(12) United States Patent
`Krishnan et al.
`
`US007039001 B2
`(10) Patent No.:
`US 7,039,001 B2
`(45) Date of Patent:
`May 2, 2006
`
`(54) CHANNEL ESTIMATION FOR OFDM
`COMMUNICATION SYSTEMS
`
`(56)
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`(75) Inventors: Ranganathan Krishnan, San Diego,
`CA (US); Tamer Kadous, San Diego,
`CA (US)
`
`rsr rr
`(73) Assignee: gym, Incorporated, San Diego,
`
`(*) Notice:
`
`-
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 48 days.
`
`(21) Appl. No.: 10/340,130
`(22) Filed:
`Jan. 10, 2003
`(65)
`Prior Publication Data
`
`US 2004/0203442 A1 Oct. 14, 2004
`
`Related U.S. Application Data
`(60) Provisional application No. 60/422,362, filed on Oct. 29.
`2002, and provisional application No. 60/422.368, filed on
`Oct. 29, 2002.
`(51) Int. Cl.
`H04 II/00
`
`(2006.01)
`
`(52) U.S. Cl. ....................... 370/203; 370/210; 370/207;
`370/208: 370/342; 370/343; 370/335; 370/480;
`455/63. 1; 455/450; 455/67.11; 455/67.16;
`455/464; 375/340; 375/342; 375/346; 375/347
`(58) Field of Classification Search .............. 455/67.11,
`455/67.16,703, 464, 450, 63.1375/340,
`375/346, 347, 260: 370/203, 210, 342, 347,
`370/348, 480
`See application file for complete search history.
`
`6,473,393 B1 * 10/2002 Ariyavisitakul et al. .... 370/203
`6,477,210 B1 * 1 1/2002 Chuang et al. ............. 375/340
`6,545,997 B1 * 4/2003 Bohnke et al. ............. 370/347
`6,549,561 B1 * 4/2003 Crawford .................... 375/137
`6,563,858 B1 * 5/2003 Fakatselis et al. .......... 375,148
`6,567,374 B1 * 5/2003 Bohnke et al. ............. 370/203
`6,597,745 B1 * 7/2003 Dowling ...........
`... 375,296
`6,603,801 B1 * 8/2003 Andren et al. .............. 375/147
`6,618,454 B1 * 9/2003 Agrawal et al. ............ 375/347
`6,633,616 B1 * 10/2003 Crawford .................... 375/326
`6,636,568 B1 * 10/2003 Kadous
`... 375,225
`6,654,429 B1 * 1 1/2003 Li .............................. 375.316
`ck
`12/2003 Sindhushayana et al. ... 375/144
`6,661,832 B1
`ck
`* cited by examiner
`Primary Examiner Marceau Milord
`(74) Attorney, Agent, or Firm—Sandip (Micky) S. Minhas:
`Philip Wadsworth
`ABSTRACT
`(57)
`Techniques to estimate the frequency response of a wireless
`channel in an OFDM system. In one method, an initial
`estimate of the frequency response of the wireless channel is
`obtained for a first group of Subbands based on a pilot
`transmission received via the Subbands in the first group. An
`estimate of the impulse response of the wireless channel is
`then derived based on the initial frequency response esti
`mate. An enhanced estimate of the frequency response of the
`wireless channel is then derived for a second group of
`subbands based on the impulse response estimate. The first
`and second groups may each include all or only a Subset of
`the usable subbands. Subband multiplexing may be used to
`allow simultaneous pilot transmissions by multiple termi
`nals on their associated groups of Subbands.
`27 Claims, 5 Drawing Sheets
`
`
`
`600
`
`Obtain initial frequency response
`estimate A, for the wireless
`channel based on received pilot
`
`62
`
`Form DFT matrix W, for the
`subbands used for the received pilot
`
`614
`
`Derive east square impulse
`Ris
`response estimateh for the
`wireless channel based on the initial
`channel frequency response
`and the matrixW,
`estimate
`
`Form DFT matrix W.
`for the subbands to be
`used for data transmission
`
`Derive enhanced frequency
`response estimate
`for the
`wireless channel based on the least
`square channel impulse response
`estimate and the matrix W.
`
`616
`
`68
`
`620
`
`1
`
`GM 1025
`
`

