US 20040087324A1
`
`(19) United States
`(12) Patent Application Publication (10) Pub. N0.: US 2004/0087324 A1
`(43) Pub. Date: May 6, 2004
`
`Ketchum et al.
`
`(54) CHANNEL ESTIMATION AND SPATIAL
`PROCESSING FOR TDD MlMO SYSTEMS
`
`(76)
`
`Inventors: John W. Ketchum, Harvard, MA (US);
`Mark S. Wallace, Bedford, MA (US);
`J. Rodney Walton, Carlisle, MA (US);
`Steven J. Howard, Ashland, MA (US)
`
`Correspondence Address:
`Qualcomm Incorporated
`Patents Department
`5775 Morehouse Drive
`
`San Diego, CA 92121-1714 (US)
`
`(21) Appl. N0.:
`
`10/693,171
`
`(22)
`
`Filed:
`
`Oct. 23, 2003
`
`Related US. Application Data
`
`(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.
`
`Publication Classification
`
`Int. Cl.7 ............................... H04B 7/00; H04Q 7/20
`(51)
`(52) use. ......................................... 455/513;455/67.11
`
`(57)
`
`ABSTRACT
`
`Channel estimation and spatial processing for a TDD MIMO
`system. Calibration may be performed to account for dif-
`ferences in the responses of transmit/receive chains at the
`access point and user terminal. During normal operation, a
`MIMO pilot is transmitted on a first link and used to derive
`an estimate of the first
`link channel response, which is
`decomposed to obtain a diagonal matrix of singular values
`and a first unitary matrix containing both left eigenvectors of
`the first link and right eigenvectors of a second link. A
`steered reference is transmitted on the second link using the
`eigenvectors 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.
`
`I 10
`V“
`
`Agggss Pain;
`
`114
`
`Pilot
`
`
`
`120
`
`Controller
`
`
`
`
`
`RX
`Processor
`
`RX Spatial
`Processor
`
`
`
`
`
`TX Data
`TX Spatial
`Processor I Processor
`
`
`
`
`K"
`
`
`User Terminal
`
`170
`
`RX Data
`Processor
`
`180
`
` 190
`
`D
`TX Spatial
`I'l-
`
`Page 1 of21
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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 0f 6
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`US 2004/0087324 A1
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`Patent Application Publication
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`Patent Application Publication
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`May 6, 2004 Sheet 5 0f 6
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`US 2004/0087324 A1
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`Patent Application Publication
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`May 6, 2004 Sheet 6 0f 6
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`US 2004/0087324 A1
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`Acc 55 Point
`
`U_s_rT_mm
`
` Estimate calibrated downlink
`
`channel response based on
`the downlink MIMO pilot
`
`
`
`
`
`
`
`
`526
`
`Decompose the calibrated
`downlink channel response
`
`estimate Hnto obtain diagonal
`matrix 2 and unitary matrix V
`
`
`530
`
`
`
`
`Transmit a steered reference
`on the calibrated uplink
`
`
`channel using the matrix V
`
`542
`
`Receive and spatially process
`received symbols with matrix v:
`
`550
`
`
`Spatially process symbols
`with matrix y_m and transmit
`
`
`to the access point
`
`
`
`532
`
`
`Receive and process
`the uplink steered reference
`
`
`to obtain diagonal matrix 2
`
`
`and unitary matrix Up
`
`
`540
`
`
`Spatially process symbols
`with matrix Upand transmit
`
`
`to the user terminal
`
`
`552
`
`Receive and spatially process”
`received symbols with matrix U’;
`
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`US 2004/0087324 A1
`
`May 6, 2004
`
`CHANNEL ESTIMATION AND SPATIAL
`PROCESSING FOR TDD MIMO SYSTEMS
`
`techniques to efficiently perform channel estimation and
`spatial processing in a TDD MIMO system.
`
`CLAIM OF PRIORITY UNDER 35 U.S.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 US. Application Serial No. 60/421,462,
`entitled “Channel Calibration for a Time Division Duplexed
`Communication System,” and provisional US. 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 by ref-
`erence.
`
`BACKGROUND
`
`[0002]
`
`1.rfie1d
`
`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) multiple-input multiple-output
`(MIMO) communication systems.
