US007012881B2
`
`(12) United States Patent
`Kim
`
`(10) Patent N0.:
`(45) Date of Patent:
`
`US 7,012,881 B2
`Mar. 14, 2006
`
`(54) TIMING AND FREQUENCY OFFSET
`ESTIMATION SCHEME FOR OFDM
`SYSTEMS BY USING AN ANALYTIC TONE
`
`-
`.
`75
`(
`) Inventor‘ Dong Ky“ Klm’ Pusan (KR)
`
`.
`_
`.
`(73) Asslgnee~ iillllllgglgggilicégmc Co" Ltd"
`_
`
`4/2002 Lee .......................... .. 370/503
`6,373,861 B1 *
`5/2002 Eilts ..... ..
`375/340
`6,393,073 B1 *
`6/2002 Tal et al. .................. .. 375/350
`6,400,782 B1 *
`7/2002 Vishwanath et al. ...... .. 375/139
`6,418,158 B1 *
`6,470,030 B1 * 10/2002 Park et al. ................ .. 370/480
`6,487,252 131* 11/2002 Kleider et a1. ...... ..
`375/260
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`6,538,986 B1 *
`6,539,063 B1 *
`6,614,864 B1 *
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`3/2003 Isaksson et al. .... ..
`3/2003 Peyla et a1. ......... ..
`9/2003 Raphaeli et al. .... ..
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`370/207
`375/267
`375/371
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`*
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`(
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`_
`
`) Notice:
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`_
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`_
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`_
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`_
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`SubJect to any d1scla1mer,the term of this
`patent 1s extended or adjusted under 35
`U.S.C. 154(b) by 822 days.
`
`6,643,336 B1 * 11/2003 Hsieh et al. .... ..
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`375/343
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`375/260
`6,647,066 B1 4 11/2003 szajnowski
`375/341
`6,678,339 B1 *
`1/2004 Lashkarian
`370/208
`6,714,511 B1 *
`3/2004 Sudo et al.
`375/259
`6,765,969 B1 *
`7/2004 Vook et al. ..... ..
`375/343
`6,807,241 B1 * 10/2004 Milbar et al.
`370/206
`6,891,792 B1 *
`5/2005 Cimini et al.
`2002/0065047 A1* 5/2002 Moose ...................... .. 455/63
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`W0
`
`FOREIGN PATENT DOCUMENTS
`W0 00 77961 A1 12 2000
`/
`/
`* cited by examiner
`_
`_
`Primary Exammer—Bob A. Phunkulh
`(74) Attorney) Agent) 0’ Firm—sughme M1°n> PLLC
`
`ABSTRACT
`
`57
`(
`)
`.
`.
`.
`.
`Atimmg and frequency offset estimation method for~OFD~M
`use an analytic tone in calculating timing offset estimation
`.
`.
`.
`.
`and a frequency offset est1mat1on.An analytic tone includes
`a signal that contains only one subcarrier and has charac
`teristics of a uniform magnitude and a uniform phase
`rotation. The estimation algorithm With an analytic tone is
`based correlation function. By changing the interval
`betWeen tWo samples in correlation, the maximum estima
`tion range for the frequency Offset can be extended to IN/2
`subcarrier spacing, Where N is the number of total subcar
`riers. Thus, the frequency synchronization scheme for
`OFDM systems has a Wider range and a more simple
`complexity than traditional ones requiring separate ?ne and
`Coarse synchromzanon'
`
`(21) Appl. N0.: 09/750,128
`
`(22) Filed;
`
`Dec_ 29, 2000
`
`(65)
`
`Prior Publication Data
`
`US 2002/0126618 A1
`
`Sep. 12, 2002
`
`(51) Int. Cl.
`(200601)
`H04J 11/00
`(52) US. Cl. ..................................... .. 370/208; 375/344
`
`(56)
`
`(58) Field of Classi?cation Search .............. .. 375/362,
`375/366, 137, 139, 267, 260, 340, 341, 326,
`375/344, 354, 355, 371, 259, 343, 350; 370/208,
`370/210, 503, 347, 350, 491, 520, 203, 324,
`_
`370/330, 480, 455/63
`h h.
`1
`?l f
`.
`1.
`S
`66 app lcanon e or Comp ete Seam lstory'
`,
`References Clted
`US PATENT DOCUMENTS
`5
`h h
`5
`9/1998 G 05 ...................... .. 37 /344
`,802,117 A *
`59917289 A : 11/1999 Huang et al'
`370/350
`' ' ' "
`2 *
`gcGlbni’yl ' ' ' ' ' '
`uange fa‘ """"""" "
`323E211: éltlealet a1‘ "" "
`i
`6,332,008 B1 * 12/2001 Giallorenzi et a1. ...... .. 375/356
`
`’
`
`’
`
`6,353,642 B1 *
`6,363,084 B1 *
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`3/2002 Asahara et al. ........... .. 375/344
`] g
`3/2002 De'on he ................. .. 370/480
`
`g
`40 Claims, 12 Drawin Sheets
`
`7
`
`TIMING OFFSET
`ESTIMATOR
`
`1
`
`SLIDING WINDOW
`CORRELATION
`SUMMING DEVICE
`S
`3
`
`9
`
`-
`
`FREQUENCY OFFSET
`ESTIMATOR & ANALYTIC
`TONE'PHASE
`COMPARISON DEVICE
`5 5
`
`ERIC-1004
`Ericsson v IV
`Page 1 of 21
`
`

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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 1 0f 12
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`US 7,012,881 B2
`
`FIG. 1A
`
`0 1
`
`_ _ _ _ : 8 6 4 2 0
`
`0.2 -
`
`SUBCARRIER INDEX [k]
`
`X REAL PART
`+ IMAGINARY PART
`
`SAMPLE INDEX [n]
`
`REAL PART
`""" IMAGINARY PART
`
`ERIC-1004 / Page 2 of 21
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`

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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 2 0f 12
`
`US 7,012,881 B2
`
`. A 0
`
`0 0
`
`_ _ .l 3 2. 1 0
`
`0.
`
`FIG. 1C
`
`3'2
`0
`SAMPLE INDEX
`
`6'4
`
`90
`
`FIG. 1D
`
`=2 me; 365
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`1_ _ q — _ __
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`III
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`M
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`2 3
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`I
`
`0
`32
`SAMPLE INDEX
`
`64
`
`96
`
`ERIC-1004 / Page 3 of 21
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`

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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 3 0f 12
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`US 7,012,881 B2
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`FIG. 2
`
`7
`
`S
`
`TIMING OFFSET
`
`' ESTIMATOR
`
`i
`
`1
`
`SLIDING WINDOW
`CORRELATION
`SUMMING DEVICE
`
`2
`
`FREQUENCY OFFSET
`ESTIMATOR & ANALYTIC
`TONE-PHASE
`COMPARISON DEVICE
`
`5 5
`
`‘
`
`7
`
`9
`
`__
`
`ERIC-1004 / Page 4 of 21
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`U.S. Patent
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`ERIC-1004 / Page 5 of 21
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`

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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 5 0f 12
`
`US 7,012,881 B2
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`FIG. 4
`
`RECEIVE INPUT SIGNAL,
`$1
`\ AND CONVERT FROM
`ANALOG TO DIGITAL SIGNAL
`
`S2
`I
`GENERATE SLIDING
`WINDOW CORRELATION SUM
`
`$3
`I
`I
`CALCULATE TIMING OFFSET
`ESTIMATION (DETECT
`ANALYTIC TONE AS A
`REFERENCE SYMBOL)
`
`S4
`k CALCULATE FREQUENCY
`OFFSET ESTIMATION
`
`END
`
`S5
`
`N
`
`EXTEND
`ESTIMATION
`RANGE ?
`Y
`
`S6
`K ADJUST CORRELATION
`INTERVAL BETWEEN SAMPLES
`
`ERIC-1004 / Page 6 of 21
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`

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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 6 0f 12
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`US 7,012,881 B2
`
`0.4
`
`0.3
`
`0.2—
`
`0.1
`
`SUM OF PRODUCT
`
`0-0
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`PROBABILITY
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`ESTIMATED TIMING [SAMPLES]
`
`FIG. 5C
`
`
`
`[SAMPLE SQUARE]
`
`+ 16 SAMPLES
`—B— 32 SAMPLES
`+ 48 SAMPLES
`
`
`
`
`
`ESTIMATION ERROR VARIANCE
`
`ERIC-1004 / Page 7 of 21
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`

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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 7 0f 12
`
`US 7,012,881 B2
`
`FIG. 6A
`
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`ERIC-1004 / Page 8 of 21
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`

`
`U.S. Patent
`
`Mar. 14, 2006
`
`Sheet 8 0f 12
`
`US 7,012,881 B2
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`ERIC-1004 / Page 9 of 21
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`

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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 9 0f 12
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`US 7,012,881 B2
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`ERIC-1004 / Page 10 of 21
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`

`
`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 10 0f 12
`
`US 7,012,881 B2
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`ERIC-1004 / Page 11 of 21
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`ERIC-1004 I Page 12 of 21
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`ERIC-1004 / Page 12 of 21
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`U.S. Patent
`
`Mar. 14, 2006
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`Sheet 12 0f 12
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`US 7,012,881 B2
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`ERIC-1004 / Page 13 of 21
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`

`
`US 7,012,881 B2
`
`1
`TIMING AND FREQUENCY OFFSET
`ESTIMATION SCHEME FOR OFDM
`SYSTEMS BY USING AN ANALYTIC TONE
`
`1. FIELD OF THE INVENTION
`
`The present invention relates to a system and method for
`using an analytic tone to calculate the timing offset and
`frequency offset estimations in an orthogonal frequency
`division multiplexing (OFDM) system.
`
`10
`
`2. BACKGROUND OF THE INVENTION
`
`2
`interval, Which increases the subcarrier spacing by a factor
`of tWo. HoWever, a tWo-step synchronization process (i.e.,
`coarse synchronization and ?ne synchronization) is still
`required.
`The above-described tWo-step synchronization sequence
`requires a tWo-symbol training sequence, usually at the
`beginning of a frame. Each symbol is preceded by a guard
`interval for dealing With multipath effects, and each frame
`begins With a number of system symbols, including a zero
`symbol used for frame synchronization and to determine
`channel properties, and a training symbol for initial phase
`reference.
`The symbol/frame timing is found by searching for a
`symbol, Where the ?rst half is identical to the second half in
`the time domain. Then, the carrier frequency offset is
`corrected according to the prior art coarse and ?ne frequency
`synchronization. As noted above, tWo symbols are required
`in the prior art system to estimation the frequency offset, and
`each symbol has tWo halves, With a portion of each training
`symbol copied from the ?rst half to the second half, as
`illustrated in FIG. 8.
`FIG. 8 illustrates a signal architecture for a Wireless local
`area netWork (WLAN) according to the prior art OFDM
`system, according to the IEEE Supplement. A guard interval
`G1, G2, G3, G4, G5 is provided at the beginning of each
`training symbol R1, R2, R3, R4 an data symbol D1. The ?rst
`training symbol R1 is used for signal detection and gain
`control, the second training symbol R2 is used for ?ne and
`coarse frequency synchronization, the third training symbol
`R3 is used for timing synchronization and the fourth training
`symbol R4 is used for channel estimation. Then, the data
`symbols D1 folloW. For example, in each of the symbols, the
`guard interval is N/4, Where N=64, such that the length of
`the guard symbol is 16. For the ?rst and second training
`symbols, the pattern Will repeat 10 times, in the manner as
`noted above and in Schmidl and Cox.
`FIG. 9 illustrates a second prior art data structure accord
`ing to T. Keller and L. Hanzo, “Orthogonal Frequency
`Division Multiplexing Synchronization Techniques for
`Wireless Local Area Networks,” Proc. Of PIMRC ’96, pp.
`963—967, 1996, Which is incorporated herein by reference. A
`null symbol N0 having no signal is provided as the ?rst
`symbol, and is folloWed by a ?rst training symbol R1 for
`timing and coarse and ?ne frequency synchronization, fol
`loWed by a second training symbol R2 for channel estima
`tion, and then the data symbols D1. A guard interval G is
`provided at the beginning of each of the data symbols and
`the second training symbol. HoWever, the null symbol NO
`and the ?rst training R1 symbol do not have a guard interval
`G.
`FIG. 10 illustrates a prior art OFDM system transmitter
`and receiver for the prior art data architectures illustrated in
`FIG. 8 and FIG. 9. Fine synchronization occurs before FFT
`at B, and coarse synchronization occurs after FFT at A. After
`?ne synchronization occurs at B, the guard interval G is
`removed from each symbol by counting to detect each
`symbol’s starting point, and the remaining symbols Without
`the guard interval are subjected to a serial to parallel
`converter, and then the FFT. Next, the symbols go through
`coarse frequency synchronization at A, and are further
`processed to yield a serial data output at the receiver.
`FIG. 11 illustrates the timing and ?ne frequency offset
`estimation of the prior art OFDM system at B of FIG. 10.
`After an analog-to-digital conversion (ADC) 51, a frequency
`offset for the ?ne synchronization is accomplished by a
`delayer 53 and conjugator 55 mixed With the output ADC
`signal at a mixer 57. Amoving sum 59 is then calculated and
`
`15
`
`25
`
`35
`
`A prior art multiplexing method knoWn as OFDM (Or
`thogonal Frequency Division Multiplexing) has been
`applied extensively to high data rate digital transmission,
`such as digital audio/T V broadcasting and Wireless LANs.
`Prior art OFDM receivers must Work properly under varying
`conditions such as speed, temperature and humidity at a
`reasonable cost. Since demodulation is sensitive to fre
`quency deviations, and because frequency deviations With
`respect to the suppressed carrier Will result in a shift in the
`received spectrum, a need exists to control the frequency
`deviations. In the prior art OFDM systems, fast Fourier
`transform (FFT) techniques have been used to determine the
`frequency deviation.
`Because the above-described prior art OFDM technique is
`very sensitive to varying conditions and synchronization
`errors, a prior art method for frequency synchronization of
`OFDM systems has been proposed that includes a tWo-step
`process consisting of coarse synchronization and ?ne syn
`chronization. Coarse synchronization compensates for a
`frequency offset of an integer number of the subcarrier
`spacing, While ?ne synchronization corrects for a frequency
`offset smaller than one-half of the subcarrier spacing. The
`coarse synchronization and the ?ne synchronization must be
`performed separately for the prior art frequency synchroni
`zation, because the maximum estimation range of the ?ne
`synchronization is one-half of subcarrier spacing. Examples
`of prior art algorithms for coarse synchronization include
`GIB (Guard Interval Based) and PB (Pilots Based).
`Coarse synchronization can be accomplished by compar
`ing the position of the received spectral lines With the initial
`reference peak positions (i.e., expected positions). Coarse
`synchronization provides an accuracy of 0.5 of the fre
`quency spacing of the data carriers. HoWever, various leak
`age components (e.g., unWanted harmonics) are generated
`When the FFT WindoW does not ?t With an integer number
`of periods of the received signal. Consequently, ?ne syn
`chronization is required to compensate for that problem,
`thus requiring both coarse and ?ne synchronization to solve
`the aforementioned problems.
`In Timothy M. Schmidl and Donald C. Cox, “Robust
`Frequency and Timing Synchronization for OFDM,” IEEE
`Trans. on Communication, Vol. 45, No. 12, pp.1613—1621,
`December 1997, the contents of Which is incorporated
`herein by reference, Schmidl and Cox propose a prior art
`OFDM symbol for synchronization Which repeats an iden
`tical pattern tWice in a single OFDM symbol to increase the
`estimation range by one subcarrier spacing. Further, IEEE,
`Supplement to Standard for Telecommunications and Infor
`mation Exchange Between Systems-LAN/IVIAN Speci?c
`Requirements-Part 11: Wireless MAC and PHY Speci?ca
`tions: High Speed Physical Layer in the S-GHZ Band,
`P802.11a/D7.0, July 1999, the contents of Which is also
`65
`incorporated herein by reference, de?nes the training OFDM
`symbol such that the repetition period is 1/4 of the useful data
`
`40
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`45
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`55
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`ERIC-1004 / Page 14 of 21
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`

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`US 7,012,881 B2
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`3
`output to the frequency offset calculator 61 and timing offset
`calculator 63. The maximum value of the timing offset is
`then detected, and the frequency offset is calculated in
`accordance With the timing offset estimation. HoWever,
`additional coarse synchronization is required in the prior art
`OFDM system after the timing and frequency offset have
`been estimated in the ?ne synchroniZation, as illustrated in
`FIG. 10 at A.
`The prior art OFDM system and method has various
`problems and disadvantages. For example, the estimation
`ranges are insuf?cient to overcome the need for both the
`coarse and ?ne synchroniZation steps. Further, the prior art
`OFDM system must process all of the subcarriers for timing
`and frequency synchroniZation. As noted above, both coarse
`and ?ne synchroniZation are required to synchroniZe the
`frequency. Further, the timing offset estimation depends on
`the frequency offset estimation.
`The prior art OFDM system must also repeat the same
`pattern tWice in one OFDM symbol to increase the estima
`tion range by 1 subcarrier spacing. For example, 1A of the
`useful data interval is required to increase subcarrier spacing
`by 2. HoWever, these estimation ranges are also insuf?cient
`to overcome the need for both the coarse and ?ne synchro
`niZation steps. Increasing the interval has the additional
`disadvantage of decreasing sum length and accordingly,
`decreasing performance.
`
`SUMMARY OF THE INVENTION
`
`It is an object of the present invention to overcome the
`problems and disadvantages of the prior art.
`It is another object of the present invention to eliminate
`the need for coarse synchroniZation in a frequency synchro
`niZation process, and simplify the mathematical calculations
`required to calculate the frequency offset estimation.
`It is still another object of the present invention to
`calculate the timing offset estimation independently of the
`frequency offset estimation.
`It is yet another object of the present invention to perform
`frequency synchroniZation using an analytic signal as a
`training symbol positioned in a single subcarrier of the
`overhead portion of a data packet.
`To achieve the aforementioned objects, a system for
`estimating frequency offset in an orthogonal frequency
`division multiplexing (OFDM) system is provided, compris
`ing a sliding WindoW correlation summing device that
`receives an input in accordance With a training symbol and
`generates a sliding WindoW correlation sum, and a frequency
`offset estimator that is coupled to said sliding WindoW
`correlation summing device and receives said sliding Win
`doW correlation sum and calculates a frequency offset esti
`mation in accordance With a timing offset estimation,
`Wherein said training symbol comprises an analytic tone
`located in only one subchannel of said training symbol.
`Another system for estimating frequency offset in an
`orthogonal frequency-division multiplexing (OFDM) sys
`tem is provided, comprising a sliding WindoW correlation
`summing device that receives an input in accordance With a
`symbol and generates a sliding WindoW correlation sum, and
`a frequency offset estimator coupled to said sliding WindoW
`correlation summing device and receiving said sliding Win
`doW correlation sum and calculates a frequency offset esti
`mation in accordance With a timing offset estimation. The
`frequency offset estimator comprises an analytic tone-phase
`compensation device that receives said sliding WindoW
`correlation sum and performs a phase compensation opera
`tion to a generate a phase-compensated output, and a fre
`
`15
`
`25
`
`35
`
`40
`
`45
`
`55
`
`65
`
`4
`quency offset estimation calculator that receives that said
`phase-compensation output and calculates said frequency
`offset estimation, Wherein an analytic tone is used in a
`correlation function. The system also comprises a timing
`offset estimator that receives said input signal and generates
`said timing offset estimation independent of said frequency
`offset estimation, Wherein an estimation range can be
`extended by adjusting a correlation interval betWeen
`samples, said analytic tone has at least one of a uniform
`magnitude and a uniform phase rotation, and no coarse
`synchroniZation is required.
`Additionally, a system for estimating frequency offset in
`an orthogonal frequency-division multiplexing (OFDM)
`system is provided, comprising a sliding WindoW correlation
`summing device that receives an input in accordance With a
`training symbol and generates a sliding WindoW correlation
`sum, and a frequency offset estimator that is coupled to said
`sliding WindoW correlation summing device and receives
`said sliding WindoW correlation sum to calculate a frequency
`offset estimation in accordance With a timing offset estima
`tion, Wherein an analytic tone is used in a correlation
`function.
`Further, a method for frequency offset estimation is pro
`vided, comprising the steps of (a) generating an analytic tone
`located on only one subcarrier of a training symbol in
`accordance With an input, (b) generating a sliding WindoW
`correlation sum in accordance With said analytic tone, and
`(c) calculating a frequency offset estimation of said sliding
`WindoW correlation sum in accordance With a timing offset
`estimation, Wherein a correlation interval is adjusted such
`that no coarse synchroniZation is required.
`Also, a method for frequency offset estimation is pro
`vided, comprising the steps of (a) generating an analytic tone
`located on only one subcarrier of a training symbol in
`accordance With an input, and (b) generating a sliding
`WindoW correlation sum in accordance With said analytic
`tone. Said step (b) comprises delaying said input in accor
`dance With a frequency offset interval to generate a ?rst
`delayed output, performing an operation on said ?rst
`delayed output to generate a conjugated output, and mixing
`said conjugated output and said input signal to generate a
`mixed output.
`Further, the method comprises calculating a frequency
`offset estimation of said sliding WindoW correlation sum in
`accordance With a timing offset estimation, said calculating
`step comprising, (a) performing a phase compensation
`operation on said sliding WindoW correlation sum to gener
`ate a phase-compensated output, (b) performing a ?rst
`mathematical operation to generate a ?rst calculated output,
`and (c) receiving said ?rst calculated output and generating
`said frequency offset estimation. Additionally, the method
`comprises extending an estimation range by adjusting a
`correlation interval betWeen samples, Wherein a correlation
`interval is adjusted such that no coarse tuning is required.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`The accompanying draWings, Which are included to pro
`vide a further understanding of preferred embodiments of
`the present invention and are incorporated in and constitute
`a part of this speci?cation, illustrate embodiments of the
`invention and together With the description serve to explain
`the principles of the draWings.
`FIG. 1(a) illustrates a sample input value for complex and
`real numbers for an analytic tone according to the preferred
`embodiment of the present invention;
`
`ERIC-1004 / Page 15 of 21
`
`

`
`US 7,012,881 B2
`
`5
`FIG. 1(b) illustrates a sample train of successive outputs
`and sample indices for the analytic tone according to the
`preferred embodiment of the present invention;
`FIG. 1(a) illustrates a magnitude diagram of the analytic
`tone according to the preferred embodiment of the present
`invention;
`FIG. 1(LD illustrates a phase diagram of the analytic tone
`according to the preferred embodiment of the present inven
`tion;
`FIG. 2 illustrates a block diagram of an apparatus for
`calculating a timing offset estimation and a frequency offset
`estimation according to the preferred embodiment of the
`present invention;
`FIG. 3 illustrates a detailed diagram of the apparatus for
`calculating the timing offset estimation and the frequency
`offset estimation according to the preferred embodiment of
`the present invention;
`FIG. 4 illustrates a method of calculating the timing offset
`estimation and the frequency offset estimation according to
`the preferred embodiment of the present invention;
`FIGS. 5(a)—5(c) illustrate graphical representations of
`simulation results for the performance of timing offset
`estimation according to the preferred embodiment of the
`present invention;
`FIGS. 6(a)—6(e) illustrate graphical representations of
`simulation results for the performance of frequency offset
`estimation according to the preferred embodiment of the
`present invention;
`FIGS. 7(a) and 7(b) illustrate data structures according to
`the preferred embodiment of the present invention;
`FIG. 8 illustrates a ?rst data structure according to the
`prior art;
`FIG. 9 illustrates a second data structure according to the
`prior art;
`FIG. 10 illustrates a prior art reception and transmission
`system; and
`FIG. 11 illustrates a prior art ?ne frequency synchroni
`Zation and timing estimation system.
`
`DETAILED DESCRIPTION OF THE
`INVENTION
`
`Reference Will noW be made in detail to the preferred
`embodiment of the present invention, examples of Which are
`illustrated in the accompanying draWings. In the present
`invention, the terms are meant to have the de?nition pro
`vided in the speci?cation, and are otherWise not limited by
`the speci?cation.
`The preferred embodiment of the present invention uses
`an analytic signal as the training symbol for frame synchro
`niZation of the OFDM systems and the timing and frequency
`offset estimation algorithms. The analytic signal is a com
`plex function having only positive or negative frequencies.
`Because the analytic signal only uses one subcarrier, it is
`hereafter referred to as an analytic tone. The analytic tone is
`generated easily by using inverse fast Fourier transform
`(IFFT), and has characteristics of uniform magnitude and
`?xed phase rotation, and depends on the frequency index
`used. Therefore, the analytic signal is not affected by various
`other factors (e.g., nonlinearity of ampli?ers). Further, by
`changing the correlation interval of the product, the maxi
`mum estimation range for frequency offset can be extended
`to N/2 in a single step. Thus, the prior art need for a tWo-step
`synchroniZation process is eliminated.
`The preferred embodiment of the present invention
`applies the analytic tone to a training symbol for synchro
`niZation. Because the OFDM technique already uses IFFT/
`FFT, the analytic tone is easily generated. HoWever, the
`
`6
`present invention only uses one subcarrier for the analytic
`tone. Table 1 illustrates the inputs of IFFT With 11 subcar
`riers to generate it.
`
`TABLE 1
`
`Inputs of IFFT for generation of an analytic tone.
`
`Sub-
`
`carrier
`index, k
`
`—5
`—4
`—3
`—2
`—1
`O
`1
`2
`3
`4
`5
`
`Input value Xk
`
`Ca
`se 1
`
`O + jO
`O + jO
`O + jO
`O + jO
`O + jO
`O + jO
`:VN—u+jO
`O+j0
`O + jO
`O+j0
`O + jO
`
`ca
`se 2
`
`O + jO
`O + jO
`O + jO
`O + jO
`O + jO
`O + jO
`O+j0
`1VN§+jO
`O + jO
`O+j0
`O + jO
`
`ca
`se 3
`
`O + jO
`O + jO
`O + jO
`O + jO
`O + jO
`O + jO
`O+j0
`O+j0
`O + jO
`:VN—u+jO
`O + jO
`
`Case 1 in Table 1 uses the ?rst subcarrier, Which is
`modulated by \/N;+j0 or —\/N;+j0 for the analytic tone.
`Cases 2 and 3 respectively use the second and fourth
`subcarriers for the analytic tone. Nu represents the number of
`the subcarrier used in the OFDM symbols other than the
`analytic tone among a total of N subcarriers. For example,
`52 subcarriers are used among total of 64 subcarriers. The
`average poWer of each subcarrier is poWer-normaliZed to a
`value of 1, and the total poWer of one OFDM symbol
`becomes Nu. Thus, to make the poWer of the training symbol
`Which is the analytic tone equal to the poWer of the other
`OFDM symbols, the single subcarrier used in the analytic
`tone is modulated by :\/N;+j0.
`FIGS. 1(a)—1(¢0 illustrate characteristics of the analytic
`tone according to the preferred embodiment of the present
`invention. The training symbols carry out signal detection,
`automatic gain control, synchroniZation and channel esti
`mation. FIG. 1(a) shoWs an example of the input complex
`value for the analytic tone of the preferred embodiment of
`the present invention. The symbols of “.times.” and “+” in
`FIG. 1(a) represent respective real and imaginary parts of
`each complex IFFT input.
`FIG. 1(b) illustrates the sample train of successive three
`IFFT outputs that represent 3 training symbols. The sample
`indexes of the analytic tone are from 0 to 63, and the other
`samples represent typical OFDM symbols not having the
`analytic tone. In FIG. 1(b), the solid line and the dashed line
`represent the respective real and imaginary parts of each
`sample based on the IFFT output.
`FIGS. 1(a) and 1(LD respectively illustrate the magnitude
`and the phase diagram of the training symbols of FIG. 1(b).
`FIG. 1(a) illustrates that the analytic tone has a uniform
`magnitude, A, and FIG. 1(LD illustrates that the analytic tone
`has a ?xed phase rotation betWeen the adjacent samples, (Pb.
`The magnitude depends of the training symbols depends on
`the IFFT input, and the phase rotation depends on the
`subcarrier index of a tone. Equation (1) calculates the phase
`rotation betWeen the adjacent samples in the analytic tone:
`
`(1)
`
`10
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`15
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`25
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`35
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`40
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`45
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`55
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`65
`
`Where b is the frequency index of the tone used. For
`example, if b is 1 and N is 64 as illustrated in FIG. 1, (Pb
`becomes 313/32 rad.
