EFFICIENT FILTER WEIGHT COMPUTATION FOR A

MIMO SYSTEM

BACKGROUND

I. Field

[0001] The present disclosure relates generally to communication, and more specifically to techniques for computing filter weights in a communication system.

II. Background

[0002] A multiple-input multiple-output (MIMO) communication system employs multiple (T) transmit antennas at a transmitting station and multiple (R) receive antennas at a receiving station for data transmission. A MBvIO channel formed by the T transmit antennas and the R receive antennas may be decomposed into S spatial channels, where S < min {T, R} . The S spatial channels may be used to transmit data in a manner to achieve higher overall throughput and/or greater reliability. [0003] The transmitting station may simultaneously transmit T data streams from the T transmit antennas. These data streams are distorted by the MIMO channel response and further degraded by noise and interference. The receiving station receives the transmitted data streams via the R receive antennas. The received signal from each receive antenna contains scaled versions of the T data streams sent by the transmitting station. The transmitted data streams are thus dispersed among the R received signals from the R receive antennas. The receiving station would then perform receiver spatial processing on the R received signals with a spatial filter matrix in order to recover the transmitted data streams.

[0004] The derivation of the weights for the spatial filter matrix is computationally intensive. This is because the spatial filter matrix is typically derived based on a function that contains a matrix inversion, and direct calculation of the matrix inversion is computationally intensive.

[0005] There is therefore a need in the art for techniques to efficiently compute the filter weights.

SUMMARY

[0006] Techniques for efficiently computing the weights for a spatial filter matrix are described herein. These techniques avoid direct computation of matrix inversion. [0007] In a first embodiment for deriving a spatial filter matrix M , a Hermitian matrix P is iteratively derived based on a channel response matrix H , and a matrix inversion is indirectly calculated by deriving the Hermitian matrix iteratively. The Hermitian matrix may be initialized to an identity matrix. One iteration is then performed for each row of the channel response matrix, and an efficient sequence of calculations is performed for each iteration. For the i-th iteration, an intermediate row vector a _; is derived based on a channel response row vector h, , which is the z-th row of the channel response matrix. A scalar r _t is derived based on the intermediate row vector and the channel response row vector. An intermediate matrix C,- is also derived based on the intermediate row vector. The Hermitian matrix is then updated based on the scalar and the intermediate matrix. After all of the iterations are completed, the spatial filter matrix is derived based on the Hermitian matrix and the channel response matrix. [0008] In a second embodiment, multiple rotations are performed to iteratively obtain a first matrix P and a second matrix B for a pseudo-inverse matrix of the channel response matrix. One iteration is performed for each row of the channel response matrix. For each iteration, a matrix Y containing the first and second matrices from the prior iteration is formed. Multiple Givens rotations are then performed on matrix Y to zero out elements in the first row of the matrix to obtain updated first and second matrices for the next iteration. After all of the iterations are completed, the spatial filter matrix is derived based on the first and second matrices. [0009] In a third embodiment, a matrix X is formed based on the channel response matrix and decomposed (e.g., using eigenvalue decomposition) to obtain a unitary matrix V and a diagonal matrix λ . The decomposition may be achieved by iteratively performing Jacobi rotations on matrix X . The spatial filter matrix is then derived based on the unitary matrix, the diagonal matrix, and the channel response matrix. [0010] Various aspects and embodiments of the invention are described in further detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The features and nature of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify correspondingly throughout. [0012] FIGS. 1, 2 and 3 show processes for computing an MMSE spatial filter matrix based on the first, second, and third embodiments, respectively. [0013] FIG. 4 shows a block diagram of an access point and a user terminal.

DETAILED DESCRIPTION

[0014] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment or design described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments or designs.

