ao) United States
`a2) Patent Application Publication co) Pub. No.: US 2006/0092054 Al
`
`
`(43) Pub. Date:Li et al. May 4, 2006
`
`US 20060092054A1
`
`(54) RECURSIVE REDUCTION OF CHANNEL
`STATE FEEDBACK
`
`(22)
`
`Filed:
`
`Sep. 8, 2004
`
`Publication Classification
`
`(76)
`
`Inventors: Qinghua Li, Sunnyvale, CA (US),
`Int. Cl.
`(51)
`Xintian E. Lin, Mountain View, CA
`(US) HO3M=7/40 (2006.01)
`
`
`(52) WS. CM.
`cacssssssssssssssesonntnesetntntneteretnsnee 341/67
`
`Correspondence Address:
`LeMoine Patent Services, PLLC
`c/o PortfoliolP
`P.O. Box 52050
`Minneapolis, MIN 55402 (US)
`
`(21) Appl. No.:
`
`10/937,097
`
`(57)
`
`ABSTRACT
`
`Feedback bandwidth may be reduced in a closed loop
`MIMOsystem by Householder transformations and vector
`quantization using codebooks.
`
`ESTIMATE CHANNEL STATE INFORMATION|310
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`QUANTIZE A COLUMN OF A BEAMFORMING
`MATRIX USING A CODEBOOK
`
`PERFORM A HOUSEHOLDER REFLECTION
`ON THE BEAMFORMING MATRIX TO
`REDUCE THE DIMENSIONALITY OF THE
`BEAMFORMING MATRIX
`
`340
`
`320
`
` 330
`
`
`
`
`
`
`
`
`
`
`RECURSIVELY REPEAT THE QUANTIZING
`AND PERFORMING OF HOUSEHOLDER
`
`REFLECTION
`
`390
`
`TRANSMIT QUANTIZED COLUMN VECTORS
`
`360
`
`300
`
`1
`
`HUAWEI 1007
`
`1
`
`HUAWEI 1007
`
`

`

`Patent Application Publication May 4,2006 Sheet 1 of 7
`
`US 2006/0092054 Al
`
`104
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`ry
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`

`

`Patent Application Publication May 4,2006 Sheet 2 of 7
`
`US 2006/0092054 Al
`
`3
`
`

`

`Patent Application Publication May 4,2006 Sheet 3 of 7
`
`US 2006/0092054 Al
`
`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 MATRIXTO
`
`
`REDUCE THE DIMENSIONALITY OF THE
`
`BEAMFORMING MATRIX
`
`—|_340
`
`
`
`RECURSIVELY REPEAT THE QUANTIZING|350
`AND PERFORMING OF HOUSEHOLDER
`
`REFLECTION
`
`
`
`
`
`TRANSMIT QUANTIZED COLUMN VECTORS
`
`FIG. 3 |
`
`360
`
`300
`
`4
`
`

`

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

`

`Patent Application Publication May 4,2006 Sheet 5 of 7
`
`US 2006/0092054 Al
`
`950
`
`lay ©
`ty
`f=
`WW =
`
`18
`ny
`Se
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`FIG.5
`
`6
`
`

`

`Patent Application Publication May 4,2006 Sheet 6 of 7
`
`US 2006/0092054 Al
`
`nt=3 n2=4 energy=0.9888
`
`FIG. 6
`
`7
`
`

