asy United States
`a2) Patent Application Publication (10) Pub. No.: US 2004/0087324 Al
`(43) Pub. Date: May6, 2004
`
`Ketchum etal.
`
`US 20040087324A1
`
`(54) CHANNEL ESTIMATION AND SPATIAL
`PROCESSING FOR TDD MIMO SYSTEMS
`
`(76)
`
`Inventors: John W. Ketchum, Harvard, MA (US),
`MarkS. Wallace, Bedford, MA (US);
`J. Rodney Walton, Carlisle, MA (US);
`Steven J. Howard, Ashland, MA (US)
`
`Publication Classification
`
`(51) HM. C17 cacccssscsssseeseseeen H04B 7/00; H04Q 7/20
`(52) US. Ch.
`cessssssssssesatseesseeesse 455/513; 455/67.11
`
`(57)
`
`ABSTRACT
`
`Channel estimation and spatial processing for a TDD MIMO
`Correspondence Address:
`system. Calibration may be performed to account for dif-
`Qualcomm Incorporated
`ferences in the responses of transmit/receive chains at the
`Patents Department
`5775 Morehouse Drive
`access point and user terminal. During normal operation, a
`MIMOpilot is transmitted onafirst link and used to derive
`San Diego, CA 92121-1714 (US)
`an cstimate of the first
`link channel response, which is
`decomposed to obtain a diagonal matrix of singular values
`10/693,171
`(21) Appl. No.:
`andafirst unitary matrix containing bothleft eigenvectors of
`the first link and right eigenvectors of a second link. A
`(22)
`Filed:
`Oct. 23, 2003
`steered reference is transmitted on the second link using the
`cigenvectors in the first unitary matrix, and is processed to
`obtain the diagonal matrix and a second unitary matrix
`containing both left eigenvectors of the second link and right
`eigenvectors of the first link. Each unitary matrix may be
`used to perform spatial processing for data transmission/
`reception via both links.
`
`(60) Provisional application No. 60/421,428,filed on Oct.
`25, 2002. Provisional application No. 60/421,462,
`filed on Oct. 25, 2002. Provisional application No.
`60/421,309,filed on Oct. 25, 2002.
`
`Related U.S. Application Data
`
`110
`
`Access Point
`
`User Terminal
`
`150
`
` 114
`
`TX Data
`
`
`
`
`
`170
`160
`
`
`Pilot
`120
`Processor
`
`
`RX Data
`TX Spatial
`RX Spatial
`Processor
`
`Processor — Processor
`
`180
`
`
`
`Controller
` Controller
`152ut
`
`
`
`
`
`154ut
`
`
`_ [restese
`
`RX
`Processor
`
`RX Spatial
`Processor
`
`190
`
`D
`
`TX Spatial
`
`188
`
`TX Data
`Processor
`
`186
`
`Data
`
`Source
`
`Page 1 of 21
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`SAMSUNG EXHIBIT 1023
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`SAMSUNG EXHIBIT 1023
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`Patent Application Publication
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`May 6, 2004 Sheet 1 of 6
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`US 2004/0087324 Al
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`Patent Application Publication
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`May6, 2004 Sheet 4 of 6
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`US 2004/0087324 Al
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`Patent Application Publication
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`May 6, 2004 Sheet 5 of 6
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`US 2004/0087324 Al
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`

`Patent Application Publication
`
`May6, 2004 Sheet 6 of 6
`
`US 2004/0087324 Al
`
`Acc ss Point
`UsrTrminal
`
` Estimate calibrated downlink
`
`
`channel response based on
`the downlink MIMOpilot
`
`
`526
`
`
`
`Decomposethecalibrated
`downlink channel response
`
`
`estimateAA, to obtain diagonal
`matrix &‘and unitary matrix v.
`
`
`530
`
`
`
`Transmit a steered reference
`
`
`on the calibrated uplink
`
`channelusing the matrix Vv.