[0015] The filter weight computation techniques described herein may be used for a single-carrier MEVIO system and a multi-carrier MEVIO system. Multiple carriers may be obtained with orthogonal frequency division multiplexing (OFDM), interleaved frequency division multiple access (IFDMA), localized frequency division multiple access (LFDMA), or some other modulation technique. OFDM, IFDMA, and LFDMA effectively partition the overall system bandwidth into multiple (K) orthogonal frequency subbands, which are also called tones, subcarriers, bins, and frequency channels. Each subband is associated with a respective subcarrier that may be modulated with data. OFDM transmits modulation symbols in the frequency domain on all or a subset of the K subbands. EFDMA transmits modulation symbols in the time domain on subbands that are uniformly spaced across the K subbands. LFDMA transmits modulation symbols in the time domain and typically on adjacent subbands. For clarity, much of the following description is for a single-carrier MEVIO system with a single subband.

[0016] A MDVlO channel formed by multiple (T) transmit antennas at a transmitting station and multiple (R) receive antennas at a receiving station may be characterized by an R x T channel response matrix H , which may be given as:

where h _u , for z = l, ..., R and 7 = 1, ...,T , denotes the coupling or complex channel gain between transmit antenna j and receive antenna i; and h, is a IxT channel response row vector for receive antenna i, which is the z-th row of H .

For simplicity, the following description assumes that the MEVIO channel is full rank and that the number of spatial channels (S) is given as: S = T < R . [0017] The transmitting station may transmit T modulation symbols simultaneously from the T transmit antennas in each symbol period. The transmitting station may or may not perform spatial processing on the modulation symbols prior to transmission. For simplicity, the following description assumes that each modulation symbol is sent from one transmit antenna without any spatial processing.

[0018] The receiving station obtains R received symbols from the R receive antennas in each symbol period. The received symbols may be expressed as:

r = H- s + n , Eq (2)

where s is a TxI vector with T modulation symbols sent by the transmitting station; r is an R xI vector with R received symbols obtained by the receiving station from the R receive antennas; and n is an R x 1 vector of noise.

For simplicity, the noise may be assumed to be additive white Gaussian noise (AWGN) with a zero mean vector and a covariance matrix of ^■ I , where is the variance of the noise and I is the identity matrix.

[0019] The receiving station may use various receiver spatial processing techniques to recover the modulation symbols sent by the transmitting station. For example, the receiving station may perform minimum mean square error (MMSE) receiver spatial processing, as follows:

I = (^I + H* HT ¹ H" r = P H ^H r = M r , Eq (3)

where M is a T xR MMSE spatial filter matrix;

P is a TxT Hermitian covariance matrix for the estimation error s-s ; I is a T x 1 vector that is an estimate of s ; and " ^ff " denotes a conjugate transpose.

The covariance matrix P may be given as P = E[(s-s) - (s -s) ^H ] , where E[ ] is an expectation operation. P is also a Hermitian matrix whose off-diagonal elements have the following properties p _j<t = where " * " denotes a complex conjugate.

[0020] As shown in equation (3), the MMSε spatial filter matrix M has a matrix inverse calculation. Direct calculation of the matrix inversion is computationally intensive. The MMSε spatial filter matrix may be more efficiently derived based on the embodiments described below, which indirectly calculate the matrix inversion with an iterative process instead of directly calculating the matrix inversion. [0021] In a first embodiment of computing the MMSε spatial filter matrix M , the Hermitian matrix P is computed based on the Riccati equation. Hermitian matrix P may be expressed as:

P . εq (4)

[0022] A TxT Hermitian matrix P,- may be defined as:

[0023] The matrix inversion lemma may be applied to equation (5) to obtain the following:

where r _t is a real-valued scalar. Equation (6) is referred to as the Riccati equation.

Matrix P, may be initialized as P ₀ = — • I . After performing R iterations of equation

(6), for i = 1, ..., R , matrix P _R is provided as matrix P , or P = P _R . [0024] Equation (6) may be factored to obtain the following:

£, =£,-* - ^ ^{1 h} " ^{h £ l} and r _t = σ _n ² +U ₁ -P^ -Uf , Eq (7) ^r ,

where matrix P, is initialized as P ₀ = I and matrix P is derived as P = — y • P _R .

