US 7,492,829 B2
`(10) Patent No.:
`a2) United States Patent
`Lin et al.
`(45) Date of Patent:
`Feb. 17, 2009
`
`
`US007492829B2
`
`(54) CLOSED LOOP FEEDBACK IN MIMO
`SYSTEMS
`
`(75)
`
`Inventors: Xintian E. Lin, Mountain View, CA
`(US); Qinghua Li, Sunnyvale, CA (US):
`Ada S.Y. Poon San Leeadre CA (US).
`;
`Intel Corporation, Santa Clara, CA
`(US)
`Subject to any disclaimer, the term ofthis
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 814 days.
`.
`
`(73) Assignee:
`
`(*) Notice:
`
`2002/0150109 AL* 10/2002 Agee wo... eee 370/400
`2003/0085832 Al
`5/2003 Yu
`et al.
`2003/0086366 Al
`5/2003 Brandlund
`meee
`7/2003 Walton etal.
`2003/0125040 Al
`11/2003 Onggosanusiet al.
`2003/0210750 Al
`6/2004 Goranssonet al.
`2004/0121810 Al
`11/2004 Hugletal.
`2004/0235433 Al
`2004/0235529 A1* 11/2004 Tarokh et alo... 455/562.1
`5
`.
`woosaeeeas ‘ ooo : Se etal
`/
`oon
`2006/0056531 Al
`3/2006 Li etal.
`3/2006 Lietal.
`2006/0068718 Al
`
`(21) Appl. No.: 10/939,130
`
`(22) Filed:
`
`Sep. 10, 2004
`
`2006/0068738 Al
`2006/0092054 Al
`
`3/2006 Lietal.
`5/2006 Li etal.
`
`
`
`(65)
`
`(51)
`
`(56)
`
`Prior Publication Data
`US 2006/0056335 Al
`Mar. 16, 2006
`Int.Cl
`(2006.01)
`HO04B 7/02
`(52) US. C1. ccc cee cseenecseeresereennres 375/267
`
`sees 375/267,
`(58) Field of Classification Search ...
`375/347, 349, 358, 354, 357, 369, 372, 373,
`375/374, 215, 294, 327, 376; 700/53; 455/101,
`455/132-141, 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 Proakisetal.
`12/1999 Whinnett
`7/2003 Kuwaharaetal.
`1/2005 Liu
`8/2005 Vooketal.
`6/2007 Li ctal.
`4/2008 Lietal.
`
`.....0.... 375/347
`
`4,559,605 A
`5,844,951 A *
`5,999,826 A
`6,597,678 Bl
`6,847,805 B2
`6,927,728 B2
`7,236,748 B2
`7,362,822 B2
`
`FOREIGN PATENT DOCUMENTS
`WO-2006041595 Al
`4/2006
`
`WO
`
`OTHER PUBLICATIONS
`
`Roh et al. Multiple Antenna Channels With Partial Channel State
`Information at the Transmitter, IEEE, vol. 3, No. 2, Mar. 2004.*
`
`(Continued)
`Primary Examiner—Sam K Al
`(74) Attorney, Agent, or Firm—Dana B. Lemoine; Lemoine
`Patent Services, PLLC
`
`(57)
`
`ABSTRACT
`
`Feedback bandwidth maybe reduced in a closed loop MIMO
`system by factoring non essential information out of a beam-
`forming matrix.
`
`16 Claims, 6 Drawing Sheets
`
`
`ESTIMATE CHANNELSTATEINFORMATION |_2¥”
`FROM RECEIVED SIGNALS
`
`220
`
`
`~
`
`
`|_.
`DETERMINEA BEAMFORMINGMATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`FACTORA PHASEANGLE OUTOF EACH
`|_.73
`COLUMNOF THEBEAMFORMING MATRIX
`
`FACTORADDITIONAL PHASE
`
`INFORMATIONFROM THEBEAMFORMING |_240MATRIX TO VIELDA PHASE MATRIXANDA
`MAGNITUDEMATRIX
`
`REPRESENT THEPHASEMATRIXANDA
`MAGNITUDE MATRIX USINGNF-2 |
`PARAMETERS, WHERE N ISA NUMBER OF
`SPATIAL CHANNELS
`
`25
`
`QUANTIZE THEPARAMETERS
`
`TRANSMIT THEPARAMETERS
`
`~
`
`Page 1 of 14
`
`SAMSUNG EXHIBIT 1012
`
`Page 1 of 14
`
`SAMSUNG EXHIBIT 1012
`
`

