1111111111111111 IIIIII IIIII 11111 1111111111 11111 111111111111111 11111 11111 1111111111 11111111
`US 20060068718Al
`
`c19) United States
`c12) Patent Application Publication
`Li et al.
`
`c10) Pub. No.: US 2006/0068718 Al
`Mar. 30, 2006
`(43) Pub. Date:
`
`(54) COMPACT FEEDBACK FOR CLOSED LOOP
`MIMO
`
`(22) Filed:
`
`Sep. 28,2004
`
`(76)
`
`Inventors: Qinghua Li, Sunnyvale, CA (US);
`Xintian E. Lin, Palo Alto, CA (US)
`
`Correspondence Address:
`The Law Offices of John C. Scott, LLC
`c/o PortfolioIP
`P.O. Box 52050
`Minneapolis, MN 55402 (US)
`
`(21) Appl. No.:
`
`10/952,505
`
`Publication Classification
`
`(51)
`
`Int. Cl.
`7100
`H04B
`(2006.01)
`H04B 1102
`(2006.01)
`H04M 1100
`(2006.01)
`(52) U.S. Cl. ......................... 455/69; 455/562.1; 455/101
`
`ABSTRACT
`(57)
`Compact feedback schemes are presented for use in closed
`loop multiple input, multiple output systems.
`
`10
`\
`
`12
`
`TRANSMITTER
`
`16
`
`18
`
`20
`
`22
`
`14
`
`RECEIVER
`
`24
`
`26
`
`28
`
`30
`
`ZTE, Exhibit 1005-0001
`
`

`

`Patent Application Publication Mar. 30, 2006 Sheet 1 of 4
`
`US 2006/0068718 Al
`
`00
`N
`
`0
`M
`
`00 -
`
`0
`N
`
`_,;,,
`
`0
`'1"""-1
`
`N
`.......
`
`0::
`u.J
`E-
`
`en
`
`f--, -~
`~ ~
`
`ZTE, Exhibit 1005-0002
`
`

`

`Patent Application Publication Mar. 30, 2006 Sheet 2 of 4
`
`US 2006/0068718 Al
`
`40
`\
`
`DATA
`SYMBOL
`STREAMS
`
`42
`
`MATRIX
`MULTIPLIER
`
`44
`
`46
`
`48
`
`50
`
`68
`
`MATRIX
`RECONSTRUCTION
`
`FEEDBACK
`PARAMETERS
`
`66
`
`CONTROLLER
`
`V,
`
`Fig. 2
`
`. Fig. 3
`
`60
`,I
`
`TO
`TRANSMIT
`ANTENNAS
`
`V,
`
`62
`
`TRANSMITTER
`
`64
`
`FROM
`RECEIVE
`ANTENNAS
`
`RECEIVER
`
`ZTE, Exhibit 1005-0003
`
`

`

`Patent Application Publication Mar. 30, 2006 Sheet 3 of 4
`
`US 2006/0068718 Al
`
`FROM
`RECEIVE
`
`ANTENNAS --
`
`72
`
`RECEIVER
`
`TO
`TRANSMIT
`
`ANTENNAS4(cid:141) - - -1
`
`70
`
`I
`
`FEEDBACK
`PARAMETERS
`
`76
`
`CONTROLLER
`
`78
`
`CHANNEL MA TRIX
`DETERMINATION
`
`SVD
`
`80
`
`82
`
`PARAMETER
`EXTRACTION
`
`Fig. 4
`
`ZTE, Exhibit 1005-0004
`
`

`

`Patent Application Publication Mar. 30, 2006 Sheet 4 of 4
`
`US 2006/0068718 Al
`
`Imaginary
`!
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`
`-
`
`-
`
`"90
`
`____ pJ2
`..
`\
`
`____ ..a,_ ________ _
`
`':a,
`..... -
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`-
`
`- ..,. Real
`
`Fig. 5
`
`ZTE, Exhibit 1005-0005
`
`

