(19) United States
`(12) Patent Application Publication (10) Pub. No.: US 2006/0092054 A1
`
`Li et al. May 4, 2006 (43) Pub. Date:
`
`
`US 20060092054A1
`
`(54) RECURSIVE REDUCTION OF CHANNEL
`STATE FEEDBACK
`
`(22)
`
`Filed:
`
`Sep. 8, 2004
`
`Publication Classification
`
`(76)
`
`Inventors: Qinghua Li, Sunnyvale, CA (US);
`Xintian E. Lin, Mountain View, CA
`(US)
`
`Correspondence Address:
`LeMoine Patent Services, PLLC
`c/o PortfolioIP
`PO. Box 52050
`
`Minneapolis, MN 55402 (US)
`
`(21) App]. No.:
`
`10/937,097
`
`(51)
`
`Int. Cl-
`(2006.01)
`H03M 7/40
`(52) US. 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
`
`310
`
`FROM RECEIVED SIGNALS
`
`
`
`
`
`DETERMINE A BEAMFORMING MATRIX
`
`320
`
`FROM THE CHANNEL STATE INFORMATION
`
`QUANTIZE A COLUMN OF A BEAMFORMING
`MATRIX USING A CODEBOOK
`
`330
`
`PERFORM A HOUSEHOLDER REFLECTION
`
`ON THE BEAMFORMING MATRIX TO
`
`340
`
`REDUCE THE DIMENSIONALITY OF THE
`
`BEAMFORMING MATRIX
`
`
`
`RECURSIVELY REPEAT THE QUANTIZING
`
`350
`
`AND PERFORMING OF HOUSEHOLDER
`
`REFLECTION
`
`
`
`'TRANSMIT QUANTIZED COLUMN VECTORS
`
`6
`3 0
`
`300
`
`1
`
`HUAWEI 1007
`
`1
`
`HUAWEI 1007
`
`

`

`Patent Application Publication May 4, 2006 Sheet 1 0f 7
`
`US 2006/0092054 A1
`
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`

`Patent Application Publication May 4, 2006 Sheet 2 0f 7
`
`US 2006/0092054 A1
`
`
`
`3
`
`

`

`Patent Application Publication May 4, 2006 Sheet 3 of 7
`
`US 2006/0092054 A1
`
`ESTIMATE CHANNEL STATE INFORMATION
`
`310
`
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`
`320
`
`FROM THE CHANNEL STATE INFORMATION
`
`QUANTIZE A COLUMN OF A BEAMFORMING
`MATRIX USING A CODEBOOK
`
`330
`
`
`PERFORM A HOUSEHOLDER REFLECTION
`ON THE BEAMFORMING MATRIX TO
`REDUCE THE DIMENSIONALITY OF THE
`
`
`
`BEAMFORMING MATRIX
`
`
`
`
`
`
`
`RECURSIVELY REPEAT THE QUANTIZING
`AND PERFORMING OF HOUSEHOLDER
`REFLECTION
`
`
`
`
`340
`
`350
`
`’TRANSMIT QUANTIZED COLUMN VECTORS
`
`6
`
`3 0
`
`FIG. 3 .
`
`300
`
`4
`
`

`

`Patent Application Publication May 4, 2006 Sheet 4 0f 7
`
`US 2006/0092054 A1
`
`RECEIVE QUANTIZED COLUMN VECTORS
`
`410
`
`
`
`
`
`
`
`INDEX INTO A CODEBOOK USING THE
`
` 420
`
`QUANTIZED COLUMN VECTORS TO YIELD
`
`A PLURALITY OF COLUMN VECTORS
`
`
`DETERMINE A T LEAST ONE
`HOUSEHOLDER MATRIX FROM THE
`
`430
`
`PLURALI TY OF COLUMN VECTORS
`
`RECURSIVELY APPLY THE ATLEAST ONE
`
`HOUSEHOLDER MATRIX TO THE
`
`PLURALI TY OF QUANTIZED COLUMN
`
`440
`
`
`
`
`
`VECTORS TO GENERATE A BEAMFORMING
`MATRIX
`
`
`FIG. 4
`
`400
`
`5
`
`