`

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

`

`US 2006/0092054 Al
`
`May4, 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)systemstypically transmit channel state informa-
`tion from a receiver to a transmitter. Transmitting the
`channel state information consumes bandwidth that might
`otherwise be available for datatraffic.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`[0003] FIG. 1 shows a diagram of two wireless stations;
`
`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 basestation
`or a subscriber unit. Although only two stations are shown
`in FIG, 1, any number ofstations 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 mayoperate partially in compliance with any
`
`other standard, such as any future IEEE personal area
`network standard or wide area network standard.
`
`[0004] FIG. 2 showsa 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,
`
`[0007] FIG. 6 shows distributions of codewords in a
`plane;
`
`[0008] FIG. 7 showsa partition of a codebook according
`to a parameter; and
`
`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 manypossible signal paths. For example, when
`[0006] FIG.5shows an electronic system in accordance
`stauions 102 and 104 are in an environment with many
`with various embodiments of the present invention;
`“reflectors” (e.g. walls, doors, or other obstructions), many
`signals may arrive from different paths. This condition is
`knownas “multipath.” In some embodiments, stations 102
`and 104 utilize multiple antennas to take advantage ofthe
`multipath and to increase the communications bandwidth.
`Yor example, in some embodiments, stations 102 and 104
`may communicate using Multiple-Input-Multiple-Output
`[0009] FIG.8showsa partition ofa portion of a codebook
`(MIMO)techniques. In general, MIMO systems offer higher
`according to a parameter.
`capacitics by utilizing multiple spatial channels made pos-
`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.
`
`DESCRIPTION OF EMBODIMENTS
`
`In the following detailed description, reference is
`[0010]
`madeto 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 understoodthat 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 descriptionis, therefore, not to be taken in a limiting
`sense, and the scope of the present invention is defined only
`by the appended claims, appropriatcly 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 ofstations 102 and 104
`may be an access point ina WLAN.Also for example, one
`or moreofstations 102 and 104 may be a mobilestation such
`as a laptop computer, personaldigital assistant (PDA), or the
`
`
`
`In some embodiments, stations 102 and 104 may
`[0014]
`communicate using orthogonal frequency division multi-
`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 moreflat
`channel characteristic. Scaling appropriate for each sub-
`channel may be implemented to correct any attenuation
`caused bythe subchannel. Further, the data carrying capacity
`of each subchannel may be controlled dynamically depend-
`ing on the fading characteristics of the subchannel.
`
`[0015] MIMOsystems 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 channelstate
`information can be employed for various enhancements such
`as transmit beamforming and adaptive modulation. The
`communications bandwidth used for this purposeis referred
`to herein as “feedback bandwidth.” When feedback band-
`width is reduced in closed loop MIMO systems, more
`bandwidth is available for data communications.
`
`9
`
`

`

`US 2006/0092054 Al
`
`May4, 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,
`different size codebooks are used for different ones of the
`
`in some
`transmit beamforming vectors. For example,
`embodiments,
`three beamforming vectors are quantized
`using three small codebooksof 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 eigenmodeis usually punctured.
`Additionally, in some embodiments the mean (and variance)
`of eigenvalues for each active spatial channelis fed back for
`adaptive modulation, where the mean (and variance) is
`computed over the sorted eigenvalues on OFDM subchan-
`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 supportingall 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 (SVD) of the channel
`state matrix H as follows:
`
`Fn= Ummmen ‘nxn
`Xnxt=Vinenbared
`
`(1)
`(2)
`
`[0019] where dis 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 beamformed, 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 andonly thefirst k columnsare needed to be fed
`back. Equation (2) is the beamformingact 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 v,, the first column of V, where V is n by
`k; n is the numberoftransmit antennas; k is the number of
`spatial streams. The P matrix has the property that the first
`columnofthe product, PV, is [e'™ 0... OJ. Andthefirst row
`of PV becomes [e!” 0. .
`. 0] due to orthogonality. Then, the
`quantization of an n by k V matrix is converted into the
`quantization ofn-vector v, and the quantization of an n-1 by
`k-1 matrix V,. This conversion reduces overhead and
`quantization complexity. The process is repeated to quantize
`V, and convert the problem to the quantization of (n-1)-
`
`vector v, and n-2 by k-2 matrix V,. This repeats k-1 times.
`Finally, the quantization of V is converted to the quantiza-
`tion of v,, V>,..., V, that are k unit vectors of dimensions
`n,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 thefirst k
`columns of the V matrix, which corresponds to the k
`strongest eigenmodesof H. This offers an additional reduc-
`tion in feedback bandwidth. The degree of freedom of H is
`2n? while the degree offreedom ofV is n?—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 recetver may only
`quantize the first two columnsof V in the scheme depicted
`next.
`
`In some embodiments, the V matrix is quantized
`[0023]
`column by columnandrecursively. 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:
`
`Vir Viz Vi3
`
`V22
`Ve Vor
`V32
`V31
`Var Var
`
`-V23
`<V33
`V43
`
`(3)
`
`the first column of V denoted as v, may be be
`[0024]
`quantized as follows.
`
`Vj=arg MAXpec[YI]
`
`(4)
`
`[0025] where C, is a codebook containing unit 4-vectors
`for quantization shownat the bottomof this description. v,
`has the maximum innerproduct amongall 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 codewordis set to be real for the next step.
`
`[0026] A Householder reflection matrix is constructed as
`follows
`
`i)
`
`10
`
`10
`
`