Equations (6) and (7) are different forms of a solution to equation (5). For simplicity, the same variables P, and r _t are used for both equations (6) and (7) even though these variables have different values in the two equations. The final results from equations

(6) and (7), i.e., P _R for equation (6) and — ^- -P _R for equation (7), are equivalent.

However, the calculations for the first iteration of equation (7) are simplified because

P ₀ is an identity matrix.

[0025] Each iteration of equation (7) may be performed as follows:

a, = h _; P _^1 , Eq (8a)

r, = σ _n ² +a, -h? , Eq (Sb)

C ₁ = a? a, , and Eq (8c)

P ₁ = P ₁ - _I - ^ - C, , Eq (Sd)

where a, is a IxT intermediate row vector of complex-valued elements; and C, is a T x T intermediate Hermitian matrix.

[0026] In equation set (8), the sequence of operations is structured for efficient computation by hardware. Scalar η is computed before matrix C ₁ . The division by η in equation (7) is achieved with an inversion and a multiply. The inversion of η may be performed in parallel with the computation of C, . The inversion of r _t may be achieved

with a shifter to normalize η and a look-up table to produce an inverted η value. The normalization of η may be compensated for in the multiplication with C, . [0027] Matrix P ₁ is initialized as a Hermitian matrix, or P ₀ = I , and remains Hermitian through all of the iterations. Hence, only the upper (or lower) diagonal matrix needs to be calculated for each iteration. After R iterations are completed,

matrix P is obtained as P = — r- ^■ P _R . The MMSE spatial filter matrix may then be

computed as follows:

[0028] FIG. 1 shows a process 100 for computing the MMSE spatial filter matrix M based on the first embodiment. Matrix P ₁ is initialized as P ₀ = 1 (block 112), and index i used to denote the iteration number is initialized as i - \ (block 114). R iterations of the Riccati equation are then performed.

[0029] Each iteration of the Riccati equation is performed by block 120. For the i- th iteration, the intermediate row vector a, is computed based on the channel response row vector h, and the Hermitian matrix P _1-1 from the prior iteration, as shown in equation (8a) (block 122). The scalar η is computed based on the noise variance , the intermediate row vector a, , and the channel response row vector h, , as shown in equation (8b) (block 124). Scalar η is then inverted (block 126). Intermediate matrix C, is computed based on the intermediate row vector a, , as shown in equation (8c) (block 128). Matrix P ₁ is then updated based on the inverted scalar η and the intermediate matrix C ₁ , as shown in equation (8d) (block 130).

[0030] A determination is then made whether all R iterations have been performed (block 132). If the answer is 'No', then index i is incremented (block 134), and the process returns to block 122 to perform another iteration. Otherwise, if all R iterations have been performed, then the MMSE spatial filter matrix M is computed based on the Hermitian matrix P _R for the last iteration, the channel response matrix H, and the noise variance σ _n ² , as shown in equation (9) (block 136). Matrix M may then be used for receiver spatial processing as shown in equation (3).

[0031] In a second embodiment of computing the MMSE spatial filter matrix M , the Hermitian matrix P is determined by deriving the square root of P , which is P ^1/2 , based on an iterative procedure. The receiver spatial processing in equation (3) may be expressed as:

i

= H ^P r

where is a (R +T) x T augmented channel matrix;

V_ ^p is a T x (R +T) pseudo-inverse matrix obtained from a Moore-Penrose inverse or a pseudo-inverse operation on U , or U ^p = (U" • U) ^] • V" ; 0 _Tx2 is a TxI vector of all zeros; and H^ is a T x R sub-matrix containing the first R columns of U ^p .

[0032] QR decomposition may be performed on the augmented channel matrix, as follows:

where Q is a (R +T) x T matrix with orthonormal columns; R is a T x T matrix that is non-singular; B is an R xT matrix containing the first R rows of Q ; and Q ₂ is a TxT matrix containing the last T rows of Q .