`

`US 2006/0068718 Al
`
`Mar. 30, 2006
`
`1
`
`COMPACT FEEDBACK FOR CLOSED LOOP
`MIMO
`
`TECHNICAL FIELD
`
`[0001] The invention relates generally to wireless com(cid:173)
`munications and, more particularly, to multiple input mul(cid:173)
`tiple output (MIMO) based systems.
`
`BACKGROUND OF THE INVENTION
`
`[0002] Multiple input multiple output (MIMO) is a radio
`communication technique in which both a transmitter and a
`receiver use multiple antennas to wirelessly communicate
`with one another. By using multiple antennas at the trans(cid:173)
`mitter and receiver, the spatial dimension may be taken
`advantage of in a manner that improves overall performance
`of the wireless link. MIMO may be performed as either an
`open loop or a closed loop technique. In open loop MIMO,
`a transmitter has no specific knowledge of the condition of
`the channel before signals are transmitted to a receiver. In
`closed loop MIMO, on the other hand, channel-related
`information is fed back from the receiver to the transmitter
`to allow the transmitter to precondition transmit signals
`before they are transmitted to better match the present
`channel state. The amount of feedback information that is
`delivered from a receiver to a transmitter in a system using
`closed loop MIMO can be very large. There is a general need
`for strategies to reduce the overall amount of feedback used
`in a closed loop MIMO system.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`[0003] FIG. 1 is a block diagram illustrating an example
`wireless communication link in a MIMO-based wireless
`system in accordance with an embodiment of the present
`invention;
`
`[0004] FIG. 2 is a block diagram illustrating the multipli(cid:173)
`cation of data by a beam forming matrix (precoder) in a
`wireless transmitter in accordance with an embodiment of
`the present invention;
`
`[0005] FIG. 3 is a block diagram illustrating an example
`communication device that may be used to transmit data to
`a remote receiver in accordance with an embodiment of the
`present invention;
`
`[0006] FIG. 4 is a block diagram illustrating an example
`communication device that may be used to receive data from
`a remote transmitter in accordance with an embodiment of
`the present invention; and
`
`[0007] FIG. 5 is a graph illustrating a geometric relation(cid:173)
`ship that may be used during beam steering matrix recon(cid:173)
`struction in a transmitter in accordance with an embodiment
`of the present invention.
`
`DETAILED DESCRIPTION
`
`[0008]
`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 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(cid:173)
`ments of the invention, although different, are not necessar(cid:173)
`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.
`
`[0009] FIG. 1 is a block diagram illustrating an example
`wireless communication link 10 in a MIMO-based wireless
`system in accordance with an embodiment of the present
`invention. As illustrated, a wireless transmitter 12 is com(cid:173)
`municating with a wireless receiver 14 via a wireless chan(cid:173)
`nel. The transmitter 12 has four transmit antennas 16, 18, 20,
`22 and the receiver 14 has four receive antennas 24, 26, 28,
`30. The wireless channel is a multiple input, multiple output
`(MIMO) channel. Although illustrated with four transmit
`antennas 16, 18, 20, 22 and four receive antennas 24, 26, 28,
`30 in FIG. 1, it should be appreciated that any number (i.e.,
`greater than 1) of transmit antennas and any number (i.e.,
`greater than 1) of receive antennas may be used to form a
`MIMO channel. The wireless link 10 of FIG. 1 may utilize
`"closed loop" MIMO techniques. That is, the receiver 14
`may transmit channel-related feedback information to the
`transmitter 12 for use by the transmitter 12 in developing
`transmit signals. The same antennas may (or may not) be
`used for the reverse direction link that are used for the
`forward direction link. By utilizing knowledge of the chan(cid:173)
`nel, the transmitter 12 can tailor the transmit signals to the
`channel in a manner that simplifies receiver processing in
`and/or improves the performance of the receiver 14. The
`receiver 14 can generate the channel-related feedback infor(cid:173)
`mation by, for example, appropriately processing training
`information received from the transmitter 12.
`
`[0010] Various methods of developing channel-related
`feedback information are known in the art. One method of
`developing channel-related feedback information makes use
`of a mathematical technique known as singular value
`decomposition (SYD). When SYD is utilized in a MIMO(cid:173)
`based system, the overall technique may be referred to as
`SVD-MIMO. In at least one embodiment, features of the
`present invention are implemented within a multicarrier
`communication system (although applications in single car(cid:173)
`rier systems also exist). One type of multicarrier technique
`that is gaining popularity is orthogonal frequency division
`multiplexing (OFDM). In a multicarrier system, a series of
`relatively narrow "sub-carriers" may be used to transmit
`data across a wireless channel. To facilitate understanding
`and simplify notation, the discussion that follows may be
`with respect to a single subcarrier in a multicarrier system
`(e.g., an OFDM system). It should be appreciated, however,
`that the below described functions may be performed for
`each of the subcarriers within a multicarrier system. Inter(cid:173)
`polation between subcarriers may also be used to reduce the
`amount of calculation and feedback.
`
`[0011]
`In a MIMO-based system, a wireless channel may
`be characterized using an nRXxn= channel matrix H, where
`
`ZTE, Exhibit 1005-0006
`
`

