IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 6, NOVEMBER 2007
`
`3469
`
`Synchronization and Cell-Search Technique Using
`Preamble for OFDM Cellular Systems
`
`Kwang Soon Kim, Senior Member, IEEE, Sung Woong Kim, Student Member, IEEE,
`Yong Soo Cho, Senior Member, IEEE, and Jae Young Ahn, Member, IEEE
`
`Abstract—In this paper, a novel preamble structure, including
`a synchronization field (S-field) and a cell-search field (C-field),
`is proposed for orthogonal-frequency-division-multiplexing-based
`cellular systems. An efficient algorithm for downlink synchro-
`nization and cell search using the preamble is also proposed.
`The synchronization and cell-search process includes the initial
`symbol-timing estimation using continuously or, at least, period-
`ically transmitted downlink signal, the frame detection, the fine
`symbol-timing estimation, the frequency-offset estimation using
`the preamble S-field, and the cell identification using the preamble
`C-field. Performance of each synchronization and cell-search step
`is analyzed and verified by computer simulation. The overall
`performance of the synchronization and cell search is then ana-
`lyzed in terms of the mean acquisition time. It is shown that the
`proposed preamble with the corresponding synchronization and
`cell-search algorithm can provide a very robust synchronization
`and cell-search capability, even in bad cellular environments.
`
`search, cellular, orthogonal-frequency-
`Index Terms—Cell
`division multiplexing (OFDM), preamble, synchronization.
`
`I. INTRODUCTION
`
`R ECENTLY, orthogonal-frequency-division multiplexing
`
`(OFDM) has been widely accepted as the most promising
`radio transmission technology for the next-generation wireless
`systems due to its advantages such as robustness to multi-
`path fading, granular resource allocation capability, and no
`intracell interference. Among the conventional OFDM-based
`wireless systems, digital audio broadcasting, IEEE 802.11a,
`and Hiperlan/2 are well known [1]–[5]. For cellular systems,
`it is one of the most important requirements to provide ro-
`bust synchronization and cell-search capability. For example,
`the wideband code-division multiple-access (WCDMA) system
`provides a hierarchical three-step cell search using the primary
`
`Manuscript received April 19, 2005; revised April 5, 2006, November 30,
`2006, and January 17, 2007. This work was supported in part by the MIC,
`Korea, under the ITRC support program supervised by the IITA under Grant
`IITA-2006-(C1090-0602-0011) and in part by the Ubiquitous Computing and
`Network (UCN) Project, MIC 21st Century Frontier R&D Program in Korea.
`The review of this paper was coordinated by Dr. E. Larsson.
`K. S. Kim is with the Department of Electrical and Electronic Engineering,
`Yonsei University, Seoul 120-749, Korea (e-mail: ks.kim@yonsei.ac.kr).
`S. W. Kim is with the Samsung Electronics Company, Ltd., Suwon 442-742,
`Korea.
`Y. S. Cho is with the School of Electrical and Electronic Engineering,
`Chung-Ang University, Seoul 156-756, Korea.
`J. Y. Ahn is with the Electronics and Telecommunications Research Institute,
`Daejeon 305-350, Korea.
`Digital Object Identifier 10.1109/TVT.2007.901053
`
`synchronization code and the secondary synchronization code
`in the synchronization channel (SCH) and the common pilot
`channel (CPICH) [6]. However, the synchronization schemes
`used in such conventional OFDM schemes are not appropriate
`for a cellular system since they cannot discriminate signals
`from different cells unless their carrier frequencies are different.
`Thus, devising a new synchronization and cell-search technique
`for OFDM-based cellular systems is required.
`Recently, synchronization and cell-search techniques have
`been proposed for
`asynchronous OFDM–code-division-
`multiplexing cellular systems having a channel structure
`similar to the WCDMA [7], [8]. The differentially encoded
`SCH uses equally spaced subcarriers in every OFDM symbol
`and is common for every cell, while CPICH is spread by a
`cell-specific code in both the time and the frequency domains.
`However, asynchronous cellular systems generally suffer
`from longer cell-search time, particularly for a neighbor-cell
`search. Thus, synchronous cellular systems using the global
`positioning system (GPS) are considered to be more attractive
`for the next-generation cellular systems. In this paper, a novel
`preamble-based synchronization and cell-search technique
`for synchronous OFDM-based cellular systems using a novel
`preamble structure, which is comprised of a synchronization
`field (S-field) and a cell-search field (C-field), is proposed.