[0033] The QR decomposition in equation (11) decomposes the augmented channel matrix into an orthonormal matrix Q and a non-singular matrix R . An orthonormal matrix Q has the following property: Q ^H - Q = I , which means that the columns of the orthonormal matrix are orthogonal to one another and each column has unit power. A non-singular matrix is a matrix that an inverse can be computed for.

[0034] The Hermitian matrix P may then be expressed as:

Q ⁸ Q E) ^"1 , Eq (12)

= (R ^B -R) ^"1 =R^-R ^"l '=P ^1/a -P" ^/a •

R is the Cholesky factorization or matrix square root of P . Hence, P is equal to

R ^"1 and is called the square-root of P .

[0035] The pseudo-inverse matrix in equation (10) may then be expressed as:

U" = P-[H" σ -I] = (R —1 - fR-fc —H \ * -|-j H g~ _\ H \ γ _% —\ *-* H • Eq (13)

Sub-matrix H^. , which is also the MMSE spatial filter matrix, may then be expressed as:

H!: =M=P" ² -B" Eq (14)

[0036] Equation (10) may then be expressed as:

S = H: -r = P ,1/2 -B "τ = M-r Eq (15)

[0037] Matrices P ^1/2 and B may be computed iteratively as follows:

= Z,. , oi Eq (16)

where Y ₁ . is a (T + R + l)x(T + l) matrix containing elements derived based on P , _M 1/2 ,

B _M and h,- ; θ _; is a (T + 1) x (T + 1) unitary transformation matrix;

Z, is a (T + R + 1) x (T + 1) transformed matrix containing elements for P, ^1/2 ,

B, and r, ; e, is an R xI vector with one (1.0) as the i-th element and zeros elsewhere; and k, is a TxI vector and I ₁ is an R xI vector, both of which are non-essential.

Matrices P ^1/2 and B are initialized as P ₀ ^1/2 = 1 and B ₀ = Q _RxT .

[0038] The transformation in equation (17) may be performed iteratively, as described below. For clarity, each iteration of equation (17) is called an outer iteration. R outer iterations of equation (17) are performed for the R channel response row vectors h _; , for i = l, ..., R . For each outer iteration, the unitary transformation matrix θ, in equation (17) results in the transformed matrix Z ₁ containing all zeros in the first row except for the first element. The first column of the transformed matrix Z ₁ contains rl ¹² , k, , and I ₁ . The last T columns of Z, contain updated P, ^1/2 and B, . The first column of Z ₁ does not need to be calculated since only P ₁ and B, are used in the next iteration. P, ^1/2 is an upper triangular matrix. After R outer iterations are completed, P _R ^/2 is provided as P ^m , and B _R is provided as B . The MMSE spatial filter matrix M may then be computed as based on P ^1/2 and B , as shown in equation

(14).

[0039] For each outer iteration i, the transformation in equation (17) may be performed by successively zeroing out one element in the first row of Y ₁ at a time with a 2 x 2 Givens rotation. T inner iterations of the Givens rotation may be performed to zero out the last T elements in the first row of Y ₁ .

[0040] For each outer iteration i, a matrix Y _{1 ;} may be initialized as Y ₁₄ = Y ₁ . For each inner iteration j, for j = l, ...,T , of outer iteration i, a (T + R + l)x2 sub-matrix

Y^ _1J containing the first and (j + 1) -th columns of Y _ii7 is initially formed. The Givens rotation is then performed on sub-matrix Y^ to generate a (T + R + l)x2 sub-matrix

Y" _tJ containing a zero for the second element in the first row. The Givens rotation may be expressed as:

X^ = YVS,., , Eq (18)

where G ₁ ^ is a 2x2 Givens rotation matrix for the j-th inner iteration of the ϊ-th outer iteration and is described below. Matrix Y, ₇₊₁ is then formed by first setting X _ι . _j+1 ⁼ Y _{ι,7 »} then replacing the first column of Y, _iJ+1 with the first column of Y^ , and then replacing the (j + l) -th column of Y ₁ ^ ₊₁ with the second column of Y^ . The Givens rotation thus modifies only two columns of Y, _; in the j-th inner iteration to produce Y _{1 J+1} for the next inner iteration. The Givens rotation may be performed in- place on two columns of Y ₁ for each inner iteration, so that intermediate matrices Y _{1 ;} , Y _{-Ij >} Y^ _1J ^an( i Y, _,j+ i ^{aχe n} °t needed and are described above for clarity. [0041] For the j-th inner iteration of the z-th outer iteration, the Givens rotation matrix G _tJ is determined based on the first element (which is always a real value) and the (j ^' + l) -th element in the first row of Y ₁ ^ . The first element may be denoted as a, and the ( j + 1) -th element may be denoted as b • e ^jθ . The Givens rotation matrix G _{1 ;} may then be derived as follows:

- s 1 0 c - s

&., = s - e -jβ c- e ,-Jθ Eq (19)

0 e ^~jθ S C

a where c = • and s = for equation (19).

[0042] FIG. 2 shows a process 200 for computing the MMSE spatial filter matrix

M based on the second embodiment. Matrix P ₁ is initialized as P , ₀ 1/2 = 1 , and

matrix B ₁ is initialized as B ₀ = 0 (block 212). Index i used to denote the outer iteration number is initialized as i = 1 , and index j used to denote the inner iteration number is initialized as j = 1 (block 214). R outer iterations of the unitary transformation in equation (17) are then performed (block 220). [0043] For the i-th outer iteration, matrix Y ₁ is initially formed with the channel response row vector h, and matrices P _1- .', ² and B _1-1 , as shown in equation (17) (block 222). Matrix Y, is then referred to as matrix Y _I>; for the inner iterations (block 224). T inner iterations of the Givens rotation are then performed on matrix Y, ₇ (block 230).

[0044] For the j-th inner iteration, the Givens rotation matrix G _(J is derived based on the first and (j + ϊ) -th elements in the first row of Y_ _tJ , as shown in equation (19) (block 232). The Givens rotation matrix G _(J is then applied to the first and (j + 1) -th columns of Y ₁ . _ _; to obtain Y,- _,J+ i , as shown in equation (18) (block 234). A determination is then made whether all T inner iterations have been performed (block 236). If the answer is 'No', then index j is incremented (block 238), and the process returns to block 232 to perform another inner iteration.

[0045] If all T inner iterations have been performed for the current outer iteration and the answer is 'Yes' for block 236, then the latest Y ₁ . _J+1 is equal to Z ₁ - in equation

(17). Updated matrices P, ^1/2 and B ₁ - are obtained from the latest Y, _J+1 (block 240). A determination is then made whether all R outer iterations have been performed (block 242). If the answer is 'No', then index i is incremented, and index j is reinitialized as j = l (block 244). The process then returns to block 222 to perform another outer iteration with P, ^1/2 and B, . Otherwise, if all R outer iterations have been performed and the answer is 'Yes' for block 242, then the MMSE spatial filter matrix M is computed based on P ₁ ¹ ' ² and B,- , as shown in equation (14) (block 246). Matrix M may then be used for receiver spatial processing as shown in equation (15).

[0046] In a third embodiment of computing the MMSE spatial filter matrix M, eigenvalue decomposition of P ^" is performed as follows:

P ^"1 = σ ² -I + H ^H -H = V -λ -V ^H , Eq (20)

where V is a TxT unitary matrix of eigenvectors; and

λ is a TxT diagonal matrix with real eigenvalues along the diagonal.