`

`US 2006/0068718 Al
`
`Mar. 30, 2006
`
`2
`
`nRX is the number of receive antennas and n= is the number
`of transmit antennas. Using SYD, the channel matrix H may
`be decomposed as follows:
`
`H-UDv"
`where U and V are unitary matrices (i.e., matrices with
`orthonormal colunms and unit amplitude), D is a diagonal
`matrix, and yH is the Hermitian of matrix V. A unitary matrix
`U has the following property:
`
`u"u-1
`where I is the identity matrix. In the channel matrix decom(cid:173)
`position set out above, the matrix V may be referred to as the
`beam forming matrix (precoder). This beam forming matrix
`V may be generated in the receiver 14 by first determining
`the channel matrix H (using, for example, received training
`information) and then decomposing the matrix H using SYD
`techniques (or other similar techniques). The beam forming
`matrix V may then be transmitted back to the transmitter 12
`to be used in the generation of a subsequent transmit signal.
`A separate matrix V may be required for each subcarrier in
`a multicarrier system.
`
`[0012] After receiving the beam forming matrix V from
`the receiver 14, the transmitter 12 may use the matrix to
`generate a subsequent transmit signal. For example, the
`transmitter 12 may multiply a vector X of complex symbols
`to be transmitted by the transmitter 12 by matrix V before
`transmission. FIG. 2 is a block diagram illustrating such a
`scenario. As shown, a matrix multiplier 42 receives a
`number of data symbol streams and a beam forming matrix
`V; at inputs thereof. The matrix multiplier 42 multiplies a
`vector of data symbols X by the beam forming matrix V; as
`follows:
`z-v,x
`where Z represents the symbols that will be transmitted. The
`outputs of the matrix multiplier 42 are directed to multiple
`transmit antennas. In the illustrated embodiment, four trans(cid:173)
`mit antennas 44, 46, 48, 50 are used. Although not shown,
`additional processing functionality ( e.g., an inverse discrete
`Fourier transform unit, a power amplifier, etc.) may be
`present between the matrix multiplier 42 and each corre(cid:173)
`sponding transmit antenna 44, 46, 48, 50. After transmis(cid:173)
`sion, the transmitted symbols Z are acted upon by the
`channel Hand are also subject to noise in the channel. Thus,
`the signal Y received by the receiver at the other side of the
`MIMO channel (e.g., receiver 14 in FIG. 1) may be repre(cid:173)
`sented as:
`
`Y-HVX+N
`where N is the additive noise. From the channel expression
`given above, it is found that:
`
`HV-UDv"V-UDI-UD
`Therefore, Y may be expressed as:
`
`Y-UDX+N
`
`In the receiver, the received signal Y can be matrix multi(cid:173)
`plied by UH to achieve the following result:
`
`u"Y-u"UDX+u"N-IDX+u"N-DX+u"N
`
`Thus, if the diagonal matrix Dis known, the symbols X may
`be recovered. The above-described technique essentially
`diagonalizes the channel and allows the original symbols X
`to be recovered using relatively simple linear algebra tech(cid:173)
`niques in the receiver. The elements of the diagonal matrix
`
`D are known as the singular values ( or eigenvalues) of the
`channel matrix H. It should be appreciated that there are
`many other receiver techniques that may be used. For
`example, the receiver can use a minimum mean square error
`(MMSE) filter instead of multiplying by UH, etc.
`
`[0013]
`In a straightforward SYD implementation, a rela(cid:173)
