(12)
`
`United States Patent
`US 7,236,748 B2
`(10) Patent No.:
`Jun. 26, 2007
`(45) Date of Patent:
`Li et al.
`
`
`US007236748B2
`
`(54) CLOSED LOOP FEEDBACK IN MIMO
`SYSTEMS
`
`(75)
`
`Inventors: Qinghua Li, Sunnyvale, CA (US);
`Xintian E. Lin, Palo Alto, CA (US)
`Intel Corporation, Santa Clara, CA
`(US)
`
`(73) Assignee:
`
`7/2003 Walton et al. oo... 455/454
`2003/0125040 Al*
`2003/0210750 Al* 11/2003 Onggosanusi et al.
`...... 375/295
`2004/0235433 AL* 11/2004 Hugl et al. oe. 455/101
`2005/0101259 Al
`5/2005 Tong et al.
`20060056335 AL
`32006. Linetal
`specoesig aT Feo0e rt . v
`2006/0092054 Al
`5/2006 Lit al.
`
`455/60
`
`(*) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`USC. 154(b) by 363 days.
`.
`(21) Appl. No.: 10/955,826
`(22)
`Filed:
`Sep. 30, 2004
`oo.
`.
`(65)
`Prior Publication Data
`US 2006/0068738 Al
`Mar. 30, 2006
`Int. Cl
`‘
`(2006.01)
`HO4B 1/38
`(2006.01)
`HO04M 1/00
`(52) US. Ch.
`ceccccccceesssscssecsstestessseessees 455/69; 455/562.1
`(58) Field of Classification Search .................. 455/69,
`455/562.1, 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
`5,999,826 A * 12/1999 Whinnett ......ee 455/561
`6,597,678 B1*
`7/2003 Kuwahara et al.
`.......... 370/342
`6,847,805 B2*
`1/2005 Lit oo... eee ceseeeeeeeeees 455/69
`6,927,728 B2
`8/2005 Vook etal.
`
`(51)
`
`(56)
`
`ritten
`
`pinion o
`
`©
`
`lnterma-
`
`nternationa
`
`Care.
`
`eport
`
`an
`
`OTHER PUBLICATIONS
`Int
`f the
`International Search Report
`and Written
`Ovini
`tional Seraching Authority; Dated Jan. 31, 2006; PCT/US2005/
`031585, 1-13.
`International Search Report and Written Opinion of the Interna-
`tional S
`hing
`Authority; Dated Sep. 16, 2005; PCT/US2005/
`01774,15Pages uthoritys
`Dated
`Sep.
`16,
`2005;
`“PCT Search Report”, PCT/US2005/031979, (Jan. 23, 2006), 12
`pages.
`Jihoon, C. , “Interpolation based transmit beamforming for MIMO-
`OFDM with Limited Feedback”, IEEE 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
`« “ne
`i
`—-* cited by examiner
`Primary Examiner—Neuyen T. Vo
`(74) Attorney, Agent, or Firm—LeMoine Patent Services,
`PLLC; Dana B. LeMoine
`
`ABSTRACT
`O7)
`Feedback bandwidth may be reduced in a closed loop
`veins©systemByrepresenting a beamforming matrix using
`gona"
`s
`
`23 Claims, 4 Drawing Sheets
`
`
`ESTIMATE CHANNEL STATE INFORMATION|270
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`220
`
`MATRICES
`
`1
`
`HUAWEI 1004
`
`

`

`U.S. Patent
`
`Jun. 26, 2007
`
`Sheet 1 of 4
`
`US 7,236,748 B2
`
`
`
`STATION2
`
`
`
`STATION4
`
`104
`
`102
`
`FIG.1
`
`2
`
`

`

`U.S. Patent
`
`Jun. 26, 2007
`
`Sheet 2 of 4
`
`US 7,236,748 B2
`
`ESTIMATE CHANNEL STATE INFORMATION
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`MATRICES
`
`REPRESENTA BEAMFORMING MATRIX
`USING A SUM OF WEIGHTED GENERATOR
`
`210
`
`220
`
`930
`
`
`
`FEED BACK PARAMETERS THAT DESCRIBE|949
`
`THE WEIGHTING OF THE GENERATOR
`MATRICES
`
`3
`
`

`

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

`

`U.S. Patent
`
`Jun. 26, 2007
`
`Sheet 4 of 4
`
`US 7,236,748 B2
`
`0p|AMON
`JOVIYSINI
`LINUFHLI
`
`097
`
`09|YOSS300YdOvAHd
`
`vb08
`OpANf/'N
`
`“
`
`bOla
`
`5
`
`
`

`

`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. The transmitter may then utilize the
`information to do beam forming. Transmitting the channel
`state information consumes bandwidth that might otherwise
`be available for data traffic.
`
`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.
`
`20
`
`25
`
`DESCRIPTION OF EMBODIMENTS
`
`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 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 ina WLAN.Also for example, one or more of
`stations 102 and 104 may be a mobile station such as a
`
`2
`the 1999
`limited to,
`including, but not
`802.11 standard,
`edition. Also for example, stations 102 and 104 may operate
`partially in compliance with any other standard, such as any
`future JEEE personal area network standard or wide area
`network standard.
`Stations 102 and 104 each include multiple antennas.
`Each of stations 102 and 104 includes “‘n” antennas, where
`n may be 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 many possible signal paths. For example, when
`stations 102 and 104 are in an environment with many
`“reflectors” (e.g. walls, doors, or other obstructions), many
`signals may arrive from different paths. This condition is
`known as “multipath.” In some embodiments, stations 102
`and 104 utilize multiple antennas to take advantage of the
`multipath and to increase the communications bandwidth.
`For example, in some embodiments, stations 102 and 104
`may communicate using Multiple-Input-Multiple-Output
`(MIMO) techniques. In general, MIMO 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 frequency division multiplexing
`(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
`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 recerving 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 channelstate 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 may be represented
`by an n by n unitary beamforming matrix V determined
`using a singular value decomposition (SVD) algorithm, and
`
`6
`
`

`

`US 7,236,748 B2
`
`V =expléCod,2ws a,G,|=ely
`
`n2-1
`
`k= -
`
`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 generator
`bases. For example, multiple hermitian generator matrices
`known to both the transmitter and receiver may be utilized
`to represent the beamforming matrix. Further, the numbers
`are also angles from -x to x of an (n°—1)-dimension polar
`coordinate, which facilitate a fine control of quantization
`error.
`
`
`
`
`
`10
`
`15
`
`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 MIMO sys-
`tems.
`
`Atransmit beamforming matrix may be found using SVD
`as follows:
`
`20
`
`H=UDV'
`
`x=Vd
`
`(1)
`
`(2)
`
`25
`
`where det(V)=1 and p is a global phase. In some embodi-
`ments, yp is not fed back to the transmitter. The term e’” can
`be factored out from V in equation (4) and absorbed by the
`data vector d in equation (2). The 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, ip 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 numbers ofbits
`prior to feeding back the parameters.
`In embodiments in which n*—1 angles (i.e. a, ...a,2_,) are
`fed back, the feedback angles are computed by the 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 andVare unitary; D is a diagonal matrix with
`30
`above are not included in the feedback, the numberof angles
`H’s eigenvalues; V is n by n, and n is the numberofspatial
`fed back is reduced to n?-n parameters.
`channels. To obtain V at the transmitter, the transmitter may
`Feeding back n?-1 parameters instead 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 may be 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'=L, is a unitary matrix. All n by n unitary
`n-1 angles, and the interpolation may make useofthis extra
`matrices may be considered to form a group U(n). Its generic
`information.
`representation may be written as:
`
`The feedback angles may be computed as follows.
`1) Singular value decomposition of the channel matrix H
`
`35
`
`40
`
`45
`
`(3)
`
`V =explé
`
`ne
`
`k=l
`
`ay Gy
`
`where G, is the k-th hermitian generator matrix; a, is the
`angle of the k-th rotation and it is between -a and 7; and 1
`is the square root of -1. Example generator matrices for n=2,
`3, and 4 are provided at the end of this description. lt should
`
`55
`
`where ' is the conjugate transpose operation.
`2) Eigenvalue decomposition of matrix V
`
`50
`
`H-UDV'
`
`V=M DM"!
`
`(5)
`
`(6)
`
`where D is a diagonal matrix with norm 1 diagonal
`elements.
`
`7
`
`

`

`5
`The receiver may transmit (a, .. . a,,2_,) to the transmitter,
`which may then reconstruct the beamforming matrix V as
`follows.
`
`6
`We can expand V in series as
`
`US 7,236,748 B2
`
`(15)
`
`For 2x2 matrix V, (15) can be simplified by using
`
`n=-l
`Az i> a, Gi
`k=l
`
`A= PAP"
`
`V = Pdiaglexp(A,) +++ exp(a,)|P-!
`
`(9)
`
`(10)
`
`(11)
`
`and the transmitter may perform transmit beamforming
`
`as:
`
`x=Vd
`
`(12)
`
`Various embodiments of the present invention also reduce
`the range of the quantized feedback numbers from (—2, 0%)
`to (-m, a]. For example, real numbers included in a beam-
`forming matrix generally take on values of (-%, 9), while
`the angles a, may take on values of (-m, a]. In some
`embodiments, the range of (-7, 1] can be represented with
`fewer bits, and in other embodiments, greater precision 1s
`provided because of the smaller range.
`
`Compact Feedback Formats for 2x2 MIMO Systems
`As described above, various embodiments of the present
`invention provide compact feedback formats for n by n
`MIMO systems, where n may be of any size. 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.
`Two compact feedback schemesare described below. The
`first scheme feeds back one sign bit and three real numbers
`between —1 and 1. The computation of the numbers utilizes
`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
`[O,2), [0,00), and (-2,2t]. Two of the three ranges are smaller
`than the more general case described above and leads to a
`smaller quantization error under the same number of quan-
`tization bits.
`
`As described above, any unitary matrix V can be written
`
`as
`
`V =exp(icoa,>ws
`
`-y
`
`k=l
`
`
`
`aG,|=e"V
`
`(13)
`
`2
`
`3
`
`k=l
`
`
`
`bs nyGy =,
`
`to yield:
`
`V=cos(®)G,ti sin(@)(7G+2)G54+3G3)
`
`(16)
`
`ln this representation, we can limit ® in [0, m) and n, are
`real between [-1,1]. Using the orthogonal and unitary prop-
`erty, we have:
`
`_
`1
`cos(y) = 3 trace (VG4)
`
`=
`Mm =>
`2sin(y)
`
`vo
`trace (VG) for k= 1, 2,3
`
`(17)
`
`(18)
`
`35
`
`is a real, unit 3-vector,
`Since (n,, n, 03)
`described by two angles 9, as follows.
`
`it can be
`
`n=sin(8)cos()
`
`n5=sin(O)sin(p)
`
`n3=cos(8)
`
`(19)
`
`(20)
`
`(21)
`
`is between [-7, 2).
`where 0 is between [0, 1) and
`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 doesn’t require
`sine and cosine functions during reconstruction. Scheme 2
`sends back ®, @ and #, which are between [0, 2), [0, 7), and
`[0,27), respectively. This scheme utilizes sine and cosine
`functions during reconstruction. In some embodiments, the
`angles may be quantized at low resolution to reduce over-
`head, and existing 64 or 128 FFT tables in 802.11 OFDM
`baseband systems may be used to approximate the sine and
`cosine functions. The schemesare illustrated next.
`
`8
`
`

`

`US 7,236,748 B2
`
`7
`3) Compute feedback numbers
`
`1 9
`cos(y) = 3 trace(V G4)
`
`uh, = ———————— trace
`=
`trace(VG{)
`2¥ 1 — cos? (g)
`‘
`‘
`
`(24)
`
`(>)
`
`4) Receiver quantizes cos(®), n,, n,, and sends back with
`sign(n, )
`The transmitter may then reconstruct V using cos(®), n,
`n, and sign(n,)
`
`a2
`ny=sign(# ))V1—-n5°—ny
`
`(26)
`
`(27)
`
`P=cos(@)G,-1V1-cos?(@) (2G,+1>GytnG3)
`
`Scheme 2 is illustrated as follows.
`1) Singular value decomposition of the channel matrix H
`
`H=UDV'
`
`where ' is the conjugate transpose operation.
`2) Remove the global phase of the unitary matrix V
`
`
`ye
`~ Vder(V)
`
`3) Compute feedback numbers
`
`1 a
`cos(y) = qirace(V G4)
`
`ne = tecG1)
`~ 2¥1 — cos? (w)
`‘
`
`4) Calculate angle @ and o
`
`8 = arecos(n3), 8c [0, x)
`
`arctan(—}, Ay =O
`o=)Ay
`arctan|=| +7, ny <0
`Ay
`
`(28)
`
`(29)
`
`(30)
`
`G1)
`
`(32)
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`5) Receiver quantizes and feeds back ®, 6 and o
`The transmitter may then reconstruct V using ®, 8 and o
`
`n,=sin(O)cos()
`
`no=sin(8)sin(p)z3=cos(8)
`
`(33)
`
`G34)
`
`55
`
`8
`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 from received signals.
`The channelstate information may include the channel state
`matrix H 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 generator 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,
`.
`.
`. 4,,2_1);
`and in embodiments that utilize equation (16), the param-
`eters may include coefficients such as cos(®), n,, n,, and the
`sign of n,. Further, in some embodiments that utilize equa-
`tions (16)-(21), the parameters may include ®, 0 and 9.
`In some embodiments, n’-1 parameters are chosen to
`represent the weighting of generators matrices. For example,
`in a 2 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 embodiments that
`feed back (a, .. . a,2_,), the angles a, can be quantized in the
`range [-7, 1). Further,
`in embodiments that feed back
`cos(®), nj, n,, and the sign of n,, the parameters may be
`quantized in the range of [-1, 1). In still further embodi-
`ments, the parameters P, 9 and ¢ may be quantized between
`[0, =),
`[0, =), and [0,2 2), respectively. The quantized
`parameters may be transmitted using any type of protocol or
`any type of communications link, including a wireless link
`such as a wireless link betweenstations 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-
`
`9
`
`

`

`US 7,236,748 B2
`
`9
`method 300 may be performed in the order presented, or
`may be performed in a different order. Further,
`in some
`embcdiments, someactions listed in FIG. 3 are omitted from
`method 300.
`Method 300 is shown beginning at block 310 in which at
`least one parameter is recetved. In some embodiments, this
`may correspond to a transmitter receiving one or more
`parameters that represent a sum of rotated 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 4, or
`coefficients such as cos(®), n,, n,, 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. For 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 subcarriers 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 may be 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 MIMOsystem. For example, electronic
`system 400 may beutilized in a wireless network as station
`102 or station 104 (FIG. 1). Also for example, electronic
`system 400 may be a station 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.
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`10
`cation (LNA), filtering, frequency conversion or the like.
`Further, in some embodiments, PHY 430 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 control
`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 performs actions in response thereto.
`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 example, 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
`ofarticle that includes a medium readable by processor 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. For
`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 may be 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.
`Ethernet
`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
`
`10
`
`

`

`US 7,236,748 B2
`
`11
`
`12
`
`Generator Matrices
`For U(2) group, the generator matrices are:
`
`10
`0
`1
`0 -i
`01
`a(, oe, » }e=(, i} @=(y |
`
`For UG) group, the generator matrices are:
`
`0
`0
`1
`0-70
`010
`Gy=|1 0 O},G,=)% 0 O},G;=/0 -1 0},
`a0 0
`0.90 9
`0
`0
`9
`
`000
`00 -i
`1
`G,-|0 0 Ola;=|0 0 OL aG-=lo 0 1],
`0
`0
`70 0
`010
`
`oOF©
`
`PeOoOG
`
`For U(4) group, the generator matrices are:
`
`-continued
`100 0
`
`100 0
`
`1/0 10 06
`1);0 100
`“= —=lo o
`1
`o f= Glo 01 0
`000-3
`0001
`
`Whatis claimedis:
`1. A method comprising:
`representing a beamforming matrix using a sum of
`weighted hermitian generator matrices; and
`feeding back parameters that describe the weighting of the
`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 comprises feeding back parameters for less than all
`orthogonal frequency division multiplexing (OFDM) sub-
`carriers in a multiple input multiple output (MIMO) system.
`3. The method of claim 1 wherein feeding back comprises
`transmitting parameters for less than all OFDM subcarriers
`in a MIMOsystem.
`4. The methodof claim 1 further comprising removing a
`global phase from the beamforming matrix.
`5. The method of claim 1 wherein the beamforming
`matrix comprises two rows and two columns.
`6. A method comprising:
`representing a beamforming matrix using a sum of
`weighted hermitian generator matrices; and
`feeding back parameters that describe the weighting of the
`hermitian generator matrices, wherein the parameters
`comprise coefficients to weight the hermitian generator
`matrices and wherein the parameters comprise at least
`two of n,, 0.4, and n,, wherein
`F=cos(®)G,+i sin(P)(7G+17.G5+n3G3),
`
`°
`
`10
`
`Is
`
`50
`
`25
`
`30
`
`35
`
`40
`
`V is the beamforming matrix, G,, G,, G,, and G, are
`hermitian generator matrices, and i is the square root of -1.
`7. The method of claim 6 wherein the parameters further
`45 comprise cos(®).
`8. The method of claim 6 further comprising removing a
`global phase from the beamforming matrix.
`9. The method of claim 6 wherein the parameters com-
`prise n,, n;, and the sign of n,.
`5°10. A method comprising:
`projecting a function of a beamforming matrix to a
`plurality of hermitian generator matrices;
`removing a global phase from the beamforming matrix;
`and
`
`55
`
`OooOofCFe
`oOorfS
`ooor |
`oFD2
`
`G3 =
`
`OoOo
`on
`
`:
`Gy = ococoFe
`reOOCOSG
`
`G2 =
`
`
`
`OoOo2f oo.colU6c8
`
`un
`
`o
`
`OQ
`
`o2Oo
`2
`
`|
`
`OoOoOoff
`
`|
`
`~Oo
`aooo
`
`oroned
`ooond
`
`ooond
`aor22
`
`aooOofcSG
`aooca
`oooo
`oooer
`aococKF& ocoOoG&G
`Qocr8S I
`
`i)
`
`0.0
`
`OooOofc
`
`OooO°OGf
`
`OooO°OGf
`
`-i
`0
`o,7
`0
`
`Oo
`
`o
`
`o™2
`OoOoOoff
`
`11
`
`

`

`US 7,236,748 B2
`
`13
`13. A method comprising:
`receiving at least one parameter, wherein the at least one
`parameter includes a sign bit and a second parameter,
`wherein the sign bit is used to reduce a range of the
`second parameter; and
`least one hermitian
`combining a weighted sum of at
`generator matrix using information derived from the at
`least one parameter to arrive at a beamforming matrix.
`14. The method of claim 13 wherein:
`the beamforming matrix comprises n rows and n columns;
`and
`receiving at least one parameter comprises receiving n,-1
`parameters.
`15. The method of claim 13 wherein receiving comprises
`receiving at least one parameter for less than all OFDM
`subcarriers in a MJMO system.
`16. The method of claim 15 wherein combining comprises
`combining a weighted sum of at least one hermitian gen-
`erator matrix for the less than all OFDM subcarriers.
`17. The method of claim 16 further comprising interpo-
`lating to arrive at additional beamforming matrices.
`18. An article comprising:
`a machine-readable medium encoded with computer
`executable instructions that when accessed result in a
`machine representing a beamforming matrix using a
`sum of weighted hermitian generator matrices, and
`feeding back parameters that describe the weighting of
`the hermitian generator matrices, wherein the param-
`eters comprise at least two of n,, nj, and n;, wherein
`
`F=cos(P)Gyti sin(P)(7;G ,+5G5+4G,),
`
`10
`
`15
`
`20
`
`25
`
`14
`V is the beamforming matrix, G,, Gj, G,, and G, are
`hermitian generator matrices, and i is the square root of —1.
`19. The article of claim 18 wherein the parameters com-
`prise n,, n;, and the sign of n,.
`20. The article of claim 19 wherein the parameters further
`comprise cos(@).
`21. An electronic system comprising:
`n antennas;
`a processor coupled to the n antennas;
`an Ethernet interface; and
`an article having a machine-readable medium encoded
`with computer executable instructions
`that when
`accessed result in the processor receiving at least one
`parameter, and combining a weighted sum ofat least
`one hermitian generator matrix using information
`derived from the at least one parameter to arrive at a
`beamforming matrix, wherein the at least one param-
`eter comprises at least two of n,, n,, and n,, wherein
`
`F=cos(®)G,ti sin(D)(#,G ,+7,G54+n3G,),
`
`V is the beamforming matrix, G,, G5, G,, and G, are
`hermitian generator matrices, and i is the square root of -1.
`22. The electronic system of claim 21 wherein receiving
`comprises receiving at least one parameter for less than all
`OFDMsubcarriers in a MIMOsystem.
`23. The electronic system of claim 22 wherein the instruc-
`tions, when accessed, further result in the processor inter-
`polating to arrive at OFDM subcarrier beamforming matri-
`ces for which no parameters were received.
`*
`*
`*
`*
`*
`
`12
`
`

`

`UNITED STATES PATENT AND TRADEMARKOFFICE
`CERTIFICATE OF CORRECTION
`
`: 7,236,748 B2
`PATENT NO.
`APPLICATION NO. : 10/955826
`DATED
`: June 26, 2007
`INVENTOR(S)
`: Liet al.
`
`Page | of 1
`
`It is certified that error appears in the above-identified patent and that said Letters Patentis
`hereby corrected as shownbelow:
`
`On the Title page, in field (56), under “Other Publications”, in column 2, line 2, delete
`“Seraching” andinsert -- Searching--, therefor.
`
`In column 13, line 12, in Claim 14, delete “n,-1” and insert -- n’-1 --, therefor.
`
`Signed and Sealed this
`
`Fourth Day of September, 2007
`
`
`
`13
`
`