`

`US7,492,829 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-
`OFDMwith 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.
`“PCT Search Report”, PCT/US2005/031979, (Jan. 23, 2006), 12
`pages.
`
`Choi, Jihoon,et al., “Interpolation Based Transmit Beamforming for
`MIMO-OFDMwith Limited Feedback”, IEEE Communications
`Society, (Jun. 20, 2004),249-253.
`Holtinen, A.
`, et al., “Transmit Diversity Using Fillered Feedback
`Weights In The FDD/WCDMASystem”. IEEE 2000, (Feb. 15,
`2000), 15-17.
`Zoltowski, Michael D., et al., “Simultaneous Sector Processing via
`Root-Music for Large Sensor Arrays”, School ofElectrical Engineer-
`ing, Purdue University., 1990), pp. 372-376.
`Van Der Veen, Alle-Jan “Algebraic Methods For Deterministic Blind
`Beamforming”, Proceedings ofthe IEEE, vol. 86, No. 10, Oct. 1998,
`1987-2008.*
`
`* cited by examiner
`
`Page 2 of 14
`
`Page 2 of 14
`
`

`

`U.S. Patent
`
`Feb. 17, 2009
`
`Sheet1 of 6
`
`US 7,492,829 B2
`
`104
`
`
`
`STATION2
`
`
`
`STATION1
`
`FIG.1
`
`102
`
`Page 3 of 14
`
`Page 3 of 14
`
`

`

`U.S. Patent
`
`Feb. 17, 2009
`
`Sheet2 of 6
`
`US 7,492,829 B2
`
`ESTIMATE CHANNEL STATE INFORMATION|21?
`FROM RECEIVED SIGNALS
`
`DETERMINE A BEAMFORMING MATRIX
`FROM THE CHANNEL STATE INFORMATION
`
`220
`
`FACTORA PHASEANGLE OUT OFEACH|.°%
`COLUMN OF THE BEAMFORMING MATRIX
`
`FACTOR ADDITIONAL PHASE
`INFORMATION FROM THE BEAMFORMING|240
`MATRIX TO YIELD A PHASE MATRIX AND A
`MAGNITUDE MATRIX
`
`200
`
`260
`
`270
`
`REPRESENT THE PHASE MATRIX AND A MAGNITUDE MATRIX USING N2— 2
`
`PARAMETERS, WHERENS A NUMBER OF
`SPATIAL CHANNELS
`
`QUANTIZE THE PARAMETERS
`
`TRANSMIT THE PARAMETERS
`
`~ 200
`
`FIG. 2
`
`Page 4 of 14
`
`Page 4 of 14
`
`

`

`U.S. Patent
`
`Feb. 17, 2009
`
`Sheet3 of 6
`
`US 7,492,829 B2
`
`RECEIVE AT LEAST ONE ANGLE
`PARAMETER
`
`370
`
`DETERMINE MAGNITUDES OF ENTRIES IN
`A BEAMFORMING MATRIX FROM THE AT
`LEAST ONE ANGLE PARAMETER
`
`
`
`
`
`320
`
`
`
`
`
`
`RECEIVE AT LEAST ONE PHASE
`PARAMETER
`
`330
`
`
` 340
`APPLY THE AT LEAST ONE PHASE
`
`PARAMETER TO AT LEAST ONE ROW IN
`THE BEAMFORMING MATRIX
`
`\ 300
`
`FIG. 3
`
`Page 5 of 14
`
`Page 5 of 14
`
`

`

`U.S. Patent
`
`Feb. 17, 2009
`
`Sheet4 of 6
`
`US 7,492,829 B2
`
`450
`oX
`fp Li
`a
`Ly <>
`==}|2
`co
`Li
`Se oh
`©
`i=
`&
`Wu =
`
`FIG.4
`
`Page 6 of 14
`
`Page 6 of 14
`
`

