1111111111111111 IIIIII IIIII 11111 1111111111 11111 1111111111 11111 lllll 111111111111111 11111111
`US 20060092054Al
`
`c19) United States
`c12) Patent Application Publication c10) Pub. No.: US 2006/0092054 Al
`May 4, 2006
`Li et al.
`(43) Pub. Date:
`
`(54) RECURSIVE REDUCTION OF CHANNEL
`STATE FEEDBACK
`
`(22) Filed:
`
`Sep. 8, 2004
`
`(76)
`
`Inventors: Qinghua Li, Sunnyvale, CA (US);
`Xintian E. Lin, Mountain View, CA
`(US)
`
`Correspondence Address:
`LeMoine Patent Services, PLLC
`c/o PortfolioIP
`P.O. Box 52050
`Minneapolis, MN 55402 (US)
`
`(21) Appl. No.:
`
`10/937,097
`
`Publication Classification
`
`(51)
`
`Int. Cl.
`H03M 7140
`(2006.01)
`(52) U.S. Cl. ................................................................ 341/67
`
`(57)
`
`ABSTRACT
`
`Feedback bandwidth may be reduced in a closed loop
`MIMO system by Householder transformations and vector
`quantization using codebooks.
`
`ESTIMATE CHANNEL STATE INFORMATION
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`QUANTIZE A COLUMN OF A BEAMFORMING
`MATRIX USING A CODEBOOK
`
`10
`3
`
`~
`
`320
`I-/
`
`330
`
`._/
`
`PERFORM A HOUSEHOLDER REFLECTION
`ON THE BEAMFORMING MA TRIX TO
`REDUCE THE DIMENSIONALITY OF THE
`BEAMFORMING MATRIX
`
`340
`I-/
`
`RECURSIVELY REPEAT THE QUANTIZING
`AND PERFORMING OF HOUSEHOLDER
`REFLECTION
`
`350
`I-/
`
`TRANSMIT QUANTIZED COLUMN VECTORS
`
`360
`
`' 300
`
`

`

`Patent Application Publication May 4, 2006 Sheet 1 of 7
`
`US 2006/0092054 Al
`
`I
`I
`I
`I
`I
`I
`I
`I
`I
`
`I +
`
`.......
`
`

`

`Patent Application Publication May 4, 2006 Sheet 2 of 7
`
`US 2006/0092054 Al
`
`FIG. 2
`
`

`

`Patent Application Publication May 4, 2006 Sheet 3 of 7
`
`US 2006/0092054 Al
`
`310
`ESTIMATE CHANNEL STA TE INFORMATION ~
`FROM RECEIVED SIGNALS
`
`320
`DETERMINE A BEAMFORMING MATRIX ~
`FROM THE CHANNEL STATE INFORMATION
`
`330
`QUANTIZE A COLUMN OF A BEAMFORMING ~
`MATRIX USING A CODEBOOK
`
`PERFORM A HOUSEHOLDER REFLECTION
`ON THE BEAMFORMING MA TRIX TO
`REDUCE THE DIMENSIONALITY OF THE
`BEAMFORMING MATRIX
`
`340
`
`~
`
`RECURSIVELY REPEAT THE QUANTIZING
`AND PERFORMING OF HOUSEHOLDER
`REFLECTION
`
`350
`
`..J
`
`360
`TRANSMIT QUANTIZED COLUMN VECTORS ~
`
`I 300
`
`FIG. 3
`
`

`

`Patent Application Publication May 4, 2006 Sheet 4 of 7
`
`US 2006/0092054 Al
`
`RECEIVE QUANTIZED COLUMN VECTORS
`
`___,410
`
`INDEX INTO A CODEBOOK USING THE
`QUANTIZED COLUMN VECTORS TO YIELD
`A PLURALITY OF COLUMN VECTORS
`
`420
`__.,
`
`DETERMINE AT LEAST ONE
`HOUSEHOLDER MA TRIX FROM THE
`PLURALITY OF COLUMN VECTORS
`
`430
`__.,
`
`RECURSIVELY APPLY THE AT LEAST ONE
`HOUSEHOLDER MA TRIX TO THE
`PLURALITY OF QUANTIZED COLUMN
`VECTORS TO GENERATE A BEAMFORMING
`MATRIX
`
`440
`__.,
`
`I 400
`
`FIG. 4
`
`