`tively large amount of feedback information is delivered
`from the receiver to the transmitter. That is, each complex
`element of the beam forming matrix V needs to be fed back
`for each subcarrier (in a multicarrier embodiment). As each
`complex element includes two real numbers (i.e., a modulus
`and an angle), the total number of real numbers to be fed
`back in a straightforward implementation for an nxn matrix
`is 2n2 for each subcarrier, where n is the number of spatial
`streams. In addition, each of these real numbers can be
`anywhere between -oo to +oo. As will be appreciated, this
`large amount of feedback data can have a deleterious effect
`on overall system throughput. In one aspect of the present
`invention, techniques and structures are presented that are
`capable of significantly reducing the amount of data that
`needs to be fed back in a closed loop SYD MIMO channel
`to achieve an operative version of the beam forming matrix
`V within the transmitter. In at least one embodiment, a
`scheme for use with a 4x4 beam forming matrix is provided
`that only requires two sign bits, 9 "real number" parameters
`between O and 1, and 4 angles between -Jt or and +it. This
`is only 13 total parameters (plus two sign bits) as opposed
`to 32 parameters (i.e., 2n2 =2x4 2 =32) for the straightforward
`implementation. Other embodiments also exist.
`
`[0014] FIG. 3 is a block diagram illustrating an example
`communication device 60 that may be used to transmit data
`to a remote receiver in accordance with an embodiment of
`the present invention. The communication device 60 is
`configured for use in a closed loop SYD MIMO based
`the communication device 60
`system. As
`illustrated,
`includes: a wireless transmitter 62, a wireless receiver 64, a
`controller 66, and a matrix reconstruction unit 68. The
`transmitter 62 is operative for wirelessly transmitting data to
`the remote receiver via multiple transmit antennas. The
`transmitter 62 (or some other element) may include, among
`other things, a matrix multiplier to multiply data symbol
`vectors by a beam forming matrix V before transmission
`(e.g., see matrix multiplier 42 of FIG. 2). The wireless
`receiver 64 is operative for, among other things, receiving
`feedback information (via receive antennas) from the remote
`receiver that may be used in generating subsequent transmit
`signals within the communication device 60. The feedback
`information may include, for example, information describ(cid:173)
`ing a beam forming matrix to be used. In at least one
`embodiment of the present invention, the feedback infor(cid:173)
`mation that is received by the wireless receiver 64 that
`describes the beam forming matrix is in a compact form (i.e.,
`it is a reduced amount of data from the amount that would
`be transmitted in a straightforward SYD MIMO implemen(cid:173)
`tation). This compact feedback information may be used
`within the communication device 60 to reconstruct a corre(cid:173)
`sponding beam forming matrix. In some embodiments, the
`feedback information may also include eigenvalue informa(cid:173)
`tion for use in performing adaptive bit loading (ABL) within
`the communication device 60.
`
`[0015] The controller 66 may control the operation of
`some or all of the elements within the communication device
`60. When the controller 66 receives compact feedback
`
`ZTE, Exhibit 1005-0007
`
`