`
`542
`Receive and spatially process_
`received symbols with matrix ve
`
`550
`
`
`
`Spatially process symbols
`with matrix V,, and transmit
`
`
`to the accesspoint
`
`
`
`Transmit a MIMOpilot on the
`calibrated downlink channel
`
`532
`
`
`
`Receive and process
`the uplink steered reference
`
`
`to obtain diagonal matrix &
`
`
`and unitary matrix G,,
`
`
`540
`
`
`
`Spatially process symbols
`with matrix G.p and transmit
`
`
`to the user terminal
`
`
`552
`Receive and spatially process|
`received symbols with matrix or
`
`|
`
`Page 7 of 21
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`

`

`US 2004/0087324 Al
`
`May6, 2004
`
`CHANNEL ESTIMATION AND SPATIAL
`PROCESSING FOR TDD MIMO SYSTEMS
`
`techniques to efficiently perform channel estimation and
`spatial processing in a TDD MIMOsystem.
`
`CLAIM OF PRIORITY UNDER35 USS.C. §119
`
`[0001] This application claims the benefit of provisional
`US. Application Serial No. 60/421,428, entitled “Channel
`Estimation and Spatial Processing for TDD MIMO Sys-
`tems,” provisional U.S. Application Serial No. 60/421,462,
`entitled “Channel Calibration for a Time Division Duplexed
`Communication System,” and provisional U.S. Application
`Serial No, 60/421,309, entitled “MIMO WLAN System,”all
`of which are filed on Oct. 25, 2002, assigned to the assignee
`of the present application, and incorporated herein byref-
`erence.
`
`BACKGROUND
`
`[0002]
`
`1. Field
`
`invention relates generally to data
`[0003] The present
`communication, and more specifically to techniques to per-
`form channel estimation and spatial processing in time-
`division duplexed (TDD) multiplc-input multiple-output
`(MIMO) communication systems.
`
`[0004]
`
`2. Background
`
`[0005] A MIMOsystem employs multiple (N,) transmit
`antennas and multiple (N,) receive antennas fordata trans-
`mission. A MIMO channel formed by the Ny transmit and
`N_
`reecive antennas may be decomposed into Ng indepen-
`dent channels, with Ne=min{Ny, Ng}. Each of the Ng
`independent channels is also referred to as a spatial sub-
`channel or an eigenmode of the MIMO channel and corre-
`sponds to a dimension. The MIMO system can provide
`improved performance (c.g., inercased transmission capac-
`ity) if the additional dimensionalities created by the multiple
`transmit and receive antennas are utilized.
`
`In order to transmit data on onc or morc of the Ng
`[0006]
`eigenmodes of the MIMO channel,it is necessary to perform
`spatial processing at the receiver and typically also at the
`transmitter. The data streams transmitted from the N, trans-
`mit antennas interfere with each other at the receive anten-
`nas. The spatial processing attempts to scparate out the data
`streams at
`the receiver so that they can be individually
`recovered.
`
`SUMMARY
`
`‘Techniques are provided herein to perform channel
`[0009]
`estimation and spatial processing in an efficient mannerin a
`TDD MIMOsystem. I'or the TDD MIMO system,
`the
`reciprocal channel characteristics can be exploited to sim-
`plify the channel estimation and spatial processing at both
`the transmitter and receiver. Initially, an access point and a
`user terminal
`in the system may perform calibration to
`determine differences in the responses of their transmit and
`receive chains and to obtain correction factors used to
`account for the differences. Calibration may be performedto
`ensure that the “calibrated” channel, with the correction
`factors applied, is reciprocal. In this way, a more accurate
`estimate of a sccond link may be obtaincd based on an
`estimate derived for a first link.
`
`[0010] During normal operation, a MIMOpilot is trans-
`mitted (e.g., by the access point) on the first link (e.g., the
`downlink) and used to derive an estimate of the channel
`response for the first link. The channel response estimate
`maythen be decomposed (e.g., by the user terminal, using
`singular value decomposition) to obtain a diagonal matrix of
`singular values anda first unitary matrix containing both the
`left eigenvectors of the first link and the right eigenvectors
`of the second link (e.g., the uplink). The first unitary matrix
`may thus be used to perform spatial processing for data
`transmission received on the first link as well as for data
`transmission to be sent on the second link.
`
`[0011] A steered reference may be transmitted on the
`secondlink using the eigenvectors in the first unitary matrix.
`Astcered reference(orsteeredpilot) is a pilot transmitted on
`specific eigenmodes using the eigenvectors used for data
`transmission. This steered reference may then be processed
`(e.g., by the access point) to obtain the diagonal matrix and
`a second unitary matrix containing both the left eigenvectors
`of the secondlink and the right cigenvectors ofthe first link.