`

`US 2006/0092054 Al
`
`May4, 2006
`
`In some embodiments, the householderreflection
`[0027]
`matrix is determined as a function of the original column
`vector, in which case
`
`Way ep =
`
`vyy—-1
`Vai
`V3
`Val
`
`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
`
`ty, —1
`Sar
`¥31
`Val
`
`If v,=v,. Householder reflection converts the first column
`and row ofV into [e'*! 0.0 OJ’ and e'*[1 0 0] as shownin (6),
`where @, is the phase of v,,. Since usually v,=v,, there will
`be nonzero residuals in the off diagonal entries of the first
`column and row.
`
`is worth noting that the phases ¢, 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 codebooksize 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 columns of the beamforming matrix V,
`where k is the numberofactive spatial channels.
`2. Let V=V.,., which is a temporary matrix and is formed
`by the first k columnsof V.
`
`3. For i=1: min(k,n-1)
`
`3.1. Let v=V.,, which is the first column of V.
`[0033]
`3.2. Quantizev, by finding v,=arg maXx,<clu"vjl|,
`[0034]
`where C; is a codebook of unit n-i+1 vectors.
`
`3.3. Record the index of ¥, in the codebook for
`[0035]
`feedback.
`
`[0036]
`as
`
`3.4. Construct a Householder reflection matrix
`
`2
`Fp =1-—wit!
`Ibwill
`
`(6)
`
`FiV =!
`
`0.0
`
`el
`0.0
`0.0
`0.0
`
`0.0
`[ti
`S12
`Por Fo
`$31
`932
`
`%
`
`the
`[0028] where two properties are employed to get
`result, i.e. V,, is real and the unitary property ofV. Since both
`F, and Vare unitary, V, is unitary. From
`
`(6), we see that the size of V, is 3x2 and it is
`[0029]
`reduced from that of V, by one on both row and column
`dimensions. Recursively, we repeat the actions in (4),
`
`(5), and (6) on V,as follows. First, we quantize the
`[0030]
`first column of V, denoted as v5, using another codebook of
`unit 3-vectors shownat the bottom ofthis description, whose
`first element of each codewordis real. Then, we construct a
`Householder reflection matrix and multiply it with V, as
`follows.
`
`e®2
`
`0.0
`
`7)
`
`where w,=v,-e, and e, 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=E,V. ‘To reduce complexity, one only needs to com-
`pute columns and rows of V otherthan the first one.
`
`3.6. Update VaV5a1 occ:
`
`[0039]
`4. End
`
`[0040] For small matrix V, the SVD computation above
`can be skipped as follows. The vector codebooks C, for v;
`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 performanceis as follows.
`
`1. Apply the beamforming matrix undertest, V(t),
`[0041]
`to the channel matrix H, where V(t) is the t-th codeword in
`C. The combined channel matrix after the beamformingis as
`G=HV(0)
`(8)
`
`Vir
`0.0
`FyVp =
`0.0|Fay
`[0042]
`2. The signal
`to interference plus noise ratios
`(SINR) of this beamformed channel G can be computed in
`order to estimate the performance of V(t). For linear receiv-
`ers such as MMSEandzero-forcing receiver, the computa-
`tion of the SINR for each spatial stream is known.
`
`[0031] Finally, we quantize the vector V, using a code-
`book of unit 2-vectors shownat the bottom ofthis descrip-
`tion. ‘The quantization indexes of v,, v2, and v; are fed back
`to the access point, i.e. the transmitter, for beamforming. It
`
`3. Compare the sets of SINRs corresponding to
`[0043]
`V(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 Al
`
`May4, 2006
`
`4
`
`streams, or minimum estimated packet error rate. We find
`and feed the quantization index correspondingto the optimal
`vo.
`[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 [louseholder 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 be different from the original V by a global
`phase on each column andthis is fine with closed loop
`MIMO. First, two vectors, v, and v., 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. as
`
`hate!
`epee
`
`ap
`
`is the reconstructed first
`[0047] where w=v,-e, and ¢,
`col
`of V. Finally.
`the beamforming matrix V is
`given b
`,
`¥
`e
`&
`y
`
`10 6
`0
`.
`ver 0
`0
`
`(12)
`
`2,
`Foal ime”?
`
`(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=¥,-e, and ¥, is the reconstructed 3-vec-
`tor; F; can be stored beforehand to reduce computation.
`‘Third, V, 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.
`
`Receive indices n,,i = 1,...,N,, where N, is the number of feedback indices.
`1.
`2
`If k <n, where k and n are the numbers ofspatial streams and transmit
`antennas respectively, do
`2.1
`=
`Let V = %y, the ny-th vector of the codebook of (n—k + 1) dimension
`
`unit vector.
`2.2
`T=No-1.
`
`Else
`
`3.1
`
`3.2
`
`=
`Let V=1.
`J=N,.-
`End
`fori = J:-1:1
`
`3.
`
`4
`5.
`
`st
`vector
`
`5.2
`
`3.3
`
`6.
`
`End
`
`(10)
`
`0
`
`Vo =F/0 $5
`
`[0046] Fourth, we reconstruct thefirst column of Vusing
`the quantization index and compute a Householder matrix as
`
`9, = the nj-th vector of the codebook of (n— 1 +1) dimension unit
`
`FE =[- — www = tj —e.
`IIwil
`
`V=Fi
`
`10
`|.
`0
`Vv
`
`[0050] Quantization of large unit vector can be done as
`follows. It should be noticedthat the quantization of the unit
`vector in (4) is computational intensive for unit vectors of
`large size. Three schemes are proposed for the quantization
`oflarge unit vectors.
`
`[0051] Schemel
`[0052] We quantize each element of the unit vector using
`scalar quantization. For example, we may quantize unit
`vector v=-[v, .. . v,]' as follows. Wefirst normalize the
`
`12
`
`12
`
`