`

`US 2006/0068718 Al
`
`Mar. 30, 2006
`
`3
`
`information from the receiver 64, it may pass the informa(cid:173)
`tion to the matrix reconstruction unit 68. The matrix recon(cid:173)
`struction unit 68 may then reconstruct the corresponding
`beam forming matrix using the compact feedback informa(cid:173)
`tion. In a multicarrier system, a reconstruction may be
`performed for each subcarrier. The matrix reconstruction
`unit 68 may then deliver the beam forming matrix ( or
`matrices) to the transmitter 62 ( or elsewhere) where it may
`be matrix multiplied with data symbols to be transmitted.
`The receive antennas coupled to the receiver 64 and the
`transmit antennas coupled to the transmitter 62 may be the
`same or different antennas.
`
`[0016] FIG. 4 is a block diagram illustrating an example
`communication device 70 that may be used to receive data
`from a remote transmitter in accordance with an embodi(cid:173)
`ment of the present invention. The communication device 70
`is configured for use in a closed loop SYD MIMO type
`the communication device 70
`system. As
`illustrated,
`includes: a wireless receiver 72, a wireless transmitter 74, a
`controller 76, a channel matrix determination unit 78, an
`SYD unit 80, and a parameter extraction unit 82. The
`wireless receiver 72 is operative for, among other things,
`receiving data from a remote transmitter via a MIMO
`channel. One type of data that may be received is training
`data that allows the communication device 70 to determine
`a channel matrix describing the MIMO channel. When the
`controller 76 detects training data, it may pass the training
`data to the channel matrix determination unit 78 which uses
`the data to determine the channel matrix. Techniques for
`determining a MIMO channel matrix using training data are
`well known in the art. The channel matrix determination unit
`78 passes the channel matrix to the SYD unit 80 which
`decomposes the channel matrix using, for example, singular
`value decomposition techniques (or another similar tech(cid:173)
`nique). As part of the decomposition, the SYD unit 80
`determines a beam forming matrix that is to be used by the
`remote transmitter to transmit data to the communication
`device 70 in a future data transmission operation. The SYD
`unit 80 passes the beam forming matrix to the parameter
`extraction unit 82 which extracts parameters from the beam
`forming matrix for delivery to the remote transmitter as
`feedback information. The parameters that are extracted
`from the beam forming matrix are intended to describe the
`beam forming matrix in a relatively compact form and may
`be used in the transmitter to reconstruct the beam forming
`matrix for use therein. The parameter extraction unit 82 may
`pass the extracted parameters to the controller 76 which may
`
`is fed back to the remote transmitter may also include
`eigenvalue information for use in performing adaptive bit
`loading (ABL). Other types of information may also be fed
`back.
`
`[0017]
`In the description that follows, a compact feedback
`solution is developed for use with a 4x4 beam forming
`matrix. The solution includes a determination of the type of
`information to be fed back to a transmitter from a receiver
`in an SYD MIMO link and techniques for reconstructing an
`associated beam forming matrix within the transmitter. After
`the 4x4 solution is presented, a more general solution is
`developed for the case of an nxn beam forming matrix.
`
`[0018] Any complex, unit 4 vector may be expressed as
`follows:
`
`VJ
`
`a1
`
`a2ei02
`
`a3ei03
`
`where
`llvll2 = llvill2 + llv2112 + llv,112 + llv4112 = l; a1, a2, a,c[O, l];
`
`and
`
`Similarly, any unitary 4x4 matrix, can be expressed as:
`
`V=[ v1 v2v3 v4]=[ e'8'ia,)
`
`where v'ivi=l and v'ivk=0 for j,k=l, 2, 3, 4. The phases on the
`first row and the first colunm can be factored as:
`
`V=
`
`0
`
`i/021
`
`0
`
`0
`
`0
`
`0
`
`0
`
`0
`
`0
`
`eifl31
`
`0
`
`0
`
`0
`
`0
`
`eifl41
`
`PL
`
`\I
`
`,ei011
`
`0
`
`0
`
`0
`
`0
`
`,ei012
`
`0
`
`0
`
`0
`
`0
`
`ei013
`
`0
`
`0
`
`0
`
`0
`
`eifl14
`
`PR
`
`[Equation 1]
`
`with matrix V being expressed as follows:
`
`V=
`
`au
`
`a21
`
`a31
`
`a12
`
`1iP22a22
`
`,/r.p32a32
`
`a13
`
`,l.P23a23
`
`,/r.p33a33
`
`✓ 1 - af1 - a~1 - a~1
`
`eir.p42 ✓ 1 - af2 - a~2 - a~2
`
`eir.p43 ✓ 1 - af3 - a~3 - a~3
`
`✓ 1 - af 1 - af2 - af3
`i/lfl24 ✓ 1 - a~ 1 - a~2 - a~3
`,/P34 ✓ 1 - ai1 - ai2 - ai3
`eir.p44 ✓ 1 - a~ 1 - a~2 - a~3
`
`[Equation 2]
`
`then deliver the parameters to the remote transmitter via
`local transmitter 74. In a multicarrier system, a set of
`parameters may be fed back for each subcarrier or interpo(cid:173)
`lation may be used to reduce feedback overhead. Quantiza(cid:173)
`tion techniques may be used to describe the parameters. As
`described above, in some embodiments, the information that
`
`where aik E[0,1] and cjl~=8;i-8il-8 1i. Since phase facto~za(cid:173)
`tion does not change the unitary property, the matrix Y is
`still unitary. Although the phases of the first row and the first
`colunm are factored out in the above example, it should be
`appreciated that the phases associated with any row and
`colunm may be factored.
`
`ZTE, Exhibit 1005-0008
`
`