`The second unitary matrix may thus be used to perform
`spatial processing for data transmission received on the
`second link as well as for data transmissionto be sent on the
`first link.
`
`[0012] Various aspects and embodiments of the invention
`are described in further detail below.
`
`[0007] To perform spatial processing, an accurate estimate
`of the channel response betweenthe transmitter and receiver
`is typically required. For a TDD system, the downlink (ie.,
`forward link) and uplink (i.e., reverse link) between an
`access point and a user terminal both share the same
`frequency band.
`In this case,
`the downlink and uplink
`channel responses may be assumedto be reciprocal of one
`[0014] FIG.1is a block diagram of an access point and a
`another, after calibration has been performed (as described
`user terminal ina TDD MIMOsystem, in accordance with
`below) to accountfor differencesin the transmit and receive
`one embodimentof the invention;
`chains at the access point and user terminal. That is, if H
`represents the channel response matrix from antenna array A
`to antennaarray B, then a reciprocal channel impliesthat the
`coupling from array B to array A is given by H", where M
`denotes the transpose of M.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`[0013] The various aspects and features of the present
`invention are described below in conjunction with the fol-
`lowing drawings, in which:
`
`[0015] FIG.2A showsa block diagram ofthe transmit and
`receive chains at
`the access point and user terminal,
`in
`accordance with one embodiment of the invention;
`
`[0016] FIG. 2B showsapplication of correction matrices
`to account for differences in the transmit/receive chains at
`the access point and user terminal, in accordance with one
`embodimentof the invention;
`
`[0008] The channel estimation and spatial processing for a
`MIMOsystem typically consume a large portion of the
`system resources. There is therefore a need in the art for
`
`Page 8 of 21
`
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`

`US 2004/0087324 Al
`
`May6, 2004
`
`[0017] FIG. 3 showsthe spatial processing for the down-
`link and uplink for a spatial multiplexing mode, in accor-
`dance with one embodiment of the invention;
`
`[0018] FIG. 4 showsthe spatial processing for the down-
`link and uplink for a beam-stecring mode, in accordance
`with one embodiment of the invention; and
`
`[0019] FIG. 5 shows a process for performing channel
`estimation and spatial processing at the access point and user
`terminal, in accordance with one embodiment of the inven-
`tion.
`
`DETAILED DESCRIPTION
`
`FIG.1 is a block diagram of an cmbodimentof an
`[0020]
`access point 110 and a user terminal 150 in a TDD MIMO
`system 100. Access point 110 is equipped with N,,, transmit/
`receive antennas for data transmission/reception, and user
`terminal 150 is equipped with N,,, transmit/receive antennas.
`
`[0021] On the downlink, at access point 110, a transmit
`(TX) data processor 114 receives traffic data (ie., informa-
`tion bits) from a data source 112 and signaling and other data
`from a controller 130. TX data processor 114 formats, codes,
`interleaves, and modulates (i.e., symbol maps) the data to
`provide modulation symbols. A TX spatial processor 120
`receives the modulation symbols from TX data processor
`114 and performsspatial processing to provide N,,, streams
`oftransmit symbols, one stream for each antenna. TX spatial
`processor 120 also multiplexes in pilot symbols as appro-
`priate (c.g., for calibration and normal opcration).
`
`{0022] Each modulator (MOD) 122 (which includes a
`transmit chain) receives and processes a respective transmit
`symbolstream to provide a corresponding downlink modu-
`lated signal. The N,, downlink modulated signals from
`modulators 122¢ through 122ap are then transmitted from
`N,, antennas 124a through 124ap,respectively.
`[0023] At user terminal 150, N., antennas 152a through
`152ut receive the transmitted downlink modulated signals,
`and cach antenna provides a reccived signal to a respective
`demodulator (DEMOD) 154. Each demodulator 154 (which
`includes a receive chain) performs processing complemen-
`tary to that performed at modulator 122 and provides
`received symbols. A receive (RX) spatial processor 160 then
`performsspatial processing on the received symbols from all
`demodulators 154a through 154ur to provide recovered
`symbols, which are estimates of the modulation symbols
`sent by the access point. An RX data processor 170 further
`processes (e.g., symbol demaps,deinterleaves, and decodes)
`the recovered symbols to provide decoded data. The
`decoded data may include recoveredtraffic data, signaling,
`and so on, which maybe provided to a data sink 172 for
`storage and/or a controller 180 for further processing.
