United States Patent
`US 7,236,748 B2
`(10) Patent No.:
`(12)
`Li et al.
`(45) Date of Patent:
`Jun. 26, 2007
`
`
`US007236748B2
`
`(54) CLOSED LOOP FEEDBACK IN MIMO
`SYSTEMS
`
`(75)
`
`Inventors: Qinghua Li, Sunnyvale, CA (US),
`.
`.
`.
`Xintian E. Lin, Palo Alto, CA (US)
`:
`:
`(73) Assignee:
`Intel Corporation, Santa Clara, CA
`(US)
`
`(*) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`,
`U.S.C, 154(b) by 363 days.
`.
`(21) Appl. No.: 10/955,826
`ag.
`(22) Filed:
`Sep. 30, 2004
`ous
`.
`,
`Prior Publication Data
`.
`US 2006/0068738 Al
`Mar. 30, 2006
`Int. Cl
`(5 1)
`~ 7
`3006.01)
`ntapp
`J
`.
`l'
`(52) US. C1.
`cesceecssecsssstesssseteessneesssnees 455/69; 455/562.1
`(58) Field of Classification Search oe 455/69,
`495/562.1, 561, 101, 103, 272-273, 276.1,
`455/277.1, 277.2; 375/299, 347, 370/208
`See application file for complete search history.
`References Cited
`U.S. PATENT DOCUMENTS
`
`(65)
`
`(56)
`
`5,999,826 A *
`6,597,678 B1*
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`
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`8/2005 Vooket al.
`
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`poe)oetces “I
`boobs ne et al.
`oon
`2006/0056335 Al
`3/2006 Linet al.
`2006/0056531 Al
`3/2006 Li etal.
`2006/0068718 Al*
`3/2006 Li et al. veces 455/69
`2006/0092054 Al
`5/2006. Liet al.
`
`
`
`OTHER PUBLICATIONS
`Int
`f the
`International Search Report
`and Written
`Opin;
`Intema-
`he
`care.
`epoit
`ani
`ritten
`pinion oO
`Ntemationa:
`tional Seraching Authority; Dated Jan. 31, 2006; PCT/US2005/
`031585, 1-15.
`International Search Report and Written Opinion of the Interna-
`tional Searching Authority; Dated Sep. 16, 2005; PCT/US2005/
`017774; 15 Pages,
`“PCT Search Report”, PCT/US2005/031979, (Jan. 23, 2006), 12
`pages.
`Jihoon, C. , “Interpolation based transmit beamforming for MIMO-
`OFDM with Limited Feedback”, JEFF International Conference on
`Paris, France, Piscataway, NJ, USA., P20442PCT—PCT Search
`Report Written Opinion from PCT application serial No. PCT/
`US2005/031585,(Jun. 20, 2004),249-253.
`.
`.
`_—* cited by examiner
`Primary Examiner—Nguyen T. Vo
`(74) Attorney, Agent, or Firm—LeMoine Patent Services,
`PLLC; Dana B. LeMoine
`
`ABSTRACT
`(57)
`Feedback bandwidth may be reduced in a closed loop
`MIMOsystem by representing a beamforming matrix using
`orthogonal generator matrices.
`
`23 Claims, 4 Drawing Sheets
`
`
`ESTIMATE CHANNEL STATE INFORMATION|210
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`220
`
`REPRESENT A BEAMFORMING MATRIX
`USING A SUM OF WEIGHTED GENERATOR
`MATRICES
`
`230
`
`MATRICES
`
`FEED BACK PARAMETERS THAT DESCRIBE|249
`THE WEIGHTING OF THE GENERATOR
`
`\ 200
`
`Page 1 of 13
`
`SAMSUNG EXHIBIT 1018
`
`Page 1 of 13
`
`SAMSUNG EXHIBIT 1018
`
`

`

`U.S. Patent
`
`Jun. 26, 2007
`
`Sheet 1 of 4
`
`US 7,236,748 B2
`
`
`
`STATION2
`
`
`
`STATION1
`
`104
`
`102
`
`FIG.1
`
`Page 2 of 13
`
`Page 2 of 13
`
`