`

`US 2006/0068718 Al
`
`Mar. 30, 2006
`
`4
`
`G41 =Yl-au 2-a212-a312
`
`2
`a42= V 1-a 12
`
`2
`-a22
`
`2
`-a32
`
`G43=Yl-a13 2_a23 2_a332
`
`[0021] Since v2 is orthogonal to vi, it follows that v\ v 2 =0.
`This relationship can be expressed as:
`
`where:
`
`[Equation 5]
`
`[Equation 6]
`
`[0022] FIG. 5 is a graph illustrating a geometric relation(cid:173)
`ship 90 that is representative of Equation 5 above. In FIG.
`5, a 1 is the angle of vector c1 92, cp32 is the angle of vector
`c2 94, and cp42 is the angle of vector c3 96. The values of c2
`and C3 are greater than or equal to zero. Using trigonometry,
`the solutions for cp32 and cp42 may be calculated as follows:
`
`where Lxy is the angle formed by vectors x and y in the
`direction from x toy and sign(Lxy) is the sign of Lxy. The
`parameter Lxy is positive (i.e., sign (Lxy)=l) if Lxy is
`counterclockwise in [O, it]. Similarly, the parameter Lxy is
`negative (i.e., sign(Lxy)=-1) if Lxy is clockwise in [O, it).
`[0023] To solve for the third colunm v3 ofV, the following
`procedure may be followed. Since v 3 is orthogonal to v 1 and
`v2 , it follows that v\v3 =0 and v'2v3 =0. These relationships
`may be expressed as follows:
`
`[Equation 7]
`
`[Equation 8]
`
`where:
`
`[0019]
`It can be shown that only PL and Vin Equation 1
`above, and not PR, need to be fed back to the transmitter to
`appropriately process a transmit signal therein. This is
`because matrix PR can be absorbed into D, the diagonal
`matrix in SYD, and may thus be taken care of in the training
`process. The angles 821 , 831 , and 841 , determine PL and the
`angles Bu, 8 12 , 813 , and 8 14 determine PR. It can also be
`shown that the matrix V, as set out in Equation 2 above, can
`be described by (and reconstructed from) only 9 parameters.
`However, there are many different 9 parameter combinations
`that may be used. Each of these combinations is a subset of
`all of the variables of V. Different combinations result in
`different complexities in the reconstruction of V in the
`transmitter. In general, the complexity of extracting the
`parameters ofV is relatively low compared to the complex(cid:173)
`ity of reconstructing V based on these parameters. An
`example of the extraction process is set out below in
`Equation 3. In this example, the 9 extracted parameters are:
`
`a 11=/V 1i/,a21 =/V2if,a31=/V31I
`
`[Equation 3]
`
`a12=/V12/,a22=/V22/,a32=/Vd
`a 13=/V 13/,an=/V n/, a33=fV 331
`where lxl denotes the absolute value of x. Instead of sending
`parameters back directly, functions of the selected param(cid:173)
`eters may be sent. The functions may include, for example,
`common trigonometric functions such as arcsin( ), arccos( ),
`and arctan( ) or square( ). Any design of a closed loop SYD
`MIMO feedback technique should address the dual goals of:
`1) reducing the amount of data that needs to be fed back; and
`2) achieving a low matrix reconstruction complexity in the
`transmitter.
`
`[0020]
`In at least one embodiment of the present inven(cid:173)
`tion, the following parameters from the expression for V in
`Equation 2 are included as feedback: aii=l,2,3 andj=l,2,3),
`cp 22 , and the signs of cp 32 and cp33 . The parameters aii=l ,2,3
`and j=l,2,3) and cp22 may be quantized before they are fed
`back. In addition, the angles 821 , 831 , and 841 from PL may
`also be fed back. These parameters may also be quantized
`before they are fed back. As will be described in greater
`detail, the reconstruction ofV in the transmitter ( e.g., within
`the matrix reconstruction unit 68 of FIG. 3) may then be
`carried out in the following manner: (1) compute the
`unknown aii based on the unit vector condition; (2) compute
`cp 32 and cjl42 to reconstruct the second colunm v2 ofV; (3)
`compute the third colunm v3 of V based on the unitary
`property ofV; and (4) compute the fourth colunm v4 ofV
`based on the row orthogonality ofV. The matrix V may be
`rewritten as follows:
`
`au
`
`a12
`
`a13
`
`a14
`
`[Equation 4]
`
`V=
`
`a21
`
`1/P22a 22
`
`a31 1/P32a32
`
`G4!
`
`i/P4la42
`
`,l.P23a23
`,l.P33 a33
`i/P43 l43
`
`i/Pl4 a24
`
`i/P34 a34
`
`i/P44l144
`
`b1=a12a13
`
`b2=a22a23 e-i,t,22
`
`b3=a32a33 e-i,t,32
`
`b4=a42a43 e-i-42
`
`To compute the remaining a;i, using the fed back a;i, the
`following equations may be used:
`
`Elimination of ei<l>n using Equations 7 and 8 results in:
`
`[Equation 9]
`
`where:
`
`d1=a1bra2b1
`
`d2=a3bra2b3
`
`d3=a4bra2b4
`
`ZTE, Exhibit 1005-0009
`
`

