(12) United States Patent
`US 7,492,829 B2
`(10) Patent N0.:
`Lin et a1.
`(45) Date of Patent:
`Feb. 17, 2009
`
`USOO7492829B2
`
`10/20 2 Agee .......................... 370/400
`5/20 3 Yu
`
`5/20 3 Brandlund et a1.
`7/20 3 Walton et a1,-
`11/20 3 Onggosanus1 et a1.
`6/20 4 Goransson et a1.
`11/20 4 Hugl et al.
`11/20 4 Tarokh et a1.
`5/20 5 T
`t
`1.
`12/20 5 Poon
`ong e a
`_
`3/20 6 Li et a1.
`3/20 6 Li et al.
`
`............ 455/562.l
`
`3/20 6 Li et a1.
`5/20 6 Li et a1.
`
`
`
`2002/0150109 A1 *
`2003/0085832 A1
`
`7
`2003/0086366 A1
`2003/0125040 A1
`2003/0210750 A1
`2004/0121810 A1
`2004/0235433 A1
`2004/0235529 A1 *
`2005/0101259 A1
`2005/0286663 A1
`
`2006/0056531 A1
`2006/0068718 A1
`
`2006/0068738 A1
`2006/0092054 A1
`
`(54)
`
`CLOSED LOOP FEEDBACK IN MIMO
`SYSTEMS
`
`(75)
`
`11ven ors:
`I
`
`I
`
`(73)
`
`Assignee:
`
`.
`Notice:
`
`(*)
`
`2 111 Ian .
`1n
`Dun am 1ew
`a
`:
`CA
`K'
`t_
`E L' M t
`, V'
`(US); Qinghua Li, Sunnyvale, CA (Us),
`Ada S. YI P0011 San Leandro CA (Us)
`,
`Intel Corporation, Santa Clara, CA
`(US)
`.
`.
`.
`.
`.
`.
`Subject to any d1scla1mer, the term of this
`patent is extended or adjusted under 35
`U S C 154(1)) by 814 davs
`l
`
`(21)
`
`Appl. N0.: 10/939,130
`
`(22)
`
`Filed:
`
`Sep. 10, 2004
`
`(65)
`
`Prior Publication Data
`
`US 2006/0056335 A1
`
`Mar. 16, 2006
`
`Int. Cl.
`(2006.01)
`H04B 7/02
`U.S. Cl.
`...................................................... 375/267
`
`375/267,
`Field Of Classification Search
`375/347, 349, 358, 354, 337, 369, 372, 373,
`375/374, 215, 294, 327, 376; 700/53; 455/101,
`455/1327141, 69, 265, 180.3, 266; 370/328,
`370/395.62, 507, 503; 702/89; 713/375,
`713/400; 342/103
`See application file for complete search history.
`References Cited
`U.S. PATENT DOCUMENTS
`,
`12/1985 Norsworthy
`12/1998 Proakis et al.
`12/1999 Wh'
`tt
`7/2003 KUJVIEIZM et 31.
`1/200 5 Liu
`8/2005 Vook et a1.
`6/2007 Li ct a1.
`4/2008 Li et a1.
`
`4,559,605 A
`5,844,951 A *
`5,999,826 A
`6,597,678 B1
`6 847 805 B2
`6,927,728 B2
`7,236,748 B2
`7,362,822 B2
`
`.............. 375/347
`
`(56)
`
`r
`W0
`
`FOREIGN PATENT DOCUMENTS
`_7
`/2
`r
`WO 2006041595 Al
`4 006
`
`OTHER PUBLTCATIONS
`
`Roh et a1. Multiple Antenna Channels With Partial Channel State
`Information at the Transmitter, IEEE, vol. 3, No. 2, Mar. 2004*
`.
`(Contlnued)
`Primary Exam inerisam K Ahn
`(74) Attorney, Agent, or FirmiDana B. Lemoine; Lemoine
`Patent Services, PLLC
`
`(57)
`
`ABSTRACT
`
`,
`,
`Feedback bandwidth may be reduced 1n a closed loop MIMO
`system by factorlng non essential 1nf0rmat10n out ofa beam-
`”mung mamx'
`
`16 Claims, 6 Drawing Sheets
`
`
`ESHMATECHANNELSTATEINFORMATION 4270
`FROM RECEIVED SIGNALS
`
`ID
`
`ETERMINEABEAMFORMWGMATRIX J7”
`FROM me CHANNEL smTE WORM/1now
`
`FACTORAPHASEANGLEOUTOFEACH J23”
`
`COLUMNOF THEHEM/FORMING MATRW
`
`FACTORADDIT/ONAL PHASE
`
`)NFORMATIONFROMTHEBEAMFORMING J24”MATRIX TO WED/4 PHASE MATRIXANDA
`
`mew/momma
`
`
`REPRESENT THEPEASEMATRIXAND/1
`MAGN/T'JDEMA1R/XUSINGN1-2 J
`PARAMETERS, WHERE N 13A NUMBER OF
`
`sum/.1 CHANNELS
`
`250
`
`
`
`QUANTIZETHEPARAMETERS
`
`TRANSMTTHEPARAMETERS
`
`4m
`
`Jm
`
`\ 200
`
`Page 1 of 14
`
`SAMSUNG EXHIBIT 1012
`
`Page 1 of 14
`
`SAMSUNG EXHIBIT 1012
`
`