`
`[0024] The processing for the uplink may be the same or
`different from the processing for the downlink. Data and
`signaling are processed (e.g., coded, interleaved, and modu-
`lated) by a TX data processor 188 and further spatially
`processed by a TX spatial processor 190, which also mul-
`tiplexesin pilot symbols as appropriate (e.g., for calibration
`and normal opcration). The pilot and transmit symbols from
`TX spatial processor 190 are further processed by modula-
`tors 1544 through 154ur to generate N,, uplink modulated
`signals, which are then transmitted via antennas 152a
`through 152ur to the access point.
`
`[0025] At access point 110, the uplink modulated signals
`are received by antennas 1244 through 124ap, demodulated
`by demodulators 122a@ through 1224p, and processed by an
`RX spatial processor 140 and an RX data processor 142 in
`a complementary manner to that performed at
`the user
`terminal. The decoded data for the uplink may be provided
`to a data sink 144 for storage and/or controller 130 for
`further processing.
`
`[0026] Controllers 130 and 180 control the operation of
`various proccssing units at the access point and uscr termi-
`nal, respectively. Memory units 132 and 182 store data and
`program codes used by controllers 130 and 180, respec-
`tively.
`
`1. Calibration
`
`[0027] Tora TDD system, since the downlink and uplink
`share the same frequency band, a high degree of correlation
`normally exists between the downlink and uplink channel
`responses. Thus, the downlink and uplink channel response
`matrices maybe assumedto bereciprocal(i.e., transpose) of
`each other. Ilowever, the responses of the transmit/receive
`chains at the access point are typically not equal to the
`responsesof the transmit/receive chains at the user terminal.
`For improved performance, the differences may be deter-
`mined and accounted for via calibration.
`
`[0028] FIG.2A showsa block diagram ofthe transmit and
`receive chains at access point 110 and user terminal 150, in
`accordance with one embodimentof the invention. For the
`
`downlink, at access point 110, symbols (denoted by a
`“transmit” vector x,,,) are processed by a transmit chain 214
`and transmitted from N,,, antennas 124 over the MIMO
`channel. At user terminal 150,
`the downlink signals are
`received by N,, antennas 152 and pracessed by a receive
`chain 254 to provide received symbols (denoted by a
`“receive” vector r,,). For the uplink, at user terminal 150,
`symbols (denoted by a transmit vectorx,,,) are processed by
`a transmit chain 264 and transmitted from N,,, antennas 152
`over the MIMO channel. At access point 110, the uplink
`signals are received byN,,, antennas 124 and processed by
`a receive chain 224 to provide received symbols (denoted by
`a receive vectorr,,,).
`[0029] For the downlink, the receive vector r,,, at the user
`terminal (in the absence of noise) may be expressed as:
`Eq @)
`Tu=R EL,pty
`[0030] where x,,, is the transmit vector with N,,, entries for
`the downlink;
`
`[0031]
`
`14, is the receive vector with N,, entries;
`
`‘I.is an N,,,xN,p diagonal matrix with entries
`[0032]
`for the complex gains associated with the transmit
`chain for the N,,, antennas at the access point;
`
`[0033] R,,, is an N,,xN,, diagonal matrix with entries
`for the complex gains associated with the receive
`tat
`chain for the N_,,
`antennas at the user terminal; and
`
`[0034] H is an N,,xN,,, channel response matrix for
`the downlink.
`
`[0035] The responses of the transmit/receive chains and
`the MIMO channelare typically a function of frequency. For
`simplicity, a flat-fading channel (i-e., with a flat frequency
`response) is assumed for the following derivation.
`
`Page 9 of 21
`
`Page 9 of 21
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`

`

`US 2004/0087324 Al
`
`May6, 2004
`
`Forthe uplink, the receive vectorr,,, at the access
`[0036]
`point (in the absence of noise) may be expressed as:
`Eq (2)
`Typ=RapHl"Lakup»
`[0037] where x,,, is the transmit vector with N,,entries for
`the uplink;
`[0038]
`Lup is the receive vector with N,,, entries;
`[0039] T.,, isan N,.xN,, diagonal matrix with entries
`for the complex gains associated with the transmit
`chain for the N,, antennas at the user terminal;
`[0040]
`_R,,, is an N,,,xN.,, diagonal matrix with entries
`for the complex gains associated with the receive
`chain for the N,,, antennas at the access point; and
`[0041] H" isan NapXN,, Channel response matrix for
`the uplink.