`

`U.S. Patent
`
`May 2, 2006
`
`Sheet 1 of 5
`
`US 7,039,001 B2
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`
`
`i spueqans
`
`2
`
`

`

`U.S. Patent
`
`May 2, 2006
`
`Sheet 2 of 5
`
`US 7,039,001 B2
`
`-(-1-0 -(-N-0 --->
`
`h N
`
`(NX1)
`
`(NXN)
`FIG. 2A
`
`(Nx1)
`
`W
`<-N->
`
`
`
`a-N-D
`
`M
`
`W.
`
`N
`
`H ls
`
`O
`
`f S L
`
`(MX 1)
`
`(MXL)
`
`(LX 1)
`
`3
`
`

`

`U.S. Patent
`
`May 2, 2006
`
`Sheet 3 of 5
`
`US 7,039,001 B2
`
`--N-D-
`
`S . {
`
`N
`
`FIG. 4A
`
`-(-1-D
`
`-(- - -D -(-1->
`
`
`
`W.
`
`M o
`
`(Mx1)
`
`(MXL)
`
`(LX 1)
`
`4
`
`

`

`U.S. Patent
`
`May 2, 2006
`
`Sheet 4 of 5
`
`US 7,039,001 B2
`
`600
`
`Obtain initial frequency response
`estimate A, for the wireless
`channel based on received pilot
`
`612
`
`Form DFT matrix W, for the
`Subbands used for the received pilot
`
`614
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Derive least Square impulse
`response estimateh for the
`wireless channel based On the initial 616
`channel frequency response
`estimate A, and the matrix W,
`
`Form DFT matrix W.
`for the Subbands to be
`used for data transmission
`
`Derive enhanced frequency
`response estimate H for the
`Wireless channel based On the least
`Square channel impulse response
`estimate hand the matrix W.
`
`618
`
`620
`
`FIG. 6
`
`5
`
`

`

`U.S. Patent
`U.S. Patent
`
`May2, 2006
`
`Sheet 5 of 5
`
`eyedXY
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`eyedXL
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`JOSS@001
`
`US 7,039,001 B2
`US 7,039,001 B2
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`