`The initial result of this work has been presented in [9]. The
`proposed preamble-based synchronization and cell search is
`fully analyzed, and the performance of the proposed algorithm
`is then verified by computer simulations in this paper. In
`addition, the overall performance of the proposed cell search is
`analyzed in terms of the mean acquisition time (MAT).
`
`II. PROPOSED PREAMBLE STRUCTURE
`
`A. Design Motivation
`
`In conventional OFDM-based wireless systems, such as
`IEEE 802.11a or Hiperlan/2, the functionality required for an
`initial synchronization includes signal detection, frame-timing
`estimation, and frequency-offset estimation. In order to achieve
`the above functionality, the most commonly used preamble
`structure in conventional OFDM-based wireless systems is to
`repeat a pattern, which is a sequence with a good autocorrela-
`tion property (autocorrelation function is close to the Kronecker
`delta function), a few times in a preamble symbol. Such a struc-
`ture can provide a good time and frequency synchronization
`capability and has been successfully used in many commer-
`cial systems (see [5] and [11] for more detailed discussion).
`
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`3470
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`IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 6, NOVEMBER 2007
`
`However, for a cellular system (in a single-frequency network
`as in commercial cellular systems), neighboring cells should
`use different preambles so that a mobile station can discriminate
`signals from different cells. Thus, the functionality required
`for the synchronization and cell search includes frame-timing
`estimation, frequency-offset estimation, and cell identification.
`Note that the signal detection is not required since a cellular
`system is not a burst transmission system. Once the cell number
`is obtained, a receiver can receive the broadcasting channel
`of the cell, and the whole cell information can be retrieved.
`A straightforward way to obtain the above functionality in an
`OFDM-based cellular system is to use different sequences, as
`many as the number of different cells, as the repetitive patterns
`of the preambles. Unfortunately, such a preamble design results
`in a formidable complexity of the synchronization and cell
`search (the number of candidates is the number of samples in
`a frame times the number of different cells). Thus, a preamble
`structure for a cellular system should not only provide robust
`capability of synchronization and cell search but also enable
`us to use a low-complexity hierarchical synchronization and
`cell-search algorithm. Thus, the motivation of the proposed
`preamble design is as follows.
`1) It should provide an acceptable acquisition time even in a
`very bad cellular environment where the mobile speed is
`quite fast and the average signal-to-noise ratio (SNR) is
`very low.
`2) It should allow a low-complexity hierarchical algorithm.
`
`3) A natural way to perform a low-complexity hierarchical
`estimation is as follows:
`a) estimating a rough symbol timing;
`b) determining the location of the S-field symbol;
`c) estimating the exact frame timing.
`4) Step a) above can easily be done using the cyclic prefix
`(CP). In addition, Step c) can be done using the autocor-
`relation property of the S-field. Thus, the remaining task
`is to give the S-field a unique structure that differentiates
`the S-field from other ordinary OFDM symbols. This can
`be fulfilled by using the inverted postfix structure of the
`S-field.
`
`The preamble C-field is used for the cell-number identi-
`fication, and each cell with a different cell number uses a
`different preamble C-field. Then, the detailed requirements and
`the design approach of the preamble C-field are as follows.
`
`1) The best way to make OFDM signals is to use different
`subcarriers. Thus, the C-fields of adjacent cells should use
`different sets of subcarriers.
`2) To increase the number of different cells, the different
`cells (not adjacent) may use the same set of subcarriers
`with different sequences (with a good cross-correlation
`property) on these subcarriers.
`3) Even to accommodate a higher number of different cells,
`the C-field can be comprised of more than one OFDM
`symbol.
`
`The detailed preamble design from the above design strategy
`is as follows. The downlink frame structure considered in this
`paper and the proposed preamble structure (both in the time
`and the frequency domains) are shown in Fig. 1. A preamble,
`with length Tp, is located at the beginning of the frame and
`is followed by a number of data slots, where pilot symbols
`are well spread both in the time and the frequency domains.
`The length of the S-field is Tps, which is equal to the OFDM
`symbol duration Ts. The S-field signal is composed of one S
`(cid:1)
`(cid:1)
`symbol. The IS
`symbol is the first TCP-
`symbol and one IS
`length part of the π-phase-rotated version of the S symbol, and
`the S symbol is comprised of NSsym repetitive Sa symbols.