`

`U.S. Patent
`
`Feb. 17, 2009
`
`Sheet 5 of 6
`
`US 7,492,829 B2
`
`FACTORA 2X2 BEAMFORMING MATRIX
`INTO A PLURALITY OF MATRICES, A FIRST
`OF THE PLURALITY OF MATRICES HAVING
`ENTRIES THAT INCLUDE MAGNITUDE
`INFORMATION FROM THE BEAMFORMING|_910
`MATRIX, WHEREIN THE PLURALITY OF
`MATRICES FURTHER INCLUDES TWO
`MATRICES WITH PHASE INFORMATION,
`AND WHEREIN ONE OF THE TWO
`MATRICES IS REPRESENTED BY A
`SECOND PARAMETER, AND THE OTHER OF
`
`THE TWO MATRICESIS DISCARDED REPRESENTTHE FIRST OF THE
`
`PLURALITY OF MATRICES WITH A FIRST
`PARAMETER
`
`TRANSMIT THE FIRST PARAMETER
`
`920
`
`530
`
`NN 500
`
`FIG. 5
`
`Page 7 of 14
`
`Page 7 of 14
`
`

`

`U.S. Patent
`
`Feb. 17, 2009
`
`Sheet6 of 6
`
`US 7,492,829 B2
`
`FACTOR A PHASE ANGLE FROM EACH
`COLUMN OF A 3X3 BEAMFORMING MATRIX
`
`USING SIX PARAMETERS TRANSMIT THE SIX PARAMETERS
`
`REPRESENT THE BEAMFORMING MATRIX
`
`XN 600
`
`FIG. 6
`
`Page 8 of 14
`
`Page 8 of 14
`
`

`

`US 7,492,829 B2
`
`1
`CLOSED LOOP FEEDBACK IN MIMO
`SYSTEMS
`
`FIELD
`
`10
`
`20
`
`40
`
`45
`
`The present invention relates generally to wireless net-
`works, and morespecifically to wireless networksthatutilize
`multiple spatial channels.
`
`BACKGROUND
`
`Closed loop multiple-input-multiple-output (MIMO)sys-
`tems typically transmit channel state information from a
`receiver to a transmitter. ‘Lhe transmitter may then utilize the
`information to do beam forming. Transmitting the channel
`stale information consumes bandwidth that might otherwise
`be available for datatraffic.
`
`
`
`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 drawingsthat show, by way ofillustration,
`specific embodiments in which the invention may be prac-
`ticed. These embodimentsare described in sufficient detail to
`
`enablethose skilled in the art to practice the invention.It is to
`be understoodthat the various embodiments ofthe 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 scopeofthe invention. In addition, it is to
`be understood that the location or arrangementof individual
`elements within each disclosed embodiment may be modified
`without departing, fromthe spirit and scope of the invention.
`The following detailed description is, therefore, not to be
`taken in a limiting sense, and the scopeofthe present inven-
`tion is defined only by the appended claims, appropriately
`interpreted, along with the full range of equivalents to which
`the claimsare entitled. In the drawings, like numerals refer to
`the same or similar functionality throughout the several
`views.
`
`FIG. 1 showsa diagram of two wireless stations: station:
`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 mobilestation suchas a laptop
`computer, personal digital assistant (PDA), or the like. I'ur-
`ther, in some embodiments, stations 102 and 104are 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 Ldition, although this
`is nota 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
`
`2
`partially in compliance with any other standard, such as any
`future IKEE 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 remainderofthis
`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 manypossible signal paths. For example, whensta-
`tions 102 and 104 are in an environment with many “reflec-
`tors”(c.g. walls, doors, or other obstructions), manysignals
`may arrive fromdifferent paths. This condition is known as
`“multipath.” In some embodiments, stations 102 and 104
`utilize multiple antennas to take advantage ofthe multipath
`and to increase the communications bandwidth. or example,
`in some embodiments, stations 102 and 104 may communi-
`cate using Multiple-Input-Multiple-Output (MIMO) tech-
`niques. In general, MIMO systemsoffer 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 impairmentslike
`inter-symbolinterference ([S]). OFDM is effective at com-
`bating frequency selective fading in part because OFDM
`breaks each spatial channel into small subchannels suchthat
`each subchannel exhibits a more flat 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.
`MIMOsystems mayoperate either “open loop”or “closed
`loop.” In open loop MIMOsystems, a station estimates the
`state of the channel without receiving channel state informa-
`tion directly from anotherstation. In general, open loop sys-
`tems employ exponential decoding complexity to estimate
`the channel. In closed loop systems, communications band-
`widthis 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 MIMOsystems, more bandwidthis
`available for data communications.
`The current channel state information maybe represented
`by an NxN unitary beamforming matrix V determined using
`a singular value decomposition (SVD) algorithm, and the
`transmitter may process an outgoing signal using, the beam-
`forming matrix Vto transmit into multiple spatial channels. In
`a straightforward implementation, the receiver sends cach
`element of the unitary matrix V back to transmitter. This
`schemeinvolves sending information related to the 2N? real
`numbers for any NxN complex unitary matrix, where N is the
`numberofspatial channels in MIMOsystem.
`In some embodiments ofthe present invention, the beam-
`forming matrix V is represented by N?—N real numbers
`instead of 2N? real numbers. By sending N?-N real numbers
`instead of 2N? real numbers to represent the beamforming
`matrix, the feedback bandwidth may be reduced. Non-essen-
`tial information may be factored out of the beamforming
`matrix and discarded prior to quantizing parameters that are
`used to represent the beamforming matrix. For example, non-
`
`Page 9 of 14
`
`Page 9 of 14
`
`

