(12) United States Patent
`US 7,236,748 BZ
`(10) Patent N0.:
`
` Li et al. (45) Date of Patent: Jun. 26, 2007
`
`
`USOO7236748B2
`
`(54) CLOSED LOOP FEEDBACK IN MIMO
`SYSTEMS
`
`(75)
`
`Inventors: Qinghua Li, Sunnyvale, CA (US);
`.
`.
`.
`Xlntlan E“ L'"’ Palo Alto” CA (Us)
`.
`Intel corporat‘m santa C1ara= CA
`(US)
`
`.
`.
`(73) ASSlgnee‘
`
`( * ) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U'S'C' 15403) by 363 days‘
`
`_
`(21) Appl. NO” 10/955’826
`.
`.
`(22) Filed.
`
`Sep. 30, 2004
`_
`_
`_
`Prior Publication Data
`
`US 2006/0068738 A1
`Int Cl
`'
`'
`(200601)
`H043 ”38
`(2006.01)
`H04M 1/00
`(52) us. Cl.
`...................................... 455/69; 455/562.1
`(58) Field of Classification Search .................. 455/69,
`455/562'13 561= 1013 103= 272’2733 27617
`. 455/277.I, 2772; 375/299, 347.; 370/208
`See application file for complete search history.
`References Cited
`
`(65)
`
`(51)
`
`(56)
`
`Man 30’ 2006
`
`U.S. PATENT DOCUMENTS
`5,999,826 A * 12/1999 Whinnctt
`.................... 455/561
`6,597,678 31*
`7/2003 Kuwahara et a1.
`.......... 370/342
`6,847,805 B2*
`1/2005 Liu ............................. 455/69
`6,927,728 B2
`8/2005 Vook et al.
`
`.............. 455/454
`7/2003 Walton et al.
`2003/0125040 A1*
`2003/0210750 A1* 11/2003 Onggosanusi et a1.
`...... 375/295
`2004/0235433 A1* 11/2004 Hugl et al.
`................. 455/101
`iggg/gégéégg 21
`13/388; gong at 31'
`0011
`2006/0056335 A1
`3/2006 Lin et a1.
`2006/0056531 A1
`3/2006 Li et al.
`2006/0068718 A1*
`3/2006 Li et a1.
`2006/0092054 A1
`5/2006 Li et a1.
`
`....................... 455/69
`
`OTHER PUBLICATIONS
`t
`f th 1
`h R
`1 S
`t'
`1 t
`it
`d W 'tt
`0 _
`_
`e n erna-
`epo
`H erna 10113.
`1'1 en
`plnlOIl 0
`earc
`an
`tional Seraching Authority; Dated Jan. 31, 2006; PCT/Uszoos/
`031585, 1-13.
`International Search Report and Written Opinion of the Interna-
`tional Searching Authority; Dated Sep. 16, 2005; PCT/USZOOS/
`017774; 15 Pages.
`“PCT Search Report”, PCT/US2005/03I979, (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, P20442PCT7PCT Search
`Report Written Opinion from PCT application serial No. PCT/
`U82005/031585,(Jun. 20, 2004),249—253.
`.
`.
`* 01th by exammer
`Primary Examiner—Nguyen T. V0
`(74) Attorney, Agent, or Firm—LeMoine Patent Services,
`PLLC; Dana B. LeMoine
`
`(57)
`
`ABSTRACT
`
`Feedback bandwidth may be reduced in a closed loop
`231%Ooiiitegiigiifgffiiifiggsg abeamformlng matnx uglng
`g
`g
`'
`
`23 Claims, 4 Drawing Sheets
`
` ESTIMATE CHANNEL STATE INFORMATION
`FROM RECEIVED SIGNALS
`
`210
`
`DETERMINE A BEAMFORMING MATRIX
`
`FROM THE CHANNEL STA TE INFORMATION
`
`MATRICES
`
`REPRESENTA BEAMFORMING MATRIX
`USING A SUM OF WEIGHTED GENERATOR
`
`MATRICES
`
`FEED BACK PARAMETERS THAT DESCRIBE
`THE WEIGHT/N0 OF THE GENERATOR
`
`220
`
`230
`
`240
`
`\ 200
`
`LG 1004
`
`1
`
`LG 1004
`
`

