Ausarbeitung_Schuh

SeminarAusgewhlte Kapitel der Nachrichtentechnik, WS 2009/2010

LTE:Der Mobilfunk der Zukunft

Synchronization and Cell SearchFabian Schuh

February 4, 2010

Abstract In this work time and frequency synchronization as well as sector andcell search for 3GPP Long Term Evolution (LTE) are considered. The synchroniza-tion procedure described is compliant to the most recent 3GPP specifications andmakes use of the Primary and Secondary Synchronization Sequence (PSS/SSS)and the cell-specific reference signal. Some mathematical aspects of the Zadoff-Chu sequences used in the PSS are considered and two search procedures, theMaximum Likelihood correlation based method and the cyclic prefix correlationtracking will be introduced. A close look into the SSS gives a hint on how the cellsearch is realized. Finally a closed concept for synchronization and cell search willbe presented.

1 Introduction

The Long Term Evolution (LTE) is an upcoming mobile communication standard that isspecified by the 3rd Generation Partnership Project (3GPP). The proposed E-UTRAN systemuses OFDMA for the downlink what allows data rates of several hundred Mbps.However, it is well known that OFDM systems are very sensitive when it comes to carrierfrequency offset (CFO) and errors in sample timing. In order to transfer data correctly the userequipment (UE) must perform a synchronization with the serving cell. With the help of thePrimary Synchronization Signal (SSS) the UE can estimate the CFO and the OFDM symboltiming. Furthermore the beginning of an LTE radio frame (BOF) must be found to allow anycommunication. The Second Synchronization Signal can be used to identify the cell-ID whichis needed to register the UE with the basestation what is required to receive incoming phonecalls. The full synchronization and cell identification procedure needs to be complete as fast aspossible [Myu08].

2 Fabian Schuh

0 5 10 15 20 25 30 35 40 45 50 55 601,5

1

0,5

0

0,5

1

1,5

k

Figure 1: Real part of Zadoff-Chu Sequence L = 63 and M = 1. Red circles for k IN. Blueline for k IR

2 Theory of Zadoff-Chu sequences

The following section gives a mathematical overview on Zadoff-Chu (ZC) sequences whichare used in LTEs Primary Synchronization Signal [FZH62]. The ZC sequences allow preciseappreciation of its position in time and in frequency domain. However they are easy to calculatein the UE and have a fixed length of 63 in LTE.

2.1 Definition of Zadoff-Chu sequences

Zadoff-Chu (ZC) sequences are defined as samples of a complex exponential function as shownin equation 1. There, ZCNZC ,M [k] denotes a sequences of length NZC and M denotes the family.In the case of NZC relative prime to M the definition results in a Zadoff-Chu sequence. Twonumbers are relative prime if there is no common divider for both numbers except 1.

ZCNZC ,M [k] =

exp

(jMpik2

NZC

)for NZC integer even

exp(jMpik(k+1)

NZC

)for NZC integer odd

(1)

Figure 1 shows the real part of Zadoff-Chu sequence of family M = 1 and illustrates itsgeneralized chirp-like characteristic [Pop92]. The red circles show the real value of the sequencefor k IN, whereas the blue line indicates the real part for k IR showing the chirp-like characterof a ZC sequence.

Synchronization and Cell Search 3

70 60 50 40 30 20 10 0 10 20 30 40 50 60 70

0

0,2

0,4

0,6

0,8

1

Auto-Correlat

ion

Figure 2: Auto-Correlation of a ZC sequence wit M = 29 showing a single dirac impulse

2.2 Properties of ZC sequences

The ZC sequences have three important properties that are exploited during the synchronizationprocess of LTE [STB09].First of all the definition shows clearly that a ZC sequence has a constant amplitude. Also itsNZC-point DFT has a constant amplitude. This property limits the Peak-to-Average Ratio andgenerates bounded and time-flat interference to other uses.The second property shows that the cyclic auto-correlation of each ZC sequence results in asingle dirac-impulse (see Figure 2) at time offset zero (Equation 2).

kk() =NZC1n=0

ak(n)ak(n+ ) = () [0, NZC ] (2)

This property later allows the receiver to easily find the timing offset by correlation.Furthermore the cross-correlation of two different ZC sequences of family M1 and M2 with M1relative prime to M2 is constant. This property can later be exploited to identify a sector of acell, because only a single ZC sequence generates a maximum during cross-correlation.