`

`US 7,492,829 B2
`
`3
`essential phase information may be factored from each col-
`umn in the beamforming matrix, and then N?-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
`MIMOsystems. In the 2x2 closed loop MIMO example, two
`anglesin [0, 2/2] and(x, -71] 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 fromeight real
`numbersto two real numberspersubcarrier. In the 3x3 closed
`loop MIMO example, one sign bit plus four angles between
`[0, 2/2] and two angles between [-2, a] are used as feedback
`parameters. Compared to thestraightforward example above,
`the various embodiments ofthe present invention represented
`by the 3x3 example below reduce the amount offeedback
`from 18 real numbersto six real numbersper subcarrier.
`A transmit beamforming matrix may be found using SVD
`as follows:
`
`H=-UDV'
`
`x-Vd
`
`(1)
`
`(2)
`
`4
`consisting of scalar quantities that represent the magnitudes
`ofthe entries of V. Since b, ,?+b,.7=1, ¥ can be written as
`
`cos?
`siné
`\—sind cosd } where 0 €
`
`(
`
`~
`
`[0, =).
`
`(6)
`
`In various embodiments of the present invention, only two
`angles 1.e., 0 and 9, ;-,, are fed back to the transmitter. (530,
`FIG. 5) Thefirst angle, 6, unambiguously represents V, and
`the second angle, $,,-~2,, unambiguously represents P,.
`(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 8 maybe fed back as a param-
`eter to represent ¥. In still further embodiments, another
`parameter may be selected that may unambiguously describe
`¥.
`
`20
`
`The phase information in P, may be discarded. Equation
`(1) can be rewritten as
`
`H=UDV
`
`(7)
`
`whered is the N-vector of codebits 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=UDV'; U and
`V are unitary; D is a diagonal matrix with H’s eigenvalues; V
`is NxN,andNis the numberofspatial 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.
`
`= UD(PLVPr)
`= UDP,(P,V)
`
`2x2 Beamforming Matrices
`Any complex 2x2 matrix may be written as
`
`40
`
`where wehave usedthe fact that D and P', are diagonal and
`therefore commute.It should be noted that H=UDVis also a
`singular value decomposition of H. For the SVD algorithm,
`the change from U to U only changes the multiplication
`matrix on the receiver side. When H is a mxn matrix with
`mzn, we can still write H=URV'and the effect of beam
`forming with V amountsto a rotation in the I/Q plane, which
`may be taken care of by the training process. Therefore,
`feeding back V to the transmitter is sufficient for the SVD
`(3)
`bye byel¥12
`algorithm. SinceVis fully determined by 6 and $, ,-@,,, only
`two angles are required to feedback and they are between
`
`~ |bye?21 bye'#22 |
`
`45
`IfVis unitary 1.e., VV'=I, then
`
`bye?12
`bye
`=be*21 by ehP12+821-F11!
`
`)
`
`where b,,°+b,,°=1. We can further limit b,, €[0,1]. b,,
`€[0,1],
`0;, €[-2,7) without loss of generality. There are 4
`degrees of freedom in V. After factoring the commonphases
`for each row and column,the unitary matrix V can be written
`as
`
`and (-0, at].
`Asstated above, the unitary matrix V may be factored into
`the product of three matrices:
`
`1
`
`0
`
`Vv -(, gid Ou)
`
`1
`
`0
`
`= 0 e¢a41)
`
`( bu-by
`
`( cos?—sind
`
`bp
`
`fe’
`
`0
`
`elfi2 |
`bu | 0
`ol 0 vis |
`
`sing
`
`fel 0)
`
`(8)
`
`=
`1
`Ve Q
`
`9
`el~ri-vin}
`
`bu
`bn
`fet
`(<r. | 0
`
`0
`eff
`
`=P,V¥
`-
`= PLVPe
`
`60
`
`(5)
`
`where 6 and @3,-#,, are between
`
`where P, and P, are pure phase matrices and diagonal.
`(510, FIG. 5) P, 1s generated by factoring phase values from
`each column of V, and P, is found by factoring phase values
`from each rowofV. ¥ is a magnitude matrix that has entries
`
`3]
`
`Page 10 of 14
`
`Page 10 of 14
`
`