`

`Patent Application Publication May 4, 2006 Sheet 5 0f 7
`
`US 2006/0092054 A1
`
`550
`
`LLIO
`EEE
`FE
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`
`.
`
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`cx.
`
`FIG.5
`
`6
`
`

`

`Patent Application Publication May 4, 2006 Sheet 6 0f 7
`
`US 2006/0092054 A1
`
`n1=3 n2=4 energy=0.9888
`
`
`
`FIG. 6
`
`7
`
`

`

`Patent Application Publication May 4, 2006 Sheet 7 0f 7
`
`US 2006/0092054 A1
`
`FIG. 7
`
`FIG. 8
`
`8
`
`

`

`US 2006/0092054 A1
`
`May 4, 2006
`
`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
`
`multiple-input-multiple-output
`loop
`[0002] Closed
`(MIMO) systems typically transmit channel state informa-
`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
`
`In the following detailed description, reference is
`[0010]
`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-
`
`ments of the invention, although different, are not necessar-
`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-
`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 eomoliance with any
`
`other standard, such as any future IEEE personal area
`network standard or wide area network standard.
`
`Stations 102 and 104 may include any number of
`[0013]
`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” (eg. 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-
`sible by multipath. The channel between stations 102 and
`104 is described by the cham1el state matrix, H, that includes
`entries describing the complex chamiel gains between each
`transmit and receive antenna pair.
`
`
`
`In some embodiments, stations 102 and 104 may
`[0014]
`communicate using orthogonal frequency division multi-
`plexing (OEDM) in each spatial chalmel. 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 OEDM breaks each spatial channel
`into small
`subchannels such that each subchamiel exhibits a more flat
`chamiel characteristic. Scaling appropriate for each sub—
`chamiel may be implemented to correct any attenuation
`caused by the subchannel. Further, the data carrying capacity
`of each subchannel may be controlled dynamically depend-
`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-
`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-
`width is reduced in closed loop MIMO systems, more
`bandwidth is available for data eommtmieations.
`
`9
`
`