`
`[0004]
`
`2. Background
`
`[0005] A MIMO system employs multiple (NT) transmit
`antennas and multiple (NR) receive antennas for data trans-
`mission. A MIMO channel formed by the NT transmit and
`NR receive antennas may be decomposed into NS indepen-
`dent channels, with Nsémin{NT, NR}. Each of the NS
`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 (e.g., increased transmission capac-
`ity) if the additional dimensionalities created by the multiple
`transmit and receive antennas are utilized.
`
`In order to transmit data on one or more of the NS
`[0006]
`eigemnodes 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 NT trans-
`mit antennas interfere with each other at the receive anten—
`nas. The spatial processing attempts to separate out the data
`streams at
`the receiver so that they can be individually
`recovered.
`
`[0007] To perform spatial processing, an accurate estimate
`of the channel response between the transmitter and receiver
`is typically required. For a TDD system, the downlink (i.e.,
`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 assumed to be reciprocal of one
`another, after calibration has been performed (as described
`below) to account for differences in the transmit and receive
`chains at the access point and user terminal. That is, if E
`represents the channel response matrix from antenna array A
`to antenna array B, then a reciprocal channel implies that the
`coupling from array B to array A is given by HT, where MT
`denotes the transpose of M.
`
`[0008] The channel estimation and spatial processing for a
`MIMO system typically consume a large portion of the
`system resources. There is therefore a need in the art for
`
`SUMMARY
`
`[0009] Techniques are provided herein to perform channel
`estimation and spatial processing in an efficient manner in a
`TDD MIMO system. For 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 performed to
`ensure that the “calibrated” channel, with the correction
`factors applied, is reciprocal. In this way, a more accurate
`estimate of a second link may be obtained based on an
`estimate derived for a first link.
`
`[0010] During normal operation, a MIMO pilot 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
`may then be decomposed (e.g., by the user terminal, using
`singular value decomposition) to obtain a diagonal matrix of
`singular values and a 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
`second link using the eigenvectors in the first unitary matrix.
`A steered reference (or steered pilot) 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 second link and the right eigenvectors of the 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 transmission to be sent on the
`first link.
`
`[0012] Various aspects and embodiments of the invention
`are described in further detail below.
`
`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:
`
`[0014] FIG. 1 is a block diagram of an access point and a
`user terminal in a TDD MIMO system, in accordance with
`one embodiment of the invention;
`
`[0015] FIG. 2A shows a block diagram of the transmit and
`receive chains at
`the access point and user terminal,
`in
`accordance with one embodiment of the invention;
`
`[0016] FIG. 23 shows application of correction matrices
`to account for differences in the transmit/receive chains at
`the access point and user terminal, in accordance with one
`embodiment of the invention;
`
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`US 2004/0087324 A1
`
`May 6, 2004
`
`[0017] FIG. 3 shows the 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 shows the spatial processing for the down—
`link and uplink for a beam-steering 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
`
`[0020] FIG. 1 is a block diagram of an embodiment of an
`access point 110 and a user terminal 150 in a TDD MIMO
`system 100. Access point 110 is equipped with NaF transmit/
`receive antennas for data transmission/reception, and user
`terminal 150 is equipped with Nut transmit/receive antennas.
`
`[0021] On the downlink, at access point 110, a transmit
`(TX) data processor 114 receives tralIic data (i.e., 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 performs spatial processing to provide Nup streams
`of transmit symbols, one stream for each antenna. TX spatial
`processor 120 also multiplexes in pilot symbols as appro—
`priate (e.g., for calibration and normal operation).
`
`[0022] Each modulator (MOD) 122 (which includes a
`transmit chain) receives and processes a respective transmit
`symbol stream to provide a corresponding downlink modu-
`lated signal. The N810 downlink modulated signals from
`modulators 122a through 12201) are then transmitted from
`
`Nap antennas 1240 through 124ap, respectively.
