                          
                            
                              
                                K
                                _
                              
                              ^
                            
                            ap
                          
                          ⁡
                          
                            (
                            k
                            )
                          
                        
                        ⁢
                        
                          
                            
                              
                                U
                                _
                              
                              ^
                            
                            ap
                            *
                          
                          ⁡
                          
                            (
                            k
                            )
                          
                        
                        ⁢
                        
                          
                            
                              s
                              _
                            
                            dn
                          
                          ⁡
                          
                            (
                            k
                            )
                          
                        
                      
                      +
                      
                        
                          
                            n
                            _
                          
                          dn
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                    
                    ⁢
                    
                      

                    
                    ⁢
                    
                      
                    
                    ≈
                    
                      
                        
                          
                            
                              
                                H
                                _
                              
                              ^
                            
                            cdn
                          
                          ⁡
                          
                            (
                            k
                            )
                          
                        
                        ⁢
                        
                          
                            
                              
                                U
                                _
                              
                              ^
                            
                            ap
                            *
                          
                          ⁡
                          
                            (
                            k
                            )
                          
                        
                        ⁢
                        
                          
                            
                              s
                              _
                            
                            dn
                          
                          ⁡
                          
                            (
                            k
                            )
                          
                        
                      
                      +
                      
                        
                          
                            n
                            _
                          
                          dn
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                    
                  
                  ⁢
                  
                    

                  
                  ⁢
                  
                    
                  
                  =
                  
                    
                      
                        
                          
                            
                              V
                              _
                            
                            ^
                          
                          ut
                          *
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                      ⁢
                      
                        
                          
                            ∑
                            _
                          
                          ^
                        
                        ⁢
                        
                          
                            (
                            k
                            )
                          
                          ⁢
                          
                            
                              
                                
                                  U
                                  _
                                
                                ^
                              
                              ap
                              T
                            
                            ⁡
                            
                              (
                              k
                              )
                            
                          
                          ⁢
                          
                            
                              
                                
                                  U
                                  _
                                
                                ^
                              
                              ap
                              *
                            
                            ⁡
                            
                              (
                              k
                              )
                            
                          
                          ⁢
                          
                            
                              
                                s
                                _
                              
                              dn
                            
                            ⁡
                            
                              (
                              k
                              )
                            
                          
                        
                      
                    
                    +
                    
                      
                        
                          n
                          _
                        
                        dn
                      
                      ⁡
                      
                        (
                        k
                        )
                      
                    
                  
                
              
            
            )
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            
              
                
                  
                    
                      V
                      _
                    
                    ^
                  
                  ut
                  *
                
                ⁡
                
                  (
                  k
                  )
                
              
              ⁢
              
                
                  
                    ∑
                    _
                  
                  ^
                
                ⁢
                
                  
                    (
                    k
                    )
                  
                  ⁢
                  
                    
                      
                        s
                        _
                      
                      dn
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                
              
            
            +
            
              
                
                  n
                  _
                
                dn
              
              ⁡
              
                (
                k
                )
              
            
          
        
        ,
        
          
            for
            ⁢
            
              
            
            ⁢
            k
          
          ∈
          
            K
            .
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          19
          )
        
      
    
  




A weighted matched filter matrix Mut(k) for the downlink transmission from the access point may be expressed as:

Mut(k)={circumflex over (Σ)}−1(k){circumflex over (V)}utT(k), for k∈ K.  Eq (20)

The spatial processing (or matched filtering) at the user terminal for the received downlink transmission may be expressed as:





  
    
      
        
          
            
              
                
                  s
                  _
                
                ^
              
              dn
            
            ⁡
            
              (
              k
              )
            
          
          =
          
            
              
                
                  
                    ∑
                    _
                  
                  ^
                
                
                  -
                  1
                
              
              ⁢
              
                
                  (
                  k
                  )
                
                ⁢
                
                  
                    
                      
                        V
                        _
                      
                      ^
                    
                    ut
                    T
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    
                      r
                      _
                    
                    dn
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
              
            
            ⁢
            
              

            
            ⁢
            
              
            
            =
            
              
                
                  
                    ∑
                    _
                  
                  ^
                
                
                  -
                  1
                
              
              ⁢
              
                
                  (
                  k
                  )
                
                ⁢
                
                  
                    
                      
                        V
                        _
                      
                      ^
                    
                    ut
                    T
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  (
                  
                    
                      
                        
                          
                            
                              V
                              _
                            
                            ^
                          
                          ut
                          *
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                      ⁢
                      
                        
                          
                            ∑
                            _
                          
                          ^
                        
                        ⁢
                        
                          
                            (
                            k
                            )
                          
                          ⁢
                          
                            
                              
                                s
                                _
                              
                              dn
                            
                            ⁡
                            
                              (
                              k
                              )
                            
                          
                        
                      
                    
                    +
                    
                      
                        
                          n
                          _
                        
                        dn
                      
                      ⁡
                      
                        (
                        k
                        )
                      
                    
                  
                  )
                
              
            
          
        
        ,
        
          
            for
            ⁢
            
              
            
            ⁢
            k
          
          ∈
          K
        
        ,
        
          

        
        ⁢
        
          
        
        ⁢
        
          =
          
            
              
                
                  s
                  _
                
                dn
              
              ⁡
              
                (
                k
                )
              
            
            +
            
              
                
                  
                    n
                    ~
                  
                  _
                
                dn
              
              ⁡
              
                (
                k
                )
              
            
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          21
          )
        
      
    
  




Table 1 summarizes the spatial processing at the access point and user terminal for data transmission and reception.