2.3 Fourier Duality

As already shown, the Zadoff-Chu Sequences have remarkable qualities. Additionally, eachsequences also holds a Fourier dual. This means, that the DFT of a ZC sequence xu[k] is aweigthed cyclicly-shifted ZC sequence Xw[k] such that w = 1u modNZC . There is an easy prooffor this Fourier Duality with M = 1 given in [LH07].This property is useful in practical systems, as it allows the generation of ZC sequences directlyin frequency domain without any DFT operation. Even more important, the correlation may bedone in frequency domain and/or in time domain accordingly.

4 Fabian Schuh

3 Synchronization Signal

Several targets must be achieved before the first higher level connection can be establishedwith the cellular network. First of all the UE needs to find the carrier frequency offset betweenthe UE and the base station. Than the OFDM symbol timing must be estimated. Finally thebeginning of an LTE frame needs to found.

The 3rd Generation Partnership Project (3GPP) therefore specified a number of synchronizationsignals along with a cell-specific reference signal to allow synchronization and cell identificationin the UE. They are now described in detail, as a basic knowledge is required to understand thesynchronization and cell-search procedure.

3.1 Signal location

0 1 2 3 4 5 6 7 8 9

radio frame = 10 ms

0 1 2 3 4 5 6 7 8 9 10 11 12 13

PSS (Primary Synchronization Signal)

SSS (Secondary Synchronization Signal)

RS (Reference Symbol)

Figure 3: Location of both, the Synchronization and the Reference signal in the resource block

Before going into detail an overview on the signal location in the resource block is given. Figure 3shows a full LTE radio frame with 10 ms comprising 10 subframes. The PSS and SSS are sentin subframe index 0 and 5. It will be shown later in this report that the SSS differs dependingon its subframe position. Furthermore each subframe contains the cell-specific reference signalseveral times on different subcarriers. This signals allows identifying the serving cell.

The following section will describe these three signals in detail and introduces the necessaryfundamentals of the synchronization concept which is specified afterwards.


3.2 PSS: Primary Synchronization Signal

...... ......

......

DC

c31c30c29c28c27c26c3c2c1c0 c32 c33 c34 c35 c36 c59 c60 c61 c62

-1-2-3-4-5 0 1 2 3 4 5 59 60-61 -60 -28-29-30-31-32 28 29 30 31 32

128 Subcarriers

ZC-Sequence:

Figure 4: PSS mapping of a Zadoff-Chu sequence.

The PSS is designed to use oneout of three possible Zadoff-Chu se-quences. They have length 63 anddiffer im family. The specificationallows M {25, 29, 34}. There isa mapping applied to construct thePSS in frequency domain out of a ZCsequence (see Figure 3.2).

It needs to be pointed out, that timeindex k = 31 is mapped on the DC

slice and therefore is forced to 0. Thus there is no direct current at the receiver after down-mixingfrom the carrier frequency into baseband.

3.2.1 Correlation results

As of this zero forcing the sequence cannot be ideal anymore. Figure 5 illustrates the auto-correlation of a PSS mapped Zadoff-Chu sequence. However, the correlation still generates asignificant maximum at = 0 and therefore estimation of timing offset at the receiver is stillpossible.

70 60 50 40 30 20 10 0 10 20 30 40 50 60 70

0

0,2

0,4

0,6

0,8

1

Auto-Correlat

ion

Figure 5: Autocorrelation of a PSS Signal constructed by a ZC sequence L = 63 and M = 29

An auto-correlation of a PSS with a CFO and a timing offset is shown in Figure 6(a). It becomesclear that with a CFO of one subcarrier spacing (i.e. 15 kHz) no correlation peak can be foundat any time. This results leads to a required maximum carrier frequency offset of less than halfthe carrier spacing respectively 7.5 kHz.