`

`US 2006/0092054 Al
`
`May4, 2006
`
`average power of each element of v to be unity, i.e. Vnv.
`Then, we may quantize each element of Viv 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
`
`ayy
`b=].
`eeanuy
`
`.
`
`[0053] Scheme2
`
`[0054] Wefirst 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]
`,, as
`
`1: Partition the vector into two sub-vectors, ti, and
`
`[0068] The numberof sub-vectors in Scheme 3 can be
`generalized to L that is greater than 2 as follows.
`
`[0069]
`
`Scheme3.1
`
`[0070] Quantization Acts
`
`[0071]
`t,, as
`
`1: Partition the vector into L sub-vectors, ty, ...,
`
`2: Normalize i, as t,=a,u, for i=1,..., L where
`[0072]
`|ju;|=1, Zlla|/P=1, and a;20. 2\a,|?=1 is because v is a unit
`vector.
`
`3: Quantize u,, fori=1,...,L. If we employ vector
`[0073]
`quantization, we may employ different codebooks depend-
`ing on the valueof 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 of u, as 0;. The quanti-
`zation index for each u, is fed back to the transmitter.
`
`4: Compute the global phase difference between u;
`[0074]
`and 0, for i=1,...,L as $,=phase(t',u;). These phases may
`already be computed in 3 during the quantization of u,.
`
`5: Compute $;=;,-9, forj=2, ..., L, where 9; is the
`[0075]
`phase difference between sub-vector, u; and u,.
`
`6: Quantize >; forj=2,...,L, and L-1 ofa;for i=1,
`[0076]
`..., L jointly or separately. Feed back the quantization
`indexes.
`
`2: Normalize fi, as f,=a,u,; for i=1,2, where||u,||=1,
`[0058]
`llay||?+\lao[|?=1, and a; 20. |a,||?+\\a5||?=1 is because v is a unit
`vector.
`
`3: Quantize u, and u, . If we employ vector quan-
`[0059]
`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, and u, as i, and 0,
`respectively. The quantization indexes for u, and u, are fed
`back to the transmitter.
`
`4: Compute the global phase difference between u,
`[0060]
`and 0, fori=1, 2 as 9;=phase(t',u,). These phases may already
`be computed in 3 during the quantization of u, and u,.
`
`If the dimension of the unit vector is large, the
`[0077]
`vector can be partitioned into multiple sub-vectors and
`Scheme3 can also be applied recursively to quantize the unit
`vector as follows.
`
`5: Compute $=$,-,, which is phase difference
`[0061]
`between the lower and upper sub-vectors, u, and u,.
`
`6: Quantize @ and one of a, and a, jointly or
`[0062]
`separately. Feed back the quantization indexes.
`
`[0063] Reconstruction Acts
`
`[0064]
`1: Reconstruct a;. If a, is quantized and fed back,
`then 4,=V¥1-4,*, where 4, is the reconstructed a, from the
`feedback index. Similarly, ifa, is quantized, then 4,=¥1-a,”.
`
`2: Reconstruct @ and denote the reconstructed
`[0065]
`phaseas 6.
`
`3: Reconstruct u, and u, using the quantization
`[0066]
`indexes. Denote the reconstructed vectors as t, and ,.
`
`[0078]
`
`Scheme 3.2
`
`[0079] Quantization Acts
`
`[0080]
`t,, as
`
`1: Partition the vector into L sub-vectors, fi,,...,
`
`2: Normalize i, as ti,=a,u; for i=1,..., L where
`[0081]
`|ju;|=1, da|?=1, and a;20. dIa,|?=1 is because v is a unit
`vector.
`
`13
`
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`
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`