`

`1.
`CHANNEL ESTMLATION FOR OFDM
`COMMUNICATION SYSTEMS
`
`US 7,039,001 B2
`
`RELATED APPLICATIONS
`This application is related to both U.S. Provisional Patent
`Application Ser. No. 60/422,362, filed Oct. 29, 2002,
`entitled “Channel Estimation For OFDM Communication
`Systems.” and to U.S. Provisional Patent Application Ser.
`No. 60/422.368, entitled “Uplink Pilot And Signaling Trans
`mission. In Wireless Communication Systems, filed on Oct.
`29, 2002, which are incorporated herein by reference in its
`entirety for all purposes.
`This application is related to U.S. patent application Ser.
`No. 60/422.368, entitled “Uplink Pilot And Signaling Trans
`mission. In Wireless Communication Systems, filed on Oct.
`29, 2002, which is incorporated herein by reference in its
`entirety for all purposes.
`
`10
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`15
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`30
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`35
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`40
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`45
`
`BACKGROUND
`I. Field of the Invention
`The present invention relates generally to data
`communication, and more specifically to techniques for
`estimating the response of a wireless channel in a commu
`nication system with multiple Subbands, such as an orthogo
`25
`nal frequency division multiplexing (OFDM) system.
`II. Background
`Wireless communication systems are widely deployed to
`provide various types of communication Such as voice,
`packet data, and so on. These systems may be multiple
`access systems capable of Supporting communication with
`multiple users by sharing the available system resources.
`Examples of Such multiple-access systems include code
`division multiple access (CDMA) systems, time division
`multiple access (TDMA) systems, and orthogonal frequency
`division multiple access (OFDMA) systems.
`OFDM effectively partitions the overall system band
`width into a number of (N) orthogonal subbands. These
`Subbands are also referred to as tones, frequency bins, and
`frequency subchannels. With OFDM, each subband is asso
`ciated with a respective subcarrier upon which data may be
`modulated. Each subband may thus be viewed as an inde
`pendent transmission channel that may be used to transmit
`data.
`In a wireless communication system, an RF modulated
`signal from a transmitter may reach a receiver via a number
`of propagation paths. For an OFDM system, the N subbands
`may experience different effective channels due to different
`effects of fading and multipath and may consequently be
`associated with different complex channel gains.
`An accurate estimate of the response of the wireless
`channel between the transmitter and the receiver is normally
`needed in order to effectively transmit data on the available
`subbands. Channel estimation is typically performed by
`sending a pilot from the transmitter and measuring the pilot
`at the receiver. Since the pilot is made up of symbols that are
`known a priori by the receiver, the channel response can be
`estimated as the ratio of the received pilot symbol over the
`transmitted pilot symbol for each subband used for pilot
`transmission.
`Pilot transmission represents overhead in the OFDM
`system. Thus, it is desirable to minimize pilot transmission
`to the extent possible. However, because of noise and other
`artifacts in the wireless channel, a Sufficient amount of pilot
`needs to be transmitted in order for the receiver to obtain a
`reasonably accurate estimate of the channel response.
`
`50
`
`55
`
`60
`
`65
`
`2
`Moreover, the pilot transmissions need to be repeated to
`account for variations in the channel over time due to fading
`and changes in the multipath constituents. Consequently,
`channel estimation for an OFDM system normally consumes
`a noticeable portion of the system resources.
`In the downlink of a wireless communication system, a
`single pilot transmission from an access point (or a base
`station) can be used by a number of terminals to estimate the
`response of the distinct downlink channels from the access
`point to each of the terminals. However, in the uplink, each
`terminal needs to send a pilot transmission separately in
`order to enable the access point to estimate the uplink
`channel from the terminal to the access point. Consequently,
`the overhead due to pilot transmissions is exacerbated due to
`uplink pilot transmissions.
`There is therefore a need in the art for techniques to more
`efficiently estimate the channel response in an OFDM
`system, particularly in the uplink.
`SUMMARY
`Techniques are provided herein to estimate the frequency
`response of a wireless channel in a communication system
`with multiple subbands (e.g., an OFDM system). It is
`recognized that the impulse response of the wireless channel
`can be characterized by L. taps, where L is typically much
`less than the N total subbands in the OFDM system. Because
`only L. taps is needed for the channel impulse response, the
`frequency response of the wireless channel lies in a subspace
`of dimension L (instead of N) and may be fully characterized
`based on the channel gains for as few as L appropriately
`selected subbands (instead of all N subbands). Moreover,
`even when more than L channel gains are available, the
`property described above may be used to obtain an enhanced
`estimate of the frequency response of the wireless channel
`by Suppressing the noise components outside this subspace,
`as described below.
`In one embodiment, a method is provided for estimating
`the frequency response of the wireless channel (e.g., in the
`OFDM system). In accordance with the method, an initial
`estimate of the frequency response of the wireless channel is
`obtained for a first group of Subbands based on a pilot
`transmission received via the Subbands in the first group.
`The first group may include all or only a subset of the
`Subbands usable for data transmission. An estimate of the
`impulse response of the wireless channel is then derived
`based on the initial frequency response estimate and a first
`discrete Fourier transform (DFT) matrix for the subbands in
`the first group. The impulse response estimate may be
`derived as a least square estimate, as described below. An
`enhanced estimate of the frequency response of the wireless
`channel is then derived for a second group of Subbands
`based on the impulse response estimate and a second DFT
`matrix for the Subbands in the second group. The second
`group may include all or a Subset of the usable Subbands, and
`would include at least one additional subband not included
`in the first group if this first group does not include all usable
`subbands.
`Various aspects and embodiments of the invention are
`described in further detail below.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`The features, nature, and advantages of the present inven
`tion will become more apparent from the detailed descrip
`tion set forth below when taken in conjunction with the
`drawings in which like reference characters identify corre
`spondingly throughout and wherein:
`
`7
`
`