TABLE 1







Uplink
Downlink


















User
Transmit:
Receive:


Terminal
xup (k) = {circumflex over (K)}ut (k){circumflex over (V)}ut (k)sup (k)
ŝdn (k) = {circumflex over (Σ)}−1 (k){circumflex over (V)}utT (k)rdn (k)


Access
Receive:
Transmit:


Point
ŝup (k) = {circumflex over (Σ)}−1 (k)ÛapH (k)rup (k)
xdn (k) = {circumflex over (K)}ap (k)Ûap* (k)sdn (k)









In the above description and as shown in Table 1, the correction matrices {circumflex over (K)}ap(k) and {circumflex over (K)}ut(k) are applied on the transmit side at the access point and user terminal, respectively. The correction matrices {circumflex over (K)}ap(k) and {circumflex over (K)}ut(k) may also be combined with other diagonal matrices (e.g., such as weight matrices Wdn(k) and Wup(k) used to achieve channel inversion). However, the correction matrices may also be applied on the receive side, instead of the transmit side, and this is within the scope of the invention.
FIG. 3 is a block diagram of the spatial processing for the downlink and uplink for the spatial multiplexing mode, in accordance with one embodiment of the invention.
For the downlink, within a TX spatial processor 120x at access point 110x, the data vector sdn(k), for k∈ K , is first multiplied with the matrix Ûap*(k) by a unit 310 and then further multiplied with the correction matrix {circumflex over (K)}ap(k) by a unit 312 to obtain the transmit vector xdn(k). The vector xdn(k), for k K, is then processed by a transmit chain 314 within modulator 122x and transmitted over the MIMO channel to user terminal 150x. Unit 310 performs the spatial processing for the downlink data transmission.
At user terminal 150x, the downlink signals are processed by a receive chain 354 within demodulator 154x to obtain the receive vector rdn(k), for k∈ K. Within an RX spatial processor 160x, the receive vector rdn(k), for k∈ K , is first multiplied with the matrix {circumflex over (V)}utT(k) by a unit 356 and further scaled by the inverse diagonal matrix {circumflex over (Σ)}−1(k) by a unit 358 to obtain the vector ŝdn(k), which is an estimate of the data vector sdn(k). Units 356 and 358 perform the spatial processing for the downlink matched filtering.
For the uplink, within a TX spatial processor 190x at user terminal 150x, the data vector sup(k), for k∈ K, is first multiplied with the matrix {circumflex over (V)}ut(k) by a unit 360 and then further multiplied with the correction matrix {circumflex over (K)}ut(k) by a unit 362 to obtain the transmit vector xup(k). The vector xup(k), for k∈ K, is then processed by a transmit chain 364 within modulator 154x and transmitted over the MIMO channel to access point 110x. Unit 360 performs the spatial processing for the uplink data transmission.
At access point 110x, the uplink signals are processed by a receive chain 324 within demodulator 122x to obtain the receive vector rup(k), for k∈ K. Within an RX spatial processor 140x, the receive vector rup(k), for k∈ K , is first multiplied with the matrix ÛapH(k) by a unit 326 and further scaled by the inverse diagonal matrix {circumflex over (Σ)}−1(k) by a unit 328 to obtain the vector ŝup(k), which is an estimate of the data vector sup(k). Units 326 and 328 perform the spatial processing for the uplink matched filtering.
3. Beam-Steering
For certain channel conditions, it is better to transmit data on only one wideband eigenmode—typically the best or principal wideband eigenmode. This may be the case if the received signal-to-noise ratios (SNRs) for all other wideband eigenmodes are sufficiently poor so that improved performance is achieved by using all of the available transmit power on the principal wideband eigenmode.
Data transmission on one wideband eigenmode may be achieved using either beam-forming or beam-steering. For beam-forming, the modulation symbols are spatially processed with the eigenvectors {circumflex over (v)}ut,1(k) or ûap,1(k), for k∈ K, for the principal wideband eigenmode (i.e., the first column of {circumflex over (V)}ut(k) or Ûap(k), after the ordering). For beam-steering, the modulation symbols are spatially processed with a set of “normalized” (or “saturated”) eigenvectors {tilde over (v)}ut(k) or ũap(k), for k∈ K, for the principal wideband eigenmode. For clarity, beam-steering is described below for the uplink.
For the uplink, the elements of each eigenvector {circumflex over (v)}ut,1(k), for k∈ K, for the principal wideband eigenmode may have different magnitudes. Thus, the preconditioned symbols for each subband, which are obtained by multiplying the modulation symbol for subband k with the elements of the eigenvector {circumflex over (v)}ut,1(k) for subband k, may then have different magnitudes. Consequently, the per-antenna transmit vectors, each of which includes the preconditioned symbols for all data subbands for a given transmit antenna, may have different magnitudes. If the transmit power for each transmit antenna is limited (e.g., because of limitations of power amplifiers), then beam-forming may not fully use the total power available for each antenna.
Beam-steering uses only the phase information from the eigenvectors {circumflex over (v)}ut,1(k), for k∈ K, for the principal wideband eigenmode and normalizes each eigenvector such that all elements in the eigenvector have equal magnitudes. The normalized eigenvector {tilde over (v)}ut(k) for the k-th subband may be expressed as:

{tilde over (v)}ut(k)=[Aejθ1(k)Aejθ2(k) . . . AejθNut(k)]T,  Eq (22)

where A is a constant (e.g., A=1); and

θi(k) is the phase for the k-th subband of the i-th transmit antenna, which is given as:




  
    
      
        
          
            θ
            i
          
          ⁡
          
            (
            k
            )
          
        
        =
        
          
            ∠
            ⁢
            
              
                
                  v
                  ^
                
                
                  ut
                  ,
                  1
                  ,
                  i
                
              
              ⁡
              
                (
                k
                )
              
            
          
          =
          
            
              
                tan
                
                  -
                  1
                
              
              ⁡
              
                (
                
                  
                    Im
                    ⁢
                    
                      {
                      
                        
                          
                            v
                            ^
                          
                          
                            ut
                            ,
                            1
                            ,
                            i
                          
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                      }
                    
                  
                  
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    e
                    ⁢
                    
                      {
                      
                        
                          
                            v
                            ^
                          
                          
                            ut
                            ,
                            1
                            ,
                            i
                          
                        
                        ⁡
                        
                          (
                          k
                          )
                        
                      
                      }
                    
                  
                
                )
              
            
            .
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          23
          )
        
      
    
  




As shown in equation (23), the phase of each element in the vector {tilde over (v)}ut(k) is obtained from the corresponding element of the eigenvector {circumflex over (v)}ut,1(k) (i.e., θi(k) is obtained from {circumflex over (v)}ut,1,i(k), where {circumflex over (V)}ut,1(k)=[{circumflex over (v)}ut,1,1(k){circumflex over (v)}ut,1,2(k) . . . {circumflex over (v)}ut,1,Nut(k)]T). 

A. Uplink Beam-Steering
The spatial processing by the user terminal for beam-steering on the uplink may be expressed as:

{tilde over (x)}up(k)={circumflex over (K)}ut{tilde over (v)}ut(k)sup(k), for k├K,  Eq (24)

where sup(k) is the modulation symbol to be transmitted on the k-th subband; and {tilde over (x)}up(k) is the transmit vector for the k-th subband for beam-steering.

As shown in equation (22), the Nut elements of the normalized steering vector {tilde over (v)}ut(k) for each subband have equal magnitude but possibly different phases. The beam-steering thus generates one transmit vector {tilde over (x)}up(k) for each subband, with the Nut elements of {tilde over (x)}up(k) having the same magnitude but possibly different phases.
The received uplink transmission at the access point for beam-steering may be expressed as:




  
    
      
        
          
            
              
                
                  r
                  ~
                
                _
              
              up
            
            ⁡
            
              (
              k
              )
            
          
          =
          
            
              
                
                  
                    H
                    _
                  
                  up
                
                ⁡
                
                  (
                  k
                  )
                
              
              ⁢
              
                
                  
                    
                      x
                      ~
                    
                    _
                  
                  up
                
                ⁡
                
                  (
                  k
                  )
                
              
            
            +
            
              
                
                  n
                  _
                
                up
              
              ⁡
              
                (
                k
                )
              
            
          
        
        ,
        
          
            for
            ⁢
            
              
            
            ⁢
            k
          
          ∈
          K
        
        ,
        
          

        
        ⁢
        
          
        
        ⁢
        
          =
          
            
              
                
                  
                    
                      H
                      _
                    
                    up
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    
                      
                        K
                        ^
                      
                      _
                    
                    ut
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    
                      
                        v
                        ~
                      
                      _
                    
                    ut
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    s
                    up
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
              
              +
              
                
                  
                    n
                    _
                  
                  up
                
                ⁡
                
                  (
                  k
                  )
                
              
            
            ⁢
            
              

            
            ⁢
            
              
            
            =
            
              
                
                  
                    
                      H
                      _
                    
                    cup
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    
                      
                        v
                        ~
                      
                      _
                    
                    ut
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    s
                    up
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
              
              +
              
                
                  
                    n
                    _
                  
                  up
                
                ⁡
                
                  (
                  k
                  )
                
              
            
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          25
          )
        
      
    
  




where {tilde over (r)}up(k) is the received vector for the uplink for the k-th subband for beam-steering.

A matched filter row vector {tilde over (m)}ap(k) for the uplink transmission using beam-steering may be expressed as:

{tilde over (m)}ap(k)=(Hcup(k){tilde over (v)}ut(k))H, for k∈0 K.  Eq (26)

The matched filter vector {tilde over (m)}ap(k) may be obtained as described below. The spatial processing (or matched filtering) at the access point for the received uplink transmission with beam-steering may be expressed as:





  
    
      
        
          
            
              
                
                  
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                ⁡
                
                  (
                  k
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              =
              
                
                  
                    
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                ⁢
                
                  
                
                ⁢
                
                  (
                  27
                  )
                
              
            
          
        
        
          
            
              
                =
                
                  
                    
                      
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              ,
              
                
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                  ⁢
                  
                    
                  
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                K
              
              ,
            
          
        
        
          
            
              =
              
                
                  
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                    up
                  
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                    (
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where {tilde over (λ)}up(k)=(Hcup(k){tilde over (v)}ut(k))H(Hcup(k){tilde over (v)}ut(k)) (i.e., {tilde over (λ)}up(k) is the inner product of {tilde over (m)}ap(k) and its conjugate transpose),

    
    
        ŝup(k) is an estimate of the modulation symbol sup(k) transmitted by the user terminal on the uplink, and
        ñup(k) is the post-processed noise.
    