6 Fabian Schuh

(a) Auto-Correlation results with frequency and tim-ing offset (M = 29)

(b) Crosscorrelation of different sequences with fre-quency and timing offset (M1 = 25, M2 = 29,NZC = 63)

Figure 6: Auto- and cross-correlation results

In Figure 6(b) the cross-correlation between two different ZC sequence if plotted over frequencyand timing offset. It shows that the orthogonality still exists. Therefore the receiver cannotdecide for a wrong sequence even if there is a large CFO.

3.2.2 Time & Frequency Synchronization procedure

For practical purposes there are two different methods for time and frequency synchronization.The more intuitive PSS Maximum Likelihood correlation based estimation and the cyclic prefixcorrelation based tracking. Both will be described briefly.

The maximum likelihood (ML) detector [TZ07] finds the timing offset mM that corresponds tothe position of the maximum in the correlation.

mM = argmaxm{N1

i=0Y [i+m]SM [i]

2} (3)i: Time indexm: Timing offsetN : PSS time domain signal lengthY [i]: Received signalSM [i]: PSS signal with ZC family M

This procedures needs to be done twice. In frequency domain to estimate the CFO and in timedomain to detect the OFDM symbol timing.

The cyclic prefix correlation based tracking [SHRC09] autocorrelates the received signal. Thecorrelation generates a maximum on the cyclic prefix position as this element appears twice foreach OFDM symbol.

mM = argmaxm {2|(m)| (m)}


(m) =m+L+1k=m

r(k)r(k +N) (Correlation)

(m) =m+L+1k=m

|r(k)|2 + |r(k +N)|2 (Energy)

This method allows a very precise estimation of the OFDM symbol timing, but gives noinformation on the LTE frame begin. In addition the cyclic prefix based method remainsunaffected by the presence of high CFO.

3.3 SSS: Secondary Synchronization Signal

The Secondary Synchronization Signal is used by the UE to determine the cell-ID of the servingcell. In contrast to the PSS the SSS depends on the nodeB that is broadcasting it. As the PSSdoes not directly imply the beginning of a LTE radio frame the UE can only estimate it usingthe SSS. Therefore the SSS must be distinguishable between subframe index 0 and subframeindex 5. The following section will describe how this is achieved and how the UE can find thecell-ID through the SSS.

3.3.1 Individual Cell Information

Cell Area

Omni Cell

Cell Area

Site (3 sectors)

3 sector site

Figure 7: The difference between an omni celland a three sector site

The cell itself can be identified by the cell-IDwhich depends on two other IDs, the sector-IDand the group-ID. The sector-ID Ns identifieseach sector of a cell using the PSS. One physicalbase station site typically consists of three sectors(see Figure 7) that are served. Each of the sectorshas its own sector-ID which are described byone of the three available Zadoff-Chu sequencesM {25, 29, 34}.The group-ID Ng is a numerical classification andis a value between 0 and 167.

The cell-ID finally identifies the cell and is re-quired for the UE to register to the cell. It isdefined as Nc = 3Ng +Ns and thus depends onsector-ID and group-ID.

8 Fabian Schuh

3.3.2 Secondary Synchronization Signal

...

...

...

...

s 0(n

)s 1(n

) Interlea

vedPN

sequence

Figure 8: Interleaving of s0 and s1 in fre-quency domain

The Secondary Synchronization Signal dependson the group-ID and the sector-ID. To each pos-sible group-ID a pair of numbers m0 and m1is assigned. Through those numbers there canbe generated two sequences s0 and s1 using alength 31 linear feedback shift register. Thosemaximum-length sequences are than interleavedin frequency domain as shown in figure 8.Afterwards there is a scrambling applied on theeven and the odd subcarrier entries separately.For the scrambling two additional sequences c0and c1 are generated that are both based on abase scrambling code c. The shift value betweenthe sequences indicate the sector-ID Ns. Furtherinformation about the generation of the basescrambling can be found in the 3GPP specifica-tion TS 36.201.A second scrambling is applied using the codeszm01 and zm11 that are also based on c. This timethe shift depends on the group-ID Ng. However,this scrambling is only applied to the odd sub-carrier entries of the SSS.Finally, to distinguish the SSS in subframe 0 fromthe one in 5 the sequences s0 and s1 as well asthe sequences in the second scrambling are swapped for subframe index 5. This leads to twoequations describing the SSS:

d[2n] =s0[n]c0[n] in subframe 0s1[n]c0[n] in subframe 5 (4)

d[2n+ 1] =s1[n]c1[n]z

m01 [n] in subframe 0

s0[n]c1[n]zm11 [n] in subframe 5(5)

Where s0 and s1 denote the group-ID shifted base sequence that is interleaved in time domain.The primary scrambling sequences c0 and c1 have a shift depending in the sector-ID, whereaszm01 and zm11 describe the second scrambling sequences.

3.4 RS: Cell-specific reference signals

As already stated in the introduction the cell-specific reference signal is broadcasted much morefrequently and can be found on multiple subcarriers (see Figure 3). The complex-valued signal


itself can be described as in equation 6 using two length 31 gold sequences c[n]. To obtaindifferent reference signals for different base stations the cell-ID is coded into the signal. Theinitialization vector of the gold code generator is specified in equation 6 and contains the cell-IDNc. The cell-specified reference signal will later be used to confirm the estimated cell-ID.

P [n] = 12(1 2 c[2n]) + j 12(1 2 c[2n+ 1]) (6)cinit = 210 (7 (ns + 1) + l + 1) (2 Nc + 1) + 2 Nc +NCP (7)

Nc is the cell-IDn resource element indexns to be the slot-indexNCP 0 if extended CP, else 1

4 Concept: Cell Search procedure

Synchronization

Primary Signaldetection

Secondary Signaldetection

CellConfirmation

Nocell-ID

confi

rmation

afterseverals

ubfram

es

Nocell-ID

after

severaliteration

s

Symbol timingCFO (fractional)

Sector-ID

Group-ID Cell-IDCFO (integer), BOF

Successfull Synchronizationand cell search

Figure 9: Synchronization and cell searchprocedure as described in [MGEJ+09]

The following part describes a closed concept forsynchronization and cell search in 3GPP LTEsystems [MGEJ+09]. It contains a full time andfrequency synchronization of the UE and the cellidentification. The estimated cell identity is after-wards verified by a cell confirmation [TZGO07].

First of all the UE calculates all three possibleZadoff-Chu sequences and performs the DC zeroforcing to obtain the three PSS. Afterwards thesesequences are cross-correlated with the receivedsignal. By maximizing the correlation over car-rier frequency offset the CFO can be estimated.The OFDM symbol timing can be found by maxi-mizing over time offset. The correlation with thestrongest maximum is chosen for further analysis.This selection yields the sector-ID (Figure 4) asthere is a fixed relation to the family of the ZCsequence. The relative time position of the cor-relation peak gives the time offset to the radioframe begin with uncertainty between first andsixth subframe.

Ns = argmaxi

{[n]}After that, the Secondary Synchronization Signal

can be extracted and separated into even and odd subcarrier entries d(2n) and d(2n + 1).

10 Fabian Schuh

The even entries may than be divided through c0 as it depends only on the already estimatedsector-ID. The result sref is afterwards autocorrelated to exploit the cyclic shift and obtainm0. With m0 the second scrambling sequence z(m0)1 can be computed and afterwards divide theodd subcarrier entries d(2n+ 1) through c1 and the z(m0)1 . The cross-correlation of the resultwith sref shows a significant maximum, which indicates m1. The pair of estimated m0 and m1identifies the group-ID Ng. The cell-ID can than be calculated with Nc = 3Ng + Ns.

This procedure is performed for several cyclic shifts of the received signal d(n), in order todetect the integer CFO.