`

`US 7,039,001 B2
`
`3
`FIG. 1 shows an OFDM Subband structure;
`FIG. 2A shows the relationship between the frequency
`response and the impulse response of a wireless channel;
`FIG. 2B Shows a DFT matrix for the N total Subbands in
`the OFDM system:
`FIG. 3A shows the relationship between the DFT matrices
`for the Musable Subbands and the N total Subbands in the
`OFDM system:
`FIG. 3B shows derivation of an enhanced frequency
`response estimate based on an impulse response estimate
`derived from pilot transmission on the Musable subbands:
`FIG. 4A shows the relationship between the DFT matrices
`for S assigned subbands and the N total Subbands;
`FIG. 4B shows derivation of the enhanced frequency
`response estimate based on an impulse response estimate
`derived from pilot transmission on the S assigned Subband;
`FIG. 5 shows an OFDM subband structure that supports
`Subband multiplexing;
`FIG. 6 shows a process for estimating the frequency
`response of the wireless channel; and
`FIG. 7 shows a block diagram of an access point and a
`terminal.
`
`10
`
`15
`
`25
`
`30
`
`4
`corresponding OFDM symbol, which is then transmitted
`over a wireless channel.
`The length of the cyclic prefix (i.e., the amount to repeat)
`for each OFDM symbol is dependent on the delay spread of
`the system. The delay spread for a given transmitter is the
`difference between the earliest and latest arriving signal
`instances at a receiver for a signal transmitted by the
`transmitter. The delay spread of the system is the expected
`worst-case delay spread for all terminals in the system. To
`effectively combat ISI, the cyclic prefix should be longer
`than the delay spread of the system.
`Each transformed symbol has a duration of N sample
`periods, where each sample period has a duration of (1/W)
`usec. The cyclic prefix may be defined to include Cp
`samples, where Cp is a Suitable integer selected based on the
`delay spread of the system. In particular, Cp is selected to be
`greater than or equal to the number of taps (L) for the
`impulse response of the wireless channel (i.e., Cp2L). In
`this case, each OFDM symbol would include N+Cp
`samples, and each symbol period would span N+Cp sample
`periods.
`The N subbands of the OFDM system may experience
`different channel conditions (i.e., different effects due to
`fading and multipath) and may be associated with different
`complex channel gains. An accurate estimate of the channel
`response is normally needed in order to properly process
`(e.g., decode and demodulate) data at the receiver.
`The wireless channel in the OFDM system may be
`characterized by either a time-domain channel impulse
`response, h, or a corresponding frequency-domain channel
`frequency response, H. The channel frequency response His
`the discrete Fourier transform (DFT) of the channel impulse
`response h. This relationship may be expressed in matrix
`form, as follows:
`
`is
`
`Eq. (1)
`where h is an (Nx1) vector for the impulse response of the
`wireless channel between the transmitter and the receiver in
`the OFDM system:
`H is an (Nx1) vector for the frequency response of the
`wireless channel; and
`W is an (NXN) matrix used to perform the DFT on the
`vector h to obtain the vector H.
`The matrix W is defined such that the (nm)-th entry, w,
`is given as:
`
`Winn F