`US 2006/0092054 Al
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`May4, 2006
`
`3: Quantize u,, for i=1,...,L. If we employ vector
`[0082]
`quantization, we may employ different codebooks depend-
`ing 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 of u, as 0;. The quanti-
`zation index for each u, is fed back to the transmitter.
`
`4: Compute the global phase difference between u,,
`[0083]
`and fi, as 6=phase(t',u,). Let I=a,, fi=u,, and v=6,.
`
`[0084]
`
`5: For i=L-1:-1:1 Do
`
`the global phase difference
`5.1 Compute
`[0085]
`between u, and t, as ,=phase(t'u,).
`[0086]
`5.2 Compute »=$-¢; and
`
`6 = tan} — |.
`a
`
`(3)
`
`5.3 Quantize cos(®) and sin(6)e jointly or
`[0087]
`respectively, and feed back quantization indexes.
`
`[0088]
`
`5.4 Let
`
`u;
`= _jand y=
`u
`
`
`
`cos(O)a;
`~ al
`sine
`
`[0089]
`
`where 6 and @ are quantized » and 0.
`
`[0090]
`
`5.4 Compute =phase(v'ti) and T=||¥||.
`
`[0091] End
`
`in accordance with
`[0092] FIG. 3 shows a flowchart
`invention. In some
`various embodiments of the present
`embodiments, method 300 may be usedin,orfor, a wireless
`system that utilizes MIMO technology. In some embodi-
`ments, method 300, or portions thereof, is performed bya
`wireless communications device, embodiments of which are
`shownin the variousfigures. In other embodiments, method
`300 is performed by a processor or electronic system.
`Method300 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 maybe performedin 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 channelstate 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 (1). 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
`columnvector. For example, the operations described above
`
`with reference to equation (4) may be utilized to search a
`code book.In various embodimentsofthe present invention,
`the size of the codebook, and therefore the numberof 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 householderreflection operations of 330 and 340 are
`recursively repeated. As the operations are recursively
`repeated, each of the columnvectors may be quantized using,
`the same codebook ordifferent 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 beutilized
`such that the column vectors are quantized 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 Householderreflection is recursively performed until a
`smal] 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
`then cach of the sub-vectors may be quantized using one or
`more codebooks. Thepartition 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 powerof 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
`embodiments, method 400 may be usedin,or for, a wireless
`system that utilizes MIMO technology. In some embodi-
`ments, method 400, or portions thereof, is performed by a
`wireless communications device, embodiments of which are
`shownin 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 sofiware element performing the method. The various
`actions in method 400 may be performed in the order
`presented, or may be performedin 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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`
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`
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`

`US 2006/0092054 Al
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`May4, 2006
`
`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
`columnvectors 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 operations of 440 may correspondto the actions
`described above with respect to equations (10) and (12).
`Further, in some embodiments, the operations of method 400
`may correspondto the operations represented by the pseudo-
`code appearing above after equation (12). After the beam-
`forming matrix is reproduced,
`the apparatus performing
`method 400 may utilize the beamforming matrix to operate
`on transmitted signals in a MIMOsystem.
`
`[010