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A complete cell search and synchronization in LTE
 Sriharsha M.R.^{1}Email authorView ORCID ID profile,
 Sreekanth Dama^{1} and
 Kiran Kuchi^{1}
https://doi.org/10.1186/s1363801708863
© The Author(s) 2017
 Received: 25 October 2016
 Accepted: 14 May 2017
 Published: 31 May 2017
Abstract
The initial process of identifying any available base station (BS) by a user equipment (UE) that wants to communicate is termed as cell search. To ensure a reliable communication, any UE has to be synchronized with the BS both in time and frequency domains. Cell search process is said to be complete once cell ID associated with longterm evolution (LTE) BS is decoded successfully. This paper presents a series of cell search and synchronization algorithms, which efficiently estimated time and frequency offsets as well as cell ID. The synchronization signals present in LTE, namely, primary synchronization signal (PSS) and secondary synchronization signal, that carry cell ID are critically exploited in the algorithms. The aforementioned algorithms are classified into two modules, namely, module I and module II, based on their computation complexity.
In module I, a cyclic prefix (CP)based maximum likelihood (ML) estimator is employed to obtain a coarse estimate of time and fractional frequency offset; however, the estimates are refined using synchronization signals. A joint estimation of timing, integer frequency offset (IFO), and PSS ID (sector ID) is carried out in module II. Both the modules operate on the crosscorrelation approach of PSS with the received signal for obtaining timing and sector ID. IFO as a part of module II is detected from a finite hypotheses set using synchronization signals. Extensive simulations are carried out on a timevarying frequencyselective channel to analyze the performance of the algorithms.
Keywords
 LTE
 Synchronization
 Cell search
 CFO
1 Introduction
Third generation partnership project (3GPP) has developed longterm evolution (LTE) technology to achieve high data throughput and better spectrum utilization. Supporting varied range of bandwidths from 1.4 to 20 MHz makes this technology more flexible. LTE aims at data rates up to 100 Mbps in downlink (DL) and 50 Mbps in uplink (UL) with a bandwidth (BW) of 20 MHz excluding carrier aggregation and spatial multiplexing [1]. Orthogonal frequency division multiplexing (OFDM) makes a perfect choice in the DL because of its competence in dealing channel frequency selectivity and its flexibility to handle different channel BWs. Singlecarrier frequency division multiplexing (SCFDM) is adopted in UL to reduce the peak to average power ratio (PAPR). A cyclic prefix (CP) is inserted in every OFDM and SCFDM symbol. LTE base station (BS) supports normal and extended CP to combat delay spreads. LTE cell operates on either time division duplexing (TDD) or frequency division duplexing (FDD) mode.
BS in a LTE cellular network are differentiated by their unique IDs. They are identified by 504 such distinct IDs called as cell ID. The deployment of these cells is done in such a way that the BSs having the same cell ID are placed far apart. The user equipment (UE) trying to communicate has to primarily decode the cell ID of the nearest BS. The process of attaining timing and frequency synchronization and cell ID of a BS is called as cell search [2]. Under this process of cell search, UE has to acquire basic information including cell ID, duplexing mode, timing, and frequency related to the BS.
1.1 LTE frame and cell ID
The data transmission in LTE is carried out with duration of 10 ms for each frame on a given bandwidth. Each frame is divided into 10 subframes of each 1 ms which are further divided into two slots of equal duration. Each slot consists of six or seven OFDM symbols depending on the CP length. A resource block (RB) is the smallest timefrequency resource unit which can be allocated to users. Each RB comprises of seven or six symbols with 12 resource elements in each symbol [3]. A resource element (RE) is the resource provided by one subcarrier in an OFDM symbol.
 1.
Acquisition of the symbol and frame timing is the operation by which UE determines the start of each symbol, i.e., the precise set of samples that has to be fed to the DFT for OFDM demodulation. Frame timing determines the boundaries of the frame.
 2.
Carrier frequency offset (CFO) estimation involves synchronizing UE to BS carrier frequency by eliminating the frequency offsets generated at the RF section due to lossy oscillator or due to Doppler frequency shift.