    


B. Downlink Beam-Steering
The spatial processing by the access point for beam-steering on the downlink may be expressed as:

{tilde over (x)}dn(k)={circumflex over (K)}apũap(k)sdn(k), for k├K,  Eq (28)

where ũap(k) is the normalized eigenvector for the k-th subband, which is generated based on the eigenvector ûap,1*(k), for the principal wideband eigenmode, as described above.

A matched filter row vector {tilde over (m)}ut(k) for the downlink transmission using beam-steering may be expressed as:

{tilde over (m)}ut(k)=(Hcdn(k)ũap(k))H, for k├K.  Eq (29)

The spatial processing (or matched filtering) at the user terminal for the received downlink transmission may be expressed as:





  
    
      
        
          
            
              
                
                  
                    s
                    ^
                  
                  dn
                
                ⁡
                
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                  k
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              =
              
                
                  
                    
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                    k
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                        _
                      
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                    dn
                  
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                    (
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                ⁢
                Eq
                ⁢
                
                  
                
                ⁢
                
                  (
                  30
                  )
                
              
            
          
        
        
          
            
              
                =
                
                  
                    
                      
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                          (
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              ,
              
                
                  for
                  ⁢
                  
                    
                  
                  ⁢
                  k
                
                ∈
                K
              
              ,
            
          
        
        
          
            
              =
              
                
                  
                    s
                    dn
                  
                  ⁡
                  
                    (
                    k
                    )
                  
                
                +
                
                  
                    
                      n
                      ~
                    
                    dn
                  
                  ⁡
                  
                    (
                    k
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where {tilde over (λ)}dn(k)=(Hcdn(k)ũap(k))H(Hcdn(k)ũap(k)) (i.e., {tilde over (λ)}dn(k) is the inner product of {tilde over (m)}ut(k) and its conjugate transpose).

Beam-steering may be viewed as a special case of spatial processing in which only one eigenvector for one eigenmode is used for data transmission and this eigenvector is normalized to have equal magnitudes.
FIG. 4 is a block diagram of the spatial processing for the downlink and uplink for the beam-steering mode, in accordance with one embodiment of the invention.
For the downlink, within a TX spatial processor 120y at access point 110y, the modulation symbol sdn(k), for k∈ K, is first multiplied with the normalized eigenvector ũap(k) by a unit 410 and then further multiplied with the correction matrix {circumflex over (K)}ap(k) by a unit 412 to obtain the transmit vector {tilde over (x)}dn(k). The vector {tilde over (x)}dn(k), for k∈ K, is then processed by a transmit chain 414 within modulator 122y and transmitted over the MIMO channel to user terminal 150y. Unit 410 performs spatial processing for the downlink data transmission for the beam-steering mode.
At user terminal 150y, the downlink signals are processed by a receive chain 454 within demodulator 154y to obtain the receive vector {tilde over (r)}dn(k), for k∈ K. Within an RX spatial processor 160y, a unit 456 performs an inner product of the receive vector {tilde over (r)}dn(k), for k∈ K, with the matched filter vector {tilde over (m)}ut(k). The inner product result is then scaled by {tilde over (λ)}dn−1(k) by a unit 458 to obtain the symbol ŝdn(k), which is an estimate of the modulation symbol sdn(k). Units 456 and 458 perform spatial processing for the downlink matched filtering for the beam-steering mode.
For the uplink, within a TX spatial processor 190y at user terminal 150y, the modulation symbol sup(k), for k∈ K, is first multiplied with the normalized eigenvector {tilde over (v)}ut(k) by a unit 460 and then further multiplied with the correction matrix {circumflex over (K)}ut(k) by a unit 462 to obtain the transmit vector {tilde over (x)}up(k). The vector {tilde over (x)}up(k), for k∈ K, is then processed by a transmit chain 464 within modulator 154y and transmitted over the MIMO channel to access point 110y. Unit 460 performs spatial processing for the uplink data transmission for the beam-steering mode.
At access point 110y, the uplink signals are processed by a receive chain 424 within demodulator 124y to obtain the receive vector {tilde over (r)}up(k), for k∈ K. Within an RX spatial processor 140y, a unit 426 performs an inner product of the receive vector {tilde over (r)}up(k), for k∈ K, with the matched filter vector {tilde over (m)}ap(k). The inner product result is then is scaled by {tilde over (λ)}up−1(k) by a unit 428 to obtain the symbol ŝup(k), which is an estimate of the modulation symbol sup(k). Units 426 and 428 perform spatial processing for the uplink matched filtering for the beam-steering mode.
4. Steered Reference
As shown in equation (15), at the access point, the received uplink vector rup(k), for k∈ K, in the absence of noise is equal to the data vector sup(k) transformed by Ûap(k){circumflex over (Σ)}(k), which is the matrix Ûap(k) of left eigenvectors of Ĥcup(k) scaled by the diagonal matrix {circumflex over (Σ)}(k) of singular values. As shown in equations (17) and (18), because of the reciprocal channel and the calibration, the matrix Ûap*(k) and its transpose are used for spatial processing of the downlink transmission and spatial processing (matched filtering) of the received uplink transmission, respectively.
A steered reference (or steered pilot) may be transmitted by the user terminal and used by the access point to obtain estimates of both Ûap(k) and {circumflex over (Σ)}(k), for k∈ K, without having to estimate the MIMO channel or perform the singular value decomposition. Similarly, a steered reference may be transmitted by the access point and used by the user terminal to obtain estimates of both {circumflex over (V)}ut(k) and {circumflex over (Σ)}(k).
A steered reference comprises a specific OFDM symbol (which is referred to as a pilot or “P” OFDM symbol) that is transmitted from all of the Nut antennas at the user terminal (for the uplink) or the Nap antennas at the access point (for the downlink). The P OFDM symbol is transmitted on only one wideband eigenmode by performing spatial processing with the set of eigenvectors for that wideband eigenmode.
A. Uplink Steered Reference
An uplink steered reference transmitted by the user terminal may be expressed as:

xup,m(k)={circumflex over (K)}ut(k){circumflex over (v)}ut,m(k)p(k), for k∈ K,   Eq (31)

where xup,m(k) is the transmit vector for the k-th subband of the m-th wideband eigenmode;