`

`US 7,492,829 B2
`Page 2
`
`OTHER PUBLICATIONS
`
`International Search Report and Written Opinion ofthe Inernational
`Searching Authority; Dated Jan. 31, 2006; PCT/US2005/031585,
`1-13.
`
`Jihoon, C. , “Interpolation based transmit beamforming for MIMO-
`OFDM with Limited Feedback”. IEEE International Conference on
`Paris, France, Piscataway, NJ, USA., P20442PCT7PCT Search
`Report \Vritten Opinion from PCT application serial No. PCT/
`U82005/031585,(Jun. 20. 2004),249-253.
`“PCT Search Report”. PCT/US2005/031979. (Jan. 23. 2006). 12
`pages.
`
`Choi, Jihoon. et al., “Interpolation Based Transmit Beamforming for
`MIMO-OFDM with Limited Feedback”, IEEE Communications
`Society, (Jun. 20, 2004),249-253.
`Hottinen. A.
`. et al.. “Transmit Diversity Using Filtered Feedback
`Weights In The FDD/WCDMA System”. IEEE 2000. (Feb. 15.
`2000),15-17.
`Zoltowski, Michael D., et a1., “Simultaneous Sector Processing Via
`Root-Music for Large SensorArrays", School ofElectrical Engineer—
`ing, Purdue University, (1990), pp. 372-376.
`Van Der Veen, Alle-Jan “Algebraic Vlethods For Deterministic Blind
`Beamforming”, Proceedings oftheIEEE, vol. 86, N0. 10, Oct. 1998,
`1987-2008.*
`
`"‘ cited by examiner
`
`Page 2 of 14
`
`Page 2 of 14
`
`

`

`US. Patent
`
`Feb. 17, 2009
`
`Sheet 1 of6
`
`US 7,492,829 B2
`
`
`
`STATION2
`
`
`104
`
`
`
`STATION1
`
`102
`
`FIG.1
`
`Page 3 of 14
`
`Page 3 of 14
`
`

`

`US. Patent
`
`Feb. 17, 2009
`
`Sheet 2 of6
`
`US 7,492,829 B2
`
`ESTIMATE CHANNEL STATE INFORMATION
`FROM RECEIVED SIGNALS
`
`DETERMINEA BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`FACTOR A PHASE ANGLE OUT OF EACH
`COLUMN OF THE BEAMFORMING MATRIX
`
`FACTOR ADDITIONAL PHASE
`INFORMATION FROM THE BEAMFORMING
`
`MAGNITUDE MATRIX
`
`MATRIX T0 YIELD A PHASE MATRIX AND A
`
`REPRESENT THE PHASE MA TRIX AND A
`MAGNITUDE MATRIX USING N2-2
`PARAMETERS, WHERE N IS A NUMBER OF
`
`SPATIAL CHANNELS
`TRANSMIT THE PARAMETERS/||
`
`OUANTIZE THE PARAMETERS
`
`FIG. 2
`
`Page 4 of 14
`
`210
`
`220
`
`23“
`
`240
`
`250
`
`260
`
`270
`
`200
`
`Page 4 of 14
`
`