`

`US 2006/0068718 Al
`
`Mar. 30, 2006
`
`5
`
`Equation 9 may be solved in a manner similar to Equation
`5 discussed previously, using trigonometric relationships.
`This results in:
`
`( ~ ~ l[
`c.p33 = sign Ld 1 d 2
`( ~ ~ l[
`[
`(df +d}-d})
`<p43 = sign Ld 1 d 2 arccos - - - - - n
`2d1d3
`
`,r - arccos - -
`d-
`2
`
`1-
`
`( df + d} - d}) [
`
`[Equation 10]
`
`d-
`-
`2
`
`above approach. This may be performed, for example,
`within the matrix reconstruction unit 48 of FIG. 3. As
`described previously, in addition to the parameters listed
`above, the parameters 82 i, 831 , and 841 may also be fed back
`to the transmitter to permit reconstruction of matrix PL
`(within, for example, matrix reconstruction unit 48). The
`matrices PL and V may then be used to generate a subsequent
`transmit signal (e.g., Z=PLVX). As mentioned previously,
`the matrix PR is not needed to achieve the desired result.
`Thus, feedback including 13 parameters and two sign bits
`allow the 4x4 beam forming matrix to be reconstructed in
`the transmitter in a relatively low complexity manner.
`
`[0026] For a more general nxn beam forming matrix, a
`similar solution approach may be taken. Any complex, unit
`n vector may be expressed as follows:
`
`v=
`
`n-!
`1- L
`j=l
`
`where llvll 2 = .L llvJll 2 = l; ajE[O, l]; and 0jE[-n, rr)for j = 1, ... , n.
`
`n
`
`j=l
`
`Similarly, any unitary nxn matrix, can be expressed as:
`V=[V1V2 ... vnJ=le'9i.kaj,kJ
`where v>i=l and v'ivk=O for j,k=l, ... ,n. The phases on the
`first row and the first column ( or any other row and colunm)
`can be factored as:
`
`Substitution of Equation 10 into Equation 7 results in the
`following solution for cp 23 :
`
`[0024] Because V is unitary, the second row of V is
`orthogonal to the first row. This leads to the following
`solution for e<1>24
`
`:
`
`3
`
`-aua21 - .L
`i/P24 = ____ 1_·~_2 - - - (cid:173)
`a14a24
`
`Similarly, e<1>34 and e<1>44 may be expressed as:
`
`3
`
`-aua31 - .L
`i/P34 = ____ 1_·~_2 - - - -
`a14a34
`
`3
`
`-aua41 - .L
`ilP44 = ____ 1_·~_2 - - - -
`a14a44
`
`[Equation 11]
`
`[Equation 12]
`
`[0025] Thus, with reference to Equation 4 above, values
`for au, a12 , a 13 , a21 , a22, a23 , a31 , a32, a33 , and cp 22, along with
`the signs of cp 32 and cp33 , may be delivered from a receiver to
`a transmitter and values for a 14, a24, a34, a4 i, a42, a43 , a44,
`, ei<l>34
`, ei<l>44 may be generated
`cjl23, <P32, cjl3 3 , <P42, <P43 , ei<l>24
`within the transmitter to reconstruct the matrix V using the
`
`with matrix V being expressed as follows:
`
`V=
`
`v
`
`n-!
`
`1- °\' ay L. .1
`
`j=l
`
`an-1,1
`
`eicp2,n
`
`n-!
`
`l - .L aJ,n-1
`
`j=l
`
`n-!
`
`1 - I a~-1,j
`
`j=l
`
`n-!
`
`1 - .L a], 1
`
`j=l
`
`!l/Pn,2
`
`n-!
`
`1 _ .L a], 2
`
`j=l
`
`. . .
`
`!l/Pn,n-1
`
`n-!
`
`1 - .L a],n- l
`
`j=l
`
`ii"cpn,n
`
`-n+l
`
`ZTE, Exhibit 1005-0010
`
`