    
    
        {circumflex over (v)}ut,m(k) is the eigenvector for the k-th subband of the m-th wideband eigenmode; and
        p(k) is a pilot modulation symbol to be transmitted on the k-th subband.

The eigenvector {circumflex over (v)}ut,m(k) is the m-th column of the matrix {circumflex over (V)}ut(k), where {circumflex over (V)}ut(k)=[{circumflex over (v)}ut,1(k){circumflex over (v)}ut,2(k) . . . {circumflex over (v)}ut,Nut(k)].

    
    


The received uplink steered reference at the access point may be expressed as:




  
    
      
        
          
            
              
                
                  
                    
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                        (
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                        m
                      
                      ⁡
                      
                        (
                        k
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                    ⁢
                    
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                        (
                        k
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                  +
                  
                    
                      
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                      (
                      k
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        ,
        
          
            for
            ⁢
            
              
            
            ⁢
            k
          
          ∈
          
            K
            .
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          32
          )
        
      
    
  




where rup,m(k) is the received vector for the uplink steered reference for the k-th subband of the m-th wideband eigenmode; and

    
    
        σm(k) is the singular value for the k-th subband of the m-th wideband eigenmode.
    
    


Techniques to estimate the channel response based on the steered reference are described in further detail below.
B. Downlink Steered Reference
A downlink steered reference transmitted by the access point may be expressed as:

xdn,m(k)={circumflex over (K)}ap(k)ûap,m*(k)p(k), for k∈ K,   Eq (33)

    
    
        where xdn,m(k) is the transmit vector for the k-th subband of the m-th wideband eigenmode; and
        ûap,m*(k) is the eigenvector for the k-th subband of the m-th wideband eigenmode.

The steering vector ûap,m*(k) is the m-th column of the matrix Ûap*(k), where Ûap*(k)=[ûap,1*(k)ûap,2*(k) . . . ûap,Nap*(k)].

    
    


The downlink steered reference may be used by the user terminal for various purposes. For example, the downlink steered reference allows the user terminal to determine what kind of estimate the access point has for the MIMO channel (since the access point has an estimate of an estimate of the channel). The downlink steered reference may also be used by the user terminal to estimate the received SNR of downlink transmission.
C. Steered Reference for Beam-Steering
For the beam-steering mode, the spatial processing on the transmit side is performed using a set of normalized eigenvectors for the principal wideband eigenmode. The overall transfer function with a normalized eigenvector is different from the overall transfer function with an unnormalized eigenvector (i.e., Hcup(k){circumflex over (v)}ut,1(k)≠Hcup(k){tilde over (v)}ut(k)). A steered reference generated using the set of normalized eigenvectors for all subbands may then be sent by the transmitter and used by the receiver to derive the matched filter vectors for these subbands for the beam-steering mode.
For the uplink, the steered reference for the beam-steering mode may be expressed as:

{tilde over (x)}up,sr(k)={circumflex over (K)}ut(k){tilde over (v)}ut(k)p(k), for k∈ K.   Eq (34)

At the access point, the receive uplink steered reference for the beam-steering mode may be expressed as:





  
    
      
        
          
            
              
                
                  
                    
                      
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                        ~
                      
                      _
                    
                    
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                      .
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                =
                
                  
                    
                      
                        
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                          _
                        
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                        (
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                  +
                  
                    
                      
                        n
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                      k
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                  +
                  
                    
                      
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                      up
                    
                    ⁡
                    
                      (
                      k
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                =
                
                  
                    
                      
                        
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                          _
                        
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                        (
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                          _
                        
                        ut
                      
                      ⁡
                      
                        (
                        k
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                      ⁡
                      
                        (
                        k
                        )
                      
                    
                  
                  +
                  
                    
                      
                        n
                        _
                      
                      up
                    
                    ⁡
                    
                      (
                      k
                      )
                    
                  
                
              
            
          
        
        ,
        
          
            for
            ⁢
            
              
            
            ⁢
            k
          
          ∈
          
            K
            .
          