`

`US. Patent
`
`Feb. 17, 2009
`
`Sheet 3 of6
`
`US 7,492,829 B2
`
`PARAMETER
`
`RECEIVE AT LEAST ONE ANGLE
`
`
`
`310
`
`
`
`A BEAMFORMING MATRIX FROM THE AT
`
`DETERMINE MAGNITUDES OF ENTRIES IN
`
`320
`
`
`
`LEAST ONE ANGLE PARAMETER
`
`
`
`
`RECEIVE AT LEAST ONE PHASE
`
`
`
`PARAMETER
`
`330
`
`APPLY THE AT LEAST ONE PHASE
`
`
` 340
`PARAMETER TO AT LEAST ONE ROW IN
`
`
`THE BEAMFORMING MATRIX
`
`\ 300
`
`FIG. 3
`
`Page 5 of 14
`
`Page 5 of 14
`
`

`

`US. Patent
`
`Feb. 17, 2009
`
`Sheet 4 of6
`
`US 7,492,829 B2
`
`E
`8
`on
`LL]
`0
`8
`Q
`
`|—_LI.J
`LL10
`3%
`0:
`'fi:”Lu
`HE
`Lu___
`
`FIG.4
`
`450
`
`Page 6 of 14
`
`Page 6 of 14
`
`

`

`US. Patent
`
`Feb. 17, 2009
`
`Sheet 5 of6
`
`us 7,492,829 32
`
`FACTOR A 2X2 BEAMFORMING MATRIX
`
`INTO A PLURALITY OF MATRICES, A FIRST
`
`OF THE PLURALITY OF MATRICES HAVING
`
`ENTRIES THATINCLUDE MAGNITUDE
`
`INFORMATION FROM THE BEAMFORMING
`
`MATRIX, WHEREIN THE PLURALITY OF
`
`MATRICES FURTHER INCLUDES TWO
`
`MATRICES WITH PHASE INFORMA TION,
`
`AND WHEREIN ONE OF THE TWO
`
`MATRICES IS REPRESENTED BYA
`
`SECOND PARAMETER, AND THE OTHER OF
`THE TWO MATRICES IS DISCARDED
`
`
`
`REPRESENT THE FIRST OF THE
`
`PLURALITY OF MATRICES WITH A FIRST
`
`PARAMETER
`
`TRANSMIT THE FIRST PARAMETER
`
`510
`
`520
`
`530
`
`\ 500
`
`FIG. 5
`
`Page 7 of 14
`
`Page 7 of 14
`
`

`

`US. Patent
`
`Feb. 17, 2009
`
`Sheet 6 of6
`
`US 7,492,829 B2
`
`FACTORA PHASEANGLE FROM EACH
`COLUMN OF A 3X3 BEAMFORIWNG MATRIX
`
`REPRESENT THE BEAMFORMING MA TRIX
`USING SIX PA RA METERS
`
`510
`
`520
`
`630 TRANSMIT THE SIX PARAMETERS
`
`\ 600
`
`FIG. 6
`
`Page 8 of 14
`
`Page 8 of 14
`
`