`

`US 2006/0092054 A1
`
`May 4, 2006
`
`[0016] Various embodiments of the present invention pro-
`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-
`zation using codebooks. In some of these embodiments,
`diiferent size codebooks are used for different ones of the
`
`in some
`transmit beamfonning vectors. For example,
`embodiments,
`three beamforming vectors are quantized
`using three small codebooks of sizes 16, 32 and 64 respec-
`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—
`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-
`nels. For example, each OFDM subchalmel 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 onc
`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 (SVD) of the channel
`state matrix H as follows:
`
`men= mmeman’nxn
`_ 7
`W
`nxl
`d
`rod—[mm
`
`(1)
`(2)
`
`[0019] where d is the n-vector of data symbols containing
`k non-zero elements, where k is the number of active spatial
`channels (see next paragraph); x is the beamfonned, trans-
`mitted signal vector on n transmit antennas; H is the channel
`matrix; H’s singular value decomposition is H=UDV'; U and
`V are unitary; D is a diagonal matrix with H’s eigenvalues;
`V is n by n and only the first k columns are needed to be fed
`back. Equation (2) is the beamforming act at the transmitter
`after the beamforming matrix V is fed back from the receiver
`to the transmitter.
`
`invention
`[0020] Various embodiments of the present
`combine Householder reflection techniques with vector
`quantization in the quantization of V, the unitary beamform-
`ing matrix. First, a Householder reflection matrix, P,
`is
`constructed from v1, the first column of V, where V is 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
`column of the product, PV, is [ejq’l 0 .
`.
`. 0]T. And the first row
`of PV becomes [eiqn 0 .
`.
`. 0] due to orthogonality. Then, the
`quantization of an n by k V matrix is converted into the
`quantization ofn-vector v1 and the quantization of an n—l by
`k—l matrix V1. This conversion reduces overhead and
`quantization complexity. The process is repeated to quantize
`V1 and convert the problem to the quantization of (n—l)-
`
`vector v2 and n—2 by k—2 matrix V2. This repeats k—l times.
`Finally, the quantization of V is converted to the quantiza-
`tion of v1, v2, .
`.
`.
`, vk that are k unit vectors of dimensions
`11, n—l,
`.
`.
`. ,n—k+l.
`
`In some embodiments, an access point may send
`[0021]
`training signals to a station and the station may compute and
`feedback the beamforming matrix V in (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-
`tion in feedback bandwidth. The degree of freedom of H is
`2n2 while the degree of freedom ofV is nZ—n for m=n. Since
`only V is useful for transmit beamforming and V contains
`less information than H, feeding back V is more eflicient
`than feeding H.
`
`[0022] Quantization of the beamforming matrix V is illus-
`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, V as shown
`above in equation (1). Next, the receiver only needs to
`quantize the first 3 columns of V 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 columns of V in the scheme depicted
`next.
`
`In some embodiments, the V matrix is quantized
`[0023]
`column by column and recursively. After the quantization of
`one column, the size of the problem is reduced by one on
`both row and column dimensions. Denoting the beamform-
`ing matrix as:
`
`V11
`
`V12
`
`V13
`
`V:
`
`V21
`V31
`V41
`
`V22
`V32
`V42
`
`’
`
`V23
`V33
`V43
`
`(3)
`
`the first column of V denoted as vl may be be
`[0024]
`quantized as follows.
`
`V1=8Ig maxueclllqurH
`
`(I4)
`
`[0025] where C 1 is a codebook containing unit 4-vectors
`for quantization shown at the bottom of this description. v1
`has the maximum inner product among all unit vectors in the
`codebook. The codebook is constructed such that the code-
`
`word vectors distribute on the n-dimension complex unit
`sphere as uniformly as possible. Additionally, the first ele-
`ment of each codeword is set to be real for the next step.
`
`[0026] A Householder reflection matrix is constructed as
`follows
`
`
`2
`
`(5)
`
`10
`
`10
`
`

`

`US 2006/0092054 A1
`
`May 4, 2006
`
`In some embodiments, the householder reflection
`[0027]
`matrix is determined as a function of the original column
`vector, in which case
`
`wl = v1 —el
`
`v11 —1
`V21
`V31
`V41
`
`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
`
`911—1
`V21
`V31
`V41
`
`lf v1=v1, Householder reflection converts the first column
`and row ofV into [64" 0 0 0]T and el“"[1 0 0] as shown in (6),
`where (I)l is the phase of v11. Since usually vlzv 1, there will
`be nonzero residuals in the off diagonal entries of the first
`colunm and row.
`
`is worth noting that the phases q), 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
`chamiel matrix H with size m by n as in equation (1), and
`obtain the first k columns 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 formcd
`by the first k columns of V.
`
`3. For i=1: min(k,n—l)
`
`[0033]
`
`3.1. Let vi=V:,1, which is the first column of V.
`
`3.2. Quantize vi by finding vi=arg maxueCiHquiH,
`[0034]
`where Ci is a codebook of unit n—i+l vectors.
`
`3.3. Record the index of vi in the codebook for
`[0035]
`feedback.
`
`[0036]
`as
`
`3.4. Construct a Householder reflection matrix
`
`2
`
`i = 1—
`
`WMF.
`
`”Will2
`
`(6}
`
`0.0
`
`8"“
`0.0
`0.0
`0'0
`
`0.0
`911
`912
`1721
`922
`\731
`932
`
`V2
`
`FIV =
`
`where wi=vi—el and el is the unit vector with
`[0037]
`all zero elements except the first equal to one.
`
`3.5. Conduct Householder reflection on V as
`[0038]
`V=FiV. To reduce complexity, one only needs to com-
`pute columns and rows of V other than the first one.
`
`[0039]
`4. End
`
`3.6. Update V472,, “Mk.
`
`[0040] For small matrix V, the SVD 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 C‘- as
`shown in (9) and (10). We can test the beamforming per-
`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.
`
`the
`[0028] where two properties are employed to get
`result, i.e. {7, 1 is real and the unitary property ofV. Since both
`F1 and V are unitary, V2 is unitary. From
`
`(6), we see that the size of V2 is 3x2 and it is
`[0029]
`reduced from that of V1 by one on both row and column
`dimensions. Recursively, we repeat the actions in (4),
`
`(5), and (6) on V2 as follows. First, we quantize the
`[0030]
`first column of V2 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 V2 as
`follows.
`
`«M 0.0
`
`F2 V2 2
`
`V11
`0.0
`0.0 ml
`V3
`
`[0031] Finally, we quantize the vector V3 using a code-
`book of unit 2-vectors shown at the bottom of this descrip-
`tion. The quantization indexes of v1, v2, and v3 are fed back
`to the access point, i.e. the transmitter, for beamforming. It
`
`1. Apply the beamforming matrix under test, V(t),
`[0041]
`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=HV(2‘)
`(:8)
`
`(7;
`
`to interference plus noise ratios
`2. The signal
`[0042]
`(SINR) of this beamformed channel G can be computed in
`order to estimate the performance of V(t). For linear receiv-
`ers such as MMSE and zero-forcing receiver, the computa-
`tion of the SINR for each spatial stream is known.
`
`3. Compare the sets of SINRs corresponding to
`[0043]
`\7(t)s, and select the best V(t), where the selection criterion
`may be maximum mean SINR averaged over spatial
`
`11
`
`11
`
`