`Here, TCP is the length of the CP. As shown in Fig. 1, one good
`example of the preamble S-field signal PS(t) is
`
`(cid:4)
`−(cid:4)
`0 ≤ t < Td
`NF −1
`k=0 g(k)ϕk(t),
`k=0 g(k)ϕk(t − Td), Td ≤ t < Tps
`NF −1
`otherwise
`
`0,
`
`(1)
`
`
`
`
`PS(t) =
`
`B. Preamble Design
`
`The rough structure of the proposed preamble to obtain
`the functionality and to meet
`the design motivation de-
`scribed in Section II-A can be determined from the following
`observations.
`1) In a synchronous system, base stations can transmit a
`common preamble for the timing-estimation stage, and
`the received signal is equivalent to the signal from a single
`transmitter through a multipath channel.
`2) We can ignore the relative frequency offset between dif-
`ferent base stations in a GPS-aided synchronous system.
`3) In order to identify the cell number, the signals from
`different base stations should be as different as possible.
`Based on the above observations, we determine to use two dif-
`ferent components, which are denoted as the preamble S-field
`and the preamble C-field, for the proposed preamble structure.
`The preamble S-field is common for all base stations and is
`used for the frame-timing estimation and the frequency-offset
`estimation. The detailed requirements and the design approach
`of the preamble S-field are as follows.
`
`where NF is the size of the fast Fourier transform (FFT),
`ϕk(t) = exp(−j2π(k− NF /2)t/Td)), Td = Ts− TCP, g(k) =
`µ(i)δK(k − iNSsym), µ(i) is a pseudorandom sequence such
`as the m-sequence, and δK(·) is the Kronecker delta function.
`1) To reduce the complexity of the cell identification, the
`Since nonzero symbol values are assigned at every NSsym
`integral part of the frequency offset should be estimated.
`subcarrier in (1), the S symbol has NSsym repetitive patterns
`This requirement can be fulfilled by using a repetitive
`(each is denoted as the Sa symbol). Among the many possible
`pattern in the preamble S-field.
`S-field signals given by (1), the signal with a low peak-to-
`2) A reliable frame-timing estimation can be fulfilled by
`average power ratio and a good correlation property can be
`designing the above repetitive pattern in the preamble
`selected as the preamble S-field.
`S-field to have a good autocorrelation property.
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`

`

`KIM et al.: SYNCHRONIZATION AND CELL-SEARCH TECHNIQUE USING PREAMBLE FOR OFDM SYSTEMS
`
`3471
`
`Fig. 1. Abstract downlink frame structure and the proposed preamble structure.
`
`The length of the C-field is equal to NcTs. The C-field signal
`C (t) is defined as
`of the mth cell P m
`
`n (k) is defined as
`5) Finally, cm
`
`
`(cid:4)NF
`(cid:4)NF
`
`
`C (t)
`P m
`
`=
`
`0,
`
`−1
`k=0
`−1
`k=0
`
`n (k)ϕk(t+Td−TCP), 0≤ t−nTs < TCP
`cm
`TCP ≤ t−nTs < Ts
`n (k)ϕk(t−TCP),
`cm
`otherwise
`
`n (k) =
`cm
`
`
` ψpn,qn(j), k = spn,c(j)
`
`(4)
`
`¯ψ(j),
`k = spn,p(j)
`0,
`otherwise
`where ψpn,qn(j), ¯ψ(j), spn,p(j), and spn,c(j) denote the
`jth elements of ψpn,qn, ¯ψ, spn,p, and spn,c, respectively.
`Here, we can see that, with the proposed C-field, M Nc
`different cells can be discriminated. As an example, let Nc = 2,
`P = 8, and G = 8. Then, the number of cells that can be
`discriminated is M Nc = 642 = 4096, which is large enough for
`a cellular system.
`
`C. Comparison With the IEEE802.16e Preamble Structure
`
`(2)
`n (k), 0 ≤ n ≤ Nc − 1, is the frequency-domain signal
`where cm
`at the kth subcarrier of the nth symbol of the C-field of the mth
`n (k) is as follows.
`cell. The construction of cm
`1) Let S = {s0, s1, . . . , sP−1} be a set of partitions of all
`used subcarriers. Furthermore, the ith partition si is di-
`vided into si,p and si,c.
`2) Let ψi,j, i = 0, . . . , P − 1, j = 0, . . . , G − 1, be the se-
`quences with good correlation properties and ¯ψ be a
`sequence used for known pilot-symbol pattern.
`3) For each symbol of the C-field, there are P different
`partitions and G different sequences. Thus, M = P G
`different symbols are prepared.
`4) Let pn and qn be the partition number and the sequence
`number for the nth symbol of the C-field, respectively.