`Fromequations (1) and (2), the “effective” down-
`[0042]
`link and uplink channel responses, H,, and H,,, which
`include the responsesof the applicable transmit and receive
`chains, may be expressed as:
`
`Eq (3)
`Hig-RulTap and Hyp=RapHTyp.
`[0043] As shownin equation (3), if the responses of the
`transmit/receive chains at the access point are not equal to
`the responses of the transmit/receive chains at
`the user
`terminal, then the effective downlink and uplink channel
`responses
`are
`not
`reciprocal
`of
`one
`another, Le., RuHL*(RopfLa)”
`[0044] Combining the two equations in equation set (3),
`the following relationship maybe obtained:
`Eq (4)
`lap
`H=Ry“Haslap“(Rap“HapLar*)"=Lur“HapBap
`[0045] Rearranging equation
`(4),
`the
`following
`is
`obtained:
`
`Hap=TRarHdnTyy*Rap=Kar“HanKap
`[0046]
`or
`Eq (5)
`Hag=(KarHanKap)"s
`[0047] where K,=T.,"Ry and K..=T,,'R,,. Because
`Tar Ru» Tap and R,,, are diagonal matrices, K,,, and K,,, are
`also diagonal matrices. Equation (5) mayalso be expressed
`as:
`
`Eq (6)
`HypKu=(inKap)”
`[0048] The matrices K,, and K,, may be viewed asinclud-
`ing “correction factors” that can account for differences in
`the transmit/receive chains at
`the access point and user
`terminal. ‘This would then allow the channel response for
`one link to be expressed by the channel response for the
`otherlink, as shown in equation (5).
`
`[0049] Calibration may be performed to determine the
`matrices K,,, and K,,. Typically, the true channel response H
`and the transmit/receive chain responses are not known nor
`can they be exactly or easily ascertained.
`Instead,
`the
`effective downlink and uplink channel
`responses, L,,,
`and H.,,, may be estimated based on MIMO pilots sent on
`the downlink and uplink, respectively. The generation and
`use of MIMOpilot are described in detail in the aforemen-
`tioned U.S. patent application Ser. No. 60/421,309.
`[0050] Estimates of thc matriccs K,, and K,,, which are
`referred to as correction matrices, KK, and K,,, may be
`derived based on the downlink and uplink channel response
`estimates, A, and Bo in various manners, including by a
`matrix-ratio computation and a minimum mean square error
`
`(MMSE) computation. For the matrix-ratio computation, an
`(N,.xN,,) matrix C is first computedasa ratio of the uplink
`and downlink channel response estimates, as follows:
`
`Sup
`nr”
`“dn
`
`Eq (7)
`
`[0051] where the ratio is taken element-by-element. Each
`element of C may thus be computed as:
`
`i
`doug
`eg =, for i= 41... Nupand j={l ...Ngp}
`Nan i,j
`
`dn ij
`are the (i,j)-th (row, column)
`[0052] where f,,, ,; andh
`element of He” and H,,,, respectively, and ¢,; is the G,j)-th
`element of C.
`
`[0053] Acorrection vector for the access point, Kp» which
`includes only the N,,, diagonal elements of Ro may be
`defined to be equal to the mean of the normalized rowsof C.
`Each row of C, ¢c;,,
`is first normalized by dividing cach
`element of the row with the first elementof the row to obtain
`a corresponding normalized row, ¢;. Thus,if ¢(k)=[¢,,...
`Cine] is the i-th row of C, then the normalized row ¢, may
`be expressedas:
`
`S®-leaW/er® ... ai(kye(W)..- Sing,
`1®]
`
`[0054] The correction vector K(k) is then set equal to the
`meanof the N,,, normalized rows of C and may be expressed
`as:
`
`y Nut
`
`Kq (8)
`
`[0055] Because of the normalization, the first element of
`k,,(k) is unity.