`

`5
`and (—<t, t]. The parameters 6 and ¢,,-, , may be obtained at
`the receiver as follows:
`
`-continued
`
`US 7,492,829 B2
`
`6=arccos(abs(v; ;)),€[0,7/2]
`
`
`+
`Im(y;;)
`arctan Roop taf2,
`
`Im(=| 3a/2,
`arctan| Rew, + 32/2,
`
`Im(vy) =O
`Imlvy) <0
`Imi
`
`by =
`
`(9)
`
`(10)
`
`5
`
`eu
`
`0
`
`0
`
`0
`)
`
`0
`efi3
`
`eMi2
`0
`
`Pp
`
`and the receiver mayquantize 0 and ,,-¢,, and feed them
`back to the transmitter as parameters that represent V. The
`transmitter may reconstruct V by determining the amplitudes
`using 6, and applying a phase rotationto the bottom row using,
`2 1-Pi,-
`
`_
`
`sind
`cos?
`| sing eGai-G cose eil?ai PL)
`
`The transmitter may then use V for beamforming:
`xeVd
`
`3x3 Beamforming Matrices
`Any complex, unit 3-vector may be written as
`
`v=]
`
`_|
`
`v1
`v2
`
`"3
`
`)/=e
`
`|= oift|
`
`cos($,)
`1)
`2,
`
`sin(dy)cos(ga)e#2
`
`/
`sin(h1)sin(paJe"3
`
`ah)
`
`(12)
`
`(13)
`
`where |[MP=ly, P+ val?4liva|7=L; 1.62 €|0.90/2] and
`81,82,03€[-2.7).
`Further, any unitary 3 by 3 matrix maybe written as
`
`1° Where P, and P, are pure phase matrices and diagonal. P, is
`generated by factoring phase values from each column of V,
`(610, FIG. 6) and P, is found by factoring phase values from
`each row ofV, and where $,,€| 0,7/2] and cos (,.), Cos (jz),
`sin (d,,)=0. ¥ is a magnitude matrix that includesall 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 P; and P, are factored out of the
`original beamforming matrix. As
`shown in the above
`example, one or more entries in a magnitude matrix may
`include phase information.It should be noted that ¥=|¥,¥,¥, |
`is still unitary since the phasefactorization docsn’t change the
`unilary property.
`two
`In various embodiments of the present invention,
`95 parameters are chosen to represent P,, four parameters are
`chosen to represent ¥, and P, is discarded. In some embodi-
`ments, the angles 6,,, 63, are selected as parameters to rep-
`resent P,. Matrix V can be determined byfour parameters and
`a sign bit, and there are many combinations ofthe four param-
`eters that are subsets of all the angles in ¥. Different combi-
`nations result in different complexities in the reconstruction
`:
`.
`.
`of extracting all the angles of ¥ is relatively low compared to
`that of the construction of ¥ based on four parameters.
`Instead of directly sending angles back, some embodiments
`may send functions of the selected four angles back. For
`example, commontrigonometric functions suchassin( ), cos(
`), and tan() may be selected. The various embodiments ofthe
`present invention contemplate all possible sets offour param-
`
`of¥atthetransmitter.Itshouldbenotedthatthecomplexity
`
`V = [vy v2 v3] =]
`
`ell cos(oi)
`2811 221 sin(i1 cos(do1)
`1131 sin(hy, )sin(do,)
`
`e12.cos($12)
`e812 e#22 sin(d12)cos(doz)
`eM12 e832 sin(}12)sin(Pr2)
`
`213 cos($i3)
`2913 e!23 sin(dy3)cos(23)
`e713 e733 sin(13)sin(dys)
`
`a4)
`
`where v'v=1 and v'v,=0 for j,k=1,2,3. The phases on the
`first row andthefirst column can befactored as the product of
`the following three matrices:
`
`5°
`
`eters to represent ¥. One set of four parameters $1,912,625
`$2, and the sign of 9,5 provide a solution that is now elabo-
`rated. The extraction of the angles 9,,,0,5-2;,2. may be
`performedas:
`$1,~arecos(Iv, 1)
`
`(16)
`
`q7)
`
`(18)
`(19)
`
`It should be noted that9, ;,, 2,02;,22 are all within [0,7/2]
`instead of [0,7] and the sign of »,, takes only one bit. In
`various embodiments, the feedback includes one angle in
`[0,70] and three angles in [0,2/2].
`
`55
`
`(15)
`
`y2arecos(I¥191)
`
`o2= arctan)
`Ivar
`
`on = arctan{ —lv22|Heel)
`
`60
`
`65
`
`1
`
`0
`
`va]0 ea
`0
`0
`
`Pr
`
`0
`
`0
`esr
`
`cos(¢i2)
`e822 sin(diz)cos(d22)
`e'?32sin(dy2 )sin(Gor)
`
`cos(pj3)
`e*#23 sin(d13)cos(b23)
`e833 sin(g,3)sin(Prs)
`
`y
`
`cos(¢i1)
`sin(dy Jeos(Pr1)
`sin($11)sin(dz1)
`
`Page 11 of 14
`
`Page 11 of 14
`
`