`Then, the cell number m is determined by the combina-
`tion of the Nc partition numbers (p0, . . . , pNc−1) and the
`Nc sequence numbers (q0, . . . , qNc−1) as
`
`Among the recently developed OFDM-based wireless sys-
`tems, IEEE802.16e [10] OFDMA physical layer adopted 114
`different preamble patterns by using cell-specific sequences
`transmitted over one of the three frequency partitions called
`segments. In addition, an optional common synchronization
`preamble can be used at the end of the downlink frame structure
`for simpler timing estimation in which a pseudorandom code
`is transmitted on even-numbered subcarriers (two repetitive
`patterns in the time domain) with an ordinary CP. The advan-
`tage of the proposed preamble structure can be summarized as
`follows.
`1) The inverted postfix structure of the proposed preamble
`(cid:1)
`symbols) is a very unique structure that enables us
`(IS
`to find the beginning point of a frame without a fine
`timing estimation. With the proposed preamble structure,
`n=0
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`
`m =
`
`(pnG + qn)M n.
`
`(3)
`
`Nc−1(cid:5)
`
`

`

`3472
`
`IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 6, NOVEMBER 2007
`
`mate the frame timing using the novel structure of the preamble
`S-field. As will be seen later, we evaluate a metric for the frame-
`timing estimation at the sample point obtained from the initial
`symbol-timing estimation for each OFDM symbol. Thus, the
`number of candidates in the frame-timing estimation is at most
`the number of OFDM symbols in a frame. Thus, the proposed
`hierarchical synchronization scheme has much lower com-
`plexity than the conventional synchronization schemes [11],
`[14]–[16]. Although the fine timing estimation is not an es-
`sential task required for a cell search, it is eventually required
`for successful data reception. Thus, a fine timing estimation is
`performed using the preamble S-field after the frame timing is
`obtained. In this paper, a cross-correlation-based method [11],
`[17] is adopted with a timing back-off for better performance
`[18]. Finally, frequency-offset estimation is performed by ap-
`plying an autocorrelation-based method, such as in [11] and
`[19], to the repetitive structure of the preamble S-field.
`
`A. Initial Symbol Timing and Frequency-Offset Estimation
`Let the sampled received signal be y(n) and z(k) be
`
`NCP−1(cid:5)
`
`r=0
`
`z(k) =
`
`1
`NCP
`
`∗
`
`y
`
`(k + r)y(k + r + NF )
`
`(5)
`
`where NCP is the number of samples in the CP. Then, the initial
`symbol timing τinit is obtained using the CP correlation as [12]
`
`(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)Ninit−1(cid:5)
`
`j=0
`
`τinit = arg max
`n
`
`(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)
`
`z(n + jNs)
`
`(6)
`
`Fig. 2. Proposed synchronization process.
`
`a low-complexity hierarchical synchronization algorithm
`similar to that in WCDMA [6] can be applied.
`2) The main preamble structure of IEEE802.16e can be
`considered as a special case of the proposed C-field.
`3) Additional advantages of the proposed C-field are as
`follows.
`a) Many more different cells can be implemented by al-
`lowing more than one OFDM symbol for the preamble
`C-field if necessary.
`b) The proposed C-field allows a flexible form of
`partitions.
`c) Performance can be improved by coherently combin-
`ing whole symbols with the aid of the known pilot
`sequence in the proposed C-field, provided that chan-
`nel estimation is reliable. In addition, when the pro-
`posed C-field uses a partition comprised of distributed
`clusters (adjacent subcarriers in a cluster), as shown in
`Fig. 1, the symbols within a cluster can be coherently
`combined without channel estimation.
`Thus, it is apparent that we can easily reduce the complexity
`of the synchronization and cell search, which is critical for
`a mobile station. In addition, we can expect that the cell-
`identification performance of the proposed preamble is better
`when both preambles use the same number of subcarriers since
`the proposed preamble allows coherent combining.
`
`III. SYNCHRONIZATION
`
`where Ns and Ninit are the number of samples in an OFDM
`symbol and the number of OFDM symbols used in the initial
`symbol-timing estimation, respectively. In addition, we can
`estimate the initial frequency offset init as [12]
`
`In Fig. 2, the synchronization process proposed in this paper
`is shown. In the conventional OFDM-based systems such as
`wireless LAN, all of the initial synchronization processes,
`including signal detection, are performed using the preamble
`[11]. However, in an OFDM-based cellular system employing
`frequency-division multiplexing (FDD), signals are transmit-
`ted continuously or, at least, periodically due to the common
`pilot symbols and common channels used for broadcasting.