`

`US 7,492,829 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, 3, 5, and 6 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 illustration,
`specific embodiments in which the invention may be prac-
`ticed. 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 embodiments of the invention,
`although different, are not necessarily 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 ofthe 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 inven-
`tion 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. Fur-
`ther, in some embodiments, stations 102 and 104 are part of a
`wireless wide area network (WWAN).
`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 ofthe present invention. As used herein, the
`term “802.11” refers to any past, present, or future IEEE
`802.11 standard, including, but not limited to, the 1999 edi—
`tion. Also for example, stations 102 and 104 may operate
`
`10
`
`15
`
`20
`
`30
`
`35
`
`40
`
`45
`
`60
`
`65
`
`2
`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 “N” 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 embodi-
`ments 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 sta-
`tions 102 and 104 are in an environment with many “reflec-
`tors” (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 communi-
`cate using Multip1e-Input-Multiple-Output (MIMO) tech-
`niques. In general, MIMO systems offer higher capacities by
`utilizing multiple spatial channels made possible by multi-
`path.
`In some embodiments, stations 102 and 104 may commu-
`nicate using orthogonal frequency division multiplexing
`(OFDM) in each spatial channel. Multipath may introduce
`frequency selective fading which may cause impairments like
`inter-symbol interference (1S1). OFDM is effective at com-
`bating frequency selective fading in part because OFDM
`breaks each spatial channel into small subchannels such that
`each subchannel exhibits a more fiat channel characteristic.
`
`Scaling appropriate for each subchannel may be implemented
`to correct any attenuation caused by the subchannel. Further,
`the data carrying capacity of each subchannel may be con-
`trolled dynamically depending on the fading characteristics
`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 informa-
`tion directly from another station. In general, open loop sys—
`tems employ exponential decoding complexity to estimate
`the channel. In closed loop systems, communications band-
`width is utilized to transmit current channel state information
`between stations, thereby reducing the necessary decoding
`complexity, and also reducing overall throughput. The com-
`munications bandwidth used for this purpose is referred to
`herein as “feedback bandwidth.” When feedback bandwidth
`is reduced in closed loop MIMO systems, more bandwidth is
`available for data communications.
`The current channel state information may be represented
`by an N><N unitary beamforrning matrix V determined using
`a singular value decomposition (SVD) algorithm, and the
`transmitter may process an outgoing signal using the beam-
`forrning matrix V to transmit into multiple spatial channels. In
`a straightforward implementation, the receiver sends each
`element of the unitary matrix V back to transmitter. This
`scheme involves sending information related to the 2N2 real
`numbers for any N><N complex unitary matrix, where N is the
`number of spatial channels in MIMO system.
`In some embodiments of the present invention, the beam-
`forrning matrix V is represented by N2—N real numbers
`instead of 2N2 real numbers. By sending NZ—N real numbers
`instead of 2N2 real numbers to represent the beamforrning
`matrix, the feedback bandwidth may be reduced. Non-es sen-
`tial information may be factored out of the beamforrning
`matrix and discarded prior to quantizing parameters that are
`used to represent the beamforrning matrix. For example, non-
`
`Page 9 of 14
`
`Page 9 of 14
`
`