`

`US 7,492,829 B2
`
`7
`In embodiments using the above parametersto represent P,
`and ¥, the receiver quantizes 9,,,03), 91501252)... and
`feeds them backto the transmitter along with sign(o,,), which
`can be found as sign(@,,.)=sign(angle(¥,,)). (620, 630, FIG.
`6)
`
`The receiver may receive the parameters, reconstruct V,
`and perform beamforming. The outline of the reconstruction
`of ¥ is now shown as: computation of $5, 32 to reconstruct
`¥.,, the second column of ¥; and computation of ¥,, the third
`column of¥ using the unitary property of ¥. We rewrite ¥ as
`
`V =|
`
`cos(d12)
`cos(di1)
`sin(Piseos($a1) e!22sin(py2)cos(b22)
`sin(o1)sin(Ga,)
`e*?32 sin($42)sin(bra)
`
`F13
`ny3
`#
`V3
`
`(20)
`
`x=P,¥d
`
`8
`
`(28)
`
`FIG. 2 shows a flowchart in accordance with various
`embodimentsofthe present invention. In some embodiments,
`method 200 may be used in, or for, a wireless sysiem that
`utilizes MIMOtechnology. 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 processoror electronic system. Method 200 is
`not limited by the particular type of apparatus or software
`element performing the method. The various actions in
`method 200 may be performedin the order presented, or may
`be performed in a different order. Further, in some embodi-
`ments, someactionslisted in FIG. 2 are omitted from method
`200.
`
`10
`
`15
`
`Since ¥, is orthogonal to ¥,, we have v',v,=0 or
`ey teze!2+e5¢432=0
`where
`
`(21)
`
`20
`
`€1=Cos(P;1)cos( 12)
`
`C2=SiN(M, 1)COS(P> 1SIN3)COS(22)
`
`(22)
`
`C3=SiN(, 1)SIN(P> ;)SiN(M;2)siN(2)
`
`The c, are all greater than or equal to zero since $11,912;
`21,2. are all within [0,2/2]. Equation (21) can be explicitly
`solved by using laws of cosine. Thesolutions of $55,035 are
`
`cf +3 — ch)
`|
`.
`
`P22 = sign(y22)/arccos tae
`.
`c+
`32 = —sign(y22}Jarccos ies
`
`(23)
`
`30
`
`35
`
`Since ¥' is also unitary, the norm of the first row is 1.
`Considering, ¥,;=cos(,3) is a posilive number, wesolve ¥,,
`as
`
`40
`
`91>J1-cos"(; 1)-Cos"(12)
`
`(24)
`
`Since ¥'is unitary, the second rowof¥ is orthogonalto the
`second row. ¥,; can be solved as
`
`45
`
`
`¥23 =
`~
`_ ~208(P11 )sin( P11cos(Pa1 ) — cos(G12)sin(Py 2)cos($2p Je"”22
`———
`V1 - cos?($11) - cos?(b12)
`
`(25)
`
`Sumnilarly, ¥,, is
`
`¥33 =
`
`
`—cos(h11 )sin(G11 Jsin(Gay ) — cos(g1)sim(Ay2))sin( oye*?32
`V 1 - cos*(bi1) — cos*(b12)
`
`(26)
`
`Remembering that
`
`1
`
`Oo
`
`0
`
`P,=|0 e210
`0
`CG. él
`
`>
`
`beamforming may be performedas:
`
`(27)
`
`60
`
`65
`
`Method 200 is shown beginning at block 210 in which
`channelstate informationis 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 performing singular value
`decomposition (SVD) as described above with reference to
`equations (1) and (7). Lhe beamforming matrix V is also
`described above.
`
`At 230, a phase angle 1s factored out of each column ofthe
`beamforming matrix. For example, as shown above in equa-
`tions (5), (8), and (15), the phase matrix P,; may be factored
`out of the beamforming matrix and discarded. At 240, addi-
`tional phase information is factored from the beamforming
`matrix to yicld a phase matrix and an magnitude matrix. Inthe
`various embodiments of the present
`invention described
`above, the additional phase informationis represented by the
`phase matrix P,, and the magnitude matrix is represented by
`¥. 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 ¥ may
`be scalars or complex numbers.
`At 250, the phase matrix and magnitude matrix are repre-
`sented using N?—N parameters, where N is a numberof spa-
`tial channels. For example, inthe 2x2 embodimentsdescribed
`above, N—2, and the phase matrix and magnitude matrix are