`[0023] At user terminal 150, Nm antennas 152a through
`152ut receive the transmitted downlink modulated signals,
`and each antenna provides a received 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. Areceive (RX) spatial processor 160 then
`performs spatial processing on the received symbols from all
`demodulators 15411 through 154141 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 recovered traffic data, signaling,
`and so on, which may be 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-
`tiplexes in pilot symbols as appropriate (e.g., for calibration
`and normal operation). The pilot and transmit symbols from
`TX spatial processor 190 are further processed by modula-
`tors 154a through 154141 to generate Nut uplink modulated
`signals, which are then transmitted via antennas 152a
`through 152m to the access point.
`
`[0025] At access point 110, the uplink modulated signals
`are received by antennas 124a through 124ap, demodulated
`by demodulators 122a through 122ap, 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 processing units at the access point and user termi-
`nal, respectively. Memory units 132 and 182 store data and
`program codes used by controllers 130 and 180, respec-
`tively.
`
`1. Calibration
`
`[0027] For a 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 may be assumed to be reciprocal (i.e., transpose) of
`each other. However, the responses of the transmit/receive
`chains at the access point are typically not equal to the
`responses of 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 shows a block diagram of the transmit and
`receive chains at access point 110 and user terminal 150, in
`accordance with one embodiment of the invention. For the
`
`downlink, at access point 110, symbols (denoted by a
`“transmit” vector xdn) are processed by a transmit chain 214
`and transmitted from N8p antennas 124 over the MIMO
`channel. At user terminal 150,
`the downlink signals are
`received by Nut antennas 152 and processed by a receive
`chain 254 to provide received symbols (denoted by a
`“receive” vector rd“). For the uplink, at user terminal 150,
`symbols (denoted by a transmit vector xup) are processed by
`a transmit chain 264 and transmitted from Nut antennas 152
`over the MIMO channel. At access point 110, the uplink
`signals are received by N8p antennas 124 and processed by
`a receive chain 224 to provide received symbols (denoted by
`a receive vector rup).
`[0029] For the downlink, the receive vector rdn at the user
`terminal (in the absence of noise) may be expressed as:
`Lm=3uiflap§mp
`Eq (1)
`
`[0030] where Eu” is the transmit vector with Nap entries for
`the downlink;
`
`[0031]
`
`rdn is the receive vector with Nut entries;
`
`lap is an N ap><N 8p diagonal matrix with entries
`[0032]
`for the complex gains associated with the transmit
`chain for the N813 antennas at the access point;
`
`[0033] Rut is an Nut><Nut diagonal matrix with entries
`for the complex gains associated with the receive
`nt
`chain for the N antennas at the user terminal; and
`
`[0034] E is an NulxNap channel response matrix for
`the downlink.
`
`[0035] The responses of the transmit/receive chains and
`the MIMO channel are typically a function of frequency. For
`simplicity, a flat-fading channel (i.e., with a flat frequency
`response) is assumed for the following derivation.
`
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`US 2004/0087324 A1
`
`May 6, 2004
`
`[0036] For the uplink, the receive vector rup at the access
`point (in the absence of noise) may be expressed as:
`Lup=Bap_HTIup_iup,
`
`Eq (2)
`
`[0037] where xup is the transmit vector with Nut entries for
`the uplink;
`
`is the receive vector with NaF entries;
`g...
`[0038]
`Int is an Nut><Nut diagonal matrix with entries
`[0039]
`for the complex gains associated with the transmit
`chain for the Nut antennas at the user terminal;
`
`gap is an Napr8p diagonal matrix with entries
`[0040]
`for the complex gains associated with the receive
`chain for the Nap antennas at the access point; and
`[0041] HT is an Naprut channel response matrix for
`the uplink.
`[0042] From equations (1) and (2), the “effective” down-
`link and uplink channel responses, fldn and EDP, which
`include the responses of the applicable transmit and receive
`chains, may be expressed as:
`
`Eq (3)
`Emanuel, and nup=aap_HTIm.
`[0043] As shown in 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
`.
`V
`.
`,
`T,
`, T
`responses
`are
`not
`reciprocal
`of
`one
`another, 1.e., l_{u Hlapyéfiapfl int) .