`

`Patent Application Publication May 4, 2006 Sheet 5 of 7
`
`US 2006/0092054 Al
`
`c::::,
`(0
`LC')
`
`a::
`0
`c,,J
`c,,J
`LU
`0
`0
`8:
`
`.,_
`c::::,
`LC')
`
`>-
`a::
`0
`~
`
`c::::,
`LC')
`LC')
`
`LU
`0
`
`1--
`LU
`<:
`i1: a::
`EE
`~
`<: -
`~
`LU
`
`c::::,
`C"')
`LC')
`
`\
`
`

`

`Patent Application Publication May 4, 2006 Sheet 6 of 7
`
`US 2006/0092054 Al
`
`1
`0.8
`0.6
`0.4
`0.2
`0
`-0.2
`-0.4
`-0.6
`-0.8
`-1
`
`n1=3 n2=4 energy=0.9888
`
`0
`
`0
`
`Q_610
`
`0
`
`0
`
`-1
`
`-0.5
`
`0
`
`0.5
`
`1
`
`FIG. 6
`
`

`

`Patent Application Publication May 4, 2006 Sheet 7 of 7
`
`US 2006/0092054 Al
`
`FIG. 7
`
`FIG. 8
`
`

`

`US 2006/0092054 Al
`
`May 4, 2006
`
`1
`
`RECURSIVE REDUCTION OF CHANNEL STATE
`FEEDBACK
`
`FIELD
`
`[0001] The present invention relates generally to wireless
`networks, and more specifically to wireless networks that
`utilize multiple spatial channels.
`
`BACKGROUND
`
`[0002] Closed
`multiple-input-multiple-output
`loop
`(MIMO) systems typically transmit channel state informa(cid:173)
`tion from a receiver to a transmitter. Transmitting the
`channel state information consumes bandwidth that might
`otherwise be available for data traffic.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`[0003] FIG. 1 shows a diagram of two wireless stations;
`
`[0004] FIG. 2 shows a constellation in accordance with
`various embodiments of the present invention;
`
`[0005] FIGS. 3 and 4 show flowcharts in accordance with
`various embodiments of the present invention;
`
`[0006] FIG. 5 shows an electronic system in accordance
`with various embodiments of the present invention;
`
`[0007] FIG. 6 shows distributions of codewords in a
`plane;
`
`[0008] FIG. 7 shows a partition of a codebook according
`to a parameter; and
`
`[0009] FIG. 8 shows a partition of a portion of a codebook
`according to a parameter.
`
`DESCRIPTION OF EMBODIMENTS
`
`[0010]
`In the following detailed description, reference is
`made to the accompanying drawings that show, by way of
`illustration, specific embodiments in which the invention
`may be practiced. These embodiments are described in
`sufficient detail to enable those skilled in the art to practice
`the invention. It is to be understood that the various embodi(cid:173)
`ments of the invention, although different, are not necessar(cid:173)
`ily mutually exclusive. For example, a particular feature,
`structure, or characteristic described herein in connection
`with one embodiment may be implemented within other
`embodiments without departing from the spirit and scope of
`the invention. In addition, it is to be understood that the
`location or arrangement of individual elements within each
`disclosed embodiment may be modified without departing
`from the spirit and scope of the invention. The following
`detailed description is, therefore, not to be taken in a limiting
`sense, and the scope of the present invention is defined only
`by the appended claims, appropriately interpreted, along
`with the full range of equivalents to which the claims are
`entitled. In the drawings, like numerals refer to the same or
`similar functionality throughout the several views.
`
`[0011] FIG. 1 shows a diagram of two wireless stations:
`station 102, and station 104. In some embodiments, stations
`102 and 104 are part of a wireless local area network
`(WLAN). For example, one or more of stations 102 and 104
`may be an access point in a WLAN. Also for example, one
`or more of stations 102 and 104 may be a mobile station such
`as a laptop computer, personal digital assistant (PDA), or the
`