`represented by two parameters. One parameter,0, is used to
`represent the magnitude matrix and one parameter, , ,-(5,, 18
`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 bysix param-
`eters and a sign bit. The phase matrix is represented by two
`parameters, and the magnitude matrix is represented by four
`parameters anda 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 $, ,-2,, are quantized between
`
`5]
`
`and (-«,70], respectively. At 270, the quantized parametersare
`transmitted. The quantized parameters may be transmitted
`using any type of protocol or any type of communications
`link, including a wirelesslink 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
`
`10
`
`15
`
`20
`
`30
`
`35
`
`10
`9
`FIG. 3 shows a flowchart in accordance with various
`array or any type of antennastructure that supports MIMO
`processing. System 400 may operate in partial compliance
`embodimentsofthe present invention. In some embodiments,
`with, or in complete compliance with, a wireless network
`method 300 may be used in, or for, a wireless system that
`standard such as an 802.11 standard.
`utilizes MIMOtechnology. In some embodiments, method
`Physical layer (PHY) 430 is coupled to antennas 410 to
`300, or portions thereof, is performed by a wireless commu-
`nications device, embodiments of which are shown in the
`interact with a wireless network. PHY 430 mayinclude cir-
`cuitry to support the transmission and reception of radio
`various figures. In other embodiments, method 300 is per-
`frequency (RF) signals. For example, in some embodiments,
`formed by a processoror electronic system. Method 300 is
`PHY 430 includes an RF receiver to receive signals and
`not limited by the particular type of apparatus or software
`perform “front end” processing such as low noise amplifica-
`element performing the method. The various actions in
`tion (LNA),filtering, frequency conversionor the like. Fur-
`method 300 may be performedin the order presented, or may
`ther,
`in some embodiments, PHY 430 includes transform
`be performed in a different order. Further, in some embodi-
`ments, someactionslisted in FIG. 3 are omitted from method
`mechanisms and beamforming circuitry to support MIMO
`300.
`signal processing. Also for example, in some embodiments,
`PHY 430 includes circuits to support frequency up-conver-
`Method 300 is shown beginning at block 310 in whichat
`sion, and an RF transmitter.
`least one angle parameter is received. This may correspond to
`Mediaaccess control (MAC)layer 440 maybe any suitable
`a transmitter receiving one or more angle parameters that
`media access control layer implementation. I'or example,
`represent a magnitude matrix. lor example, the at least one
`MAC440 may be implemented in software, or hardware or
`angle parameter may include 6 as described above with ref-
`any combination thereof. In some embodiments, a portion of
`erence to equation (6), or may include ,,,0,2,2),$22, as
`MAC 440 may be implemented in hardware, and a portion
`described above with reference to equations (15)-(19).
`may be implementedin software that is executed by processor
`At 320, magnitudesofentries ina beamforming matrix are
`460. Further, MAC 440 mayinclude a processor separate
`determined from the at
`least one angle parameter. For
`from processor 460.
`example, as shown in equation (11), the magnitude of the
`In operation, processor 460 reads instructions and data
`entrics ina 2x2 beamforming matrix may be determined from
`from memory 470 and performsactions in responsethereto.
`the angle parameter 8, and as shown in equations (20) and
`For example, processor 460 may access instructions from