`[0044] Combining the two equations in equation set (3),
`the following relationship may be obtained:
`Eq (4)
`up
`H=RmTlHdanloil=fRapilH T1151)T=T1‘FIHITTqu71-
`[0045] Rearranging equation
`(4),
`the
`following
`is
`obtained:
`
`Llup=_mBuFlfldnlap’lflaffluflflanfim
`[0046]
`or
`nup=(xu(1nd..£ap)T,
`
`Eq (5)
`
`[0047] where Elfin—13m and Eap=lap'lgap. Because
`Tm, 3“,, LI» and Rap are diagonal matrices, g1, and E” are
`also diagonal matrices. Equation (5) may also be expressed
`as:
`
`Llup_ FflmLfiQT-
`
`Eq (6)
`
`[0048] The matrices £13 and gut may be viewed as includ-
`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
`other link, as shown in equation (5).
`
`[0049] Calibration may be performed to determine the
`matrices K31) and Km. Typically, the true channel response fl
`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,
`fldn
`and flup, may be estimated based on MIMO pilots sent on
`the downlink and uplink, respectively. The generation and
`use of MIMO pilot are described in detail in the aforemen-
`tioned US. patent application Ser. No. 60/421,309.
`
`[0050] Estimates of the matrices E813 and Em, which are
`referred to as correction matrices, ESP and Km, may be
`derived based on the downlink and uplink channel response
`estimates, fldn and amp, in various manners, including by a
`matrix—ratio computation and a minimum mean square error
`
`(MMSE) computation. For the matrix-ratio computation, an
`(meNap) matrix Q is first computed as a ratio of the uplink
`and downlink channel response estimates, as follows:
`
`AT
`
`
`Eq (7)
`
`[0051] where the ratio is taken element-by-element. Each
`element of Q may thus be computed as:
`
`
`_ hut? M f
`._
`,
`. _
`CLj—A
`, orz—ll...1\1u,}a.nd J—{1...Nap},
`hdn [,1
`
`[0052] where limp 1-)]. and lid" 1-)]. are the (i,j)-th (row, column)
`_up
`element of fl T and Ed”, respectively, and cid- is the (i,j)-th
`element of Q.
`
`[0053] A correction vector for the access point, gm, which
`includes only the NSP diagonal elements of gap, may be
`defined to be equal to the mean of the normalized rows of Q.
`Each row of Q, 91-,
`is first normalized by dividing each
`element of the row with the first element of the row to obtain
`
`.
`.
`a corresponding normalized row, Q. Thus, if ci(k)=[ci_1 .
`C
`LNap] is the i-th row of Q, then the normalized row i may
`be expressed as:
`
`éi(k:)=[ci,1(k)/Ci,1(k) -
`100]-
`
`-
`
`- Ci,j(k)/Ci,1(k) -
`
`-
`
`- Ci,N,p(k:)/Ci,
`
`[0054] The correction vector kap(k) is then set equal to the
`me an of the Nm normalized rows of Q and may be expressed
`as:
`
`A
`
`
`1 Nu,
`
`Hg (3)
`
`[0055] Because of the normalization, the first element of
`kap(k) is unity.
`
`[0056] A correction vector f_<m(k) for the user terminal,
`kut(k), which includes only the Nm diagonal elements of
`5mm), may be defined to be equal to the mean of the
`inverses of the normalized columns of Q. Each column of Q,
`2]., is first normalized by scaling each element in the column
`with the j-th element of the vector tsp, which is denoted as
`Kapjfl-
`to obtain a corresponding normalized column, cj.
`Thus, if gj(k)=[cqyj .
`.
`. CNN]? is the j—th column of Q, then
`the normalized column c2]. may be expressed as:
`
`“i=[CLj/Kam -
`
`-
`
`- Cij/Kapa'j -
`
`-
`
`- Cij/Kap.j.j]T-
`
`[0057] The correction vector kap is then set equal to the
`me an of the inverses of the Nap normalized columns of Q and
`may be expressed as:
`
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`

`US 2004/0087324 A1
`
`May 6, 2004
`
`Nap
`
`Eq (9,)
`
`[0058] where the inversion of the normalized columns,
`cj(k), is performed element-wise. The calibration provides
`the correction vectors,
`[5“, and km or the corresponding
`correction matrices K4, andpKm, for the access point and user
`terminal, respectively.
`
`[0059] The MMSE computation for the correction matri-
`ces K813 and Km is described in detail in aforementioned U.S.
`patent application Ser. No. 60/421,462.