`

`U.S. Patent
`
`Jun. 26,2007
`
`Sheet 1 0f 4
`
`US 7,236,748 B2
`
`
`
`STAT/0N2
`
`
`104
`
`
`
`STATION1
`
`102
`
`FIG.1
`
`2
`
`

`

`U.S. Patent
`
`Jun. 26,2007
`
`Sheet 2 0f 4
`
`US 7,236,748 B2
`
`ESTIMATE CHANNEL STATE INFORMATION
`
`210
`
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`
`FROM THE CHANNEL STA TE INFORMATION
`
`REPRESENTA BEAMFORMING MATRIX
`USING A SUM OF WEIGHTED GENERATOR
`
`MATRICES
`
`
`
`FEED BACK PARAMETERS THAT DESCRIBE
`THE WEIGHTING OF THE GENERATOR
`
`
`MATRICES
`
`220
`
`230
`
`240
`
`\ 200
`
`FIG. 2
`
`3
`
`

`

`U.S. Patent
`
`Jun. 26,2007
`
`Sheet 3 0f 4
`
`US 7,236,748 B2
`
`RECEIVE AT LEAST ONE PARAMETER
`
`WEIGHTAT LEAST ONE GENERATOR
`
`
`
`MA TRIX USING INFORMA TION DERIVED
`
`FROM THE AT LEAST ONE PARAMETER
`
`310
`
`320
`
`
`
`
`
`
`
`
`
`MATRIX TO ARRIVE A T A BEAMFORMING
`MA TRIX
`
`
`COMBINE THE AT LEAST ONE GENERATOR
`
`330
`
`K 300
`
`FIG. 3
`
`4
`
`

`

`U.S. Patent
`
`Jun.26,2007
`
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`
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`

`

`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.
`
`DESCRIPTION OF EMBODIMENTS
`
`In the following detailed description, reference is made to
`the accompanying drawings that show, by way of illustra-
`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 description is, therefore, not to be taken in a limiting
`sense, and the scope of the present invention is defined only
`by the appended claims, appropriately interpreted, along
`with the full range of equivalents to which the claims are
`entitled. In the drawings, like numerals refer to the same or
`similar functionality throughout the several views.
`FIG. 1 shows a diagram of two wireless stations: station
`102, and station 104. In some embodiments, stations 102 and
`104 are part of a wireless local area network (WLAN). For
`example, one or more of stations 102 and 104 may be an
`access point in a WLAN. Also for example, one or more of
`stations 102 and 104 may be a mobile station such as a
`laptop computer, personal digital assistant (PDA), or the
`like. Further, in some embodiments, stations 102 and 104 are
`part of a wireless wide area network (WWAN), and still
`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. 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 fiiture IEEE
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`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 IEEE personal area network standard or wide area
`network standard.
`
`Stations 102 and 104 each include multiple antennas.
`Each of stations 102 and 104 includes “11” antennas, where
`n may be any number. In some embodiments, stations 102
`and 104 have an unequal number of 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 systems offer 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
`OFDM breaks each spatial channel into small subchannels
`such that each subchannel exhibits a more fiat 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.
`
`MIMO systems may operate either “open loop” or “closed
`loop.” In open loop MIMO systems, 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-
`
`thereby reducing the necessary
`mation between stations,
`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
`MIMO systems, 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
`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 2n2 real numbers for any n by n complex
`unitary matrix, where n is the number of spatial channels in
`the MIMO system.
`In some embodiments of the present invention, the beam-
`forming matrix V is represented by nZ—l
`real numbers
`instead of Zn2 real numbers. By sending nz—l real numbers
`instead of 2n2 real numbers to represent the beamforming
`matrix, the feedback bandwidth may be reduced. Various
`
`6
`
`