`like. Further, in some embodiments, stations 102 and 104 are
`part of a wireless wide area network (WWAN). For example,
`one or more of stations 102 and 104 may be a base station
`or a subscriber unit. Although only two stations are shown
`in FIG. 1, any number of stations may be present without
`departing from the scope of the present invention.
`
`In some embodiments, stations 102 and 104 may
`[0012]
`operate partially in compliance with, or completely in com(cid:173)
`pliance with, a wireless network standard. For example,
`stations 102 and 104 may operate partially in compliance
`with a standard such as ANSI/IEEE Std. 802.11, 1999
`Edition, although this is not a limitation of the present
`invention. As used herein, the term "802.11" refers to any
`past, present, or future IEEE 802.11 standard, including, but
`not limited to, the 1999 edition. Also for example, stations
`102 and 104 may operate partially in compliance with any
`other standard, such as any future IEEE personal area
`network standard or wide area network standard.
`
`[0013] Stations 102 and 104 may include any number of
`antennas. In the example of FIG. 1, station 102 includes four
`antennas, and station 104 includes three antennas. The
`"channel" through which stations 102 and 104 communicate
`may include many possible signal paths. For example, when
`stations 102 and 104 are in an environment with many
`"reflectors" (e.g. walls, doors, or other obstructions), many
`signals may arrive from different paths. This condition is
`known as "multipath." In some embodiments, stations 102
`and 104 utilize multiple antennas to take advantage of the
`multipath and to increase the communications bandwidth.
`For example, in some embodiments, stations 102 and 104
`may communicate using Multiple-Input-Multiple-Output
`(MIMO) techniques. In general, MIMO systems offer higher
`capacities by utilizing multiple spatial channels made pos(cid:173)
`sible by multipath. The channel between stations 102 and
`104 is described by the channel state matrix, H, that includes
`entries describing the complex channel gains between each
`transmit and receive antenna pair.
`
`In some embodiments, stations 102 and 104 may
`[0014]
`communicate using orthogonal frequency division multi(cid:173)
`plexing (OFDM) in each spatial channel. Multipath may
`introduce frequency selective fading which may cause
`impairments like inter-symbol interference (ISI). OFDM is
`effective at combating frequency selective fading in part
`because OFDM breaks each spatial channel into small
`subchannels such that each subchannel exhibits a more flat
`channel characteristic. Scaling appropriate for each sub(cid:173)
`channel may be implemented to correct any attenuation
`caused by the subchannel. Further, the data carrying capacity
`of each subchannel may be controlled dynamically depend(cid:173)
`ing on the fading characteristics of the subchannel.
`
`[0015] MIMO systems may operate either "open loop" or
`"closed loop." In open loop MIMO systems, no channel
`state information is explicitly fed back from another station.
`In closed loop systems, communications bandwidth is uti(cid:173)
`lized to transmit channel state information between stations,
`and thereby reducing overall throughput. The channel state
`information can be employed for various enhancements such
`as transmit beamforming and adaptive modulation. The
`communications bandwidth used for this purpose is referred
`to herein as "feedback bandwidth." When feedback band(cid:173)
`width is reduced in closed loop MIMO systems, more
`bandwidth is available for data communications.
`
`