`By taking these into account, we can devise a more efficient
`hierarchical synchronization and cell-search algorithm. First,
`the signal-detection step is not required in the synchroniza-
`tion of OFDM-based cellular systems using FDD. In addition,
`a symbol-timing acquisition within a certain range (roughly
`speaking, 10%–20% of the length of the CP, which corresponds
`to 1 dB–2 dB SNR loss) is enough for the cell search. Thus,
`as the first step of the synchronization and cell search, an initial
`symbol timing and an initial frequency offset are obtained using
`a simple CP-based methods such as in [12] and [13]. Note
`that the required length of the searching window in the initial
`τf (ι) = ιNs + τinit,
`symbol-timing estimation is at most over an OFDM-symbol
`τframe = τf (ι),
`period. After achieving the initial synchronization, we can esti-
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`
`
`Ninit−1(cid:5)
`
`j=0
`
` init =
`
`1
`2π
`
`arg
`
`
` .
`
`z(τinit + jNs)
`
`(7)
`
`Note that (7) can estimate only the fractional part of the
`frequency offset (normalized by the subcarrier spacing). The
`estimation of the integral part of the frequency offset will be
`taken care of using the preamble S-field.
`
`B. Frame-Timing Estimation
`
`synchronization, we have
`After obtaining the initial
`Nf (= Tframe/Ts) candidates for the frame timing. Here, we
`utilize the property of the preamble S-field where every OFDM
`symbol, except the preamble S-field, has a positive value of
`autocorrelation due to the CP, while the preamble S-field has
`a negative value of autocorrelation due to the inverted postfix
`structure. By exploiting the unique structure of the preamble
`S-field, the frame timing is estimated as
`0 ≤ ι < Nf
`if (cid:8) {zc (τf (ι))} < 0
`
`(8)
`
`

`

`KIM et al.: SYNCHRONIZATION AND CELL-SEARCH TECHNIQUE USING PREAMBLE FOR OFDM SYSTEMS
`
`3473
`
`τ0 = 0 and k = 0 represent the frame boundary without loss
`of generality. The complex channel gain of the lth path hl is
`assumed to be a complex Gaussian process with mean zero and
`variance βl (i.e., Rayleigh fading channel). Moreover, n(k) is
`assumed to be a complex Gaussian process with mean zero and
`variance 2σ2
`n. Define
`
`∗
`x
`
`(r)y(k + r).
`
`(12)
`
`R−1(cid:5)
`
`r=0
`
`1 R
`
`ζ(k) =
`
`In the case where NCP is sufficiently large, which is true for
`most OFDM cellular systems due to the large delay spread of
`outdoor environments, we can assume that z(k) and ζ(k) are
`Gaussian random processes with means mz(k) and mζ(k) and
`
`z(k) and 2σ2ζ (k), respectively, using the central
`variances 2σ2
`limit theorem (CLT). The statistics can be summarized as
`
`NF
`
`mz(k) ∼= (−1)δK((cid:10)k/Ns(cid:11)) Pxq(k)κ
`z(k) ∼=
`2σ4
`2σ2
`nPxκ
`n
`NCPNF
`NCP
`hlδK(k − τl)
`
`σ2
`
`mζ(k) = Px
`NF
`
`+
`
`L−1(cid:5)
`
`l=0
`
`σ2
`
`(13)
`
`(14)
`
`ζ (k) ∼=
`P 2
`+ σ2
`x κ
`nPx
`(cid:4)
`2RN 2
`RNF
`F
`|hl|2, and (cid:10)x(cid:11) is the greatest integer not
`L−1
`where κ =
`exceeding x. Here, q(k) = max(0, 1 − (u(k)/NCP)) denotes
`l=0
`the loss due to the initial timing-estimation error, where u(k) =
`|k − Ns · (cid:10)k/Ns + 1/2(cid:11)| represents the distance to the nearest
`OFDM-symbol starting point from k. Derivations are given in
`Appendix A.
`1) Initial Synchronization: The outage probability of the
`initial symbol timing Pr{|τinit| > τth} can be calculated from
`the statistic of z(k) by using a numerical method for a given
`threshold τth. In addition, the outage probability of the initial
`symbol-timing estimation can be reduced by increasing Ninit.
`In the sequel, we assume that the initial timing estimation is
`successful with the initial timing error equals to τinit. Further-
`more, we assume that the frequency offset is well estimated so
`that the effect of the remaining frequency offset in the following
`synchronization and cell-search procedure can be ignored.