`

`US 7,492,829 B2
`
`4
`consisting of scalar quantities that represent the magnitudes
`ofthe entries of V. Since b112+b122:l, V can be written as
`
`V =
`
`eosH sinH
`,—sm0
`e050 ], where 0 E [0, g].
`
`[
`
`(6)
`
`10
`
`15
`
`In various embodiments of the present invention, only two
`angles i.e., 6 and (1)1 141),, are fed back to the transmitter. (530,
`FIG. 5) The first angle, 6, unambiguously represents V, and
`the second angle,
`(pH—(1)21, unambiguously represents PL.
`(520, FIG. 5) In other embodiments of the present invention,
`a trigonometric function of 6 may be selected as a parameter
`to feed back. For example, cos 6 may be fed back as a param-
`eter to represent V. In still further embodiments, another
`parameter may be selected that may unambiguously describe
`V.
`
`20
`
`The phase information in PR may be discarded. Equation
`(1) can be rewritten as
`
`3
`essential phase information may be factored from each col-
`umn in the beamforming matrix, and then NZ—N parameters
`may be utilized to represent the matrix without the non-
`essential phase information.
`A mathematical background of the SVD operation is pro-
`vided below, and then examples are provided for 2x2 and 3x3
`MIMO systems. In the 2x2 closed loop MIMO example, two
`angles in [0, 75/2] and (TE, —J'E] are used as feedback parameters.
`Compared to the straightforward example above, the various
`embodiments ofthe present invention represented by the 2x2
`example below reduce the amount offeedback from eight real
`numbers to two real numbers per subcarrier. In the 3x3 closed
`loop MlMO example, one sign bit plus four angles between
`[0, 311/2] and two angles between [-J'IS, .11] are used as feedback
`parameters. Compared to the straightforward example above,
`the various embodiments ofthe present invention represented
`by the 3x3 example below reduce the amount of feedback
`from 18 real numbers to six real numbers per subcarrier.
`A transmit beamforming matrix may be found using SVD
`as follows:
`
`H:UDV'
`
`erd
`
`(1)
`
`(:2)
`
`where d is the N—vector of code bits for N data streams; x is the
`transmitted signal vector on the antennas; H is the channel
`matrix; H’s singular value decomposition is H:UD "; U and
`V are unitary; D is a diagonal matrix with H’ s eigenvalues; V
`is NxN, 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 compute the matrix V'; and
`the receiver may feedback parameters representing V to the
`transmitter. As described more fully below, the number of
`feedback parameters used to represent V may be reduced by
`factoring non—essential phase information from V‘ and dis—
`carding it prior to quantizing the parameters.
`
`2x2 Beamforming Matrices
`Any complex 2x2 matrix may be written as
`
`V =
`
`[13113011
`bu 49/121
`
`b12€i¢12]
`bzzewzz
`
`.
`
`IfV is unitary i.e., V ':I, then
`
`blzewll
`blleltmzwzrm’
`
`]
`
`(3)
`
`(4)
`
`30
`
`35
`
`40
`
`45
`
`H = DD V/
`
`= UD(PLVPR)'
`= UDPRtPLV)’
`D
`v
`
`= UP’RD( LV)’
`0
`V
`
`where we have used the fact that D and P‘R are diagonal and
`therefore commute. It should be noted that H:UDV' is also a
`singular value decomposition of H. For the SVD algorithm,
`the change from U to U only changes the multiplication
`matrix 011 the receiver side. When H is a mxn matrix with
`m¢n, we can still write H:UDV' and the effect of beam
`forming with V amounts to a rotation in the HQ plane, which
`may be taken care of by the training process. Therefore,
`feeding back V to the transmitter is sufficient for the SVD
`algorithm. Since V is fully determined by 6 and ([311 -¢21, only
`two angles are required to feedback and they are between
`
`and (—75, J13].
`As stated above, the unitary matrix V may be factored into
`the product of three matrices:
`
`1
`0
`V =[0 e“¢21¢11’
`l
`0
`= [ D
`el(¢21n¢11)
`
`511
`][—b12
`
`I712
`2711]
`
`£11911
`0
`
`0
`8“”12
`
`]
`
`[c059
`sinG] 8””
`—sin0 eos0
`0
`
`C‘
`€i¢12
`
`\
`
`(8)
`
`where 6 and (1)2141) 11 are between
`
`where b112+b122:l. We can further limit b11 e[0,l], b12
`e[0,1],
`(1),].
`€[—J'E,J'IZ) without loss of generality. There are 4
`degrees of freedom in V. After factoring the common phases
`for each row and column, the unitary matrix V can be written
`as
`
`_
`
`1
`V _ 0
`
`0
`£II¢ZI’¢III‘
`
`bu
`biz
`(-brz bll]
`
`5w”
`0
`
`0
`eid’lfi
`
`_
`
`I
`-
`_ P’“ PR
`
`60
`
`(5)
`
`where PL and PR are pure phase matrices and diagonal.
`(510, FIG. 5) PR is generated by factoring phase values from
`each column of V, and PL is found by factoring phase values
`from each row ofV. V is a magnitude matrix that has entries
`
`65
`
`Page 10 of 14
`
`Page 10 of 14
`
`