`

`US 7,236,748 B2
`
`3
`
`embodiments of the present invention exploit the structure
`
`of unitary matrixes and represent the unitary matrices by a
`combination of nz—l 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 —J1: to 31: of an (n2—1)-dimension polar
`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 MlMO sys-
`tems.
`
`Atransmit beamforming matrix may be found using SVD
`as follows:
`
`10
`
`15
`
`20
`
`H=UDV‘
`
`x:Vd
`
`(1)
`
`(2)
`
`25
`
`where d is the n-vector of code bits for 11 data streams; x is
`the transmitted signal vector on the antennas; H is the
`channel matrix; H’s
`singular value decomposition is
`HZUDV'; U and V are unitary; D is a diagonal matrix with
`H’s eigenvalues; V is n by n, and n is the number of spatial
`channels. To obtain V at the transmitter, the transmitter may
`send training symbols to the receiver;
`the receiver may
`evaluate H, compute the matrix V'; and the receiver may
`feedback parameters representing V to the transmitter. As
`described more fiJlly below, the number of feedback param-
`eters used to represent V may be reduced by representing the
`beamforming matrix using a weighted sum of orthogonal
`generator matrices.
`
`A generic n by n complex matrix satisfying the following
`condition VV':ln is a unitary matrix. All 11 by n unitary
`matrices may be considered to form a group U(n). lts generic
`representation may be written as:
`
`V = exp [i
`
`”2
`
`k:l
`
`51k Gk
`
`(3)
`
`where Gk is the k-th hermitian generator matrix; ak is the
`angle of the k-th rotation and it is between —J'IS and at; and i
`is the square root of —1. Example generator matrices for n:2,
`3, and 4 are provided at the end of this description. It should
`be noticed that the set of generator matrices for n:m is a
`subset of the set for n:m+l. 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 from the 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 of n,
`may be utilized without departing from the scope of the
`present invention.
`
`lt is noted that the last generator an in U(n) is a scaled
`identity matrix and it commutes with all other generator
`matrices. Accordingly, the unitary matrix can be written as
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`V = exp(.é0051,12)exp[r
`
`n21
`
`kzl
`
`
`
`akGk = 13wV
`
`(4)
`
`where det(V):l and It) is a global phase. In some embodi-
`ments, 1]) is not fed back to the transmitter. The term em’ can
`be factored out from V in equation (4) and absorbed by the
`data vector din equation (2). The term eN’ 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 nz—l angles (i.e. a1 .
`.
`. an2_1) are fed back. Further, in
`some embodiments, adaptive bit loading is utilized to reduce
`the feedback bandwidth further. For example, various
`parameters may be quantized with dilferent numbers of bits
`prior to feeding back the parameters.
`
`. an2_1) are
`.
`ln embodiments in which nZ—l angles (i.e. al .
`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
`feed back n231 1 angles, it can be shown that n—l of those
`angles are not needed at the transmitter since the training can
`compensate the effect. When the n—l angles referred to
`above are not included in the feedback, the number of angles
`fed back is reduced to nZ—n parameters.
`
`Feeding back n2—l parameters instead of n2—n parameters
`provides more information at the transmitter that may be
`useful in many ways. For example, in OFDM systems with
`m subcarriers, the transmitter uses a beamforming matrix for
`each of the m OFDM subcarriers. In some embodiments of
`
`the present invention, n2—1 parameters are fed back for less
`than all of the m subcarriers, and the transmitter may then
`interpolate to arrive at the beamforming matrices for the
`remaining subcarriers. Extra information is provided by the
`n—l angles, and the interpolation may make use of this extra
`information.
`
`The feedback angles may be computed as follows.
`
`1) Singular value decomposition of the channel matrix H
`
`H:U D v'
`
`where ' is the conjugate transpose operation.
`
`2) Eigenvalue decomposition of matrix V
`
`v:M D M’1
`
`(5)
`
`(6)
`
`where D is a diagonal matrix with norm 1 diagonal
`elements.
`
`3) Natural logarithm of V
`
`log( V)=M lo g(D)MF1
`
`(7)
`
`where log(D) essentially computes the phase of diagonal
`elements of D.
`
`4) Project logW) to the nZ—l generator matrixes
`
`01k = —%trace[log(V)Gila
`
`for k = l,
`
`,
`
`n2 —l
`
`(8)
`
`7
`
`