`
`[0060] FIG. 2B illustrates the application of the correction
`matrices to account for differences in the transmit/receive
`chains at the access point and user terminal, in accordance
`with one embodiment of the invention. On the downlink, the
`transmit vector xdn is first multiplied with the matrix KAI, 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 xup
`is first multiplied with the matrix Km by a unit 262. Again,
`the subsequent processing by transmit 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:
`
`_Cd.n=_dnKap and Hp=HupKut>
`
`F11 (10)
`
`[0062] where fled: and chp are estimates of the “true”
`calibrated channel response expressions in equation (6)
`From equations (6) and (10), it can be seen that pr~Uflcdn.
`The accuracy of the relationship_HmpzflcdnT is dependent on
`the accuracy of the estimates K; and Km, whichin turn is
`dependent on the quality of the downlink and uplink channel
`response estimates, Hdn and EDP. As shown above, once the
`transmit/receive chains have been calibrated, a calibrated
`channel response estimate obtained for one link (e.g., _cdn)
`may be used as an estimate of the calibrated channel
`response for the other link (e.g., chp)
`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 MIMO system, 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 modes require spatial processing
`at the transmitter and receiver.
`
`[0065] The channel estimation and spatial processing
`techniques described herein may be used for MIMO systems
`with and without OFDM. OFDM effectively partitions the
`overall system bandwidth into a number of (NF) orthogonal
`subbands, which are also referred to as frequency bins or
`subchannels. With OFDM, each subband is 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. For clarity,
`the channel estimation and spatial processing techniques are
`described below for a TDD MIMO-OFDM system. For this
`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/receive chains. The calibrated channel
`responses may be expressed as a function of frequency, as
`follows:
`
`Eq (11)
`
`Hcdn(k)=fldn(k)Kap(k) for kEK and
`Eup(k)=flup(k)Km(k)~tH_,;I;C.,m(k)poof 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 K2p(k)
`and Kmai) 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
`_ap
`matrices K (k) and Kut(k) for the “uncalibrated” subbands
`may be obtained by interpolating the matrices 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 may be “diagonalized” to obtain the NS eigenmodes for
`that subband. This may be achieved by performing either
`singular value decomposition on the channel
`response
`matrix fl(k) or eigenvalue decomposition on the correlation
`matrix of H(k), which is B(k)=HH(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, _Cnp(k), may be expressed
`as:
`
`Emp(K)=Qap(k)é(k)XmH(KL for EL
`
`liq (12)
`
`[0070] where gap(k) is an (Napr
`eigenvectors of chp(k);
`
`8p) unitary matrix of left
`
`[0071] §(k) is an (Nprul) diagonal matrix of sin-
`_cup
`gular values ofH (k), and
`
`[0072] Xut(k)is an (Nuthut) unitary matrix of right
`eigenvectors of chp(k).
`
`characterized
`is
`[0073] A unitary matrix
`property MHM=I, where I is the identity matrix
`
`by
`
`the
`
`[0074] Correspondingly, the singular value decomposition
`of the calibrated downlink channel response matrix, Hcdnfli),
`may be expressed as:
`
`flcdn(k)=¥*m(k)§(k)UapT(k) for kEK
`
`Eq (13)
`
`[0075] where the matrices yank) and U*12(k) are unitary
`matrices of
`left
`and right eigenvectors,
`respectively,
`_cdn
`of H (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
`
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`
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`

`US 2004/0087324 A1
`
`May 6, 2004
`
`matrices of right and left eigenvectors, respectVivelTy, for the
`_ut
`thher
`link. The matrices V (k), V*m(k),V_utT(k), and
`_utH(k) are different forms of the matrix Vut(k), and the
`matrices U p(k), U*ap(k),U_apT(k), and gapH(k) are also
`different forms of the matrix Q,1D(k). For simplicity, refer—
`ence to the matrices U3P(k) and Vut(k) in the following
`description may also refer to their various other forms. The
`matrices U_ap(k) and Vut(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 value 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 MIMO pilot sent by
`the access point. The user terminal may then perform
`singular value decomposition for the calibrated downlink
`channel response estimate HC1D(k), for kEK, to obtain the
`diagonal matrix :(k) and the matrix V*m(k) of left eigen-
`vectors of Hcdn(k). This singular value—decomposition may
`be given as 311k) =y*.,.(k121k10r1k1, where the hat (W)
`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 MIMO pilot sent
`by the user terminal. The access point may then perform
`singular value decomposition for the calibrated uplink chan—
`nel response estimate Hup,(k) for kEK, to obtain the diago-
`nal matrix 2(k) and the matrix _ap(k) of left eigenvectors of
`_cup(k) This singular value decomposition may be given as
`sup1k1=U1k121kLmH1k1
`[0079] However, because of the reciprocal channel and the
`calibration, the singular value decomposition only needs to
`be performed by either the user terminal or the access point.