`
`[0056] A correction vector K(k) for the user terminal,
`k,,(k), which includes only the N,, diagonal elements of
`K(k), may be defined to be equal to the mean of the
`inverses of the normalized columns of C. Each columnofC,
`¢c,, is first normalized by scaling each elementin the column
`with the j-th element of the vector k,,, which is denoted as
`K,,;; to obtain a corresponding normalized column, ¢;.
`Thus,if ¢(k)=[c,; ..- ox.il is the j-th column of C, then
`the normalized column c2, may be expressed as:
`
`CleryKapaa «+ + CiKapgg ++ + CnKapsal”
`
`[0057] The correction vector k,,, is then set equal to the
`mean ofthe inverses of the N,,, normalized columnsof C and
`may be expressed as:
`
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`US 2004/0087324 Al
`
`May6, 2004
`
`Nap
`
`Eq (9)
`
`[0058] where the inversion of the normalized columns,
`c;(k), is performed element-wise. The calibration provides
`the correction vectors, k,, and k,, or the corresponding
`correction matrices K.,,, andKin for the access point and user
`terminal, respectively.
`
`[0059] The MMSE computation for the correction matri-
`ces K and K., is described in detail in aforementioned U.S.
`patent application Ser. No. 60/421,462.
`
`FIG.2Billustrates the application of the correction
`[0060]
`matrices to account for differences in the transmit/receive
`chains at the access point and user terminal, in accordance
`with one embodimentof the invention. On the downlink, the
`transmit vector x,, is first multiplied with the matrix K,, by
`a unit 212. The subsequent processing by transmit chain 214
`and receive chain 254 for the downlink is the same as shown
`in FIG. 2A.Similarly, on the uplink, the transmit vector x,,,
`is first multiplied with the matrix K,, by a unit 262. Again,
`the subsequent processing bytransmit chain 264 and receive
`chain 224 for the uplink is the same as shown in FIG.2A.
`
`[0061] The “calibrated” downlink and uplink channel
`responses observed by the user terminal and access point,
`respectively, may be expressed as:
`
`Eq (10)
`Hean~HinKap and Houp7HapKu
`[0062] where H.,,” and H.,,, are estimates of the “true”
`calibrated channel response expressions in equation ((6).
`From equations (6) and (10),it can be seen that H..~Hoan
`The accuracyof the relationship H.,.~HoaniS dependent on
`the accuracy of the estimates Kk, and K,,, which in turn is
`dependenton the quality of the downlink and uplink channel
`responseestimates, H,,, and Hp As shown above, once the
`transmit/receive chains have been calibrated, a calibrated
`channel responseestimate obtained for one link (e.g., Aan)
`may be used as an estimate of the calibrated channel
`response for the other link (e.g., Hoop)
`is
`[0063] The calibration for TDD MIMO systems
`described in detail in the aforementioned U.S. patent appli-
`cation Ser. No. 60/421,309 and U.S. patent application Ser.
`No. 60/421,462.
`
`2. Spatial Processing
`
`[0064] For a MIMOsystem, data may be transmitted on
`one or more eigenmodes of the MIMO channel. A spatial
`multiplexing mode may be defined to cover data transmis-
`sion on multiple eigenmodes, and a beam-steering mode
`may be defined to cover data transmission on a single
`eigenmode. Both operating modesrequire spatial processing
`at the transmitter and receiver.
`
`‘lhe channel estimation and spatial processing
`[0065]
`techniques described herein may be used for MIMO systems
`with and without OFDM. OFDMeffectively partitions the
`overall system bandwidth into a numberof (N,) orthogonal
`subbands, which are also referred to as frequency bins or
`subchannels. With OFDM,each subbandis associated with
`
`a respective subcarrier upon which data may be modulated.
`For a MIMO system that utilizes OFDM (i.e., a MIMO-
`OFDM system), each eigenmode of each subband may be
`viewed as an independent transmission channel. Forclarity,
`the channel estimation and spatial processing techniques are
`described below for a TDD MIMO-OFDMsystem.Forthis
`system, each subband of the wireless channel may be
`assumed to be reciprocal.