`2) Frame-Timing Estimation: If the transmitted symbol is
`not the preamble S-field, i.e., ι (cid:13)= 0, it can be easily seen from
`(8) and the statistic of z(k) that the false-alarm probability of
`frame detection conditioned on the combined fading channel
`gain (κ) Pfa,frame(κ) is given by
`(cid:12)(cid:13)
`(cid:14)
`Pfa,frame(κ) = Pr {(cid:8) {z(ιNs + τinit) < 0}
`∼= Q
`2gγ2κ2
`2γκ + 1
`
`where (cid:8){x} is the real part of x, and zc(·) in (8) is the same
`as (5), except that the received samples after frequency-offset
`compensation with the initial frequency-offset estimate ob-
`tained in (7) yc(·) is used instead of y(·). For better
`frame-timing estimation performance, one may use τframe =
`minι (cid:8){zc(τf (ι))} instead of using (8), particularly when SNR
`is low. However, this will cause additional delay since the
`observation window should be at least one frame, which may
`degrade the performance of the whole cell-search process in
`terms of the MAT.
`
`C. Fine Symbol-Timing Estimation
`
`In the case where the frequency offset have both the inte-
`gral and the fractional parts, the frequency offset f can be
`estimated using the repetitive property of the preamble S-field
`as [11], [19]
`
`(cid:11)
`
` f = NSsym
`2π
`
`arg
`
`∗
`
`y
`
`(τs+r)y(τs+r+NF /NSsym)
`
`.
`
`r=0
`
`(9)
`
`(cid:10)
`NCP−1(cid:5)
`
`Note that (9) can estimate the normalized frequency offset in
`the range of [−NSsym/2, NSsym/2].
`After obtaining the frame timing, we can assume that the
`starting point of the preamble S-field is around the estimated
`frame timing τframe. Then, we can estimate the fine symbol
`timing τs with the timing backoff by taking the cross correlation
`between the frequency-offset compensated signal yc(·) with
`the result obtained in (9) and the preamble S-field signal as
`[11], [17]
`
`(cid:6)(cid:6)(cid:6)(cid:6)(cid:6) − NB
`
`(10)
`
`(r + Rs)yc(n + r + Rs)
`
`∗ S
`
`P
`
`(cid:6)(cid:6)(cid:6)(cid:6)(cid:6)R−1(cid:5)
`
`r=0
`
`τs = arg max
`n
`
`where PS(r) is the sampled signal of the preamble S-field,
`R is the number of samples used for the fine symbol-timing
`estimation, Rs is the starting point for accumulation, and NB
`is the number of samples for the timing back-off. In OFDM
`systems, a negative timing error (estimated timing is greater
`than true timing) causes intersymbol-interference (ISI) and
`interchannel-interference (ICI) effects, while a small positive
`timing error (less than the CP length minus the channel delay)
`does not. Thus, we can reduce the ISI and the ICI effects by
`introducing an appropriate timing backoff.
`
`(cid:4)
`D. Performance Analysis
`l=0 hlδ(t − τ c
`L−1
`l ) be the channel impulse re-
`Let h(t) =
`sponse and x(k) be the sampled transmitted signal with average
`power Px/NF . Assuming that the frequency-offset estimation
`is perfect, the received signal after sampling with sampling
`period T and frequency-offset compensation is given by
`
`L−1(cid:5)
`
`l=0
`
`y(k) =
`
`hlx(k − τl) +n( k)
`
`(11)
`
`(cid:15) ∞
`√
`where γ = Px/(2σ2
`nNF ), g = q2(τinit)NCP, and Q(x) =
`x exp(−t2/2)dt. On the other hand, if the trans-
`2π)
`(1/
`where τl, which is defined by τ c
`l /T , is assumed to be an integer.
`ι = 0,
`For notational simplicity, we use y instead of yc. In addition,
`mitted symbol
`is the preamble S-field,
`i.e.,
`the
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`
`

`

`3474
`
`IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 6, NOVEMBER 2007
`
`detection-failure probability conditioned on the combined fad-
`ing channel gain (κ) Pdf,frame(κ) is given by
`(cid:12)(cid:13)
`(cid:14)
`Pdf,frame(κ) = Pr {(cid:8) {z(τinit) > 0}
`∼= Q
`2gγ2κ2
`2γκ + 1
`
`(15)
`
`.
`
`IV. CELL IDENTIFICATION
`
`For the cell identification, we need to estimate the parti-
`tion numbers pn, n = 1, . . . , Nc and the sequence numbers
`qn, n = 1, . . . , Nc, which are used to generate the preamble
`C-field.
`In this paper, we consider a hierarchical cell-
`identification algorithm for low computational complexity. For
`each OFDM symbol in the preamble C-field, the partition
`number is estimated by calculating the received signal power
`contained in each partition and choosing the partition with the
`largest power. Then, the sequence number is estimated by com-
`paring cross-correlation values between candidate sequences
`and the received frequency symbols on the selected partition.
`Finally, we obtain the cell number from the estimated partition
`numbers and the estimated sequence numbers of the Nc OFDM
`symbols in the preamble C-field.
`
`A. Cell-Identification Algorithm
`Let Yn(k) be the received frequency-domain symbol at the
`kth subcarrier in the nth OFDM symbol. Then, for the nth
`symbol of the preamble C-field, the subcarrier partition number
`pn can be estimated as
`
`(cid:5) k
`
`ˆpn = arg max
`p
`
`|Yn(k)|2 .
`
`(18)
`
`(cid:4)
`∈sp
`l=0 hl exp(−j2πτlk/NF ) be the complex
`L−1
`Let H(k) =
`channel at
`the kth subcarrier. Then,
`from the received
`frequency-domain symbols Yn(k), k ∈ s ˆpn,p, and the known
`pilot sequence ¯Ψ, the estimated channel gain ˆH(k) can be
`obtained by applying an appropriate channel-estimation scheme
`such as the modified least-squares estimator [21]. Let χp,q be
`the cross correlation between the channel-compensated sym-
`bols in the subcarrier set sp and the sequence ψp,q, which is
`defined by
`
`|sp,c|−1(cid:5)
`
`j=0
`
`(19)
`
`∗ p
`
`(sp,c(j)) ψ
`
`,q(j)
`
`Yn (sp,c(j)) ˆH
`
`∗
`
`χp,q =
`
`|ζ(k)|2
`
`where |A| denotes the cardinality of a set A. Then, the sequence
`number of the nth symbol of the preamble C-field qn can be
`(cid:16)
`estimated as
`
`ˆqn =
`
`arg maxq (cid:8){χ ˆpn,q}, χ ˆpn,ˆqn > χth
`Detection fails,
`otherwise
`
`(20)
`
`(cid:17)(cid:17)
`|hl|
`
`n=1
`
`(−1)n+1
`
`vT w
`Rγ + vT w
`
`(cid:19)
`
`Nc−1(cid:5)
`
`where χth is the threshold for the cell identification. Finally, the
`cell number is estimated as
`
`ˆm =
`
`(ˆpnG + ˆqn)M n.
`
`(21)
`
`n=0
`
`B. Performance Analysis of the Partition Estimation
`
`Although the proposed algorithm can be applied for any
`value of Nc, any partition set S, and any sequence sets ψi,j,
`i = 0, . . . , P − 1, j = 0, . . . , G − 1, we consider a simple but
`
`v∈Vn
`Nw − NB + 1,
`× B
`vT w
`(17)
`Rγ + vT w
`where v is the L(NB) × 1 column vector whose ele-
`ments are either zero or one. In addition, w is defined by
`· · · β
`−1
`−1
`−1
`L(NB )−1]T, Vn is the collection of all v’s con-
`[β
`0 β1
`
`sisting of n elements of “one,” and B(x, y) is the beta
`function [20].
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`
`to (14) because mz(τinit) =
`Note that
`(15)
`is identical
`z(ιNs + τinit) for ι (cid:13)= 0.z(τinit) =σ 2
`−mz(ιNs + τinit), and σ2
`
`3) Fine Symbol-Timing Estimation: Although the fine
`symbol-timing estimation is not an essential part for the cell
`search, it is required for the good quality of data reception.
`In addition, it is not only required for the initial cell search
`but also required for the time tracking in an OFDM cellular
`system. Thus, it is required to analyze the performance of the
`fine symbol-timing estimation separately from the cell search in
`fading channels. In previous literature such as [15] and [18], the
`mean-square error has been used for a performance measure.
`In this paper, however, the probability that the ISI and the ICI
`occur due to the falsely estimated symbol timing is used as
`a performance measure for the fine symbol-timing estimation.
`Since the ISI and the ICI occur when a nonnegligible path exists
`before the start point of the FFT window at the receiver, we can
`define the timing-error probability Pe,timing as
`|ζ(k)|2 < max
`|ζ(k)|2
`max
`Pe,timing = Pr
`(16)
`k∈Kf
`k∈Ks
`where Ks ={k|0≤ k < NB}, Kf ={k|−N w/2≤ k < Nw/2,
`k /∈ Ks}, and Nw is the search window size of the fine
`symbol-timing estimation. Here, we assume that −(Nw/2) ≤
`τinit < (Nw/2) and that the frame-timing estimation is suc-
`cessful. Let Us be the set given by {τ0, . . . , τL(NB )−1}. Here,
`L(NB) denotes the largest integer such that τL(NB )−1 < NB.