`
`1
`(n-1)(n-1)
`- 27 Mr. At it
`8
`VN
`for n e {1 ...
`
`N} and n e {1 ... N.
`
`Eq. (2)
`
`The vector h includes one non-zero entry for each tap of the
`channel impulse response. Thus, if the channel impulse
`response includes L. taps, where L-N, then the first L entries
`of the vector h would be L non-zero values and the (N-L)
`following entries would be zeros. However, the techniques
`described herein apply equally even if the L non-zero values
`are some arbitrary selection within the N entries in the vector
`h, although Such a scenario may not arise in real systems.
`FIG. 2A graphically shows the relationship between the
`channel frequency response H and the channel impulse
`response h. The vector h includes N time-domain values for
`the impulse response of the wireless channel from the
`transmitter to the receiver. This vector h can be transformed
`to the frequency domain by pre-multiplying it with the DFT
`
`DETAILED DESCRIPTION
`The channel estimation techniques described herein may
`be used for any communication system with multiple Sub
`bands. For clarity, these techniques are described for an
`OFDM system.
`FIG. 1 shows a subband structure 100 that may be used for
`an OFDM system. The OFDM system has an overall system
`bandwidth of W MHz, which is partitioned into Northogo
`nal subbands using OFDM. Each subband has a bandwidth
`of WNMHz. In a typical OFDM system, only M of the N
`35
`total subbands are used for data transmission, where MCN.
`These M usable Subbands are also referred to as data
`subbands. The remaining N-M subbands are not used for
`data transmission and serve as guard Subbands to allow the
`OFDM system to meet spectral mask requirements. The M
`40
`usable subbands include subbands F through F+M-1.
`For OFDM, the data to be transmitted on each subband is
`first modulated (i.e., symbol mapped) using a particular
`modulation scheme selected for use for that subband. The
`signal value is set to zero for each of the N-M unused
`subbands. For each symbol period, the N symbols (i.e., the
`M modulation symbols and N-M Zeros) are transformed to
`the time domain using an inverse fast Fourier transform
`(IFFT) to obtain a “transformed symbol that includes N
`time-domain samples. The duration of each transformed
`50
`symbol is inversely related to the bandwidth of each sub
`band. For example, if the system bandwidth is W=20 MHz
`and N=256, then the bandwidth of each subband is 78.125
`KHZ (or WNMHz) and the duration of each transformed
`symbol is 12.8 usec (or N/W usec).
`OFDM can provide certain advantages, such as the ability
`to combat frequency selective fading, which is characterized
`by different channel gains at different frequencies of the
`overall system bandwidth. It is well known that frequency
`selective fading is accompanied by inter-symbol interfer
`ence (ISI), which is a phenomenon whereby each symbol in
`a received signal acts as distortion to Subsequent symbols in
`the received signal. The ISI distortion degrades performance
`by impacting the ability to correctly detect the received
`symbols. Frequency selective fading can be conveniently
`combated with OFDM by repeating a portion of (or append
`ing a cyclic prefix to) each transformed symbol to form a
`
`45
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`