`

`US 2006/0068718 Al
`
`Mar. 30, 2006
`
`6
`
`where aik E[0,1] for j,k=l, ... ,n-1 and <Pi.k E(-it,it] for j,k=2,
`... ,n. Since phase factorization does not change the unitary
`property, the matrix V is still unitary.
`
`[0027] As before, only PL and Vin Equation 11 above, and
`not PR, need to be fed back to the transmitter to appropri(cid:173)
`ately process a transmit signal therein. The angles 8i.1, j=2,
`... , n determine PL and the angles 81k, k=l, ... ,ndetermine
`PR. The unitary matrix V, as set out in Equation 12 above,
`can be described by (and reconstructed from) only (n-1)2
`parameters (e.g., aj.k, j,k=l, ... , n-1). This can be proven
`as follows. First, assume that the (n-1)2 parameters are aj.k,
`j,k=, ... , n-1. These are the magnitudes of elements in the
`upper, left sub-matrix ofV in Equation 12. The magnitudes
`at the last row and column ofV (i.e., an.k, aj.n, j=l_ ... n, k=l
`... n) can be solved using a unitary property ofV (i.e., that
`all rows and columns have unit norms). The magnitudes may
`be solved as:
`
`an.k= 1-I
`
`n-!
`
`j=l
`
`aj.n = 1-I
`
`n-!
`
`k=l
`
`k = 1, ··· , n
`
`j = 1, ··· , n-1
`
`The remaining unknown variables are the (n-1 )2 angles, <Pi,k'
`j,k=2, ... , n. These angles are the phases of each element
`ofV, excluding the first row and column. First, the angles in
`column 2 through column n-1 may be determined (i.e., <Pi,k,
`j-2, ... , n, k=2, ... , n-1). There are (n-l)(n-2) unknown
`angles in these columns. Since Vis unitary, any two columns
`between column 1 and column n-1 are orthogonal to each
`other. Using these constraints, the following (n-l)(n-2)
`equations may be obtained:
`
`[Equation 13]
`
`or
`Re{ U1Ja1,k+a2Ja2,kaei(<l>,J-<l>l.k)+ ... +anJan,kei(<l>nJ-<l>n.k)}=0
`
`Im) { U1,ja1,k+a2,ja2,kai<4'2,j-¢il,k)+ ... +an,jan,ki(4'n,j-¢in,
`k}-0
`where k=l, ... , n-2, k<j<=n-1. These equations are
`non-linear and uniquely determine the (n-l)(n-2) angles
`therein. The equations may be solved using, for example,
`numerical methods (e.g., Newton and Newton-Seidel algo(cid:173)
`rithms may be employed). Because V is unitary, the first row
`ofV is orthogonal to the other rows. Thus, the angles in the
`last column (i.e., the only remaining unsolved variables)
`may be determined as follows:
`
`'PJ.n = angl ~ I
`
`{
`
`l,n J,n k=l
`
`-l n-1
`
`j = 2, ··· , n
`
`[0028] There are many different combinations of (n-1)2
`parameters that may be used to describe the unitary matrix
`V. Each of these combinations is a subset of all of the
`variables of V set out in Equation 12 above. For example,
`the angle <Pi,k and the magnitud~ vi,k are equivalent (i.e., if
`cpi.k is a specified parameter, then vi,k is determined by solving
`
`Equation 13 above). As in the 4x4 solution described
`previously, different combinations will typically result in
`different reconstruction complexities in the transmitter.
`Again, the complexity of extracting the parameters ofV will
`typically be relatively low compared to the complexity of
`reconstructing V based on these parameters. An example of
`the extraction process for an nxn implementation follows:
`
`ai,k-/Vi,J, )-1, ... , n-1, k-1, ... , n-1
`[0029] Thus, in at least embodiment of the present inven(cid:173)
`tion, (n-1)2 parameters may be fed back from a receiver to
`a transmitter in an SYD MIMO system and then used in the
`transmitter to reconstruct an nxn matrix V. In addition, n-1
`angle parameters may also be fed back to reconstruct matrix
`PL in the transmitter. The matrices PL and V may then be
`used to generate a subsequent transmit signal (e.g., Z=PL
`VX). Therefore, feedback including n2-n parameters allows
`the nxn beam forming matrix to be reconstructed in the
`transmitter in a relatively low complexity manner.
`
`[0030] As described previously, in addition to information
`describing the beam forming matrix, the feedback from the
`receiver to the transmitter may also include eigenvalue
`information for use in performing adaptive bit loading
`(ABL) within the transmitter. For example, in at least
`embodiment, the feedback information in an nxn system
`may include n2-n parameters to describe the beam forming
`matrix and n real parameters to describe the eigenvalues in
`the matrix D.
`
`[0031] The techniques and structures of the present inven(cid:173)
`tion may be implemented in any of a variety of different
`forms. For example, features of the invention may be
`embodied within cellular telephones and other handheld
`wireless communicators, personal digital assistants having
`wireless capability, laptop, palmtop, and tablet computers
`having wireless capability, pagers, satellite communicators,
`cameras having wireless capability, audio/video devices
`having wireless capability, network interface cards (N