`

`U.S. Patent
`
`Jun. 26, 2007
`
`Sheet 2 of 4
`
`US 7,236,748 B2
`
`ESTIMATE CHANNEL STATE INFORMATION|210
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`MATRICES
`
`REPRESENT A BEAMFORMING MATRIX
`USING A SUM OF WEIGHTED GENERATOR
`
`220
`
`230
`
`
`
`FEED BACK PARAMETERS THAT DESCRIBE|240
`
`THE WEIGHTING OF THE GENERATOR
`MATRICES
`
`\ 200
`
`FIG, 2
`
`Page 3 of 13
`
`Page 3 of 13
`
`

`

`U.S. Patent
`
`Jun. 26, 2007
`
`Sheet 3 of 4
`
`US 7,236,748 B2
`
`RECEIVE AT LEAST ONE PARAMETER
`
`310
`
`
`
`
`
`
`
`COMBINE THE AT LEAST ONE GENERATOR
`MATRIX TO ARRIVE AT A BEAMFORMING
`
`MATRIX
`
`
`
`WEIGHT AT LEAST ONE GENERATOR
`MATRIX USING INFORMATION DERIVED
`FROM THE AT LEAST ONE PARAMETER
`
`320
`
`
`
`330
`
`\ 300
`
`FIG. 3
`
`Page 4 of 13
`
`Page 4 of 13
`
`

`

`U.S. Patent
`
`Jun. 26, 2007
`
`Sheet 4 of 4
`
`US 7,236,748 B2
`
`ox
`S
`2
`Lo
`©
`ce
`x
`
`h Lu
`liy CD
`= x
`oO Le
`Ly Oc
`=> UWBS
`li =
`
`FIG.4 400“
`
`450
`
`Page 5 of 13
`
`Page 5 of 13
`
`

`

`US 7,236,748 B2
`
`1
`CLOSED LOOP FEEDBACK IN MIMO
`SYSTEMS
`
`FIELD
`
`The present invention relates generally to wireless net-
`works, and more specifically to wireless networks that
`utilize multiple spatial channels.
`
`BACKGROUND
`
`Closed loop multiple-input-multiple-output (MIMO)sys-
`tems typically transmit channel state information from a
`receiver to a transmitter. ‘he transmitter may then utilize the
`information to do beam forming. Transmitting the channel
`stale information consumes bandwidth that might otherwise
`be available for data traflic.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`FIG. 1 shows a diagram of two wireless stations;
`FIGS. 2 and 3 show flowcharts in accordance with various
`embodiments of the present invention; and
`FIG. 4 shows an electronic system in accordance with
`various embodiments of the present invention.
`
`DESCRIPTION OF EMBODIMENTS
`
`10
`
`20
`
`2
`the 1999
`including, but not limited to,
`802.11 standard,
`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.
`
`Stations 102 and 104 each include multiple antennas.
`Lach of stations 102 and 104 includes “‘n” antennas, where
`n maybe any number. In some embodiments, stations 102
`and 104 have an unequal numberof antennas. The remainder
`of this description discusses the case where stations 102 and
`104 have an equal number of antennas, but the various
`embodiments of the invention are not so limited. The
`
`“channel” through which stations 102 and 104 communicate
`may include manypossible signal paths. For cxample, 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
`knownas “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 systemsoffer higher
`capacities by utilizing multiple spatial channels made pos-
`sible by multipath.
`In some embodiments, stations 102 and 104 may com-
`municate using orthogonal frequencydivision multiplexing
`(OFDM)in each spatial channel. Multipath may introduce