`

`5
`matrix W. The vector H includes N frequency-domain
`values for the complex channel gains of the N subbands.
`FIG. 2B graphically shows the matrix W, which is an
`(NXN) matrix comprised of the elements defined in equation
`(2).
`Techniques are provided herein to obtain an enhanced
`estimate of the frequency response of the wireless channel in
`the OFDM system. It is recognized that the impulse response
`of the wireless channel can be characterized by L. taps, where
`L is typically much less than the number of total subbands 10
`in the system (i.e., L-N). That is, if an impulse is applied to
`the wireless channel by the transmitter, then L time-domain
`samples (at the sample rate of W) would be sufficient to
`characterize the response of the wireless channel based on
`this impulse stimulus. The number of taps L for the channel 15
`impulse response is dependent on the delay spread of the
`system, with a longer delay spread corresponding to a larger
`value for L.
`Because only L. taps are needed for the channel impulse
`response, the channel frequency response H lies in a Sub- 20
`space of dimension L (instead of N). More specifically, the
`frequency response of the wireless channel may be fully
`characterized based on the channel gains for as few as L
`appropriately selected subbands, instead of all N Subbands.
`Even if more than L channel gains are available, an 25
`enhanced estimate of the frequency response of the wireless
`channel may be obtained by Suppressing the noise compo
`nents outside this subspace, as described below.
`The model for the OFDM system may be expressed as:
`r=Hox+n,
`Eq. (3) '
`where r is a “receive” vector with N entries for the symbols
`received on the N Subbands;
`X is a “transmit vector with N entries for the symbols
`transmitted on the N subbands (the entries for the 35
`unused Subbands are Zeros);
`n is a vector with entries for additive white Gaussian noise
`(AWGN) received on the N subbands; and
`“o denotes the Hadmard product (i.e., a point-wise
`product, where the i-th element of r is the product of the
`i-th elements of X and H).
`The noise n is assumed to have Zero mean and a variance of
`O?.
`The channel estimation techniques described herein may
`be used in conjunction with various pilot transmission
`45
`schemes. For clarity, these techniques are described for two
`specific pilot transmission schemes.
`In a first pilot transmission scheme, pilot symbols are
`transmitted on each of the M data Subbands. The transmitted
`pilot may be denoted by an (Mx1) vector X, which includes
`a specific pilot symbol for each of the M data subbands. The
`transmit power for the pilot symbol for each data subband
`may be expressed as P=X., where X is the pilot symbol
`transmitted on the k-th Subband.
`A receive vector r may be expressed for the received
`pilot, similar to that shown in equation (1). More
`Specifically, r/FHAOX,+n, where r. H. X, and n are
`(Mx1) vectors that include only M entries of the (Nx1)
`vectors r, H., X, and n, respectively. These M entries corre
`spond to the M data subbands.
`An initial estimate of the frequency response of the
`wireless channel, he cirH|ee may be expressed as:
`Hi-ra-i-Hitin/x,
`Eq. (4)
`where he cirHee is an (MX1) vector for the initial channel 65
`frequency response estimate, and a? bi-a/b a2/b2 . . .
`a/b,
`which includes M ratios for the M data subbands.
`
`5
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`US 7,039,001 B2
`
`6
`As shown in equation (4), the initial estimate he cirHee
`may be determined by the receiver based on the received and
`transmitted pilot symbols for each of the M data subbands.
`The initial estimate he cirHee is indicative of the fre
`quency response of the wireless channel for the M data
`subbands.
`As seen from equation (4), the initial estimate le.cirHee
`is distorted by a noise component n/X. An enhanced
`estimate may be obtained by observing that the channel
`frequency response H is the discrete Fourier transform of
`the channel impulse response h, and that he has L. taps,
`where L is typically less than M (i.e., L-M).
`A least square estimate of the impulse response of the
`wireless channel, he cirhee?, may be obtained based on
`the following optimization:
`i-malil -Whi,
`
`Mi
`
`2a
`
`~ -
`
`12
`
`Eq. (5)
`
`where h is an (LX1) vector for a hypothesized impulse
`response of the channel,
`Heotl Whee is an (MXL) sub-matrix of the (NXN) matrix
`W, and
`he cirhtee f is an (LX1) vector for the least square
`channel impulse response estimate.
`FIG. 3A graphically shows the relationship between the
`matrices eotl Wee and W. The M rows of the matrix
`e.ot Whee are the M rows of the matrix W corresponding
`to the M data Subbands. The L columns of the matrix
`e.ot Whee are the first L columns of the matrix W.
`The optimization in equation (5) is over all possible
`channel impulse responses h. The least square impulse
`response estimate he cirhteef is equal to the hypothesized
`impulse response h, that results in the minimum error
`between the initial frequency response estimate he cirHee
`and the frequency response corresponding to he which is
`given by teotl Whee .
`The solution to equation (5) may be expressed as:
`
`As shown in equation (6), the least Square impulse response
`estimate +e.cirh teef may be derived based on the initial
`frequency response estimatele.ciree, which is obtained
`based on the pilot received on the M data subbands. In
`particular, the estimate he cirhee f may be obtained by
`performing a “least square operation' (i.e., a pre
`multiplication with (he otl Whee 'Helotl Whee )
`he otl Whee ') on the initial estimate he cirH+ee . The
`vector he cirheef includes L entries for the L taps of the
`channel impulse response, where L-M.
`An enhanced estimate of the frequency response of the
`wireless channel, he cirHeef, may then be derived from
`the least square channel impulse response estimate,
`he cirheef, as follows:
`Eq. (7)
`+e.cir-ee f=he otl Whhee f,
`where he cirHeef is an (Mx1) vector for the enhanced
`channel frequency response estimate.
`Equation (7) indicates that the enhanced channel frequency
`response estimate he cirHeef may be obtained for all M
`data Subbands based on the least Square channel impulse
`response estimate he cirheef that includes only L entries,
`where LCM.
`FIG. 3B graphically shows the relationship between the
`enhanced channel frequency response estimate he cirH|ee
`
`9
`
`