`

`US 2006/0092054 Al
`
`May 4, 2006
`
`2
`
`[0016] Various embodiments of the present invention pro(cid:173)
`vide for closed loop MIMO with a compact feedback
`scheme, thereby saving feedback bandwidth. In some
`embodiments, feedback bandwidth is saved by feeding back
`transmit beamforming vectors instead of the channel matrix
`H. Further, in some embodiments, the elements of each
`beamforming vector are jointly quantized by vector quanti(cid:173)
`zation using codebooks. In some of these embodiments,
`different size codebooks are used for different ones of the
`transmit beamforming vectors. For example,
`in some
`embodiments, three beamforming vectors are quantized
`using three small codebooks of sizes 16, 32 and 64 respec(cid:173)
`tively. Further, in some embodiments, beamforming vectors
`are only fed back for the active spatial channels. This
`provides a significant overhead reduction in the case of
`spatial channel puncture, where the spatial channel corre(cid:173)
`sponding to the weakest eigenmode is usually punctured.
`Additionally, in some embodiments the mean ( and variance)
`of eigenvalues for each active spatial channel is fed back for
`adaptive modulation, where the mean (and variance) is
`computed over the sorted eigenvalues on OFDM subchan(cid:173)
`nels. For example, each OFDM subchannel has two active
`spatial channels that corresponds to two eigenvalues. The
`two eigenvalues are sorted for each subchannel. The mean
`(and variance) of the first sorted eigenvalues is computed
`over the subchannels and is fed back. Similarly, the mean
`(and variance) of the second sorted eigenvalues does so.
`
`[0017] The various embodiments of the present invention
`provide a systematic, uniform scheme supporting all antenna
`configurations such as 2x2, 4x2, 4x4 and beyond, and one
`set of codebooks may be shared among the various antenna
`configurations. Further, the reconstructed matrix is unitary
`without additional correction.
`
`[0018] A transmit beamforming matrix may be found
`using singular value decomposition (SYD) of the channel
`state matrix H as follows:
`
`vector v2 and n-2 by k-2 matrix V2 . This repeats k-1 times.
`Finally, the quantization of V is converted to the quantiza(cid:173)
`tion of v 1 , v 2 , . . . , vk that are k unit vectors of dimensions
`n, n-1, ... , n-k+l.
`
`[0021]
`In some embodiments, an access point may send
`training signals to a station and the station may compute and
`feedback the beamforming matrix Vin (1). If the station
`knows beforehand that the access point only employs k
`spatial streams, the station may only feed back the first k
`columns of the V matrix, which corresponds to the k
`strongest eigenmodes of H. This offers an additional reduc(cid:173)
`tion in feedback bandwidth. The degree of freedom of H is
`2n2 while the degree of freedom ofV is n2 -n for m=n. Since
`only V is useful for transmit beamforming and V contains
`less information than H, feeding back V is more efficient
`than feeding H.
`
`[0022] Quantization of the beamforming matrix Vis illus(cid:173)
`trated below by an example, in which 4 transmit antennas
`exist and 3 receive antennas exist. Although the example
`employs a 4x3 system, the various embodiments of the
`invention are not so limited. The receiver receives training
`symbols and computes the beamforming matrix, Vas shown
`above in equation (1). Next, the receiver only needs to
`quantize the first 3 colunms ofV since the channel supports
`at most three modes. If the receiver knows the transmitter
`only employs two spatial channels, the receiver may only
`quantize the first two colunms of V in the scheme depicted
`next.
`
`[0023]
`In some embodiments, the V matrix is quantized
`column by colunm and recursively. After the quantization of
`one colunm, the size of the problem is reduced by one on
`both row and colunm dimensions. Denoting the beamform(cid:173)
`ing matrix as:
`
`(1)
`
`(3)
`
`(2)
`[0019] where dis then-vector of data symbols containing
`k non-zero elements, where k is the number of active spatial
`channels (see next paragraph); x is the beamformed, trans(cid:173)
`mitted signal vector on n transmit antennas; His the channel
`matrix; H's singular value decomposition is H=UDV'; U and
`V are unitary; Dis a diagonal matrix with H's eigenvalues;
`V is n by n and only the first k colunms are needed to be fed
`back. Equation (2) is the beamforming act at the transmitter
`after the beamforming matrix Vis fed back from the receiver
`to the transmitter.
`
`[0020] Various embodiments of the present invention
`combine Householder reflection techniques with vector
`quantization in the quantization ofV, the unitary beamform(cid:173)
`ing matrix. First, a Householder reflection matrix, P, is
`constructed from v 1 , the first colunm ofV, where Vis n by
`k; n is the number of transmit antennas; k is the number of
`spatial streams. The P matrix has the property that the first
`colunm of the product, PY, is [ei<l>1 0 ... oy. And the first row
`of PV becomes [ ei<l>1 0 ... O] due to orthogonality. Then, the
`quantization of an n by k V matrix is converted into the
`quantization of n-vector v 1 and the quantization of an n-1 by
`k-1 matrix V 1 . This conversion reduces overhead and
`quantization complexity. The process is repeated to quantize
`V 1 and convert the problem to the quantization of (n-1)-
`
`V=
`
`[0024]
`the first column of V denoted as v 1 may be be
`quantized as follows.
`
`(4)
`
`[0025] where C 1 is a codebook containing unit 4-vectors
`for quantization shown at the bottom of this description. v 1
`has the maximum inner product among all unit vectors in the
`codebook. The codebook is constructed such that the code(cid:173)
`word vectors distribute on the n-dimension complex unit
`sphere as uniformly as possible. Additionally, the first ele(cid:173)
`ment of each codeword is set to be real for the next step.
`
`[0026] A Householder reflection matrix is constructed as
`follows
`
`(5)
`
`