[0047] Eigenvalue decomposition of a 2x2 Hermitian matrix X _2x2 may be achieved using various techniques. In an embodiment, eigenvalue decomposition of X _2x2 is achieved by performing a complex Jacobi rotation on X _2x2 to obtain a 2x2 matrix V _2x2 of eigenvectors of X _2x2 . The elements of X _2x2 and V _2x2 may be given as:

^X \,Z ^v u ^V l,2

£--2x2 and -J-.2X2 — Eq (21)

^X 2,l ^X 2,l ^V 2,l ^V 2,2

The elements of V _2x2 may be computed directly from the elements of X _2x2 , as follows:

r = J(Re{x _u }) ² + (Im{x _u }) ² , Eq (22a)

J ₁ = — = sin (Zx ₁₂ ) , Eq (22c)

^X 2,2 ^X \,\

T = Eq (22e)

2 - r

x = ^l + τ ² , Eq (22f)

1 t = - Eq (22g)

| τ | +x

1 c = - Eq (22h)

/IT?

if (x ₂₂ - X ₁₁ ) < 0

then _ V-_,2 _v x,2 Eq (22j)

[0048] Eigenvalue decomposition of a T xT Hermitian matrix X that is larger than 2x2 may be performed with an iterative process. This iterative process uses the Jacobi rotation repeatedly to zero out off-diagonal elements in X . For the iterative process, index i denotes the iteration number and is initialized as i = 1. X is a T x T Hermitian matrix to be decomposed and is set as X = P ^"1 . Matrix D ₁ - is an approximation of diagonal matrix λ in equation (20) and is initialized as D ₀ = X . Matrix V ₁ - is an approximation of unitary matrix V in equation (20) and is initialized as V ₀ = I .

[0049] A single iteration of the Jacobi rotation to update matrices D,- and V ₁ - may be performed as follows. First, a 2x2 Hermitian matrix D^ is formed based on the current matrix D,- , as follows:

where d is the element at location (p,q) in D,- , /?e { 1, ...,T } , qe. { 1, ...,T } , and p ≠ q . D _pq is a 2x2 submatrix of D ₁ . , and the four elements of O _pq are four elements al locations (p,p) , (p,q) , (q,p) and (q, q) in D,. . Indices p and q may be selected as described below.

[0050] Eigenvalue decomposition of J) _pq is then performed as shown in equation set (22) to obtain a 2x2 unitary matrix V _pg of eigenvectors of O _pq . For the eigenvalue decomposition of O _pq , X _2x2 in equation (21) is replaced with D _ffl , and

V _2x2 from equation (22j) or (22k) is provided as \_ _pq .

[0051] A T xT complex Jacobi rotation matrix T_ _pq is then formed with V _p(? . T_ _pq is an identity matrix with four elements at locations (p, p) , (p, q) , (q, p) and (q, q) replaced with elements V _{1 1} , V _{1 2} , V _{2 1} and V _{2 2} , respectively, in Y_ _pq .

[0052] Matrix D, is then updated as follows:

n _M =l " _η -Url _pη ■ Eq (24)

Equation (24) zeros out two off-diagonal elements at locations (p,q) and (q,p) in D,- . The computation may alter the values of other off-diagonal elements in D ₁ .. [0053] Matrix V ₁ - is also updated as follows:

V ₄₊₁ = V, - T _M . Eq (25)

V,- may be viewed as a cumulative transformation matrix that contains all of the Jacobi rotation matrices υ_ _pq used on D,- .

[0054] Each iteration of the Jacobi rotation zeros out two off-diagonal elements of D ₁ .. Multiple iterations of the Jacobi rotation may be performed for different values of indices p and q to zero out all of the off-diagonal elements of D,- . A single sweep across all possible values of indices p and q may be performed as follows. Index p is stepped from 1 through T - 1 in increments of one. For each value of p, index q is stepped from p + 1 through T in increments of one. The Jacobi rotation is performed for each different combination of values forp and q. Multiple sweeps may be performed until D,. and V ₁ - are sufficiently accurate estimates of λ and V , respectively. [0055] Equation (20) may be rewritten as follows:

P = (σ^ -I + H ^H -H) ^"1 = V - λ ^~1 - V ^H , Eq (26)

where AT ¹ is a diagonal matrix whose elements are the inverse of the corresponding elements in λ . The eigenvalue decomposition of X = P ^"1 provides estimates of λ and

V . λ may be inverted to obtain λ ^"1 .