`

`7
`f and the least square channel impulse response estimate
`he cirhtee f. The vector he cirhee f includes L. time
`domain values for the least square channel impulse response
`estimate. This vector he cirhtee f can be transformed to
`the frequency-domain by pre-multiplying it with the matrix
`he otl Whee. The resultant vector he cirH+eef includes M
`frequency-domain values for the complex gains for the M
`data Subbands.
`For clarity, the channel estimation techniques are
`described above with three distinct steps:
`1. Obtain the initial channel frequency response estimate
`te.cirHtee f:
`2. Derive the least square channel impulse response
`estimate he cirhtee f based on the initial channel
`frequency response estimate he cirHee ?, and
`3. Derive the enhanced channel frequency response esti
`mate he cirH+ee f based on the channel impulse
`response estimate he cirhtee f.
`The channel estimation may also be performed Such that a
`step may be implicitly (instead of explicitly) performed. In
`particular, the enhanced channel frequency response esti
`mate he cirHeef may be derived directly from the initial
`channel frequency response estimate he cirH|ee as fol
`lows:
`
`10
`
`15
`
`Eq. (8)
`HA-717 B-BiL.
`In equation (8), the second step is implicitly performed Such
`that the enhanced frequency response estimate he cirHee
`f is derived based on the channel impulse response esti
`mate he cirhee? that is implicitly derived is based on the
`initial frequency response estimate he cirHee .
`The mean square error (MSE) in the enhanced channel
`frequency response estimate he cirH+ee f may be
`expressed as:
`
`25
`
`30
`
`MSE = E|H, -i, I
`
`A is 2
`
`35
`
`Ed (9
`
`q (9)
`
`40
`
`45
`
`where P is the transmit power used for the pilot symbol in
`each of the M data subbands.
`It can be shown that the MSE in equation (9) is the trace
`of the noise covariance matrix after the least square opera
`tion (i.e., the covariance matrix of eotl Whee (e.ot Whee
`50
`'Helotl Whee) +e.uns Whee 'n).
`In a second pilot transmission Scheme, pilot symbols are
`transmitted on each of S designated subbands, where S-N
`and SeL. Typically, the number of designated Subbands is
`less than the number of data subbands (i.e., SCM). In this
`case, the other (M-S) data subbands may be used for other
`transmissions. For example, on the downlink, the other
`(M-S) data subbands may be used to transmit traffic data
`and/or overhead data. On the uplink, the M data subbands
`may be partitioned into disjoint groups of S Subbands, and
`each group may then be assigned to a different terminal for
`pilot transmission. This Subband multiplexing, whereby
`multiple terminals transmit concurrently on disjoint groups
`of subbands, may be used to improve system efficiency. For
`clarity, channel estimation is described below for subband
`multtiplexing whereby each designated terminal transmits a
`pilot only on its S assigned Subbands.
`
`55
`
`60
`
`65
`
`US 7,039,001 B2
`
`8
`The transmit pilot for each terminal may be denoted by an
`(Sx1) vector X, which includes a specific pilot symbol for
`each of the S subbands assigned to the terminal. The transmit
`power for the pilot symbol for each assigned Subband may
`be expressed as P=X., where X, is the pilot symbol
`transmitted on the k-th subband by terminal i.
`An initial estimate of the frequency response of the
`wireless channel, he cirH|ee , for terminal i may be
`expressed as:
`
`is
`
`Eq. (10)
`wherer, H. X, and n are (SX 1) vectors that include only S
`entries of the (NX1) vectors r, H., X, and n, respectively, with
`these S entries corresponding to the S Subbands assigned to
`terminal i, and
`e.cirH|ee is an (SX1) vector for the initial channel
`frequency response estimate for terminal i.
`The initial estimate le.cirHee, may be determined by an
`access point for terminal i based on the received and
`transmitted pilot symbols for each of the S subbands
`assigned to the terminal. The initial estimate he cirHee, is
`indicative of the frequency response of the wireless channel
`for the S Subbands assigned to terminal i. Again, the initial
`estimate he cirH|ee is distorted by a noise component n/
`X. An enhanced channel estimate may be obtained for
`terminal i as follows.
`A least square estimate of the impulse response of the
`wireless channel, he cirhtee f. for terminal i may be
`obtained based on the following optimization:
`
`M is
`i
`
`.
`
`I a...
`
`f
`
`h; = min|h,-Whil
`
`, , ,
`
`12
`
`Eq. (11)
`
`where h is an (LX1) vector for a hypothesized channel
`impulse response,
`He ovs Whee, is an (SXL) sub-matrix of the (NXN) DFT
`W, and
`he cirhee ' is an (LX1) vector for the least square
`channel impulse response estimate for terminal i.
`FIG. 4A graphically shows the relationship between the
`matrices he, ovs Wee, and W. The S rows of the matrix W.
`are the S rows of the matrix W corresponding to the S
`Subbands assigned to terminal i (which are shown as the
`unshaded rows). The L columns of the matrix elovs Wee
`are the first L columns of the matrix W. Since each terminal
`is assigned a different group of Subbands for pilot transmis
`sion on the uplink, the matrix e, ovs Wee is different for
`different terminals.
`Again, the optimization in equation (11) is over all
`possible channel impulse responses h. The least square
`channel impulse response estimate he cirhtee
`for termi
`nal i is equal to the hypothesized response h, that results in
`the minimum error between the initial frequency response
`estimate he cirH|ee and the frequency response corre
`sponding to he which is given by Whee .h,
`The solution to equation (11) may be expressed as:
`
`Eq. (12)
`+e, cir h-hee =(WW)'W' +e, cir H-hee .
`As shown in equation (12), the least square channel impulse
`response estimate he cir hee for terminal i may be
`derived based on the initial channel frequency response
`estimate +e.cir H-hee, which is obtained based on the uplink
`pilot received on only the S subbands assigned to terminal
`i. In particular, the estimate he cirhtee may be obtained
`by performing a least square operation (i.e., a pre
`
`10
`
`