`

`US 2006/0092054 Al
`
`May 4, 2006
`
`3
`
`[0027]
`In some embodiments, the householder reflection
`matrix is determined as a function of the original column
`vector, in which case
`
`Vu -1
`
`In other embodiments, the householder reflection matrix is
`determined as a function of the value of the vector selected
`from the codebook, in which case
`
`i>u -1
`
`If v 1 =v 1 , Householder reflection converts the first column
`and row ofV into [ ei<l>1 0 0 O]T and ei<l>1[1 0 O] as shown in (6),
`where cp 1 is the phase of v 11 . Since usually v i""v i, there will
`be nonzero residuals in the off diagonal entries of the first
`colunm and row.
`
`is worth noting that the phases <Pi may not be sent back. In
`some embodiments, for high speed and low complexity, the
`codebooks are generated such that their sizes are no larger
`than 64. Since the codebook size is small, the Householder
`matrix for each codeword can be stored beforehand to
`reduce computational complexity.
`
`[0032] The pseudo code of quantization algorithm for a
`general beamforming matrix is listed as follows.
`
`1. Compute singular value decomposition of the downlink
`channel matrix H with size m by n as in equation (1), and
`obtain the first k colunms of the beamforming matrix V,
`where k is the number of active spatial channels.
`
`2. Let V=V. 1-k, which is a temporary matrix and is formed
`by the first k colunms of V.
`3. For i=l: min(k,n-1)
`
`[0033] 3.1. Let vi=V. 1 , which is the first colunm ofV.
`
`[0034] 3.2. Quantize vi by finding vi=arg maxucclluHvill,
`where Ci is a codebook of unit n-i+ 1 vectors. '
`
`[0035] 3.3. Record the index of vi in the codebook for
`feedback.
`
`[0036] 3.4. Construct a Householder reflection matrix
`as
`
`el¢!
`
`0.0
`
`0.0
`
`(6)
`
`2
`H
`F; = I - ~W;W; ,
`
`[0037]
`where wi=vi-e 1 and e 1 is the unit vector with
`all zero elements except the first equal to one.
`
`[0038] 3.5. Conduct Householder reflection on V as
`V=FiV. To reduce complexity, one only needs to com(cid:173)
`pute colunms and rows of V other than the first one.
`
`[0039] 3.6. Update V=V2.n- i+l,2k·
`
`4. End
`
`[0040] For small matrix V, the SYD computation above
`can be skipped as follows. The vector codebooks Ci for vi
`uniquely defines a matrix codebook, C, for V, where each
`codeword can be constructed using codewords in Ci as
`shown in (9) and (10). We can test the beamforming per(cid:173)
`formance of the beamforming matrixes (or codewords) in C
`and select the codeword having the best performance. One
`way to test the beamforming performance is as follows.
`
`[0041] 1. Apply the beamforming matrix under test, V(t),
`to the channel matrix H, where V(t) is the t-th codeword in
`C. The combined channel matrix after the beamforming is as
`
`G=lN(t)
`(8)
`[0042] 2. The signal to interference plus noise ratios
`(SINR) of this beamformed channel G can be computed in
`order to estimate the performance ofV(t). For linear receiv(cid:173)
`ers such as MMSE and zero-forcing receiver, the computa(cid:173)
`tion of the SINR for each spatial stream is known.
`
`[0043] 3. Compare the sets of SINRs corresponding to
`V(t)s, and select the best V(t), where the selection criterion
`may be maximum mean SINR averaged over spatial
`
`0.0 I ~ll ~121
`
`F1V = 0.0
`0.0
`
`V21
`
`V22
`
`031
`
`032
`
`'2
`
`[0028] where two properties are employed to get the
`result, i.e. v 11 is real and the unitary property ofV. Since both
`F 1 and V are unitary, V 2 is unitary. From
`[0029]
`(6), we see that the size of V2 is 3x2 and it is
`reduced from that of V 1 by one on both row and colunm
`dimensions. Recursively, we repeat the actions in (4),
`
`[0030]
`(5), and (6) on V2 as follows. First, we quantize the
`first colunm ofV2 denoted as v2, using another codebook of
`unit 3-vectors shown at the bottom of this description, whose
`first element of each codeword is real. Then, we construct a
`Householder reflection matrix and multiply it with V 2 as
`follows.
`
`el¢2
`
`0.0
`
`F2V2 = 0.0 [~ll [
`V 21
`
`0.0
`
`(7)
`
`'3
`
`[0031] Finally, we quantize the vector V3 using a code(cid:173)
`book of unit 2-vectors shown at the bottom of this descrip(cid:173)
`tion. The quantization indexes of vi, v 2, and v 3 are fed back
`to the access point, i.e. the transmitter, for beamforming. It
`
`