[0056] The MMSE spatial filter matrix may then be computed as follows:

M = P- H* = V -λ ^"1 - V" U" ■ Eq (27)

[0057] FIG. 3 shows a process 300 for computing the MMSE spatial filter matrix M based on the third embodiment. Hermitian matrix P ^"1 is initially derived based on the channel response matrix H , as shown in equation (20) (block 312). Eigenvalue decomposition of P ^"1 is then performed to obtain unitary matrix V and diagonal matrix λ , as also shown in equation (20) (block 314). The eigenvalue decomposition may be iteratively performed with a number of Jacobi rotations, as described above. The MMSE spatial filter matrix M is then derived based on the unitary matrix V , the diagonal matrix λ , and the channel response matrix H , as shown in equation (27) (block 316).

[0058] The MMSE spatial filter matrix M derived based on each of the embodiments described above is a biased MMSE solution. The biased spatial filter matrix M may be scaled by a diagonal matrix D _mniϊe to obtain an unbiased MMSE

spatial filter matrix M _mmse . Matrix O _mmse may be derived as D _mmM = [diag [M ^• H]] ^-1 , where diag [M -H] is a diagonal matrix containing the diagonal elements of M ^• H . [0059] The computation described above may also be used to derive spatial filter matrices for a zero-forcing (ZF) technique (which is also called a channel correlation matrix inversion (CCMI) technique), a maximal ratio combining (MRC) technique, and so on. For example, the receiving station may perform zero-forcing and MRC receiver spatial processing, as follows:

I* = (H* -H)- ¹ -H* r = P^ -H" -r =M^ E , Eq (28)

t s _mrc = [diag (H* • H)- ¹ ] If r = [diag (P^ )] • H* • r = M _fflrc • r , Eq (29)

where M-^ is a T x R zero-forcing spatial filter matrix; M _mrc is a TxR MRC spatial filter matrix; P^ = (H" - H) ^"1 is a TxT Hermitian matrix; and [diag (P _z/ )] is a TxT diagonal matrix containing the diagonal elements of P _z/ .

A matrix inversion is needed to compute P^ directly. P _tf may be computed using the embodiments described above for the MMSE spatial filter matrix. [0060] The description above assumes that T modulation symbols are sent simultaneously from T transmit antennas without any spatial processing. The transmitting station may perform spatial processing prior to transmission, as follows:

x = W -s , Eq (30)

where x is a TxI vector with T transmit symbols to be sent from the T transmit antennas; and

W is a TxS transmit matrix.

Transmit matrix W may be (1) a matrix of right singular vectors obtained by performing singular value decomposition of H , (2) a matrix of eigenvectors obtained by performing eigenvalue decomposition of η." • H , or (3) a steering matrix selected to spatially spread the modulation symbols across the S spatial channels of the MDVIO channel. An effective channel response matrix η. _eJf observed by the modulation

symbols may then be given as εL _eff = H • W . The computation described above may be performed based on H _e# instead of H .

[0061] For clarity, the description above is for a single-carrier MBvIO system with a single subband. For a multi-carrier MBVIO system, a channel response matrix H(fc) may be obtained for each subband k of interest. A spatial filter matrix M(Jc) may then be derived for each subband k based on the channel response matrix H(Z:) for that subband.