 3.
The successful detection of cell ID by extracting the SID and GID along with duplexing mode and the CP length (L _{CP}).
After the completion of initial cell search, UE tries to decode broadcast data channel information which confirms the successful cell search procedure. Cell search procedure is said to be failed in case UE fails to decode the broadcast data channel.
1.2 Synchronization signals
1.3 Motivation and related works
The accurate synchronization in both time and frequency domains is gaining importance in the wake of new trends like carrier aggregation, HetNets, and coordinated multipoint [4]. Cell search and synchronization is a basic operation and a much powerconsuming one in any receiver. UE has to sweep over wide range of bands to establish a connection with the BS. This makes the cell search process computationally complex. The computational complexity increases further with the incorporation of technologies like carrier aggregation in LTE. So, there is a need for efficient algorithms which can balance performance with the number of computations.
There have been extensive studies on OFDM time and frequency synchronization. Works like [5, 6] have proposed estimators which make use of pilots broadcasted periodically. Two or more replicas of the PN sequences are used as the pilots in estimation of the CFO and timing. These pilots are transmitted within the coherence time. Assuming the channel is same between two pilots, the autocorrelation of the window with its replica will give the estimates of timing and frequency offsets. The pilot sequences used in LTE synchronization are ZC sequences whose structure is entirely different from the that of the sequences proposed in the prior works. The selfcorrelation method presented in [5] is not a practical choice in LTE because the transmission periodicity of the ZC signals is much higher than the coherence time. The coherence time of highspeed vehicles is much less than 5 ms.
The work in [7] proposed ML estimator for timing and fractional portion of CFO (FFO) of an OFDM signal. This is accomplished by the autocorrelation of CP present in the OFDM symbol. We make use of this estimator to find the coarse timing of the OFDM symbol and FFO for moduleI algorithms. The autocorrelation among the received samples will result in more noise terms yielding poor performance at low SNR. Averaging over multiple OFDM symbols will give better estimates of timing and FFO. The performance of this estimator is limited by the delay spread of the channel.
The works [8, 9] present algorithms for PSS timing and SID detection. These algorithms are based on crosscorrelation with all the possible PSS sequences generated at UE. Few of the above proposed algorithms follow the approach to estimate SID through time domain operations and few are based on frequency domain operations. The cross correlation approach in time domain would result in the sum of the exponentials in the presence of large CFO. It would affect the timing estimator unless the problem of large frequency offsets is addressed. The frequency domain estimation of SID presented in [10] makes the process computationally exhaustive by using DFT. Timing errors present if any would also have significant effect on the estimates in the frequency domain. Choosing the precise set of window of samples that has to be fed to DFT would be ambiguous because few of the OFDM symbols have L _{CP} of 160 instead of 144. The DC algorithm presented in [11] estimated timing using autocorrelation of PSS present twice in a frame and tried to exploit the diversity by the neighboring sectors. The diversity is exploited from the multiple neighbor sectors having the same SID. The SID is detected by differential correlation of the frequency domain data with the possible PSS sequences. The exploitation of diversity could only be possible if all the sectors of different BSs are strongly synchronized in time and frequency. The channel effects may not be the same on both PSS which are half a frame apart under high Doppler conditions. Similarly, CCSA method proposed in [9] uses the CPbased method for timing and FFO detection. Using the obtained estimates, SID is detected using the frequency domain correlation with PSS sequences. The timing and frequency selectivity effects propagates through the algorithm leading to the performance loss.
Most of the previous works like [10] and [11] and others have not generalized the case for different CP lengths and TDD/FDD modes. The algorithms including [9] and [12] were also built on the assumption of known L _{CP}.
The algorithms presented in this work are divided into two modules as module I and module II based on their computational complexity. In this paper, we propose a sequential execution of module I and module II to reduce the computational burden at the receiver. The algorithms allow to relax the oscillator restrictions as it involves the search of CFO over a large interval. During initial synchronization, devices have to sweep over a huge number of frequency bands. The devices like relays in which the oscillators are more precise do not undergo CFO effects. In the case of normal UEs, there is high probability of having hardware impairments and being less tolerant to temperature and ageing effects. The Doppler effect which contributes to the CFO will also be significant in the case of devices moving with high speeds.