`

`5
`and (—75, 7:]. The parameters 6 and (p214), 1 may be obtained at
`the receiver as follows:
`
`6
`
`-continued
`
`US 7,492,
`
`829 B2
`
`6:arccos(abst:v1l)),9£[0,n/2]
`
`
`Imtvtj)
`q
`mctan[Re(vg)] +fl/A,
`
`IIII‘IVU)
`arctan[Rewj)] + 371/2.
`
`Im(\;j) 2 O
`7
`Im(V[_/') < U
`
`W _
`
`(:9)
`
`(10)
`
`5
`
`10
`
`and the receiver may quantize 6 and (1)21 -¢11 and feed them
`back to the transmitter as parameters that represent V. The
`transmitter may reconstruct V by determining the amplitudes 15
`using 9, and applying a phase rotation to the bottom row using
`$21 "pr 1 '
`
`’ =
`
`c059
`—sin€ Eli¢2r¢rfl
`
`sin6
`.
`c050 emflwll)
`
`(11)
`
`20
`
`The transmitter may then use V for beamfor'ming:
`x:Vd
`
`(12)
`
`25
`
`3x3 Beamforming Matrices
`Any complex, unit 3-vector may be written as
`
`v = [v2 ] =#1 sin<¢lycos<¢newz
`
`609%)
`
`smwlisinwzw‘93
`
`v1
`
`Vs
`
`wherSHVHZ:HV1l2+lv2H2+Hv3l2:1;¢r.¢2 El‘lfl/Zl and
`01,62,03e[—n,n).
`
`Further, any unitary 3 by 3 matrix may be written as
`
`(13)
`
`30
`
`35
`
`2‘911
`0
`0
`
`0
`0
`am
`
`0
`6912
`0
`
`PR
`
`where PL and PR are pure phase matrices and diagonal. PR is
`generated by factoring phase values from each column of V,
`(610, FIG. 6) and Pl is fotmd by factoring phase values from
`each row ofV, and where ¢jket0,n/2J and cos (¢jk), cos (cpjk),
`sin (@QEO. V is a magnitude matrix that includes all of the
`magnitude information originally present in the entries of V.
`As used herein, the term “magnitude matrix” refers to a
`matrix that remains after PL and PR are factored out of the
`original bearnforrning matrix. As
`shown in the above
`example, one or more entries in a magnitude matrix may
`include phase information. It should be noted that v:w 19263]
`is still unitary since the phase factorization doesn’t change the
`unitary property.
`two
`In various embodiments of the present invention,
`parameters are chosen to represent PL, four parameters are
`chosen to represent V, and PR is discarded. In some embodi-
`ments, the angles 621, 631 are selected as parameters to rep-
`resent PL. Matrix V can be determined by four parameters and
`a sign bit, and there are many combinations ofthe four param—
`eters that are subsets of all the angles in V. Different combi-
`nations result in different complexities in the reconstruction
`of V at the transmitter. It should be noted that the complexity
`of extracting all the angles of V is relatively low compared to
`that of the construction of V based on four parameters.
`Instead of directly sending angles back, some embodiments
`may send functions of the selected four angles back. For
`example, common trigonometric functions suchas sin( ), cos(
`), and tan( ) may be selected. The various embodiments ofthe
`present invention contemplate all possible sets offour param-
`
`Big“ COS(¢11)
`V = [v1 v2 V3] = 2'9112'921sin(¢11)cos(¢21)
`#116931sini¢msin<¢zn
`
`69120098512)
`66126622 sin(é12,)cos(¢zz)
`#6126932sin(¢uz)sin<¢>2z>
`
`e‘913 cos(¢513)
`2‘913 2'923 sint¢13)005(¢23)
`69136933sint¢13)sin(¢23)
`
`(l4)
`
`where v'jvj:l and v'jvk:0 for j ,k:l ,2,3. The phases on the 50
`first row and the first column can be factored as the product of
`the following three matrices:
`
`eters to represent V. One set of four parameters ¢11,¢12,<|)21,
`(1)22 and the sign of q)22 provide a solution that is now elabo-
`rated. The extraction of the angles (|)11,(|)12,(|)21,(|)22 may be
`performed as:
`(puiarccosflvlll)
`
`(16)
`
`l
`= 0
`0
`
`D
`€921
`0
`
`PL
`
`0
`0
`6931
`
`COS(¢13)
`COSI¢12)
`COS(¢11)
`sin(¢11)cos(¢21) ewzzsin(¢12)cos(¢zz)
`ei¢23sin(d§13)cos(¢z3)
`
`sin(asmsinwm e‘WSZsinwinsinwzz)
`e‘wfisinwiosinwzg)
`V
`
`Page 11 of 14
`
`55
`
`[15)
`
`¢12:a.tccos(lv12l)
`
`¢12 =arctan(@)
`|V21|
`
`|V32|)
`$22 = arctan( |V22|
`
`60
`
`65
`
`(l7)
`
`(18)
`(19)
`
`It should be noted that (I)1 1,¢12,¢21,¢22 are all within [0,75/2]
`instead of [0,75] and the sign of (1)22 takes only one bit. In
`various embodiments, the feedback includes one angle in
`[0,313] and three angles in [0,75/2].
`
`Page 11 of 14
`
`

`

`US 7,492,829 B2
`
`7
`In embodiments using the above parameters to represent PL
`and V, the receiver quantizes 621,631, ¢11,¢12,¢21,¢22 and
`feeds them back to the transmitter along with sign(¢22), which
`can be found as sign(¢22):sign(angle(\”/22)). (620, 630, FIG.
`6)
`
`The receiver may receive the parameters, reconstruct V,
`and perform beamforming. The outline of the reconstruction
`of V is now shown as: computation of (1)22, (1)32 to reconstruct
`v2, the second column of V; and computation of 9,, the third
`colunm ofV using the unitary property of V. We rewrite V as
`
`0050512)
`coswu)
`V: Sin(¢11)005(¢21) PinZSinlekOSwzz) V23
`Sin(¢11)91n(¢21)
`Pi‘p329in(¢12)91n(¢22:‘
`
`(20)
`
`x:PLVd
`
`8
`
`(2 8)
`
`FIG. 2 shows a flowchart in accordance with various
`embodiments ofthe present invention. In some embodiments,
`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 commu—
`nications device, embodiments of which are shown in the
`various figures. In other embodiments, method 200 is per-
`formed by a processor or electronic system. Method 200 is
`not limited by the particular type of apparatus or software
`element perfonning the method. The various actions in
`method 200 may be performed in the order presented, or may
`be perfomied in a different order. Further, in some embodi-
`ments, some actions listed in FIG. 2 are omitted from method
`200.
`
`10
`
`15
`
`Since 62 is orthogonal to v1, we have v'lvz:0 or
`cl+c2eil22+c2ei¢32=0
`where
`
`(21)
`
`20
`
`CFCOSWiHCOSIq’iz)
`
`CZ:SiH(¢11)COS(¢2l)SiH(¢12)COS(¢22)
`
`(22)
`
`C3:SIH(¢11)SIH(¢2 1)Sin(¢12)Sin(¢22)
`
`The c] are all greater than or equal to zero since ¢11,¢12,
`(1)2 1,4)22 are all within [0,31/2]. Equation (21) can be explicitly
`solved by using laws of cosine. The solutions of ¢22,¢32 are
`
`c? + 0% 7 0% \
`A
`,
`
`5022 — 51916022) 5310005 W
`of + 0% — (‘5
`,
`‘P32 7 —51gn(4p22) ”0005 W
`
`(23)
`
`30
`
`35
`
`Since V' is also unitary, the norm of the first row is 1.
`Considering v13:cos((|)13) is a positive number, we solve 0,,
`as
`
`40
`
`‘713:\1—COSZ(¢11)—COSZ(¢12)
`
`(24)
`
`Since V' is unitary, the second row ofV is orthogonal to the
`second row. v23 can be solved as
`
`45
`
`z
`"25 =
`
`
`—COS(¢11)Sin(¢11)605(¢21) — COSI¢12)Sinl¢12)COS(¢22Jew”
`[—
`V1 — COSZ(¢11)— COSZWiz)
`
`(25)
`
`Similarly, v33 is
`
`‘733 =
`
`
`meant :51an )sin(¢21) — cosmosmtmxmrmam
`V1 — 6082mm) — 6052(6512)
`
`(26)
`
`Remembering that
`
`1
`
`o
`
`0
`
`a
`
`10506921
`0
`0
`
`0
`«2"31
`
`beamforming may be performed as:
`
`(27)
`
`60
`
`65
`
`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
`embodiments, this corresponds to perfonning singular value
`decomposition (SVD) as described above with reference to
`equations (1) and (7). The beamforming matrix V is also
`described above.
`
`At 230, a phase angle is factored out of each column ofthe
`beamforming matrix. For example, as shown above in equa—
`tions (5), (8), and (15), the phase matrix PR may be factored
`out of the beamforming matrix and discarded. At 240, addi-
`tional phase information is factored from the beamforming
`matrix to yield a phase matrix and an magnitude matrix. In the
`various embodiments of the present
`invention described
`above, the additional phase information is represented by the
`phase matrix PL, and the magnitude matrix is represented by
`V. The magnitude matrix includes the magnitude information
`from the original beamforming matrix V, and may or may not
`include phase information. Accordingly, the entries in V may
`be scalars or complex numbers.
`At 250, the phase matrix and magnitude matrix are repre-
`sented using N 2—N parameters, where N is a number of spa-
`tial channels. For example, in the 2x2 embodiments described
`above, N72, and the phase matrix and magnitude matrix are
`represented by two parameters. One parameter, 6, is used to
`represent the magnitude matrix and one parameter, (p, 1 «p, l , is
`used to represent the phase matrix. Also for example, in the
`3x3 embodiments described above, N:3, and the phase
`matrix and magnitude matrix are represented by six param-
`eters and a sign bit. The phase matrix is represented by two
`parameters, and the magnitude matrix is represented by four
`parameters and a sign bit. The choice of parameters to repre-
`sent the magnitude matrix is large.
`At 260, the parameters are quantized. They can be quan-
`tized individually or jointly. The parameters are quantized in
`the ranges appropriate for the range of the parameters
`selected. For example, in the 2x2 embodiments described
`above, 6 and 4) 114151, are quantized between
`
`and (—:r,,a't], respectively. At 270, the quantized parameters are
`transmitted. 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.
`
`Page 12 of 14
`
`Page 12 of 14
`
`

`

`US 7,492,829 B2
`
`9
`FIG. 3 shows a flowchart in accordance with various
`embodiments ofthe present invention. In some embodiments,
`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 commu-
`nications device, embodiments of which are shown in the
`various figures. In other embodiments, method 300 is per-
`formed by a processor or electronic system. Method 300 is
`not limited by the particular type of apparatus or software
`element perfomiing the method. The various actions in
`method 300 may be perfonned in the order presented, or may
`be performed in a different order. Further, in some embodi-
`ments, some actions listed in FIG. 3 are omitted from method
`300.
`Method 300 is shown beginning at block 310 in which at
`least one angle parameter is received, This may correspond to
`a transmitter receiving one or more angle parameters that
`represent a magnitude matrix. For example, the at least one
`angle parameter may include 6 as described above with ref-
`erence to equation (6), or may include ¢11,¢12,¢21,¢22, as
`described above with reference to equations (15)—(l 9).
`At 320, magnitudes of entries in a beamforming matrix are
`determined from the at
`least one angle parameter. For
`example, as shown in equation (11), the magnitude of the
`entries in a 2x2 bcamforming matrix may be determined from
`the angle parameter 6, and as shown in equations (20) and
`(24)—(26), the magnitude of the entries in a 3x3 beamforming
`matrix may be determined from the angle parameters 4) 1 1 ,q) 12,
`4’21 5 and ¢22~
`At 330, at least one phase parameter is received. This may
`correspond to the transmitter receiving one or more phase
`parameters that represent a phase matrix. For example, the at
`least one phase parameter may include ¢21'¢11 as described
`above with reference to equations (5) and (8), or may include
`¢ll,¢12,¢21,¢22, as described above with reference to equa-
`tions (15)—(l 9). At 340, the at least one phase parameter may
`be applied to at least one row in the beamfonning matrix. For
`example, the phase matrix and magnitude matrix may be
`multiplied as shown in equation (1 l) or equation (28). Fur-
`ther, the beamforming matrix may be used in beamforming as
`shown in equation (28).
`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 interface 450, pro-
`cessor 460, and memory 470. In some embodiments, elec-
`tronic system 400 may be a station capable offactoring beam—
`forming matrices and quantizing parameters as described
`above with reference to the previous figures. In other embodi-
`ments, electronic system may be a station that receives quan-
`tized 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 GWG. 1).
`Also for example, electronic system 400 may be a station
`capable of performing the calculations shown in any of the
`equations (l)-(28), above.
`In some embodiments, electronic system 400 may repre-
`sent a system that includes an access point ormobile 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 antelma
`
`10
`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 cir—
`cuitry 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 amplifica—
`tion (LNA), filtering, frequency conversion or the like. Fur-
`ther,
`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 embodiments, 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 perfonns 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 ofprocessor, 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 execu—
`tion ofthe various method embodiments ofthe presen