[0062] The computation described above for the spatial filter matrix may be performed using various types of processors such as a floating-point processor, a fixed- point processor, a Coordinate Rotational Digital Computer (CORDIC) processor, a look-up table, and so on, or a combination thereof. A CORDIC processor implements an iterative algorithm that allows for fast hardware calculation of trigonometric functions such as sine, cosine, magnitude, and phase using simple shift and add/subtract hardware. A CORDIC processor may iteratively compute each of variables r, C ₁ and S ₁ in equation set (22), with more iterations producing higher accuracy for the variable. [0063] FIG. 4 shows a block diagram of an access point 410 and a user terminal 450 in a MBvIO system 400. Access point 410 is equipped with N _ap antennas and user terminal 450 is equipped with N _ut antennas, where N _ap > 1 and N _ut > 1. On the downlink, at access point 410, a transmit (TX) data processor 414 receives traffic data from a data source 412 and other data from a controller/processor 430. TX data processor 414 formats, encodes, interleaves, and modulates the data and generates data symbols, which are modulation symbols for data. A TX spatial processor 420 multiplexes the data symbols with pilot symbols, performs spatial processing with transmit matrix W if applicable, and provides N _ap streams of transmit symbols. Each transmitter unit (TMTR) 422 processes a respective transmit symbol stream and generates a downlink modulated signal. N _ap downlink modulated signals from transmitter units 422a through 422ap are transmitted from antennas 424a through 424ap, respectively.

[0064] At user terminal 450, N _ut antennas 452a through 452ut receive the transmitted downlink modulated signals, and each antenna provides a received signal to a respective receiver unit (RCVR) 454. Each receiver unit 454 performs processing complementary to the processing performed by transmitter units 422 and provides

received pilot symbols and received data symbols. A channel estimator/processor 478 processes the received pilot symbols and provides an estimate of the downlink channel response H _dn . A processor 480 derives a downlink spatial filter matrix M _dn based on H _dn and using any of the embodiments described above. A receive (RX) spatial processor 460 performs receiver spatial processing (or spatial matched filtering) on the received data symbols from all N _ut receiver units 454a through 454ut with the downlink spatial filter matrix M _dn and provides detected data symbols, which are estimates of the data symbols transmitted by access point 410. An RX data processor 470 processes (e.g., symbol demaps, deinterleaves, and decodes) the detected data symbols and provides decoded data to a data sink 472 and/or controller 480.

[0065] The processing for the uplink may be the same or different from the processing for the downlink. Data from a data source 486 and signaling from controller 480 are processed (e.g., encoded, interleaved, and modulated) by a TX data processor 488, multiplexed with pilot symbols, and possibly spatially processed by TX spatial processor 490. The transmit symbols from TX spatial processor 490 are further processed by transmitter units 454a through 454ut to generate N _ut uplink modulated signals, which are transmitted via antennas 452a through 452ut.

[0066] At access point 410, the uplink modulated signals are received by antennas 424a through 424ap and processed by receiver units 422a through 422ap to generate received pilot symbols and received data symbols for the uplink transmission. A channel estimator/processor 428 processes the received pilot symbols and provides an estimate of the uplink channel response H _up . Processor 430 derives an uplink spatial filter matrix M _up based on H _up and using any of the embodiments described above. An

RX spatial processor 440 performs receiver spatial processing on the received data symbols with the uplink spatial filter matrix M _up and provides detected data symbols.

An RX data processor 442 further processes the detected data symbols and provides decoded data to a data sink 444 and/or controller 430.

[0067] Controllers 430 and 480 control the operation at access point 410 and user terminal 450, respectively. Memory units 432 and 482 store data and program codes used by controllers 430 and 480, respectively.

[0068] The blocks in FIGS. 1 through 4 represent functional blocks that may be embodied in hardware (one or more devices), firmware (one or more devices), software

(one or more modules), or combinations thereof. For example, the filter weight computation techniques described herein may be implemented in hardware, firmware, software, or a combination thereof. For a hardware implementation, the processing units used to compute the filter weights 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, electronic devices, other electronic units designed to perform the functions described herein, or a combination thereof. The various processors at access point 410 in FIG. 4 may also be implemented with one or more hardware processors. Likewise, the various processors at user terminal 450 may be implemented with one or more hardware processors.

[0069] For a firmware or software implementation, the filter weight computation 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 unit 432 or 482 in FIG. 4) and executed by a processor (e.g., processor 430 or 480). The memory unit may be implemented within the processor or external to the processor.

[0070] 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.

[0071] WHAT IS CLAIMED IS: