(19) United States
`(12) Patent Application Publication (10) Pub. N0.: US 2004/0047284 A1
`(43) Pub. Date:
`Mar. 11, 2004
`Eidson
`
`US 20040047284A1
`
`(54) TRANSMIT DIVERSITY FRAMING
`STRUCTURE FOR MULTIPATH CHANNELS
`
`Publication Classi?cation
`
`(76) Inventor:
`
`Donald Brian Eidson, San Diego, CA
`(Us)
`Correspondence Address:
`Semion Talpalatsky, Esq.
`CONEXANT SYSTEMS, INC.
`4311 Jamboree Road
`Newport Beach, CA 92660-3095 (US)
`
`(21) Appl. No.:
`
`10/389,272
`
`(22) Filed:
`
`Mar. 14, 2003
`
`Related US. Application Data
`
`(63) Continuation-in-part of application No. 10/099,556,
`?led on Mar. 13, 2002.
`
`(51) Im. c1? .................................................... .. H04J 11/00
`(52) Us. 01. ............................................................ ..370/203
`
`(57)
`
`ABSTRACT
`
`Systems and techniques are disclosed for framing and pro
`cessing single-carrier and/or OFDM transmit-diversity
`transmissions through delay-spread channels, as Well as for
`deframing and processing the corresponding merged signals,
`received from a plurality of antennas, to estimate the trans
`mitted information. Time-domain processing techniques
`may be used for both types of transmissions to create
`multiplexed dual signal-unit pairs, particularly When cyclic
`pre?xes are needed to reduce delay-spreading effects.
`Repetitive pilot Words may be employed in burst preambles
`and/or in payloads of transmission bursts to minimize or
`provide ?exibility in the amount of bandwidth that is con
`sumed to generate good channel response estimates under
`changing channel conditions.
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`Patent Application Publication Mar. 11, 2004 Sheet 1 0f 7
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`US 2004/0047284 A1
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`Patent Application Publication Mar. 11, 2004 Sheet 2 0f 7
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`Patent Application Publication Mar. 11, 2004 Sheet 3 of 7
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`US 2004/0047284 A1
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`Patent Application Publication Mar. 11, 2004 Sheet 4 0f 7
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`US 2004/0047284 A1
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`Patent Application Publication Mar. 11, 2004 Sheet 6 of 7
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`US 2004/0047284 A1
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`Patent Application Publication Mar. 11, 2004 Sheet 7 of 7
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`US 2004/0047284 A1
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`

`US 2004/0047284 A1
`
`Mar. 11, 2004
`
`TRANSMIT DIVERSITY FRAMING STRUCTURE
`FOR MULTIPATH CHANNELS
`
`[0001] This application is a continuation-in-part of US.
`patent application Ser. No. 10/099,556, “Transmit Multi
`plexing and Receive Processing for Delay Spread Chan
`nels,” ?led Mar. 13, 2002, the entire contents of Which is
`hereby incorporated by reference herein.
`
`BACKGROUND OF THE INVENTION
`
`[0002] 1. Field of the Invention
`
`[0003] This invention generally relates to Wireless com
`munications links, and, more speci?cally, to frame structures
`for diverse antenna transmissions.
`
`[0004] 2. Related Art
`[0005] Virtually all Wireless communication channels are
`limited in their ability to accurately communicate data by the
`signal-to-noise ratio (SNR) of the Wireless channel. Antenna
`diversity is one category of techniques that may be used to
`enhance the effective SNR of communications channels, and
`thus enhance the ability to accurately transmit data.
`
`[0006] Antenna diversity can be incorporated at the trans
`mitter, or at the receiver, or both. HoWever, for the cost
`sensitive subscriber station, diversity is much cheaper if it is
`instantiated at the base station transmitter (Where its bene?ts
`and costs may be shared by all subscribers), rather than at
`every subscriber station. In installations Where a great deal
`of diversity is required for reliable service, multiplicities of
`diversity may be achieved if the base station transmitter and
`the subscriber station receiver both possess diversity.
`Mechanisms to realiZe transmit diversity are of great utility
`for Wireless communications.
`[0007] Many transmit diversity techniques have been pro
`posed in the literature. One such technique is transmit delay
`diversity. At the transmitter, delay diversity is achieved by
`using tWo antennas that transmit the same signal, With the
`second antenna to transmitting a delayed replica of that
`transmitted by the ?rst antenna. By so doing, the second
`antenna creates diversity by establishing a second set of
`independent multipath elements that may be collected at the
`receiver. If the multipath generated by the ?rst transmitter
`fades, the multipath generated by the second transmitter may
`not, in Which case an acceptable SNR Will be maintained at
`the receiver. This technique is easy to implement, because
`only the composite TXO+TX1 channel is estimated at the
`receiver. Transmit delay diversity does not require the
`receiver to have special a-priori knoWledge that the trans
`mitter is using this type of diversity, because the receiver’s
`equaliZer compensates automatically for the additional mul
`tipath diversity induced by the second transmit antenna.
`
`[0008] Both OFDM and single carrier modulation can
`easily implement a delay diversity scheme. The biggest
`draWback to transmit delay diversity is that it increases the
`effective delay spread of the channel, and can perform
`poorly When the multipath introduced by the second antenna
`falls upon, and interacts destructively With, the multipath of
`the ?rst antenna, thereby reducing the overall level of
`diversity.
`[0009] Another transmit diversity technique of loW-to
`moderate complexity is described in “A simple transmit
`diversity scheme for Wireless communications,” S. Alam
`
`outi, IEEE Journal on SelectAreas in Communications, vol.
`16, no. 8 Oct. 1998, pp. 1451-1458. This technique provides
`tWo-Way maximal ratio-combining diversity. Unfortunately,
`the Alamouti transmit diversity scheme cannot be directly
`applied to systems experiencing delay spread, because it
`relies on an ability to isolate pairs of multiplexed symbols
`from each other, that is, the receiver must be able to process
`each pair of symbols Without signi?cant interaction from
`other pairs of symbols. In delay-spread channels, Where
`symbol energy not only overlaps other symbols, but indeed
`may span hundreds of symbols, such absence of interaction
`cannot be relied upon. A transmit diversity technique that
`overcomes some of the limitations of the foregoing is
`described herein.
`[0010] Transmit diversity techniques rely upon estima
`tions of the symbol content of received signals. Estimating
`and compensating for transfer characteristics of the Wireless
`channel, in turn, generally improves the symbol estimates.
`Irrespective of the basic transmit diversity technique used,
`techniques to enhance the symbol estimation Will improve
`the overall ability of a communication system to accurately
`transfer data. Accordingly, there is a need for techniques to
`enhance the data transmission effectiveness of basic transmit
`diversity multiplexing techniques.
`SUMMARY
`[0011] Processing techniques and framing structures to
`enhance the effectiveness of transmit-diversity Wireless
`communications, and systems employing such techniques
`and structures, are disclosed herein that may be used to
`enhance the effectiveness of communications transmitted by
`diverse antennas, particularly When the transmission chan
`nels have delay-spread characteristics. Multiplexing tech
`niques to provide a plurality of signals for a corresponding
`plurality of transmit antennas are disclosed, as Well as
`corresponding receiver combining and equaliZation tech
`niques. Data structures are also disclosed for use in con
`junction With diversity multiplexing techniques, particularly
`for delay-spread channels. Framing and processing tech
`niques are disclosed that are applicable to single-carrier
`and/or OFDM transmit-diversity transmissions and recep
`tions through delay-spread channels.
`[0012] One embodiment is a method of transmitting dual
`signal-unit pairs from diverse antennas. It includes process
`ing a plurality of N-point signal units each into a plurality of
`forms using time-domain techniques, and prepending a
`cyclic pre?x on each of the resulting forms, before trans
`mitting the pre?xed forms of the signal units in concurrent
`pairs from the diverse antennas.
`
`[0013] Another embodiment is a method of interpreting
`received signals that Were transmitted in multiplexed forms
`from diverse transmit antennas. The method includes iden
`tifying received pilot Words that include cyclically pre?xed
`?rst and second pilot signal units. The method further
`includes ignoring the cyclic pre?xes and combining forms of
`the ?rst and second pilot signal units With ?rst and second
`expected pilot symbol units to derive ?rst and second
`channel estimates. The method further includes deriving
`estimates of transmitted payload signal units by combining
`forms of the channel estimates With forms of received
`payload signal units.
`[0014] A further embodiment is a method of transmitting
`dual signal-unit pairs from diverse antennas. The method
`
`SAMSUNG 1028-0009
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`

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`US 2004/0047284 A1
`
`Mar. 11, 2004
`
`includes deriving a plurality of pilot signal units from
`portions of pilot data expected by a receiver, establishing a
`variant form of each signal unit, and cyclically pre?xing the
`signal units and their variants. The method also includes
`transmitting, substantially concurrently, appropriate pairs of
`these various cyclically pre?xed signal units. The method
`yet further includes transmitting a repetitive pilot signal unit
`by transmitting an appropriate signal unit pair one or more
`additional times, Without cyclic pre?xes, immediately after
`they have been transmitted With a cyclic pre?xes.
`
`[0015] Yet another embodiment is a system that may be
`used for transmitting dual signal-unit pairs from diverse
`antennas. The system includes ?rst and second antennas and
`a signal-unit derivation block con?gured to derive N-point
`signal-units of time-domain samples from modulated source
`information. It also includes a diversity multiplexer block
`con?gured to multiplex pairs of the derived N-point signal
`units into multiplexed dual signal-unit pairs, each having
`?rst and second N-point multiplexed-signal-units (“MSUs”)
`for the ?rst antenna, and ?rst and second N-point MSUs for
`the second antenna, Where the ?rst N-point MSU for the ?rst
`antenna is related to the second N-point MSU for the second
`antenna by complex conjugation and modulo-N sample time
`inversion, and the second N-point MSU for the ?rst antenna
`is related to the ?rst N-point MSU for the second antenna by
`complex conjugation, negation, and modulo-N sample time
`inversion. The system also includes a ?rst output processing
`block con?gured to cyclically pre?x the ?rst and second
`N-point MSUs for the ?rst antenna, and to process the
`pre?xed MSUs for sequential transmission from the ?rst
`antenna; and a second output processing block con?gured to
`cyclically pre?x the ?rst and second N-point MSUs for the
`second antenna, and to process the pre?xed MSUs for
`sequential transmission from the second antenna substan
`tially concurrently With the sequential transmission from the
`?rst antenna.
`
`[0016] Yet a further embodiment is a receiver system that
`may be used for receiving paired multiplexed signals trans
`mitted from plural antennas. The system of this embodiment
`includes a receive and alignment block con?gured to receive
`and align pre?xed multiplexed-signal-units (“MSUs”)
`received sequentially in a frame structure having a preamble
`portion and a payload portion, and a cyclic pre?x removal
`block con?gured to remove cyclic pre?xes from received
`MSUs. The system also includes a pilot Word identi?cation
`block con?gured to identify, in accordance With relative
`position Within the frame structure, J concatenated copies of
`a ?rst received pilot MSU, RPO, folloWed by P concatenated
`copies of a second received pilot MSU, RPl, that Were
`transmitted based upon a ?rst expected pilot signal-unit EPO
`and a second expected pilot signal-unit EPl, and a channel
`estimation block con?gured to combine a representation of
`RPO and a representation of RP1 With complex conjugated
`forms of EPO and EP1 to create a ?rst channel estimate HE,
`and to combine the representations of RPO and RP1 With
`forms of EPO and EP1 that are not complex conjugated to
`create a second channel estimate HE2.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`[0017] Embodiments of the present invention Will be more
`readily understood by reference to the folloWing ?gures, in
`Which like reference numbers and designations indicate like
`elements.
`
`[0018] FIG. 1 illustrates temporal organiZation of a block
`pair.
`[0019] FIG. 2 illustrates concatenation of block pairs for
`transmission.
`
`[0020] FIG. 3 is a matrix shoWing a dual block pair signal
`multiplexing relationships.
`[0021] FIG. 4 is a signal ?oW diagram of a Decision
`Feedback EqualiZer.
`
`[0022] FIG. 5 shoWs a Unique Word variation of the
`multiplexing of FIG. 3.
`
`[0023] FIG. 6 illustrates a burst transmission using a
`Unique Word preamble.
`
`[0024] FIG. 7 shoWs Pilot Words disposed in a general
`payload transmission.
`
`[0025] FIG. 8 illustrates a use of cyclic pre?xes With the
`multiplexing of FIG. 3.
`
`[0026] FIG. 9 illustrates using Unique Words for cyclic
`pre?xes in block pairs.
`
`[0027] FIG. 10 shoWs a dual block pair multiplexing
`transmission format.
`
`[0028] FIG. 11 illustrates communication system features
`including plural receivers.
`
`[0029] FIG. 12 is a block diagram of transmit diversity
`processing for single-carrier applications using time domain
`multiplexing.
`[0030] FIG. 13 illustrates dual block pair signal multi
`plexing relationships for OFDM.
`
`[0031] FIG. 14 is a block diagram of transmit diversity
`processing for OFDM applications using frequency domain
`multiplexing.
`
`[0032] FIG. 15 shoWs a modi?cation of the processing of
`FIG. 14 to use time domain multiplexing and avoid some
`FFTs.
`
`[0033] FIG. 16 is a block diagram shoWing OFDM trans
`mit diversity receive processing.
`
`[0034] FIG. 17 illustrates an example of preamble fram
`ing for OFDM transmit diversity.
`
`DETAILED DESCRIPTION
`
`[0035] Multiplexed data may be transmitted over tWo or
`more antennas, as described more fully beloW, to enhance
`the reliability of communication With a receiver (or receiv
`ers). The techniques described are particularly effective
`When the communication is conducted over multipath delay
`spread channels. TWo-antenna diversity can double the
`effective diversity level of a system operating over such
`channels. Of course, multipath, in itself, is a form of
`diversity. Thus, for example, With a system operating over a
`single channel With three multipaths and having (therefore)
`a diversity level of three; use of tWo transmit antennas (With
`one receiver) as described beloW could increase the diversity
`level to 6 (or more). Embodiments that further employ tWo
`or more receivers may increase the diversity gains even
`further.
`
`SAMSUNG 1028-0010
`
`

`

`US 2004/0047284 A1
`
`Mar. 11, 2004
`
`Single Carrier Transmnit Diversity
`
`[0036] This description assumes a communication system
`that is con?gured to transfer selected signals from a trans
`mission system having a plurality of transmit antennas to a
`receiving system having one or more antennas. The desired
`transmission signals are assumed to at least partly take the
`form of symbols de?ned in the time domain. FIG. 1 illus
`trates that a selected number B of symbols may be organiZed
`as a symbol block, such as a “Block 0”’102 or a “Block
`1”104. Ideally, a delay spread guard period 106 is provided
`before each block (e.g., 102 and 104). For convenience,
`delay spread guard periods Will typically have the same
`length, D, Which may be measured in symbol lengths or
`time. The length, D, of these delay spread guard regions
`Would typically be longer than the delay spread span of the
`channel. In one embodiment, these delay spread guard
`regions Would have a ‘cyclic pre?x’ format; i.e., they Would
`be composed of the last D symbols of the block that folloWs
`them. A combination of sequential blocks, such as the
`illustrated Block 0 and Block 1, each preceded by a delay
`spread guard having a knoWn length that may range doWn to
`Zero, fonrs a block pair 100. Note that the tWo blocks Within
`a block pair are logically paired together, but physically
`separated from themselves (or other data) by delay spread
`guard regions 106. In general, any particular block, such as
`the “Block 0”102, may be the same or different from the
`other block (e.g., “Block 1”’104) of its block pair 100. It Will
`generally be useful, for minimiZing bit error rate (BER)
`characteristics, if the channels from each antenna to the
`receiving. system do not change signi?cantly betWeen the
`beginning and end of transmission of a block pair. Note that
`the symbols Within a block should be adjacent, but that
`blocks composing a block pair do not have to be adjacent,
`although they are pictured that Way in FIGS. 1 and 2.