`
`ERIC-1004 / Page 16 of 21
`
`

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`US 7,012,881 B2
`
`7
`Additionally, the complex product With tWo transmitted
`samples Which the interval betWeen the tWo samples is a
`samples, represented by Equation (2):
`R”,..(‘)=X*”'X”+m
`
`(2)
`
`Where xn is the n”1 sample of transmited signal and * is the
`conjugate complex value. For example, if tWo samples are in
`the analytic tone, the result of product can be expressed by
`Equation (3):
`R,,’a(‘)=A2-e"“¢b=Ra(‘).
`
`(3)
`
`8
`ther, c is an integer value less than the length of the guard
`interval G. The effect of the ISI(Inter-Symbol Interference)
`for estimation of the frequency offset is minimiZed by using
`an useful data interval that is not identical to the guard
`interval.
`The estimation range depends on the interval a betWeen a
`pair of signals. For example, When a is N/2 samples, Which
`is about one-half of the useful data interval, the maximum
`estimation range equals :1 subcarrier spacing, and When a
`is 1 sample, the maximum estimation range equals :N/2
`subcarrier spacing according to Equation (10):
`
`Equation (3) shoWs that the result of the product is inde
`pendent of the sample index, n.
`For the n”1 received sample, Zn, having a timing offset, 6
`[samples] and a normaliZed frequency offset, 6, Equation (4)
`shoWs that:
`
`15
`
`z,,=x,,,
`
`(4)
`
`Where the normaliZed frequency offset is the ratio of the
`frequency offset to the subcarrier spacing given by Equation
`(5)1
`
`(5)
`
`25
`
`Thus, the complex product With tWo received samples of
`Which the interval is a samples is represented by Equation
`(6):
`
`Similarly to Equation (3), if tWo samples are in the
`analytic tone, the result of product can be expressed by
`Equation (7):
`
`Because the receiver already has the information about
`the magnitude A and the compensation of phase rotation
`el'a‘l’b, it can estimate the timing offset and the frequency
`offset in a single step using this characteristic.
`The preferred embodiment of the present invention
`includes an algorithm that uses the above-described analytic
`tone to calculate the timing offset estimation and the fre
`quency offset estimation. The method for calculating the
`timing offset estimation using the poWer (or magnitude) of
`the sum of Equation (7) is given by Equation (8)
`
`35
`
`40
`
`45
`
`N+G ail
`9=MAx
`
`2
`
`N+G ail
`or MAX
`
`a
`
`(3)
`
`t:
`
`Where G is the length of the guard interval and A means that
`the function is an estimation. Because the algorithm uses the
`exponential poWer, it is not affected by frequency offset.
`Further, increasing the value of a decreases the length of the
`sum.
`The algorithm for calculating the frequency offset esti
`mation uses the phase of the sum of Equation (7), as shoWn
`in Equation (9):
`
`55
`
`(10)
`
`The interval a betWeen the pair for the timing offset and the
`frequency offset estimation may have different values a1, a2
`instead of a substantially same interval, a.
`FIG. 2 illustrates an apparatus for calculating the fre
`quency offset estimation according to a ?rst preferred
`embodiment of the present invention. An analog-to-digital
`converter (ADC) 1 receives an input signal and converts the
`input signal from an analog signal to a digital signal. A
`sliding WindoW correlation summing device 3 receives a
`signal from the ADC 1, and generates an output received by
`a frequency offset estimator/analytic tone-phase compensa
`tion device 5, Which calculates the frequency offset estima
`tion 6 in accordance With the analytic tone. A timing offset
`estimator 7 also receives the signal” from the ADC and
`calculates the timing offset estimation 6 independently of the
`calculation of the frequency offset estimation 6 by the
`frequency offset estimator 5. The timing offset estimation 6
`is receivedhat a switch 9, such that the frequency offset
`estimation 6 is calculated in a single step using the timing
`offset estimation 6.
`FIG. 3 illustrates a more detailed diagram ofhthe apparatus
`for calculating the frequency offset estimation 6 according to
`the preferred embodiment of the present invention. The
`respective intervals for the timing and frequency offset
`estimation are a1 and a2.
`The sliding WindoW correlation summing device 3 of FIG.
`2 is illustrated in FIG. 3 as a delayer 11 and a conjugator 13
`coupled to each other in series, and in parallel betWeen an
`output of