`If performed by the user terminal, then the matrix yut(k), for
`kEK, are used for spatial processing at the user terminal and
`the matrix gap(k), for kEK, may be provided to the access
`point in either a direct form (i.e., by sending entries of the
`matrices Q,p(k)) or an indirect form (e.g., Via a steered
`reference, as described below).
`[0080] The singular values in each matrix 2(k), for kEK,
`may be ordered such that
`the first column contains the
`largest singular value, the second column contains the next
`largest singular value, and so on (i. e. ,olio2_ .
`.
`. 0N5,
`where cr- is the eigenvalue1n the1--th column of 2(k) after thsc
`ordering). When the singular values for each matrix 2(k) are
`ordered,
`the eigenvectors (or columns) of the associated
`unitary matrices Vut(k) and U][)(k) for that subband are also
`ordered correspondingly. A‘‘wideband” eigenmode may be
`defined as the set of same-order eigenmode of all subbands
`after
`the ordering (i.e.,
`the m-th wideband eigenmode
`includes the m-th eigenmode of all subbands). Each wide-
`band eigenmode is associated with a respective set of
`eigenvectors for all of the subbands. The principle wideband
`eigenmode is the one associated with the largest singular
`value in each matrix 2(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:
`XLup(k)-_Km(k)Vm(k)§up(k) for kEK
`
`F11 (14)
`
`[0083] where xup(k) is the transmit vector for the uplink
`for the k-th subband; and
`
`_up(k) is a “data” vector with 11p to NS non-
`[0084]
`zero entries for the modulation symbols to be trans—
`mitted on the Ns eigenmodes of the k-th subband.
`
`[0085] The received uplink transmission at
`point may be expressed as:
`
`the access
`
`rm, 1k): W(k)x(k) +n(,k) for/(EX.
`
`Eq115)
`
`= 3,,1k13,1k13,,1k1s,,1k1 + 3,,1k1
`
`,3,:,1k1,V1k1§,,1k1 + 3,,1k1
`
`= 3,11121k13Z1k13,,1k15,,1/<1 + 3,111
`
`: 3,,(k;1Z 1/11.:th + 3mm
`
`[0086] wherer_np(k)1s the received vector for the uplink
`for the k-th subband; and
`
`is additive white Gaussian noise
`_up(k)
`[0087]
`(AWGN) for the k—th subband.
`
`[0088] Equation (15) uses the following relationships:
`_up(k)Kup(k)=-_cup(k)~_cup(k)
`and Heup(k)=flap(k)§(k)
`VutH(k)
`
`[0089] A weighted matched filter matrix Map(k) for the
`uplink transmission from the user terminal may be expressed
`as:
`
`Map(k)=2’1 (k)gapH(k)> fOI kEK-
`
`E61 (15)
`
`[0090] The spatial processing (or matched filtering) at the
`access point for the received uplink transmission may be
`expressed as:
`
`3
`
`,,1/c1= Z 11031113,,1/(1
`
`Eq (17)
`
`2: (log”(k1(U7p(k1Z1/c1§"p(k)+nup(k1)
`for/(GK,
`3—.:W(k1 + nup(k)
`
`wheresJP
`[0091]
`(k) is an estimate of the data vectors_np(k)
`
`transmitted by the user terminal on the uplink, and gup(k)1s
`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:
`
`3m0<>=Kap(k)Q*ap(k)§dn(k), for kEK,
`
`Eq (13)
`
`[0094] where xdn(k) is the transmit vector and sdn(k) is the
`data vector