`(24)-(26), the magnitude of the entries in a 3x3 beamforming
`memory 470 and perform method embodiments of the
`matrix may be determined from the angle parameters >, |, >;
`present invention, such as method 200 (FIG. 2) or method 300
`$21, and #23.
`(FIG.3) or methods described with reference to otherfigures.
`At 330, at least one phase parameteris received. This may
`Processor 460 represents any type ofprocessor, including but
`correspond to the transmitter receiving one or more phase
`not limited to, a microprocessor, a digital signal processor, a
`parameters that represent a phase matrix. For example, the at
`microcontroller, or the like.
`least one phase parameter may include ,,-¢,, as described
`Memory 470 represents an article that includes a machine
`above with reference to equations(5) and (8), or may include
`readable medium. For example, memory 470 represents a
`©1121 2-P21:P22, aS described above with reference to equa-
`random access memory (RAM), dynamic random access
`tions (15)-(19). At 340, the at least one phase parameter may
`memory (DRAM), static random access memory (SRAM),
`be applied to at least one row in the beamforming matrix. For
`read only memory (ROM), flash memory,or any other type of
`example, the phase matrix and magnitude matrix may be
`article that includes a medium readable by processor 460.
`multiplied as shown in equation (11) or equation (28). Fur-
`Memory 470 maystore instructions for performing the execu-
`ther, the beamforming matrix may be used in beamformingas
`tion ofthe various method embodimentsofthe present inven-
`shownin equation(28).
`tion. Memory 470 may also store beamforming matrices or
`FIG. 4 shows a system diagramin accordance with various
`beamforming vectors.
`embodimentsofthe present invention. Electronic system 400
`Although the various elements of system 400 are shown
`includes antennas 410, physical layer (PHY) 430, media
`separale in FIG. 4, embodiments exist that combine the cir-
`access control (MAC)layer 440, Ethernet interface 450, pro-
`cuitry of processor 460, memory 470, Ethernet interface 450,
`cessor 460, and memory 470. In some embodiments, elec-
`and MAC 440 in a single integrated circuit. For example,
`tronic system 400 may bea station capableoffactoring beam-
`memory 470 maybe an internal memory within processor
`forming matrices and quantizing parameters as described
`460 or may be a microprogram control store within processor
`above with referenceto the previousfigures. In other embodi-
`460. In some embodiments, the various elements of system
`ments, electronic system maybe a station that receives quan-
`400 may be separately packaged and mounted on a common
`tized parameters, and performs beamforming in a MIMO
`circuit board. In other embodiments, the various elements are
`system. For example, electronic system 400 maybeutilized
`separate integrated circuit dice packaged together, such as in
`in a wireless networkas station 102 or station 104 (FIG.1).
`a multi-chip module, and in still further embodiments, vari-
`Also for example, electronic system 400 may bea station
`ous clements are on the same integrated circuit dic.
`capable of performing the calculations shown in any of the
`Ethernet
`interface 450 may provide communications
`equations (1)-(28), above.
`between electronic system 400 and other systems. For
`In some embodiments, electronic system 400 may repre-
`example, in some embodiments, electronic system 400 may
`sent a system that includes an access point or mobilestation as
`be an access point that utilizes Ethernet interface 450 to
`well as other circuits. For example, in some embodiments,
`communicate with a w