`
`[0066] The correlation between the downlink and uplink
`channel responses may be exploited to simplify the channel
`estimation and spatial processing at the access point and user
`terminal for a TDD system. This simplification is effective
`after calibration has been performed to account for differ-
`ences in the transmit/reccive chains. The calibrated channel
`responses may be expressed as a function of frequency, as
`follows:
`
`Eq (11)
`
`Hoan()=Hin(E)Kap(k), for KEK, and
`Hep(®)=H@Kuk)=(yk)Kap)", for KEK,
`[0067] where K represents a set of all subbands that may
`be used for data transmission(i.e., the “data subbands”). The
`calibration may be performed such that the matrices K.(k)
`and K,,(k) are obtained for each of the data subbands.
`Alternatively, the calibration may be performed for only a
`subset of
`all
`data
`subbands,
`in which
`case
`the
`matrices K.(k) and K,,,(k) for the “uncalibrated” subbands
`may be obtaincd by interpolating the matriccs for the
`“calibrated” subbands, as described in the aforementioned
`U.S. patent application Ser. No. 60/421,462.
`
`[0068] The channel response matrix H(k) for each sub-
`band maybe “diagonalized”to obtain the N, eigenmodesfor
`that subband. This may be achieved by performing either
`singular value decomposition on the channel
`response
`matrix H(k) or eigenvalue decomposition on the correlation
`matrix of H(k), which is R(k)=H"(k)H(k). For clarity, sin-
`gular value decomposition is used for the following descrip-
`tion.
`
`[0069] The singular value decomposition of the calibrated
`uplink channel response matrix, H.,,,(k), may be expressed
`as:
`
`Heup(K)=Uap(K)2(K)Var(kK), for KEK,
`[0070] where U,,,(k) is an (N,»x
`Nap) unitary matrix ofleft
`eigenvectors of“H.Ck);
`[0071]
` (k) is an (N,,xN,,) diagonal matrix of sin-
`gular values of H.,,,(k); and
`
`Eq (12)
`
`[0072] V.,(k) is an (N,,xN,,) unitary matrix of right
`eigenvectors of H.,,,(k).
`
`characterized
`is
`(0073] A unilary matrix
`property M"MaLwhereI is the identity matrix.
`
`by
`
`the
`
`[0074] Correspondingly, the singular value decomposition
`of the calibrated downlink channel response matrix, H.,,(k),
`maybe expressed as:
`
`Hean(Q=V*(KZ(WQUay"(k), for KEK,
`[0075] where the matrices V*,,,(k) and U*,.(k) arc unitary
`matrices of
`left
`and right eigenvectors,
`respectively,
`of H.g,(k). As shown in equations (12) and (13) and based
`on the above description,
`the matrices of left and right
`eigenvectors for one link are the complex conjugate of the
`
`Eq (13)
`
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`US 2004/0087324 Al
`
`May6, 2004
`
`matrices of right and left eigenvectors, respectively, for the
`other
`link. The matrices V.,(k), V*,.(k), Vui'(k), and
`Var(&) are different forms of the matrix V,,(k), and the
`matrices U.,(k), U*,,(k), U,,"(k), and U,."(kx) are also
`different forms of the matrix U,,(x). For simplicity, refer-
`ence to the matrices U,,(k) and V.,(k) in the following
`description mayalso refer to their various other forms. The
`matrices U,,,(k) and V,,,(k) are used by the access point and
`user terminal, respectively, for spatial processing and are
`denoted as such by their subscripts. The eigenvectors are
`also often referred to as “steering” vectors.
`[0076] Singular valuc decomposition is described in fur-
`ther detail by Gilbert Strang in a book entitled “Linear
`Algebra and Its Applications,” Second Edition, Academic
`Press, 1980.
`
`terminal can estimate the calibrated
`[0077] The user
`downlink channel response based on a MIMOpilot sent by
`the access point. The user terminal may then perform
`singular value decomposition for the calibrated downlink
`channel responseestimate FI_.,,(k), for kKEK, to obtain the
`diagonal matrix X(k) and the matrix V*_,(k) of left eigen-
`vectors of Al.,,(k). This singular value decomposition may
`be given as H.4,(kK)=V*,,(K)Z00U,,,'(k), where the hat (“””)
`above each matrix indicates that it is an estimate of the
`actual matrix.
`
`[0078] Similarly, the access point can estimate the cali-
`brated uplink channel response based on a MIMOpilot sent
`by the user terminal. The access point may then perform
`singular value decomposition for the calibrated uplink chan-
`nel response estimate Hau,(K), for kEK,to obtain the diago-
`nal matrix £(k) and the matrix 0,p(k) of left eigenvectorsof
`H,p(k). This eyvalue decomposition may be given as
`Frap(i)=O,(KS),0).
`[0079] However, becauseofthe reciprocal channel and the
`calibration, the singular value decomposition only needsto
`be performed byeither the user terminal or the access point.
`If performed bythe user terminal, then the matrix V,,,(k), for
`kK,are used for spatial processing at the user terminal and
`the matrix UU,,(k), for KEK, may be providedto the access
`pointin either a direct form (ie., by sending entries of the
`matrices U,,(K)) or an indirect form (e.g., via a steered
`reference, as described below).
`[0080] The singular values in each matrix £(k), for kEK,
`may be ordered such that
`the first column contains the
`largest singular value, the second columncontains the next
`largest singular value, and so on (1¢., 06,20,2 ... Oy
`where o;is the cigenvaluc in the i-th column of=(k) after the
`ordering). Whenthe singular values for each matrix X(k) are
`ordered,
`the eigenvectors (or columns) of the associated
`unitary matrices V,,(k) and U,,,(k) for that subbandare also
`ordered correspondingly. A ‘“wideband” eigenmode may be
`defined as the sct of same-order cigenmode ofall subbands
`after
`the ordering (ic.,
`the m-th wideband eigenmode
`includes the m-th eigenmode of all subbands). Each wide-
`band eigenmode is associated with a respective set of
`eigenvectorsforall of the subbands. The principle wideband
`eigenmode is the one associated with the largest singular
`value in each matrix X(k) after the ordering.
`[0081] A. Uplink Spatial Processing
`[0082] The spatial processing by the user terminal for an
`uplink transmission may be expressed as:
`Xp(k)=Kur(k)Vnt(k)Sup(k), for KEK,
`
`Eq (14)
`
`[0083] where x,,,(k) is the transmit vector for the uplink
`for the k-th subband; and
`
`s_.(k) is a “data” vector with up to Ng non-
`[0084]
`zero entries for the modulation symbols to be trans-
`mitted on the Ng eigenmodesof the k-th subband.
`
`[0085] The received uplink transmission at
`point may be expressedas:
`
`the access
`
`Ep lh) =
`
`up
`“upy
`Hy&yp(k) + By
`(kh), for k EK.
`
`Eq (15)
`
`= Hy OKOU, OSph + Ay)
`
`(KV (A)s,,(k) + 2,,(4)
`© Aepl ¥it OSup
`Fup
`
`“ap
`nt
`“up
`= wy woe (KW,EDS9 (K) + (8)
`
`Lup
`=f,> Ws,ph) + By
`
`(h)
`
`[0086] wherer,,,(k) is the received vector for the uplink
`for the k-th subband; and
`
`is additive white Gaussian noise
`[0087] n,.(k)
`(AWGN)for the k-th subband.
`
`[0088] Equation (15) uses the following relationships:
`H,,,OK,,(K)=H..()=H..,(s)
`and H,,,,(k)=U,,()2(6)
`Vue(k).
`
`[0089] A weighted matched filter matrix M,,(k) for the
`uplink transmission from the user terminal may be expressed
`as:
`
`Map(k)=2(QU,)"(h), for KEK,
`
`Eq (16)
`
`[0090] The spatial processing (or matched filtering) at the
`access point for the reccived uplink transmission may be
`expressed as:
`
`al
`pO=>, Owe,
`=F HOH[E,,OY Org(b+ typ(h)}
`forke K,
`
`= Syy(k) + H,,(k)
`
`Eq
`
`(17
`qn
`
`where§,,,(k) is an estimate of the data vectors,,.(k)8up
`[0091]
`
`transmitted by the user terminalon the uplink, and f,,,(k) is
`the post-processed noise.
`
`[0092] B. Downlink Spatial Processing
`
`[0093] The spatial processing by the access point for a
`downlink transmission may be expressed as:
`
`Xanlk)“Kap(U*ap(K)san(k), for KEK,
`
`Eq (18)
`
`[0094] where x,,(k) is the transmit vector and s,_(k) is the
`data vector for the downlink.
`
`Page 12 of 21
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`US 2004/0087324 Al
`
`May6, 2004
`
`[0095] The received downlink transmission at
`terminal may be expressed as:
`
`the user
`
`channel to user terminal 150x. Unit 310 perform