`If we set NB to be sufficiently large so that βl (cid:17) β0 for
`l ≥ L(NB), we can further approximate |ζ(k)|2, k ∈ Kf as an
`independent and identical central chi-square random process
`|ζ(k)|2 ∼= maxk∈Ks
`|ζ(k)|2. Then, as derived in
`and maxk∈Us
`Appendix B, the timing-error probability is given by
`(cid:17)
`
`(cid:16)
`
`(cid:17)
`
`Pe,timing
`
`Pr
`
`|ζ(k)|2 < max
`max
`k∈Kf
`k∈Us
`|ζ(k)|2 |l =arg max
`|ζ(τl)|2 < max
`k∈Kf
`0≤l<L(NB )
`(cid:5)
`
`(cid:16)
`∼= Pr
`(cid:16)
`(cid:16)
`∼= E
`= 1 − L(NB )(cid:5)
`(cid:18)
`
`

`

`3475
`
`(cid:19)
`
`− τl2)
`
`(cid:18)
`− j2π(pD + d)(τl1
`(cid:19)
`NF
`
`L−1(cid:5)
`(cid:18)
`− τl2)r
`− j2π(τl1
`Nf n
`
`∗ l
`
`2 exp
`
`hl1 h
`
`l2=0
`
`exp
`
`L−1(cid:5)
`× Nf n−1(cid:5)
`
`= PxP
`NF
`
`l1=0
`
`r=0
`
`= PxP
`NF
`
`Nf nκ
`
`(25)
`
`KIM et al.: SYNCHRONIZATION AND CELL-SEARCH TECHNIQUE USING PREAMBLE FOR OFDM SYSTEMS
`
`is the signal power contained in the dth comb set. Here, the last
`equality in (25) comes from the assumption for simplicity that
`τi − τj is not an integer multiple of Nf n for 0 ≤ i (cid:13)= j < L.
`Then, using the results in [22], we obtain an upper bound on
`the partition estimation error Pe,part(κ) as
`(cid:18)
`Pe,part(κ) = Pr{ˆpn (cid:13)= pn|κ}
`≤ P − 1
`− NF γκ
`(cid:18)
`exp
`× NF /P−1(cid:5)
`22NF /P−1
`2
`(cid:4)
`
`where C(w, r) = (1/r!)
`
`r=0
`w−r−1
`k=0
`
`C (NF /P, r)
`
`(cid:21)
`
`(cid:22)
`
`.
`
`2w−1
`k
`
`(cid:19)
`
`(cid:19)
`
`r
`
`NF γκ
`2
`
`(26)
`
`useful example for the performance analysis of the partition
`estimation and the sequence estimation shown in this and the
`next sections as follows.
`1) Assume that we use all of
`the subcarriers
`for
`simplicity.
`2) Let λ(Nf s, d), 0 ≤ d < Nf s be the dth comb set of
`subcarriers with spacing Nf s (the set of equally spaced
`subcarriers starting from the dth subcarrier with spacing
`Nf s) defined as
`λ(Nf s, d) = {k|k mod Nf s = d, 0 ≤ k < NF − 1}.
`so that D = Nf s/P and
`3) Here, we choose Nf s
`Nf n = NF /Nf s are integers.
`4) The ith partition si is composed of D consecutive comb
`sets, i.e., si = ∪D−1
`d=0 λ(Nf s, iD + d).
`located at
`5) In every partition, one comb set
`center
`is used for
`transmitting pilot sequence,
`si,p = λ(Nf s, iD + (cid:10)D/2(cid:11)).
`6) The magnitude of each element in any sequence is one,
`i.e., |ψp,q(j)| = 1, ∀j.
`Then, for the nth OFDM symbol of the preamble C-field, the
`partition number is estimated as
`
`the
`i.e.,
`
`(cid:5) k
`
`|Yn(k)|2
`
`∈sp
`Z(p)
`
`ˆpn = arg max
`p
`
`= arg max
`p
`
`where
`
`Nf n−1(cid:5)
`
`D−1(cid:5)
`
`r=0
`
`d=0
`
`Z(p) =
`
`|Yn(rNf s + pD + d)|2 .
`
`(23)
`
`Let the cell number and the corresponding partition number in
`the nth pream