        
      
    
    
      
        Eq
        ⁢
        
          
        
        ⁢
        
          (
          35
          )
        
      
    
  




To obtain the matched filter row vector {tilde over (m)}ap(k) for the uplink transmission with beam-steering, the received vector {tilde over (r)}up,sr(k) for the steered reference is first multiplied with p*(k). The result is then integrated over multiple received steered reference symbols to form an estimate of Hcup(k){tilde over (v)}cup(k). The vector {tilde over (m)}ap(k) is then the conjugate transpose of this estimate.
While operating in the beam-steering mode, the user terminal may transmit multiple symbols of steered reference, for example, one or more symbols using the normalized eigenvector {tilde over (v)}ut(k), one or more symbols using the eigenvector {circumflex over (v)}ut,1(k) for the principal eigenmode, and possibly one or more symbols using the eigenvectors for the other eigenmodes. The steered reference symbols generated with {tilde over (v)}ut(k) may be used by the access point to derive the matched filter vector {tilde over (m)}ap(k). The steered reference symbols generated with {circumflex over (v)}ut,1(k) may be used to obtain ûap,1(k), which may then be used to derive the normalized eigenvector ũap(k) used for beam-steering on the downlink. The steered reference symbols generated with the eigenvectors {circumflex over (v)}ut,2(k) through {circumflex over (v)}ut,NS(k) for the other eigenmodes may be used by the access point to obtain ûap,2(k) through ûap,NS(k) and the singular values for these other eigenmodes. This information may then be used by the access point to determine whether to use the spatial multiplexing mode or the beam-steering mode for data transmission.
For the downlink, the user terminal may derive the matched filter vector {tilde over (m)}ut(k) for the beam-steering mode based on the calibrated downlink channel response estimate Ĥcdn(k). In particular, the user terminal has ûap,1(k) from the singular value decomposition of Ĥcdn(k) and can derive the normalized eigenvector ũap(k). The user terminal can then multiply ũap(k) with Ĥcdn(k) to obtain Ĥcdn(k)ũap(k), and may then derive {tilde over (m)}ut(k) based on Ĥcdn(k)ũap(k). Alternatively, a steered reference may be sent by the access point using the normalized eigenvector ũap(k), and this steered reference may be processed by the user terminal in the manner described above to obtain {tilde over (m)}ut(k).
D. Channel Estimation Based on Steered Reference
As shown in equation (32), at the access point, the received uplink steered reference (in the absence of noise) is approximately ûap,m(k)σm(k)p(k). The access point can thus obtain an estimate of the uplink channel response based on the steered reference sent by the user terminal. Various estimation techniques may be used to obtain the channel response estimate.
In one embodiment, to obtain an estimate of ûap,m(k), the received vector rup,m(k) for the steered reference for the m-th wideband eigenmode is first multiplied with the complex conjugate of the pilot modulation symbol, p*(k), used for the steered reference. The result is then integrated over multiple received steered reference symbols for each wideband eigenmode to obtain an estimate of Ûap,m(k)σm(k), which is a scaled left eigenvector of Ĥcup(k) for the m-th wideband eigenmode. Each of the Nap entries of ûap,m(k) is obtained based on a corresponding one of the Nap entries for rup,m(k), where the Nap entries of rup,m(k) are the received symbols obtained from the Nap antennas at the access point. Since eigenvectors have unit power, the singular value σm(k) may be estimated based on the received power of the steered reference, which can be measured for each subband of each wideband eigenmode.
In another embodiment, a minimum mean square error (MMSE) technique is used to obtain an estimate of ûap,m(k) based on the received vector rup,m(k) for the steered reference. Since the pilot modulation symbols p(k) are known, the access point can derive the estimate of ûap,m(k) such that the mean square error between the received pilot symbols (obtained after performing the matched filtering on the received vector rup,m(k)) and the transmitted pilot symbols is minimized. The use of the MMSE technique for spatial processing at the receiver is described in detail in commonly assigned U.S. patent application Ser. No. 09/993,087, entitled “Multiple-Access Multiple-Input Multiple-Output (MIMO) Communication System,” filed Nov. 6, 2001.
The steered reference is sent for one wideband eigenmode in any given symbol period, and may in turn be used to obtain an estimate of one eigenvector for each subband of that wideband eigenmode. Thus, the receiver is able to obtain an estimate of one eigenvector in a unitary matrix for any given symbol period. Since estimates of multiple eigenvectors for the unitary matrix are obtained over different symbol periods, and due to noise and other sources of degradation in the transmission path, the estimated eigenvectors for the unitary matrix are not likely be orthogonal. If the estimated eigenvectors are thereafter used for spatial processing of data transmission on the other link, then any errors in orthogonality in these estimated eigenvectors would result in cross-talk among the eigenmodes, which may degrade performance.
In an embodiment, the estimated eigenvectors for each unitary matrix are forced to be orthogonal to each other. The orthogonalization of the eigenvectors may be achieved using the Gram-Schmidt technique, which is described in detail in the aforementioned reference from Gilbert Strang, or some other technique.
Other techniques to estimate the channel response based on the steered reference may also be used, and this is within the scope of the invention.
The access point can thus estimate both Ûap(k) and {circumflex over (Σ)}(k) based on the steered reference sent by the user terminal, without having to estimate the uplink channel response or perform singular value decomposition on Ĥcup(k). Since only Nut wideband eigenmodes have any power, the matrix Ûap(k) of left eigenvectors of Ĥcup(k) is effectively (Nap×Nut), and the matrix {circumflex over (Σ)}(k) may be considered to be (Nut×Nut).
The processing at the user terminal to estimate the matrices {circumflex over (V)}ut(k) and {circumflex over (Σ)}(k), for k∈ K, based on the downlink steered reference may be performed similar to that described above for the uplink steered reference.
5. Channel Estimation and Spatial Processing
FIG. 5 is a flow diagram of a specific embodiment of a process 500 for performing channel estimation and spatial processing at the access point and user terminal, in accordance with one embodiment of the invention. Process 500 includes two parts—calibration (block 510) and normal operation (block 520).