CPbased approach is used to estimate coarse timing and FFO in module I, and the estimates are refined in time domain using PSS. However, if integer CFO is present in the received signal, it will affect the estimates of module I. So, module II which is a joint timing, integer CFO, and SID estimator is used in nullifying the CFO effect. Module II is resilient to the effects caused by integer CFO and large delay spreads since it is based on the crosscorrelation with the PSS sequence over multiple integer CFO hypotheses. The residual offsets of CFO and timing are compensated using SSS and cellspecific reference signals (pilots). The proposed algorithms are simulated and evaluated under different delay spread conditions.
The remainder of this paper is as follows. The system model and problem statement are presented in Section 2. Timing, CP length, and SID and GID estimations are elaborated in Section 3 which also describes the module I and module II algorithms. Simulations conducted to study the performance of presented algorithms are explained in Section 4. Concluding remarks are presented in Section 5.
Notations: The notation ∥.∥ indicates the norm of the enclosed vector. The signals in capital letters denote frequency domain. The notation ℜe{} represents the real part of the complex quantity. Matrices and vectors are written in bold letters. Notation . is used to show the cardinality of a set.
2 System model
The causes of CFO are due to mismatch between oscillators at BS and UE as well as due to Doppler shift. The integer (multiple of subcarrier spacing) and fractional (fractional portion of subcarrier spacing) parts of ε are separately estimated for computational convenience. The integer CFO (IFO) induces subcarrier shift, whereas the fractional CFO (FFO) leads to intercarrier interference (ICI) and common phase error. The frequency offset present at any BS is very small compared to that of an UE, so the CFO contribution from the BS is not considered.
 1.
The proposed algorithm performs the CPbased correlation according to [7] to obtain the coarse timing of an OFDM symbol and FFO.
 2.
Based on the coarse results, fine timing, SID, and L _{CP} are obtained by the crosscorrelation of the PSS over decimated received signal, further refined over standard sampling rate.
 3.
After sector ID detection, SSS ID and mode are detected based on the noncoherent receiver. Once SSS ID is detected, UE will be adjusted to the frame timings.
 4.
Joint timing, SID along with IFO are detected based on MLlike search similar to that on [13].
 5.
FFO is estimated using the detected PSS by finite hypotheses search approach.
 6.
Finally, GID of the SSS along with L _{CP} are detected to complete the cell search process.
3 Timing and SID detection
The timing and SID detection of the received signal based on the two modules are explained in this section. Since the synchronization signal occupies 1.08 MHz BW at the center of the spectrum, the received signal is decimated and cell search operation is performed.
3.1 Module I
Module I is the set of computationally efficient operations for the estimation of CFO, timing, SID, and L _{CP}. This set of algorithms assumes the CFO present is only a fractional offset. CPbased estimator for CFO is used, and the estimator is averaged over multiple symbols. SID and timing are obtained by crosscorrelating with the possible PSS sequences.
3.1.1 Coarse timing and FFO estimation
3.1.2 Timing alignment, SID, and L _{ CP } detection
An observation window of halfaframe duration is considered for PSS, L _{CP}, and timing detection. The detection of L _{CP} is done by arranging the samples into two different formats of the CP length. \(N_{HF}^{D}\) are the number of samples in halfaframe obtained after decimating the received signal. Two sets are constructed using these samples. One is a set of 70 OFDM symbols each with normal CP and the other is a set of 60 OFDM symbols each with extended CP. Υ _{1} and Υ _{2} are the sets each containing 70 and 60 OFDM symbols corresponding to normal and extended CPs respectively.
𝜗 is the number of channel taps.
Similarly, the set Υ _{2} is prepared with the \(N_{HF}^{D}\) samples according to extended CP (Υ _{2} = 60). {Υ _{2}} = {X _{0},X _{2},…X _{59}}; each X _{ k } is an OFDM symbol with extended CP (\(L_{CP2}^{D}\)). The set of operations carried on Υ _{1} with s _{ M }(n) has to be repeated for Υ _{2}.