`

`US 2006/0092054 A1
`
`May 4, 2006
`
`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 V is 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-
`structed unit vector. The Ilouseholder matrix can be com-
`
`puted and stored beforehand for small codebooks. Even in
`the case that there is no quantization error, the reconstructed
`matrix could bc diffcrcnt from thc original V by a global
`phase on each column and this is fine with closed loop
`MlMO. First. two vectors. v3 and v2, 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 v2 as
`
`F1=I—
`
`
`2
`IIWII2
`
`H
`WW .
`
`(11)
`
`is the reconstructed first
`[0047] where w=\A/1—el and {/1
`column of V. Finally, the beamforrning matrix V is given by
`
`(12)
`
`H
`
`(9)
`
`Since the codebook size is less than 64, which is
`[0048]
`small, the Householder matrix for each codebook entry can
`be stored beforehand to speedup the reconstruction.
`
`[0045] where w=vZ—e1 and v2 is the reconstructed 3-vec-
`tor, F2 can be stored beforehand to reduce computation.
`'l'hird, V2 can be reconstructed as
`
`In general, the receiver of the beam forming vector
`[0049]
`index can reconstruct the beam forming vector according to
`the following algorithm.
`
`., N“, where Nn is the number of feedback indices.
`.
`i = l, .
`Receive indices Hi,
`1.
`If k < n, where k and n are the numbers of spatial streams and transmit
`2.
`antennas respectively. do
`2.1
`H
`Let V = 9N, the nN-th vector of the codebook of (n — k + l) dimension
`
`unit vector.
`2.2
`J = Nn—l.
`
`Else
`
`3.1
`
`3.2
`
`H
`Let V = l.
`J = NH.
`End
`fori=J:—l:l
`
`3.
`
`4
`5.
`
`Vi = the ni-th vector of the codebook of(n — l + l) dimension unit
`
`2
`Fj=1 —2wwH,w=v] —e1
`lIWlI
`
`v = F.
`
`0
`1
`-
`0 V
`
`.
`
`5'1
`vector
`
`5.2
`
`5.3
`
`6.
`
`End
`
`am
`
`[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.
`
`[0046] Fourth, we reconstruct the first column of V using
`the quantization index and compute a Householder matrix as
`
`[0051] Schemel
`
`[0052] We quantize each element of the unit vector using
`scalar quantization. For example, we may quantize unit
`vector v=[vl
`.
`.
`. vn]T as follows. We first normalize the
`
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`
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`