`

`US 2006/0092054 Al
`
`May 4, 2006
`
`4
`
`streams, or minimum estimated packet error rate. We find
`and feed the quantization index corresponding to the optimal
`V(t).
`[0044] At the transmitter side, the reconstruction of the
`beamforming matrix Vis as follows. It starts from the lowest
`dimension and recursively constructs the whole matrix. In
`each step, a Householder matrix is computed from a recon(cid:173)
`structed unit vector. The Householder matrix can be com(cid:173)
`puted and stored beforehand for small codebooks. Even in
`the case that there is no quantization error, the reconstructed
`matrix could be different from the original V by a global
`phase on each colunm and this is fine with closed loop
`MIMO. First, two vectors, v 3 and v 2 , are reconstructed using
`the feedback quantization indexes and the corresponding
`2-vector and 3-vector codebooks. Second, a Householder
`matrix is computed using the reconstructed v 2 as
`
`2
`F1 = I - jj;jpww ,
`
`H
`
`(11)
`
`[0047] where w=v 1 -e 1 and v 1 is the reconstructed first
`colunm ofV. Finally, the beamforming matrix Vis given by
`
`V =F1
`
`0 0
`
`0
`0 V2
`0
`
`(12)
`
`2
`H
`F2 = I - jj;jpww ,
`
`(9)
`
`[0048] Since the codebook size is less than 64, which is
`small, the Householder matrix for each codebook entry can
`be stored beforehand to speedup the reconstruction.
`
`[0045] where w=v2 -e1 and v2 is the reconstructed 3-vec(cid:173)
`tor; F 2 can be stored beforehand to reduce computation.
`Third, V 2 can be reconstructed as
`
`[0049]
`In general, the receiver of the beam forming vector
`index can reconstruct the beam forming vector according to
`the following algorithm.
`
`Receive indices ni, i = 1, ... , Nn, where Nn is the number of feedback indices.
`1.
`If k < n, where k and n are the numbers of spatial streams and transmit
`2.
`antennas respectively, do
`
`2.1
`
`Let V = vN, the nwth vector of the codebook of (n-k+ !)dimension
`
`unit vector.
`2.2
`J = N"-1.
`
`3.
`
`Else
`
`3.1
`
`3.2
`
`Let V= 1.
`J = N".
`
`End
`for i = J:-1:1
`
`4
`5.
`
`5.1
`
`vector
`
`5.2
`
`5.3
`
`6.
`
`End
`
`(10)
`
`[0046] Fourth, we reconstruct the first colunm ofV using
`the quantization index and compute a Householder matrix as
`
`v; = the n;-th vector of the codebook of (n - 1 + 1) dimension unit
`
`2
`F; = I- ~ww", w = v; - e1.
`
`[0050] Quantization of large unit vector can be done as
`follows. It should be noticed that the quantization of the unit
`vector in ( 4) is computational intensive for unit vectors of
`large size. Three schemes are proposed for the quantization
`of large unit vectors.
`[0051] Scheme!
`[0052] We quantize each element of the unit vector using
`scalar quantization. For example, we may quantize unit
`. v nY as follows. We first normalize the
`vector v=[ v 1
`.
`.
`
`