`
`[0037] FIG. 2 illustrates a sequence of block pairs, includ
`ing block pairs (m-1) 202,
`204, (m+1) 206 and (m+2)
`208, Which have been concatenated for transmission as an
`extended payload from a particular antenna. In general, any
`block pair transmitted from a particular antenna may be
`different from or identical to any other block pair transmitted
`from the same antenna at another time.
`
`[0038] Block Pair Transmit Multiplexing
`[0039] FIG. 3 indicates a block multiplexing structure that
`a tWo-antenna transmitter may use to transmit the informa
`tion of each of tWo sequences in tWo related forms over
`block pairs 302 and 304 that resemble the block pair 100
`(see FIG. 1). {so[n]} is a signal set describing a ?rst block
`306 of the block pair 302 transmitted by Transmit Antenna
`0, While {s1[n]} is a signal set that describes a second block
`308 of the block pair 302. {so[n]} and {s1[n]} each describe
`a sequence of length B symbols, 0§n<B-1, that represents
`information that is to be delivered to a receiver via the tWo
`transmit antennas.
`
`[0040] Ablock 310 is the ?rst block of the block pair 304
`transmitted by Transmit Antenna 1, While block 312 is the
`second block of the block pair 304 transmitted by Transmit
`Antenna 1. The ?rst block 306 of the block pair 302 conveys
`the same information as the second block 312 of the block
`pair 304, but in a different form. As compared to the block
`306, the block 312 is a time-inverted sequence of the
`complex conjugate of the symbols that form the symbol
`sequence {s0[n]}. Similarly, the ?rst block 310 of the block
`
`pair 304 is a time-inverted sequence of the negative complex
`conjugate of the symbols of the sequence {s1[n]}.
`
`[0041] Thus, Transmit Antenna 1 transmits blocks having
`the same information as is transmitted by related blocks of
`Transmit Antenna 0, but in reverse time order, and the blocks
`of Transmit Antenna 1 have a sequence of symbols that are
`the (positive or negative) complex conjugate of the symbols
`of the related blocks of Transmit Antenna 0 in a sequence
`that is also time-reversed cyclically about Zero, modulo-B.
`
`[0042] It should be understood that the signal sets {so[n]}
`and {s1[n]} are only nominally in an “unmodi?ed” form.
`Either or both {so[n]} and {s1[n]} may, of course, be related
`to other symbol sequences that are the actual symbols Which
`are being sent. Thus, either of these signals may in fact be,
`for example, a time-inverted, negated and/or complex-con
`jugated version of the actual desired symbols. This merely
`re?ects the generality of the signal sets {so[n]} and {s1[n]},
`and does not affect the relationship betWeen blocks that are
`diagonally positioned Within the space-time matrix of blocks
`shoWn in FIG. 3.
`
`[0043] Transmit and Receive Signal Relationships
`[0044] De?ne So(ej‘”), S1(ej‘”), No(ej‘”), N1(ej‘”), Ho(ej‘”),
`and H1(ej‘”) as the Discrete-time Fourier transforms
`(DTFTs), respectively, of the symbol sequences {so[n]} and
`{s1[n]} (each normaliZed, Without loss of generality, so that
`their average symbol energy is 1); additive White, Zero
`mean, oz-variance noise sequences {no[n]} and {no[n]}; and
`the channel impulse responses {ho[n]} and {h1[n]} that are
`associated With each transmit antenna Due to the multi
`plexed transmit signals, each received block of payload
`symbols (Which is typically separated from other blocks by
`delay spread guard intervals) includes information from both
`blocks of a received block pair. Accordingly, the information
`from individual blocks can only be extracted by combining
`information from the tWo blocks of a block pair. The
`received signals associated With each individual block of a
`block pair, interpreted in the frequency domain, are:
`
`ROM") = Howbsoww — HIWMSUW) + Now“)
`
`Eqn- 1
`
`[0045] Note that DTFTs are used for frequency domain
`descriptions for generality, but this is in no Way limiting: a
`B-point (or, more generally, an implementation using a
`K-point) Discrete Fourier Transform (DFT) Would uni
`formly sample the DTFT response over the interval (ne[0,
`2n), yielding B (or K) samples.
`
`[0046] The received signal is a merger of the concurrently
`transmitted blocks, so processing facilities should identify
`received block pairs (through their time relationship With a
`preamble, for example), and combine forms of the received
`block pairs With forms of the channel response estimates.
`Assuming that the frequency domain channel responses
`Ho(ej‘”) and H1(ej‘”) are knoWn (or estimated), a received
`block pair R0 and R1 may be ?ltered and combined accord
`ing to the frequency domain combining scheme
`
`SAMSUNG 1028-0011
`
`

`

`US 2004/0047284 A1
`
`Mar. 11, 2004
`
`[0047] Processing the block pair, R0 and R1, thus includes
`?ltering various forms of the received blocks With a form of
`a channel estimate, and in the frequency domain the ?ltering
`may consist of multiplying a form of a channel estimate by
`a form of a received block. The appropriate ?ltered results
`are then combined (in the frequency domain case, added) to
`produce a pair of combiner outputs CO and C1. Using the
`expanded representation of the received blocks provided by
`Eqn. 1, the combiner outputs are seen to be
`
`l
`
`Eqn. 8
`
`[0054] Whereas a linear equaliZer solution obtained using
`a Minimum Mean Squared Error (MMSE) optimiZation
`criterion Would be
`
`[0055] Because D is de?ned in Eqn. 4, frequency domain
`processing facilities may therefore equaliZe the combiner
`outputs by dividing each output by a quantity that re?ects a
`sum of the individual channel response magnitudes. In the
`case of MMSE, the divisor sum further includes a term 02
`that re?ects a normaliZed reciprocal of the signal to noise
`ratio (SNR) measured for the received signal. The aforesaid
`equaliZation results may be directly interpreted as estimates
`§O(ej‘”) and §1(ej‘”), Whereupon (soft) equaliZed estimates of
`the symbol sequences {so[n]} and {s1[n]} may be obtained
`directly by computing inverse DTFTs (I-DTFTs) of the
`estimates.
`
`[0056] Instead of performing frequency domain process
`ing, the facilities may perform combining and equaliZation
`in the time domain using block length-B circular convolu
`tions (denoted by the operator ‘@), Where
`
`[0049] the expressions for the ?equency domain represen
`tation of the combiner outputs CO(e]‘”) and C1(e]‘”) become
`
`[0050] In vieW of Eqn. 6, estimates of SO(ej‘”) and S1(ej‘”)
`may be obtained using any equalization technique that Will
`substantially remove the in?uence of D(e]‘”).
`[0051] Equalization
`[0052] Many equaliZation techniques exist. Alinear equal
`iZer may be used in an effort to eliminate D(ej‘”) through
`pre-multiplication by an appropriate equaliZer characteristic
`that is generally inverse to D(ej‘”):
`
`)linear
`
`)linear
`
`[0053] Linear equaliZer functions may take various forms.
`As examples, the linear equaliZer solution obtained using a
`Zero forcing (ZF) optimiZation criterion Would be
`
`[0057] and the loWer-case variables are time domain rep
`resentations of upper-case frequency domain variables.