`US 2006/0092054 A1
`
`May 4, 2006
`
`average power of each element of V to be unity, i.e. Viv.
`Then, we may quantize each element of an using the radial
`
`quantization constellation shown in Error! Reference source
`not found. The quantization indexes are feed back to the
`transmitter for reconstruction.
`
`[0067]
`
`4: Reconstruct v as
`
`\7 =
`
`“1'41
`A
`ewazuz
`
`.
`
`[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]
`uz, as
`
`1: Partition the vector into two sub-vectors, fil and
`
`[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]
`fiL, as
`
`1: Partition the vector into L sub-vectors, fil, .
`
`.
`
`.
`
`,
`
`, L where
`.
`.
`.
`2: Normalize fii as fii=aiui for i=1,
`[0072]
`|lui|l=1, Z|lai|l2=1, and ago. Z|laiH2=1 is because v is a unit
`vector.
`
`, L. Ifwe employ vector
`.
`.
`3: Quantize lli, for i=1, .
`[0073]
`quantization, we may employ different codebooks depend-
`ing on the value of a. For example, if ai is large, then we may
`employ a codebook of more entries for ui than that if ai is
`small. Dcnotc the quantized vectors of ui as fii. Thc quanti-
`zation index for each ui is fed back to the transmitter.
`
`4: Compute the global phase difl'erence between ui
`[0074]
`and fii for i=1,
`.
`.
`. ,L as ¢i=phase(fi'iui). These phases may
`already be computed in 3 during the quantization of ui.
`
`, L, where -is the
`.
`.
`for'=2, .
`5: Com ute -= -—
`0075
`1
`J
`J
`F
`J
`J
`phase diiference between sub-vector, uj and ul.
`
`, L, and L—l ofa1 for i=1,
`.
`.
`6: Quantize ¢j forj=2, .
`[0076]
`.
`.
`.
`, L jointly or separately. Feed back the quantization
`indexes.
`
`2: Normalize f1i as fli=aiui for i=1,2, where Hui-“=1,
`[0058]
`Ha1H2+Ha2H2=L and aIEO. |a1H2+Ha2H2=l is because v is a unit
`vector.
`
`3: Quantize u1 and u2 . If we employ vector quan-
`[0059]
`tization, we may employ different codebooks depending 011
`the value of a. For example, if ai is large, then we may
`employ a codebook of more entries for ui than that if ai is
`small. Denote the quantized vectors ofu 1 and u2 as 01 and €12
`respectively. The quantization indexes for 111 and u2 are fed
`back to the transmitter.
`
`4: Compute the global phase difference between 111
`[0060]
`and fii for i=1, 2 as ¢i=phase(u'iui). These phases may already
`be computed in 3 during the quantization of 111 and u2.
`
`If the dimension of the unit vector is large, the
`[0077]
`vector can be partitioned into multiple sub—vectors and
`Scheme 3 can also be applied recursively to quantize the unit
`vector as follows.
`
`5: Compute ¢=¢2—¢1, which is phase difference
`[0061]
`between the lower and upper sub-vectors, u2 and ul.
`
`6: Quantize 4) and one of a1 and a2 jointly or
`[0062]
`separately. Feed back the quantization indexes.
`
`[0063] Reconstruction Acts
`
`[0064]
`l: Reconstruct ai. If al is quantized and fed back,
`then @1241 4112, where a1 is the reconstructed al from the
`feedback index. Similarly, if a2 is quantized, then a1 =Vrl 4:122.
`
`2: Reconstruct
`[0065]
`phase as (f).
`
`(I) and denote the reconstructed
`
`3: Reconstruct 111 and u2 using the quantization
`[0066]
`indexes. Denote the reconstructed vectors as fil and €12.
`
`[0078]
`
`Scheme 3.2
`
`[0079] Quantization Acts
`
`[0080]
`fiL, as
`
`1: Partition the vector into L sub-vectors, fil, .
`
`.
`
`.
`
`,
`
`, L where
`.
`.
`.
`2: Nonnalize fii as fii=aiui for i=1,
`[0081]
`Huill=1, Ella-“2:1, and a‘éo. ZHaiH2=1 is because v is a unit
`vector.
`
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`
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`
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`