`

`US 7,039,001 B2
`
`9
`multiplication with (WW)'W') on the initial estimate
`+e.cir Hee. The vector he cirhee, includes L entries for
`the L taps of the channel impulse response, where LSS.
`An enhanced estimate of the frequency response of the
`wireless channel, he cir Heef, for terminal i may then be
`derived from the least square channel impulse response
`estimate +e.cir hitee, as follows:
`
`10
`A Sufficient condition to attain the minimum mean square
`error (MMSE) for the enhanced estimate he cirH+ee is to
`have he ovs Whee 'Helovs Whee —I, where I is the identity
`matrix. This condition can be met if (1) the number of
`Subbands in each group is S=22L, where r is an integer So
`that S is a power of twos, and (2) the S subbands in each
`group are uniformly (i.e., equally) spaced. For Such Subband
`grouping and spacing, W, is a DFT matrix of radix N/S, and
`hence he ovs Whee 'Helovs Whee =I. For this subband
`grouping and spacing, the MMSE of the enhanced channel
`frequency response estimate he cirHee
`for terminal i
`may be derived from equation (15) and expressed as:
`
`or NL
`MMSE = ().
`
`Eq. (16)
`
`It can be shown that the MSE for the enhanced estimate
`he cirHeef, which is obtained based on pilot transmission
`on only S assigned subbands, is the same as the MSE for a
`channel estimate he cirHeef, which is obtained based on
`pilot transmission on all N subbands, if the same amount of
`total power is used for pilot transmission. This can be
`achieved by increasing the transmit power for each of the S
`Subbands assigned to terminal i, as follows:
`
`N
`s
`
`Eq. (17)
`
`where P is the “average” transmit power for the N sub
`bands.
`The OFDM system may be operated in a frequency band
`that has a per MHz power constraint of PdBm/MHz. In this
`case, the total transmit power P
`for each term