`

`5
`
`. a,,,2_1) to the transmitter,
`.
`The receiver may transmit (a 1 .
`which may then reconstruct the beamforrning matrix V as
`follows.
`
`We can expand V in series as
`
`6
`
`US 7,236,748 B2
`
`(15)
`
`r1271
`A = 52 511ka
`k=1
`
`A = 13mm1
`
`l7 : Pdiag[exp(/11)
`
`expMnHP—l
`
`(9)
`
`(10)
`
`(11)
`
`and the transmitter may perform transmit beamforrning
`
`as:
`
`x=vd
`
`(12)
`
`Various embodiments of the present invention also reduce
`the range of the quantized feedback numbers from (—00, 00)
`to (—31, 31:]. For example, real numbers included in a beam-
`forming matrix generally take on values of (—00, 00), while
`the angles ak may take on values of (—75,
`31:]. 1n some
`embodiments, the range of (—313, 313] can be represented with
`fewer bits, and in other embodiments, greater precision is
`provided because of the smaller range.
`
`Compact Feedback Formats for 2x2 MlMO Systems
`
`As described above, various embodiments of the present
`invention provide compact feedback formats for n by n
`MIMO systems, where 11 may be of any size. In some
`embodiments, compact feedback formats are further devel-
`oped for the case of MlMO systems with two spatial
`channels. These compact formats may be utilized in 2 by 2
`MlMO systems, or in higher order systems that use less than
`all available spatial channels.
`
`Two compact feedback schemes are 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 scheme feeds back three angles with ranges
`[0,75), [0,70, and (—J'IS,J'IZ]. 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
`
`n
`
`271
`
`V = epricoanz)exp[£
`
`k:1
`
`
`
`akGk = 22in
`
`(13)
`
`10
`
`15
`
`20
`
`25
`
`30
`
`For 2x2 matrix V, (15) can be simplified by using
`
`2
`
`[31.0.
`
`k:1
`
`
`
`:1,
`
`to yield:
`
`I7:cos((I))G4+i sin((I))(anl+n2G2+n3G3)
`
`(16)
`
`ln this representation, we can limit (I) in [0, 31:) and nk are
`real between [—1,1]. Using the orthogonal and unitary prop-
`erty, we have:
`
`2 ,
`1
`cos(<,0) = 2 trace (VG4)
`
`—i
`11k = 2sin(t,p)
`
`trace (VGI’) for k = l, 2, 3
`
`(17)
`
`(13)
`
`35
`
`is a real, unit 3-vector,
`Since (n1, n2, n3)
`described by two angles 0,(I) as follows.
`
`it can be
`
`nl:sin(8)COS(¢)
`
`n2=sin(6)SiH(¢)
`
`n3=cos(0)
`
`(19)
`
`(20)
`
`(21)
`
`where 0 is between [0, 31:) and q) is between [—a'c, It).
`From above, we derive two schemes to feed back infor-
`mation representing the beamforrning matrix V. Scheme 1
`sends back cos((l)), n2, n3, and the sign of n1. 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 (I), 0 and (I), which are between [0, 31:), [0, 31:), and
`[0,2313), 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 schemes are illustrated next.
`Scheme 1 is illustrated as follows.
`
`1) Singular value decomposition of the channel matrix H
`
`40
`
`45
`
`50
`
`55
`
`where Gk is the k-th herrnitian generator matrix; ak is the
`angle of the k-th rotation and it is between —J': and 31:; i is the
`square root of —1; V is unitary and det(V):1; 1p is a global
`phase. V can be computed as
`
`H:UDV'
`
`60
`
`where ' is the conjugate transpose operation.
`2) Remove the global phase of the unitary matrix V
`
`V:
`
`
`V
`
`v deI(V)
`
`(14)
`
`65
`
`V:
`
`
`v
`
`x/ mm
`
`(22)
`
`(23)
`
`8
`
`