`US 2006/0092054 A1
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`
`, L. Ifwe employ vector
`.
`.
`3: Quantize ui, for i=1, .
`[0082]
`quantization, we may employ different codebooks depend-
`ing on the value of a. For example, if a1 is large, then we may
`employ a codebook of more entries for ui than that if ai is
`small. Denote the quantized vectors of ui as 0,. The quanti-
`zation index for each 111 is fed back to the transmitter.
`
`4: Compute the global phase difference between uL
`[0083]
`and fiL as ([J=phase(fi'LuL). Let l=aL, fi=uL, and v=uL.
`
`[0084]
`
`5: For i=L—l:—l:l Do
`
`the global phase difference
`5.1 Compute
`[0085]
`between ui and ui as ¢1=phase(u'iui).
`
`[0086]
`
`5.2 Compute (pat—q), and
`
`0 = tan — .
`[l]
`a;
`
`5.3 Quantize 005(6) and sin(6)ei¢ jointly or
`[0087]
`respectively, and feed back quantization indexes.
`
`[0088]
`
`5.4 Let
`
`”A.
`it = [ ~
`M
`
`
`
`and t7 =
`
`cos((fl)12;
`A
`.
`Sumatra”?
`
`.
`
`[0089]
`
`where 9 and (f) are quantized q) and 0.
`
`[0090]
`
`5.4 Compute c])=phase(v‘fi) and I=M
`
`[0091] End
`
`in accordance with
`[0092] FIG. 3 shows a flowchart
`invention. In some
`various embodiments of the present
`embodiments, method 300 may be used in, or for, a wireless
`system that utilizes MIMO technology. In some embodi-
`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—
`forming matrix is determined from the channel state infor-
`mation. In some embodiments, this corresponds to perform-
`ing singular value decomposition (SVD) as described above
`with reference to equation (I). The beamforming matrix V
`is also described above.
`
`[0094] At 330, a column of a beamforming matrix is
`quantized using a codebook. In various embodiments of the
`present invention, the actions of 330 correspond to searching
`a code block for an entry that most closely matches the
`column 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 column vectors. Also for example,
`in some
`embodiments longer column 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 column 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 column vectors
`are quantized, codebooks of descending size may be utilized
`such that the column vcctors arc quantizcd into cight 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-
`ments, large column vectors may be quantized by breaking
`the large column vectors into two or more sub-vectors, and
`thcn each of thc sub-vcctors may bc quantizcd using onc or
`more codebooks. The partition itself may be quantized using
`one or more codebooks. In still further embodiments, col-
`umn vectors or sub—vectors may be quantized by normaliz—
`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.
`
`in accordance with
`[0097] FIG. 4 shows a flowchart
`various embodiments of the present invention.
`In some
`cmbodimcnts, mcthod 400 may bc uscd in, or for, a wirclcss
`system that utilizes MIMO technology. In some embodi-
`ments, method 400, or portions thereof, is performed by a
`wireless commtmications 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 column vectors are received. At 420, one or
`more codebooks are indexed into using the quantized col-
`umn vectors to yield a plurality of column vectors. The
`actions of 420 may take many different forms. For example,
`quantized column 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
`
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`

`US 2006/0092054 A1
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`
`column vectors may be represented as quantized sub-vec-
`tors, and each quantized sub-vector may be used to index
`into one or more codebooks, and a single column vector may
`be regenerated from multiple codebook entries.
`
`[0099] At 430, at least one householder matrix is deter-
`mined from the plurality of column vectors.
`In some
`embodiments, this may correspond to performing operations
`such as those described above with reference to equations
`(9) and (11). In other embodiments, a table may be main-
`tained with a one—to—one correspondence between quantized
`column vectors and Householder matrices. In these embodi-
`
`ments, a householder matrix may be determined by indexing
`into a table using quantized column vector values.
`
`least one householder matrix is
`[0100] At 440, be at
`recursively applied to the plurality of quantized column
`vectors to generate a beamforming matrix. In some embodi-
`ments, the oper