Initially, the access point and user terminal perform calibration to determine the differences in the responses of their transmit and receive chains and to obtain correction matrices {circumflex over (K)}ap(k) and {circumflex over (K)}ut(k), for k∈ K (at block 512). The calibration only needs to be performed once (e.g., at the start of a communication session, or the very first time the user terminal is powered up). The correction matrices {circumflex over (K)}ap(k) and {circumflex over (K)}ut(k) are thereafter used by the access point and user terminal, respectively, on the transmit side as described above.
During normal operation, the access point transmits a MIMO pilot on the calibrated downlink channel (at block 522). The user terminal receives and processes the MIMO pilot, estimates the calibrated downlink channel response based on the received MIMO pilot, and maintains an estimate of the calibrated downlink channel response (at block 524). It can be shown that performance is better (i.e., less degradation) when the channel response estimate is accurate. An accurate channel response estimate may be obtained by averaging the estimates derived from multiple received MIMO pilot transmissions.
The user terminal then decomposes the calibrated downlink channel response estimate, Ĥcdn(k), for k∈ K, to obtain the diagonal matrix {circumflex over (Σ)}(k) and the unitary matrix {circumflex over (V)}ut*(k) (at block 526). The matrix {circumflex over (V)}ut*(k) contains the left eigenvectors of Ĥcdn(k) and {circumflex over (V)}ut(k) contains the right eigenvectors of Ĥcup(k). The matrix {circumflex over (V)}ut(k) can thus be used by the user terminal to perform spatial processing for data transmission received on the downlink as well as for data transmission to be sent on the uplink.
The user terminal then transmits a steered reference on the uplink to the access point using the eigenvectors in the matrix {circumflex over (V)}ut(k), as shown in equation (31) (at block 530). The access point receives and processes the uplink steered reference to obtain the diagonal matrix {circumflex over (Σ)}(k) and the unitary matrix Ûap(k), for k∈ K (at block 532). The matrix Ûap(k) contains the left eigenvectors of Ĥcup(k) and Ûap*(k) contains the right eigenvectors of Ĥcdn(k). The matrix Ûap(k) can thus be used by the access point to perform spatial processing for data transmission received on the uplink as well as for data transmission to be sent on the downlink.
The matrix Ûap(k), for k∈ K, is obtained based on an estimate of the uplink steered reference, which in turn is generated with the eigenvector that is obtained based on an estimate of the calibrated downlink channel response. Thus, the matrix Ûap(k) is effectively an estimate of an estimate. The access point may average the uplink steered reference transmissions to obtain more accurate estimate of the actual matrix Uap(k).
Once the user terminal and access point obtain the matrices {circumflex over (V)}ut(k) and Ûap(k), respectively, data transmission can commence on the downlink and/or uplink. For downlink data transmission, the access point performs spatial processing on symbols with the matrix Ûap(k) of right eigenvectors of Ĥcdn*(k) and transmits to the user terminal (at block 540). The user terminal would then receive and spatially process the downlink data transmission with the matrix {circumflex over (V)}utT(k), which is the conjugate transpose of the matrix {circumflex over (V)}*ut(k) of left eigenvectors of Ĥcdn(k) (at block 542). For uplink data transmission, the user terminal performs spatial processing on symbols with the matrix {circumflex over (V)}ut(k) of right eigenvectors of Ĥcup(k), and transmits to the access point (at block 550). The access point would then receive and spatially process the uplink data transmission with the matrix ÛapH(k), which is the conjugate transpose of the matrix Ûap(k) of left eigenvectors of Ĥcup(k) (at block 552).
The downlink and/or uplink data transmission can continue until terminated by either the access point or user terminal. While the user terminal is idle (i.e., with no data to transmit or receive), the MIMO pilot and/or steered reference may still be sent to allow the access point and user terminal to maintain up-to-date estimates of the downlink and uplink channel responses, respectively. This would then allow data transmission to commence quickly, if and when resumed.
For clarity, the channel estimation and spatial processing techniques have been described for a specific embodiment in which the user terminal estimates the calibrated downlink channel response based on a downlink MIMO pilot and performs the singular value decomposition. The channel estimation and singular value decomposition may also be performed by the access point, and this is within the scope of the invention. In general, because of the reciprocal channel for a TDD system, the channel estimation needs only be performed at one end of the link.
The techniques described herein may be used with or without calibration. Calibration may be performed to improve the channel estimates, which may then improve system performance.
The techniques described herein may also be used in conjunction with other spatial processing techniques, such as water-filling for transmit power allocation among the wideband eigenmodes and channel inversion for transmit power allocation among the subbands of each wideband eigenmode. Channel inversion and water-filling are described in the aforementioned U.S. patent application Ser. No. 60/421,309.
The channel estimation and spatial processing techniques described herein may be implemented by various means. For example, these techniques may be implemented in hardware, software, or a combination thereof. For a hardware implementation, the elements used to implement the techniques described herein may be implemented within one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, micro-controllers, microprocessors, other electronic units designed to perform the functions described herein, or a combination thereof.
For a software implementation, the channel estimation and spatial processing techniques may be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. The software codes may be stored in a memory unit (e.g., memory units 132 and 182 in FIG. 1) and executed by a processor (e.g., controllers 130 and 180). The memory unit may be implemented within the processor or external to the processor, in which case it can be communicatively coupled to the processor via various means as is known in the art.
Headings are included herein for reference and to aid in locating certain sections. These headings are not intended to limit the scope of the concepts described therein under, and these concepts may have applicability in other sections throughout the entire specification.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