`

`US 2006/0092054 Al
`
`May 4, 2006
`
`average power of each element of v to be unity, i.e. v'nv.
`Then, we may quantize each element of v'nv using the radial
`quantization constellation shown in Error! Reference source
`not found. The quantization indexes are feed back to the
`transmitter for reconstruction.
`
`[0053] Scheme2
`
`[0054] We first partition the unit vector into sub-vectors
`and quantize each sub-vector using vector quantization
`methods e.g. vector codebooks. The quantization index of
`each sub-vector is feed back to the transmitter for the
`reconstruction of the large vector.
`
`[0055] Scheme3
`
`[0056] Quantization Acts
`
`[0057] 1: Partition the vector into two sub-vectors, il 1 and
`il2 , as
`
`v=
`
`Vt }u1
`
`V;
`
`V;~J }-
`:
`U2
`
`Vn
`
`[0058] 2: Normalize il; as il;=a;U; for i=l,2, where llu;ll=l,
`lla 1 ll 2 +lla2 ll 2 =l, and a;~O. lla 1 ll 2 +lla2 ll 2 =l is because vis a unit
`vector.
`
`[0059] 3: Quantize u 1 and u2
`. Ifwe employ vector quan(cid:173)
`tization, we may employ different codebooks depending on
`the value of a;. For example, if a; is large, then we may
`employ a codebook of more entries for u; than that if a; is
`small. Denote the quantized vectors ofu 1 and u2 as u 1 and u2
`respectively. The quantization indexes for u 1 and u2 are fed
`back to the transmitter.
`
`[0060] 4: Compute the global phase difference between u;
`and u; for i=l, 2 as <P;=phase(u';u;). These phases may already
`be computed in 3 during the quantization of u 1 and u2 .
`
`[0061] 5: Compute cjl=cp2 -cp 1 , which is phase difference
`between the lower and upper sub-vectors, u2 and u 1 .
`
`[0062] 6: Quantize cp and one of a1 and a2 jointly or
`separately. Feed back the quantization indexes.
`
`[0063] Reconstruction Acts
`
`[0064] 1: Reconstruct a;. If a 1 is quantized and fed back,
`then a2 =Yl-a/, where a 1 is the reconstructed a 1 from the
`feedback index. Similarly, ifa2 is quantized, then a1 =v' 1-a/.
`
`[0065] 2: Reconstruct cp and denote the reconstructed
`phase as~-
`
`[0066] 3: Reconstruct u 1 and u2 using the quantization
`indexes. Denote the reconstructed vectors as u 1 and u2 .
`
`5
`
`[0067] 4: Reconstruct v as
`
`[0068] The number of sub-vectors in Scheme 3 can be
`generalized to L that is greater than 2 as follows.
`
`[0069] Scheme 3.1
`
`[0070] Quantization Acts
`
`[0071] 1: Partition the vector into L sub-vectors, il1 , . . . ,
`ilu as
`
`[0072] 2: Normalize il; as il;=a;U; for i=l, ... , L where
`llu;ll=l, ~lla;ll 2 =1, and a);O. ~lla;ll 2 =1 is because v is a unit
`vector.
`
`[0073] 3: Quantize u;, for i=l, ... , L. Ifwe employ vector
`quantization, we may employ different codebooks depend(cid:173)
`ing on the value ofa;. For example, ifa; is large, then we may
`employ a codebook of more entries for u; than that if a; is
`small. Denote the quantized vectors of u; as u;. The quanti(cid:173)
`zation index for each u; is fed back to the transmitter.
`
`[0074] 4: Compute the global phase difference between u;
`and u; for i=l, ... ,Las <P;=phase(u';u;). These phases may
`already be computed in 3 during the quantization of u;.
`
`[0075] 5: Compute cjli=<Pi-cp 1 for j=2, ... , L, where <Pi is the
`phase difference between sub-vector, ui and u 1 .
`[0076] 6: Quantize <Pi for j=2, ... , L, and L-1 of aJor i=l,
`... , L jointly or separately. Feed back the quantization
`indexes.
`
`[0077]
`If the dimension of the unit vector is large, the
`vector can be partitioned into multiple sub-vectors and
`Scheme 3 can also be applied recursively to quantize the unit
`vector as follows.
`
`[0078] Scheme 3.2
`
`[0079] Quantization Acts
`
`[0080] 1: Partition the vector into L sub-vectors, il1 , . . . ,
`ilu as
`
`[0081] 2: Normalize il; as il;=a;U; for i=l, ... , L where
`llu;ll=l, ~lla;ll 2 =1, and a);O. ~lla;ll 2 =1 is because v is a unit
`vector.
`
`