`

`3) Compute feedback numbers
`
`7
`
`7 /
`1
`cos(<,0) = itrace(VG4)
`
`n =— race
`_i
`t
`2V1 — (3082(50)
`k
`
`(VG’ )
`k
`
`US 7,236,748 B2
`
`8
`
`may be performed in a different order. Further, in some
`embodiments, some actions listed in FIG. 2 are omitted from
`method 200.
`
`Method 200 is shown beginning at block 210 in which
`channel state information is estimated from received signals.
`The channel state information may include the channel state
`matrix H described above. At 220, a beamforming matrix is
`determined from the channel state information. In some
`
`(24)
`
`(25)
`
`4) Receiver quantizes cos(<I>), n2, n3, and sends back with
`81941011)
`The transmitter may then reconstruct V using cos((I)), n2,
`n3 and sign(nl)
`
`10
`
`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.
`
`I7=cos(CIJ)G4—iv/1—COSZ(<IJ)(M1G1+HZG2+H3G3)
`
`Scheme 2 is illustrated as follows.
`
`(26)
`
`15
`
`(27)
`
`I) 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
`
`
`v
`V _
`_ x/detW)
`
`3) Compute feedback numbers
`
`2 ,
`1
`cos(<,o) = Etrace(VG4)
`
`n - ——itrace(VG’)
`k — 2V1 — cosz(tp)
`k
`
`4) Calculate angle 8 and (I)
`
`0 = aI‘CCOS(f’l3), 6 c [0, 7?)
`
`¢ =
`
`arctan(’2), n1 2 0
`n1
`n2
`arctan(—) +7r, 111 < O
`”1
`
`(28)
`
`(29)
`
`(30)
`
`(31)
`
`(32)
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`5) Receiver quantizes and feeds back (I), 8 and q;
`The transmitter may then reconstruct V using (I), 6 and (I)
`
`50
`
`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 coeflicients such as (a1 .
`.
`. a,,2_1),
`and in embodiments that utilize equation (16), the param-
`eters may include coefiicients such as cos((I)), n2, n3, and the
`sign of n1. Further, in some embodiments that utilize equa-
`tions (16)-(2l), the parameters may include (I), 6 and 4).
`In some embodiments, n2—1 parameters are chosen to
`represent the weighting of generators matrices. For example,
`in a 2 by 2 MIMO system, 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
`n2—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 (a1 .
`.
`. a,,2_1), the angles ak can be quantized in the
`range [—J'|Z, 7:). Further,
`in embodiments that feed back
`cos(d>), n2, I13, and the sign of n1, the parameters may be
`quantized in the range of [—l, 1). In still further embodi-
`ments, the parameters (1), 6 and (I) may be quantized between
`[0, at),
`[0, at), and [0,2 7:), 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 between stations like those described
`with reference to FIG. 1.
`
`n1:sin(6)cos(¢)
`
`n2=sin(6)sin(¢)n3=cos(6)
`
`V=cos((IJ)G4+i sin(<IJ)(anl+n2G2+n3G3)
`
`(33)
`
`(34)
`
`(35)
`
`FIG. 2 shows a flowchart in accordance with various
`
`embodiments of the present invention. In some embodi-
`ments, method 200 may be used in, 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 processor or 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
`
`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-
`rier. 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 processor or electronic system. Method 300
`is not limited by the particular type of apparatus or software
`element performing the method. The various actions in
`
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`

`US 7,236,748 B2
`
`9
`
`10
`
`method 300 may be performed in the order presented, or
`may be performed in a dilferent order. Further,
`in some
`embodiments, some actions listed in FIG. 3 are omitted from
`method 300.
`
`Method 300 is shown beginning at block 310 in which at
`least one parameter is received. 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 (I), 6 and (I), or
`coefiicients such as cos(CI>), n2, 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. For example, herrnitian generator
`matrices may be weighted and combined as shown in
`equations (9)-(ll),
`(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 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 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.
`In operation, system 400 sends and receives signals using
`antennas 410, and the signals are processed by the various
`elements shown in 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. PHY 430 may include
`circuitry to support the transmission and reception of radio
`frequency (RF) signals. For example, in some embodiments,
`PHY 430 includes an RF receiver to receive signals and
`perform “front end” processing such as low noise amplifi-
`
`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.
`
`(MAC) layer 440 may be any
`Media access control
`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
`of article that includes a medium readable by processor 460.
`Memory 470 may store instructions for performing the
`execution of the various method embodiments of the 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 common circuit 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.
`
`interface 450 may provide communications
`Ethernet
`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 of port.
`
`Although the present invention has been described in
`conjunction with certain embodiments, it is to be understood
`that modifications and variations may be 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 appended claims.
`
`10
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`15
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`20
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`25
`
`30
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`35
`
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`
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`

`US 7,236,748 B2
`
`Generator Matrices
`
`11
`
`For U(2) group, the generator matrices are:
`
`C
`
`[0 1]G [0 —i]G [10]G[10]
`l'10’2'10’3'0—1’4'01
`
`For U(3) group, the generator matrices are:
`
`010
`
`0—10
`
`100
`
`Gl_100,G2=100,G3=0—10,
`000
`000
`000
`
`001
`
`00—1
`
`000
`
`G4_000G5=OOO,G6=001,
`0
`100
`010
`
`2100
`1100
`0
`0
`07:0 —i,G8=—010Gg= 5010
`010
`300—2
`001
`
`G1:
`
`G3:
`
`Gs:
`
`0100
`
`1000
`0000
`0000
`
`1000
`0—100
`
`0000
`0000
`
`00—10
`