## Claims

1. A method of performing spatial processing in a wireless time division duplexed (TDD) multiple-input multiple-output (MIMO) communication system, comprising:
processing a first transmission received via a first link to obtain at least one eigenvector usable for spatial processing for both data transmission received via the first link and data transmission sent via a second link; and
performing spatial processing for a second transmission with the at least one eigenvector prior to transmission over the second link.

2. The method of claim 1, further comprising:
performing spatial processing on a third transmission received via the first link with the at least one eigenvector to recover data symbols for the third transmission.

3. The method of claim 1, wherein the first transmission is a steered pilot received on at least one eigenmode of a MIMO channel for the first link.

4. The method of claim 1, wherein the first transmission is a MIMO pilot comprised of a plurality of pilot transmissions sent from a plurality of transmit antennas, and wherein the pilot transmission from each transmit antenna is identifiable by a receiver of the MIMO pilot.

5. The method of claim 4, wherein the processing a first transmission includes
obtaining a channel response estimate for the first link based on the MIMO pilot, and decomposing the channel response estimate to obtain a plurality of eigenvectors usable for spatial processing for the first and second links.

6. The method of claim 5, wherein the channel response estimate for the first link is decomposed using singular value decomposition.

7. The method of claim 4, further comprising:
performing spatial processing on pilot symbols with the at least one eigenvector to generate a steered pilot for transmission on at least one eigenmode of a MIMO channel for the second link.

8. The method of claim 1, wherein the second transmission is spatially processed with one eigenvector for transmission on one eigenmode of a MIMO channel for the second link.

9. The method of claim 1, wherein the second transmission is spatially processed with a normalized eigenvector for transmission on one eigenmode of a MIMO channel for the second link, the normalized eigenvector including a plurality of elements having same magnitude.

10. The method of claim 1, wherein the first transmission is a steered pilot generated with a normalized eigenvector for one eigenmode of a MIMO channel for the first link, the normalized eigenvector including a plurality of elements having same magnitude, and wherein one eigenvector usable for spatial processing for the first and second links is obtained.

11. The method of claim 1, further comprising:
calibrating the first and second links such that a channel response estimate for the first link is reciprocal of a channel response estimate for the second link.

12. The method of claim 11, wherein the calibrating includes
obtaining correction factors for the first link based on the channel response estimates for the first and second links, and
obtaining correction factors for the second link based on the channel response estimates for the first and second links.

13. The method of claim 1, wherein the TDD MIMO communication system utilizes orthogonal frequency division multiplexing (OFDM), and wherein the processing for the first transmission and the spatial processing for the second transmission are performed for each of a plurality of subbands.

14. An apparatus in a wireless time division duplexed (TDD) multiple-input multiple-output (MIMO) communication system, comprising:
means for processing a first transmission including at least one steered pilot received on at least one eigenmode of a MIMO channel via a first link to obtain at least one eigenvector usable for spatial processing for both data transmission received via the first link and data transmission sent via a second link; and
means for performing spatial processing for a second transmission with the at least one eigenvector prior to transmission over the second link.

15. The apparatus of claim 14, further comprising:
means for performing spatial processing on a third transmission received via the first link with the at least one eigenvector to recover data symbols for the third transmission.

16. The apparatus of claim 14, wherein the first transmission is a MIMO pilot comprised of a plurality of pilot transmissions sent from a plurality of transmit antennas, and wherein the pilot transmission from each transmit antenna is identifiable by a receiver of the MIMO pilot.

17. The apparatus of claim 16, further comprising:
means for obtaining a channel response estimate for the first link based on the MIMO pilot; and
means for decomposing the channel response estimate to obtain a plurality of eigenvectors usable for spatial processing for the first and second links.

18. An apparatus in a wireless time division duplexed (TDD) multiple-input multiple-output (MIMO) communication system, comprising:
a controller operative to process a first transmission received via a first link to obtain at least one eigenvector usable for spatial processing for both data transmission received via the first link and data transmission sent via a second link; and
a transmit spatial processor operative to perform spatial processing for a second transmission with the at least one eigenvector prior to transmission over the second link.

19. The apparatus of claim 18, further comprising:
a receive spatial processor operative to perform spatial processing on a third transmission received via the first link with the at least one eigenvector to recover data symbols for the third transmission.

20. The apparatus of claim 18, wherein the first transmission is a steered pilot received on at least one eigenmode of a MIMO channel for the first link.

21. The apparatus of claim 18, wherein the first transmission is a MIMO pilot comprised of a plurality of pilot transmissions sent from a plurality of transmit antennas, and wherein the pilot transmission from each transmit antenna is identifiable by a receiver of the MIMO pilot.

22. The apparatus of claim 21, wherein the controller is further operative to obtain a channel response estimate for the first link based on the MIMO pilot and to decompose the channel response estimate to obtain a plurality of eigenvectors usable for spatial processing for the first and second links.

23. A method of performing spatial processing in a wireless time division duplexed (TDD) multiple-input multiple-output (MIMO) communication system, comprising:
performing spatial processing on pilot symbols with a normalized eigenvector for one eigenmode of a MIMO channel to generate a first steered pilot for transmission via the one eigenmode of the MIMO channel, the normalized eigenvector including a plurality of elements having same magnitude; and
performing spatial processing on data symbols with the normalized eigenvector prior to transmission on the one eigenmode of the MIMO channel.

24. The method of claim 23, further comprising:
performing spatial processing on pilot symbols with an unnormalized eigenvector for the one eigenmode to generate a second steered pilot for transmission via the one eigenmode of the MIMO channel.