`frequency selective fading which may cause impairments
`like inter-symbol interference (ISD. OFDM is effective at
`combating frequency selective fading in part because
`OFDMbreaks each spatial channel into small subchannels
`such that each subchannel exhibits a more flat channel
`characteristic. Each channel may be scaled appropriately to
`correct any attenuation caused by the subchannel. Further,
`the data carrying capacity of each subchannel may be
`controlled dynamically depending on the fading character-
`istics of the subchannel.
`
`MIMOsystems mayoperate either “open loop”or “closed
`loop.” In open loop MIMOsystems, a station estimates the
`state of the channel without receiving channel state infor-
`mation directly from another station. In general, open loop
`systems employ exponential decoding complexity to esti-
`mate the channel. In closed loop systems, communications
`bandwidth is utilized to transmit current channel state infor-
`mation between stations,
`thereby reducing the necessary
`decoding complexity. The communications bandwidth used
`for this purpose is referred to herein as “feedback band-
`width.” When feedback bandwidth is reduced in closed loop
`MIMOsystems, more bandwidth is available for data com-
`munications.
`The current channel state information maybe represented
`by an n by n unitary beamforming matrix V determined
`using a singular value decomposition (SVD) algorithm, and
`the transmitter may process an outgoing signal using the
`beamforming matrix V to transmit into multiple spatial
`channels. In a straightforward. implementation, the receiver
`sends each element of the unitary matrix V back to the
`transmitter. This
`scheme involves
`sending information
`related to the 2n? real numbers for any n by n complex
`unitary matrix, where n is the numberofspatial channels in
`the MIMOsystem.
`In some embodiments of the present invention, the beam-
`forming matrix V is represented by n°-1 real numbers
`instead of 2n? real numbers. By sending n*~1 real numbers
`instead of 2n? real numbers to represent the beamforming
`matrix, the feedback bandwidth may be reduced. Various
`
`In the following detailed description, reference is made to
`the accompanying drawings that show, by way ofillustra-
`tion, 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 descriptionis, 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.
`FIG. 1 showsa diagram of two wireless stations: station 5
`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 ina 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),andstill
`further embodiments, stations 102 and 104 are part of a
`wireless personal area network (WPAN).
`In some embodiments, stations 102 and 104 may operate
`partially in compliance with, or completely in compliance
`with, a wireless network standard. I’or example, stations 102
`and 104 mayoperate 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
`
`40
`
`45
`
`60
`
`Page 6 of 13
`
`Page 6 of 13
`
`

`

`US 7,236,748 B2
`
`2-1
`
`V=explicoa2ex ay“|=ell
`
`k=l
`
`4)
`
`3
`embodiments of the present invention exploit the structure
`of unitary matrixes and represent the unitary matrices by a
`combination of n?-1 orthogonal generator matrices, where
`the feedback numbers are the projections on the gencrator
`bases. For example, multiple hermitian generator matrices
`known to both the transmitter and recciver may be utilized
`to represent the beamforming matrix. Further, the numbers
`are also angles from -m to x of an (n?-1)-dimensionpolar
`coordinate, which facilitate a fine control of quantization
`error.
`
`A mathematical background of the SVD operation is
`provided below, and then examples are provided to describe
`various embodiments of the present invention that utilize
`hermitian generator matrices to represent beamforming
`matrices of any size. Further examples are also provided
`illustrating compact feedback formats for 2x2 MIMOsys-
`tems.
`
`Atransmit beamforming matrix maybe found using SVD
`as follows:
`
`20
`
`where det(V)=1 and wp is a global phase. In some embodi-
`ments,a is not fed backto the transmitter. The term ce” can
`be factored out from Vin equation (4) and absorbed by the
`data vector d in equation (2). ‘he term e’” rotates the QAM
`constellation of d’s elements and the rotation may be com-
`pensated by the training. Accordingly,
`in some embodi-
`ments, 1) may be dropped to reduce feedback bandwidth and
`only n?-1 angles (i.e. a, .. . a,2_,) are fed back. Further, in
`some embodiments, adaptive bit loadingis utilized to reduce
`the feedback bandwidth further. For example, various
`parameters may be quantized with different numbersofbits
`prior to feeding back the parameters.
`In embodiments in which n*-1 angles (i.e.a, ...a,?_,) are
`fed back, the feedback angles are computed bythe receiver
`that received channel training symbols. After the angles are
`computed, the receiver feeds back the angles to the trans-
`mitter of training symbols.
`Although various embodiments of the present invention
`where d is the n-vector of code bits for n data streams; x is
`feed back n731 1 angles, it can be shownthat n-1 of those
`the transmitted signal vector on the antennas; H is the
`angles are not neededat the transmitter since the training can
`channel matrix; H’s
`singular value decomposition is
`compensate the effect. When the n-1 angles referred to
`H-UDV’; U and V are unitary; D is a diagonal matrix with
`aboveare not included in the feedback, the number of angles
`H’s eigenvalues; V is n by n, andnis the numberofspatial
`fed back is reduced to n?-n parameters.
`channels. To obtain Vat the transmitter, the transmitter may
`Feeding back n?-1 parametersinstead of n?-n parameters
`send training symbols to the receiver;
`the receiver may
`provides more information at the transmitter that may be
`evaluate H, compute the matrix V'; and the receiver may
`useful in many ways. For example, in OFDM systems with
`feedback parameters representing V to the transmitter. As
`m subcarriers, the transmitter uses a beamforming matrix for
`described more fully below, the number of feedback param-
`each of the m OFDM subcarriers. In some embodiments of
`eters used to represent V maybe reduced by representing the
`the present invention, n°-1 parameters are fed back for less
`beamforming matrix using a weighted sum of orthogonal
`than all of the m subcarriers, and the transmitter may then
`generator matrices.
`interpolate to arrive at the beamforming matrices for the
`A generic n by n complex matrix satisfying the following
`remaining subcarriers. Extra information is provided by the
`condition VV'=], is a unitary matrix. All n by n unitary
`n-1 angles, and the interpolation may make use of this extra
`matrices maybe considered to form a group U(n). Ils generic
`information.
`representation may be written as:
`
`H-UDV'
`
`x=Vd
`
`(2)
`
`40
`
`V=
`
`weoS aya|
`
`kel
`
`45
`
`(3)
`
`where G,is the k-th hermitian generator matrix; a, is the
`angle of the k-th rotation and it is between - and 7; and i
`is the square root of -1. Example generator matrices for n=2,
`3, and 4 are providedat the end ofthis description. It should
`be noticed that the set of generator matrices for n=m is a
`subsetof the set for n—m+1. Therefore, a 4 by 4 system may
`store only the matrices for n=4, and matrices for n=2 and
`n=3 may be determined fromthe stored matrices. Although
`example generator matrices are only provided up to n=4, this
`is not a limitation of the present invention. Any number of
`generator matrices, corresponding to various values ofn,
`may be utilized without departing from the scope of the
`present invention.
`It is noted that the last generator G,,2 in U(n) is a scaled
`identity matrix and it commutes with all other generator
`matrices. Accordingly, the unitary matrix can be written as
`
`Page 7 of 13
`
`The feedback angles may be computed as follows.
`1) Singular value decomposition of the channel matrix H
`H=U D V'
`(5)
`
`where' is the conjugate transpose operation.
`2) Rigenvalue decomposition of matrix V
`
`V=M DM
`
`(6)
`
`where D is a diagonal matrix with norm 1 diagonal
`elements.
`
`3) Natural logarithm of V
`
`log(V)=M log(D)M!
`
`(7)
`
`where log(D) essentially computes the phase of diagonal
`elements of D.
`
`4) Project log(V) to the n?-1 generator matrixes
`
`ay = — Atrace flog(ViGi], fork=1,..., n?-1
`
`Page 7 of 13
`
`

`

`US 7,236,748 B2
`
`5
`. a,?_,) to the transmitter,
`.
`The receiver may transmit(a, .
`which may then reconstruct the beamforming matrix V as
`follows.
`
`rut
`Asi)! a Ge
`k=l
`
`A= PAP?
`
`V = Pdiaglexp(A,)--- exp(a,JP?
`
`(9)
`
`(10)
`
`ql)
`
`and the transmitter may perform transmit beamforming
`
`as:
`
`wa
`
`10
`
`15
`
`6
`We can expand V in series as
`
`|
`
`&
`
`~.Mi ag a
`
`" goS—-=
`
`Tor 2x2 matrix V, (15) can be simplified by using
`
`x=Vd
`
`(12)
`
`[i aco
`
`k=l
`
`2° 40 yield:
`V=cos(®)Gyti sin(@) (2G+1G+1363)
`
`(15)
`
`(16)
`
`Various embodiments of the present invention also reduce
`the range of the quantized feedback numbers from (-», 9)
`to (-7, m]. For example, real numbers included in a beam-
`forming matrix generally take on values of (-%, °), while
`the angles a, may take on values of (-a, a]. In some
`embodiments, the range of (-z, =] can be represented with
`fewer bits, and in other embodiments, greater precision is
`provided because of the smaller range.
`
`Compact Feedback Formats for 2x2 MIMO Systems
`Asdescribed above, various embodiments of the present
`invention provide compact feedback formats for n by n
`MIMOsystems, where n may be of any sizc. In some
`embodiments, compact feedback formats are further devel-
`oped for the case of MIMO systems with two spatial
`channels. These compact formats may be utilized in 2 by 2
`MIMOsystems, or in higher order systemsthat use less than
`all available spatial channels.
`‘lwo compact feedback schemesare described below.‘he
`first scheme feeds back one sign bit and three real numbers
`between -1 and 1. The computation of the numbersutilizes
`basic trigonometric functions which may be implemented by
`the FFT table for 802.11 OFDM modulation. The recon-
`struction of the unitary matrix utilizes a square root opera-
`tion. The second schemefeeds back three angles with ranges
`[0,7), [0,7), and (-s,2t]. Two of the three ranges are smaller
`than the more general case described above and leads to a
`smaller quantization error under the same numberof quan-
`tizationbits.
`
`Asdescribed above, any unitary matrix V can be written
`
`as
`
`tmre-1
`V = exp(icoa,2 Jexp} é
`o Le
`
`aac,
`
`
`
`|=e"V
`
`(13)
`
`where G, is the k-th hermitian generator matrix; a, is the
`angle of the k-th rotation andit is between -m and 7; 1 is the
`square root of -1; V is unitary and det(V)=1; y is a global
`phase. V can be computed as
`
`nNa
`
`30
`
`we on
`
`In this representation, we can limit ® in [0, =) and n, are
`real between [-1,1]. Using the orthogonal and unitary prop-
`erty, we have:
`
`a
`1
`cos(y) = 5 trace (VG4)
`
`my = — trace (VG)) for k= 1, 2,3
`2sin(y)
`"
`
`is a real, unit 3-vector,
`Since (n,, 1, 05)
`described by two angles 0,® as follows.
`n =sin(@)cos()
`
`(17)
`
`(18)
`
`it can be
`
`qd9)
`
`(20)
`
`@1)
`
`No=sin(O)sin()
`
`40
`
`n3=cos(@)
`
`where 6 is between [0, x) and > is between [-z, 7).
`From above, we derive two schemes to feed back infor-
`mation representing the beamforming matrix V. Scheme 1
`sends back cos(®), n,, n,, and the sign of n,. The feedback
`numbers are between [-1,1] except for the sign bit. This
`scheme limits the quantization range and docsn’t require
`sine and cosine functions during reconstruction. Scheme 2
`sends back ®, 8 and >, which are between [0, 7), [0, 7), and
`|0,27), respectively. ‘his scheme utilizes sine and cosine
`functions during reconstruction. In some embodiments, the
`angles may be quantized at lowresolution to reduce over-
`head, and existing 64 or 128 FFT tables in 802.11 OFDM
`baseband systems maybe used to approximate the sine and
`cosine functions. The schemesare illustrated next.
`Scheme 1 is illustrated as follows.
`1) Singular value decomposition of the channel matrix H
`H-UDV'
`(22)
`
`30
`
`uw an
`
`where' is the conjugate transpose operation.
`69 2) Remove the global phase of the unitary matrix V
`
`<I Ul
`Vv
`V det V)
`
`(14)
`
`65
`
`<|
`
`
`V
`VdetlV)
`
`(23)
`
`Page 8 of 13
`
`Page 8 of 13
`
`

`

`US 7,236,748 B2
`
`7
`3) Compute feedback numbers
`
`—
`1
`cos(y) = qtrace(V G4)
`-i
`~ 2v 1 - cos? (y)
`
`Nk
`
`ope
`trace(V G;)
`
`(24)
`
`(25)
`
`4) Receiver quantizes cos(®), n,, nj, and sends back with
`sign(n,)
`‘The transmitter maythen reconstruct V using cos(@), n,,
`n, and sign(n,)
`ny=sign(n )V/1-nyny"
`
`(26)
`
`F=cos(@)G,-i1-cos?(@)(n |G+2Gy+n3G3)
`Scheme2 is illustrated as follows.
`1) Singular value decomposition of the channel matrix H
`II-UDV'
`(28)
`
`(27)
`
`where ' is the conjugate transpose operation.
`2) Remove the global phase of the unitary matrix V
`
`V =
`
`Vv
`vdet(V)
`
`3) Compute feedback numbers
`
`1 —
`cos(y) = 5 race(V Gy)
`
`nm = —trace(VG4)
`‘
`2v 1 — cos? (y)
`‘
`
`4) Calculate angle @ and »
`
`8 = arccos(n3), 8c [0, 2)
`
`aretan( h ny =O
`Ay
`m
`arctan(— ) +7, 1 <0
`ny
`
`b=
`
`(29)
`
`30)
`
`31)
`
`(32)
`
`10
`
`15
`
`20
`
`30
`
`35
`
`40
`
`45
`
`5) Receiver quantizes and feeds back ®, 6 and »
`The transmitter may then reconstruct V using ®, 0 and
`n=sin(O)cos()
`(33)
`
`n=sin(0)sin()23=cos(0)
`
`(34)
`
`(35)
`V—cos(@)Gyti sin(®) (1, G+2Gp+3G3)
`FIG. 2 shows a flowchart in accordance with various
`
`embodiments of the present invention. In some embodi-
`ments, method 200 may be usedin, or for, a wireless system
`that utilizes MIMO technology.
`In some embodiments,
`method 200, or portions thereof, is performed by a wireless
`communications device, embodiments of which are shown
`in the various figures. In other embodiments, method 200 is
`performed by a processoror electronic system. Method 200
`is not limited by the particular type of apparatus or software
`element performing the method. The various actions in
`method 200 may be performed in the order presented, or
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`may be performed in a different order. Further, in some
`embodiments, someactionslisted in FIG. 2 are omitted from
`method 200.
`Method 200 is shown beginning at block 210 in which
`channelstate information is estimated fromreceived signals.
`The channelstate information may include the channelstate
`matrix IJ described above. At 220, a beamforming matrix is
`determined from the channel state information. In some
`embodiments, this corresponds to performing singular value
`decomposition (SVD) as described above with reference to
`equation (1). The beamforming matrix V is also described
`above.
`
`At 230, a beamforming matrix is represented using a sum
`of weighted gencrator matrices. For example, as shown
`above in equation(3), in some embodiments, the beamform-
`ing matrix may be represented using a sum of weighted
`hermitian generator matrices. In other embodiments,
`the
`beamforming matrix may be represented using equation
`(16). The parameters may be generated by projecting the
`beamforming matrix onto the generator matrices
`as
`described above with reference to the various embodiments
`of the present invention.
`At 240, parameters that describe the weighting of the
`generator matrices are fed back to a transmitter. For
`example,
`in embodiments that utilize equation (3),
`the
`parameters may include coefficients such as (a,
`.
`.
`. a,2_,);
`and in embodiments that utilize equation (16), the param-
`eters may include coeflicients such as cos(®), n,, n,, and the
`sign of n,. Further, in some embodiments that utilize equa-
`tions (16)-(21), the parameters may include ®, 6 and 9.
`In some embodiments, n?-1 parameters are chosen to
`represent the weighting of generators matrices. For example,
`in a2 by 2 MIMOsystem, three parameters may be used to
`represent the sum of the weighted generator matrices. In
`other embodiments, a sign bit is used in conjunction with
`n’-1 parameters to reduce the quantization range of one or
`more parameters.
`Prior to feeding back to the transmitter, the parameters
`may be quantized in the ranges appropriate for the range of
`the parameters selected. For example, in embodimentsthat
`feed back (a, ... a,2_,), the angles a, can be quantized in the
`range [-m, 1). Further,
`in embodiments that feed back
`cos(®), n,, n;, and the sign of n,, the parameters may be
`quantized in the range of [-1, 1). In still further embodi-
`ments, the parameters ®, 6 and @ may be quantized between
`[0, =),
`[0, =), and [0,2 x), respectively. The quantized
`parameters may be transmitted using any type ofprotocol or
`any type of communicationslink, including a wireless link
`such as a wireless link between stations like those described
`with reference to FIG. 1.
`
`In some embodiments, parameters are fed back for less
`than all OFDM subcarriers. For example, parameters may be
`fed back for every other OFDM subcarrier, or parameters
`may be fed back for fewer than every other OFDM subcar-
`ricr. In these embodiments, a system that receives the
`parameters may interpolate to arrive at beamforming matri-
`ces for each OFDM subcarrier.
`FIG. 3 shows a flowchart in accordance with various
`embodiments of the present invention. In some embodi-
`ments, method 300 may be used in, or for, a wireless system
`that utilizes MIMO technology.
`In some embodiments,
`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 processoror electronic system. Method 300
`is not limited bythe particular type of apparatus or software
`element performing the method. The various actions in
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`US 7,236,748 B2
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`9
`method 300 may be performed in the order presented, or
`may be performed in a different order. Further,
`in some
`embodiments, someactions listed in FIG.3 are omitted from
`method 300.
`Method 300 is shown beginning at block 310 in which at
`least one parameteris received. In some embodiments, this
`may correspond to a transmitter receiving one or more
`parameters that represent a sum ofrotated generator matri-
`ces. In some embodiments,
`the parameters may include
`coefficients with which the generator matrices are to be
`weighted, and in other embodiments, the parameters may
`include other angle parameters such as ®, @ and @, or
`coetflicients such as cos(®), n,, n3, all of which are described
`above with reference to the previous figures.
`At 320, at least one generator matrix is weighted using
`information derived from the at least one parameter, and at
`330, the generator matrices are combined to arrive at a
`beamforming matrix. or example, hermitian generator
`matrices may be weighted and combined as shown in
`equations (9)-(11),
`(26)-(27), or (33)-(35). Further,
`the
`beamforming matrix may be used in beamforming as
`described above with reference to the various embodiments
`of the present invention.
`In some embodiments, the acts of block 310 may result in
`parameters for
`less than all OFDM subcarricrs being
`received. For example, parameters may be received for
`every other OFDM subcarrier, or parameters may be
`received for fewer than every other subcarrier. In these
`embodiments, method 300 may interpolate to arrive at
`OFDM subcarrier beamforming matrices for which no
`parameters were received.
`FIG. 4 shows a system diagram in accordance with
`various embodiments of the present invention. [Electronic
`system 400 includes antennas 410, physical layer (PHY)
`
`430, media access control (MAC) layer 440, Ethernet inter-
`face 450, processor 460, and memory 470. In some embodi-
`ments, electronic system 400 maybe a station capable of
`representing beamforming, matrices using generator matri-
`ces as described above with reference to the previous
`figures. In other embodiments, electronic system 400 may be
`a station that receives quantized parameters, and performs
`beamforming in a MIMO system. For example, electronic
`system 400 may be utilized in a wireless network as station
`102 or station 104 (FIG. 1). Also for example, electronic
`system 400 may bea stalion capable of performing the
`calculations shown in any of the equations (1)-(35), above.
`In some embodiments, electronic system 400 may repre-
`sent a system that includes an access point or mobile station
`as well as other circuits. For example, in some embodiments,
`electronic system 400 may be a computer, such as a personal
`computer, a workstation,or the like, that includes an access
`point or mobile station as a peripheral or as an integrated
`unit. Further, electronic system 400 may include a series of
`access points that are coupled together in a network.
`In operation, system 400 sends and reccives signals using
`antennas 410, and the signals are processed by the various
`elements shownin FIG. 4. Antennas 410 may be an antenna
`array or any type of antenna structure that supports MIMO
`processing. System 400 may operate in partial compliance
`with, or in complete compliance with, a wireless network
`standard such as an 802.11 standard.
`
`Physical layer (PHY) 430 is coupled to antennas 410 to
`interact with a wireless network. PITY 430 may include
`circuitry to support the transmission and reception of radio
`frequency (RF) signals. For example, in some embodiments,
`PHY430 includes an RF receiver to receive signals and
`perform“front end” processing such as lownoise amplifi-
`
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`Page 10 of 13
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`10
`cation (LNA), filtering, frequency conversion or the like.
`Further, in some embodiments, PHY430 includes transform
`mechanisms and beamforming circuitry to support MIMO
`signal processing. Also for example, in some embodiments,
`PHY 430 includes circuits to support frequency up-conver-
`sion, and an RF transmitter.
`Media access control
`(MAC) layer 440 may be any
`suitable media access contro] layer implementation. For
`example, MAC 440 may be implemented in software, or
`hardware or any combination thereof. In some embodi-
`ments, a portion of MAC 440 may be implemented in
`hardware, and a portion may be implemented in software
`that is executed by processor 460. Further, MAC 440 may
`include a processor separate from processor 460.
`In operation, processor 460 reads instructions and data
`from memory 470 and performsactions in responsethereto.
`For example, processor 460 may access instructions from
`memory 470 and perform method embodiments of the
`present invention, such as method 200 (FIG. 2) or method
`300 (FIG. 3) or methods described with reference to other
`figures. Processor 460 represents any type of processor,
`including but not limited to, a microprocessor, a digital
`signal processor, a microcontroller, or the like.
`Memory 470 represents an article that includes a machine
`readable medium. For cxample, memory 470 represents a
`random access memory (RAM), dynamic random access
`memory (DRAM), static random access memory (SRAM),
`read only memory (ROM), flash memory, or any other type
`of article that includes a medium readable byprocessor 460.
`Memory 470 may store instructions for performing the
`execution of the various method embodimentsofthe present
`invention. Memory 470 may also store beamforming matri-
`ces or beamforming vectors.
`Although the various elements of system 400 are shown
`separate in FIG. 4, embodiments exist that combine the
`circuitry of processor 460, memory 470, Ethernet interface
`450, and MAC 440 in a single integrated circuit. or
`example, memory 470 may be an internal memory within
`processor 460 or may be a microprogram control store
`within processor 460. In some embodiments, the various
`elements of system 400 maybe separately packaged and
`mounted on a commoncircuit board. In other embodiments,
`the various elements are separate integrated circuit dice
`packaged together, such as in a multi-chip module, and in
`still further embodiments, various elements are on the same
`integrated circuit die.
`Ethemet
`interface 450 may provide communications
`between electronic system 400 and other systems. For
`example, in some embodiments, electronic system 400 may
`be an access point that utilizes Ethernet interface 450 to
`communicate with a wired network or to communicate with
`
`other access points. Some embodiments of the present
`invention do not
`include Ethernet
`interface 450. For
`
`
`
`example, in some embodiments, electronic system 400 may
`be a network interface card (NIC) that communicates with a
`computer or network using a bus or other type ofport.
`Although the present invention has been described in
`conjunction with certain embodiments,it is to be understood
`that modifications and variations maybe resorted to without
`departing from the spirit and scope of the invention as those
`skilled in the art readily understand. Such modifications and
`variations are considered to be within the scope of the
`invention and the appendedclaims.
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`Generator Matrices
`
`11
`
`For U(2) group, the generator matrices are:
`
`US 7,236,748 B2
`
`12
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`w
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`10
`
`30
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`35
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`40
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`65
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`-continued
`1000
`100 0
`ifo1rdac
`1fo10 0
`“= —eElo 01 0 f"Velo 01 6
`000 -3
`0001
`
`Whatis claimed is:
`
`1. A method comprising:
`representing a beamforming matrix using a sum of
`weighted hermitian generator matrices; and
`feeding back parameters that describe the weighting ofthe
`hermitian generator matrices, wherein representing a
`beamforming matrix using a sum of weighted hermitian
`generator matrices comprises projecting a natural loga-
`rithm of the beamforming matrix onto hermitian gen-
`erator matrices.
`
`2. The method of claim 1 wherein feeding back param-
`eters co