The position of subframe 0 can be determined, through the position of the maxima in thecorrelation, as the shifts between c0 and c1 is always positive. If the received signal descendsfrom subframe 5 the correlation results indicate a negative m0, respectively m1.

As cell-ID estimation is now finished the cell-specific reference signal can be calculated in thereceiver using the estimated Nc for the initialization of the gold sequence generator. The cell-IDcan than be verified by cross-correlation with the received signal. A significant peak indicates asuccessful synchronization and cell identification.

5 Conclusion

This work offered an insight into synchronization and cell search in future LTE mobil commu-nication systems. Therefore two synchronization signals, the PSS and the SSS are defined by3GPP. The PSS on the one hand allows precise estimation of the carrier frequency offset and theOFDM symbol timing. On the other hand gives some information on the LTE frame timing, asit has only two fixed positions within a radio frame. This estimation is made possible throughexploitation of the ideal cyclic auto-correlation properties of the used Zadoff-Chu sequences.

In addition the base station allows its identification by the SSS in which the sector-ID andthe group-ID allow the computation of the cell-ID. Through interleaving of multiple sequences,which have ID-depending cyclic shifts the UE is able to estimate the IDs using correlation.

Finally a slight overview of publication [MGEJ+09] shows a concept synchronization procedurefor LTE synchronization.

Literature

[FZH62] Frank, R. ; Zadoff, S. ; Heimiller, R.: Phase shift pulsecodes with good periodic correlation properties (Corresp.). In: IRETransactions on Information Theory 8 (1962), Oktober, Nr. 6, S.381382. http://dx.doi.org/10.1109/TIT.1962.1057786. DOI10.1109/TIT.1962.1057786

[LH07] Li, C.-P. ; Huang, W.-C.: A Constructive Representation for the Fourier Dualof the ZadoffChu Sequences. In: IEEE Trans. Inf. Theory 53 (2007), November,


Nr. 11, S. 42214224. http://dx.doi.org/10.1109/TIT.2007.907336. DOI10.1109/TIT.2007.907336

[MGEJ+09] Manolakis, K. ; Gutierrez Estevez, D. M. ; Jungnickel, V. ; Xu, Wen ;Drewes, C.: A Closed Concept for Synchronization and Cell Search in 3GPP LTESystems. In: Proc. IEEE Wireless Communications and Networking ConferenceWCNC 2009, 2009, S. 16

[Myu08] Myung, Hyung G.: Technical Overview of 3GPP LTE.http://hgmyung.googlepages.com/3gppLTE.pdf. Version:May 2008

[Pop92] Popovic, B. M.: Generalized chirp-like polyphase sequences with optimumcorrelation properties. In: IEEE Trans. Inf. Theory 38 (1992), Nr. 4, S. 14061409.http://dx.doi.org/10.1109/18.144727. DOI 10.1109/18.144727. ISSN00189448

[SHRC09] Shim, Myung J. ; Han, Jung S. ; Roh, Hee J. ; Choi, Hyung J.: A frequencysynchronization method for 3GPP LTE OFDMA system in TDD mode. In: Proc.9th International Symposium on Communications and Information TechnologyISCIT 2009, 2009, S. 864868

[STB09] Sesia, Stefania ; Toufik, Issam ; Baker, Matthew: LTE, The UMTS Long TermEvolution: From Theory to Practice. Wiley Publishing, 2009. ISBN 0470697164,9780470697160

[TZ07] Tsai, Yingming ; Zhang, Guodong: Time and Frequency Synchronization for3GPP Long Term Evolution Systems. In: Proc. VTC2007-Spring Vehicular Tech-nology Conference IEEE 65th, 2007. ISSN 15502252, S. 17271731

[TZGO07] Tsai, Yingming ; Zhang, Guodong ; Grieco, D. ; Ozluturk, F.: Cellsearch in 3GPP long term evolution systems. In: IEEE Veh. Technol. Mag. 2(2007), Nr. 2, S. 2329. http://dx.doi.org/10.1109/MVT.2007.912929. DOI10.1109/MVT.2007.912929. ISSN 15566072

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