`Thus, in the tine domain the combiner outputs may be based
`on forms of received blocks ?ltered by forms of channel
`estimates, just as in the frequency domain. In the time
`domain case, the various forms of the received blocks, and
`of the channel estimates, may differ by not only complex
`conjugation (positive or negative), but also by time-reorder
`ing of the symbol sequences, and in particular by cyclic time
`reversal of the time sequence of the corresponding block
`symbols. The equaliZation ?ltering may be performed by
`circular convolution betWeen block-length sequences. The
`equaliZer elinear[n] may be derived from an I-DTFT of
`E(ejw)linear if frequency domain information on the channel
`impulse responses is immediately available. If not, the time
`domain responses may be frequency transformed to generate
`Ho(ej‘”) and H1(ej‘”), and then E(ej‘”)linear May be derived, for
`example, by further processing according to Eqn. 8 or Eqn.
`9.
`
`[0058] FIG. 4 Illustrates equaliZer elements In an equal
`iZer subsystem that may be less prone, than a linear equal
`
`SAMSUNG 1028-0012
`
`

`

`US 2004/0047284 A1
`
`Mar. 11, 2004
`
`izer, to emphasize noise in frequency bands Where notches
`occur. FIG. 4 shoWs a signal to be equalized 402 progressing
`through a typical Decision Feedback Equalizer (DEE) hav
`ing tWo equalizer processing elements: a feedforWard (lin
`ear) ?lter 404, and a decision feedback ?lter 406 that
`subtracts symbol decisions made in the time domain. The
`linear feedforWard ?lter element 404 generates intermediate
`equalized results
`
`[0059] and an I-DTFT may be applied to the equalized
`results to yield time domain sequences zO[n] and z1[n]. Each
`of these sequences may then be separately operated upon in
`the time domain by the decision feedback ?lter 406, and may
`use identical feedback coef?cients f[n] to provide an equal
`ized signal 408 in the form of estimates {so[n]} and
`
`[0060] A MMSE criterion-optimizing DFE may use the
`feedforWard ?lter
`
`MMSE _ new)
`
`Eqn. 13
`
`A zero-forcing
`[0061] Where F(ej‘”) is the DTFT of
`solution Would be identical to the MMSE solution, except
`that it Would not possess the 02 found in Eqn. 13, Which
`re?ects the normalized reciprocal of the receiver SNR.
`
`[0062] The frequency domain ?ltering described in Eqn.
`12 may, in the alternative, be implemented in the time
`domain. The signal processing may ?lter the combiner
`outputs by circularly convolving them With an equalization
`sequence eFF[n]:
`
`lolnllinm = eFFlnl ‘8 Col"
`
`Z1 lnllinm = eFFlnl ® 01 [n]
`
`Eqn- 14
`
`[0063] Where eFF[n] is the I-DTFT of E(ej‘”)FF(in either its
`MMSE or zero-forcing forms).
`
`Channel Estimation
`
`[0064] It is, of course, very helpful to obtain good channel
`estimates, since the estimates of the transmitted sequences
`may depend upon the channel estimates at a number of
`stages. Manipulation of Eqn. 1 reveals that the frequency
`domain channel characteristics can be expressed as
`
`[0065] This leads to calculations that may be performed by
`the receiver signal processing facilities to obtain channel
`estimates, including the frequency domain MMSE estimates
`
`[0067] The channel estimates of Eqns. 16 and 17 are based
`upon arbitrary symbol data sequences {s0[n]} and {s1[n]}.
`Unfortunately, the arbitrary symbol data sequences must
`generally be estimated themselves, thus compounding any
`inaccuracies. It may be useful to avoid relying exclusively
`on such estimates for further deriving estimates of the
`channel response.
`
`[0068] Preambles and Pilot Words
`
`[0069] The channel estimation process Will be less reliant
`on received symbol estimates When knoWn sequences of
`symbols are transmitted at identi?able times. These knoWn
`sequences may be referred to generally as “pilot symbols,”
`although it should be understood that such sequences might
`also appear in preambles, or in other forms. In many cases,
`an identical sequence Will be consistently transmitted as
`pilot symbols, and this fact may be exploited to reduce the
`complexity of channel estimates computation according to
`algorithms Such as those listed in Eqns. 16 and 17.
`
`[0070] Pilot seq