`

`US 2006/0092054 Al
`
`May 4, 2006
`
`6
`
`[0082] 3: Quantize u;, for i=l, ... , L. Ifwe employ vector
`quantization, we may employ different codebooks depend(cid:173)
`ing on the value ofa;. For example, ifa; is large, then we may
`employ a codebook of more entries for u; than that if a; is
`small. Denote the quantized vectors of u; as u;. The quanti(cid:173)
`zation index for each u; is fed back to the transmitter.
`
`[0083] 4: Compute the global phase difference between uL
`and uL as ~=phase(u'LuL). Let I =au u=uu and v=uL.
`[0084] 5: For i=L-1:-1:1 Do
`
`[0085] 5.1 Compute
`the global phase difference
`between u; and u; as <P;=phase(u';u;).
`[0086] 5.2 Compute cjl=~-<P; and
`
`[0087] 5.3 Quantize cos(8) and sin(8)&<1> jointly or
`respectively, and feed back quantization indexes.
`
`[0088] 5.4 Let
`
`U=
`
`U;
`
`[
`
`[
`
`"
`
`andV=
`
`r cos(0)u; r
`sin( 0)e11' v '
`
`where El and ~ are quantized cp and 8.
`[0089]
`[0090] 5.4 Compute ~=phase(v'u) and I =llvll(cid:173)
`[0091] End
`
`[0092] FIG. 3 shows a flowchart in accordance with
`various embodiments of the present invention. In some
`embodiments, method 300 may be used in, or for, a wireless
`system that utilizes MIMO technology. In some embodi(cid:173)
`ments, method 300, or portions thereof, is performed by a
`wireless communications device, embodiments of which are
`shown in the various figures. In other embodiments, method
`300 is performed by a processor or electronic system.
`Method 300 is not limited by the particular type of apparatus
`or software element performing the method. The various
`actions in method 300 may be performed in the order
`presented, or may be performed in a different order. Further,
`in some embodiments, some actions listed in FIG. 3 are
`omitted from method 300.
`
`[0093] Method 300 is shown beginning at block 310 in
`which channel state information is estimated from received
`signals. The channel state information may include the
`channel state matrix H described above. At 320, a beam(cid:173)
`forming matrix is determined from the channel state infor(cid:173)
`mation. In some embodiments, this corresponds to perform(cid:173)
`ing singular value decomposition (SYD) as described above
`with reference to equation (1). The beamforming matrix V
`is also described above.
`
`[0094] At 330, a colunm of a beamforming matrix is
`quantized using a codebook. In various embodiments of the
`present invention, the actions of330 correspond to searching
`a code block for an entry that most closely matches the
`colunm vector. For example, the operations described above
`
`with reference to equation ( 4) may be utilized to search a
`code book. In various embodiments of the present invention,
`the size of the codebook, and therefore the number of bits
`used to represent the quantized vector, may vary. For
`example, in some embodiments, a large codebook may be
`used for all colunm vectors. Also for example, in some
`embodiments longer colunm vectors may be quantized using
`larger codebooks, and a smaller column vectors may be
`quantized using a smaller code book.
`
`[0095] At 340, a householder reflection is performed on
`the beamforming matrix to reduce the dimensionality of the
`beamforming matrix. In some embodiments, the actions of
`340 correspond to the operations described above with
`reference to the equations (5) and (6). At 350, the quantizing
`and householder reflection operations of 330 and 340 are
`recursively repeated. As the operations are recursively
`repeated, each of the colunm vectors may be quantized using
`the same codebook or different codebooks. For example, as
`the dimensionality of the beamforming matrix is reduced,
`smaller codebooks may be used for successive column
`vectors. In some embodiments, where three colunm vectors
`are quantized, codebooks of descending size may be utilized
`such that the colunm vectors are quantized into eight bits, six
`bits, three bits, or six bits, five bits, and four bits, or five bits,
`four bits, and three bits, although this is not a limitation of
`the present invention.
`
`In some embodiments of method 300, quantizing
`[0096]
`and Householder reflection is recursively performed until a
`small matrix remains, and the small matrix is quantized
`using a codebook of small matrices. Also in some embodi(cid:173)
`ments, large colunm vectors may be quantized by breaking
`the large column vectors into two or more sub-vectors, and
`then each of the sub-vectors may be quantized using one or
`more codebooks. The partition itself may be quantized using
`one or more codebooks. In still further embodiments, col(cid:173)
`unm vectors or sub-vectors may be quantized by normaliz(cid:173)
`ing the average power of each element, and quantizing each
`element using a radial constellation, such as the radial
`constellation shown in FIG. 2. At 360, the quantized column
`vectors are transmitted.
`
`[0097] FIG. 4 shows a flowchart in accordance with
`various embodiments of the present invention. In some
`embodiments, method 400 may be used in, or for, a wireless
`system that utilizes MIMO technology. In some embodi(cid:173)
`ments, method 400, or portions thereof, is performed by a
`wireless communications device, embodiments of which are
`shown in the various figures. In other embodiments, method
`400 is performed by a processor or electronic system.
`Method 400 is not limited by the particular type of apparatus
`or software element performing the method. The various
`actions in method 400 may be performed in the order
`presented, or may be performed in a different order. Further,
`in some embodiments, some actions listed in FIG. 4 are
`omitted from method 400.
`
`[0098] Method 400 is shown beginning at block 410 in
`which quantized colunm vectors are received. At 420, one or
`more codebooks are indexed into using the quantized col(cid:173)
`unm vectors to yield a plurality of column vectors. The
`actions of 420 may take many different forms. For example,
`quantized colunm vectors make each the represented by a
`different number of bits, and each may correspond to a
`different codebook of column vectors. Further, one or more
`
`

`

`US 2006/0092054 Al
`
`May 4, 2006
`
`7
`
`column vectors may be represented as quantized sub-vec(cid:173)
`tors, and each quantized