The maximization of Ξ over q, M, and i will give the PSS the timing location, SID, and L _{CP} as in (14). Where i is the index running over the CP size prospects. The timing obtained in (14) is based on the decimated sample of y(n). The timing is refined over the estimate obtained using \(\hat {M}\) and the PSS location. For fine timing estimate, crosscorrelation is applied over y(n) with the PSS of \(\hat {M}\) on standard sampling rate.
3.2 Module II
Where \(l~=\left \{\frac {\alpha }{2},\frac {\alpha }{2}~+~1,\ldots,\frac {\alpha }{2}\right \}\). L _{CP} detection has to be done along with the SSS detection process in this set of algorithms. The computational complexity increases with the increase in μ. Choosing μ as 5 (ν={−2,−1,..,2}) will result in 15 possible energy values of R. This approach is resilient towards the effects of large delay spread. Large delay spreads would affect the coarse timing in module I. Error propagates through fine PSS timing and SID from the affected coarse timing estimate. The PSS symbol is used in module II excluding the CP for the timing estimation. Similarly, the FFO estimation is also based on the PSS symbol without CP.
3.2.1 FFO estimation
In this section, the FFO estimation procedure is presented based on the correlation with PSS symbol. The timing and SID determined from Section 3.2 are used to estimate FFO. The PSSbased frequency offset estimation starts by compensating the received signal with the estimated IFO \(\tilde {y}_{f}(n) = \tilde {y}(n)e^{\frac {j2 \pi \hat {\nu } n}{N_{D}}}\). Once the IFO is compensated, the uncertainty span of the CFO is ε _{ f }∈ [ −0.5,0.5] which could be any real number. A near ML approach with a finite number of hypotheses is proposed in this section. k _{ f } finite number of frequency offset hypotheses that span the uncertainty of the CFO is considered for the FFO estimation. For each hypothesis test, corresponding amount of offset is removed from the \(\tilde {y}_{f}(n)\) and correlated with the PSS signal of obtained SID. A hypothesis resulting the maximum correlation sum is the residual FFO.

Prepare a set of finite number of hypotheses as \(\left \{ \epsilon ^{0}_{f}, \epsilon ^{1}_{f},..,\epsilon ^{N^{D}_{f}1}_{f} \right \}\) from the uncertainty span of FFO.

Check the correlation sum by removing an amount equal to each of the offsets in the hypotheses from \(\tilde {y}_{f}(n)\) as in (20). Obtain the offset \(\left (\epsilon ^{\hat {i}}_{f}\right)\) which maximizes the correlation sum.$$\hat{i}=\underset{i}{\mathrm{arg max}} \left\{\\Lambda(i)\^{2}\right\} $$

A new set of hypotheses is prepared based on the maximizing offset from the above step. Let us say \(\epsilon ^{2}_{f}\) maximizes the correlation energy, then the span of \(\left [\epsilon ^{1}_{f}, \epsilon ^{3}_{f}\right ]\) is further divided into \(N^{D}_{f}\) equidistant hypotheses.

The steps 2 and 3 are repeated to obtain the estimate of FFO (\(\hat {\epsilon }_{f}\)). Simulations are stopped after four repetitions. The increase in the number of repetitions decreases the error variance of the estimate.
4 Results and discussions
Simulations were carried out to analyze the performance of the cell search and synchronization algorithms. The simulation conducted follows the LTE specifications of the signal generation and transmission. Since the synchronization signals are always transmitted on single antenna in LTE, only the SISO case is considered. During initial synchronization, UE starts the cell search process without any prior information related to LTE BS. Simulations are carried out on a frequencyselective fading channel in the presence of CFO, and performance at different SNRs (in decibels) is plotted.
Simulation parameters
Parameter  Value 

Channel bandwidth  20 MHz 
Channel model  EPA, EVA, ETU (ITU models) 
Channel tap model  Jakes 
No. of Tx antennas  1 
No. of Rx antennas  1 
Frame structure  Type II (TDD) 
CFO introduced  2.06 (×15 KHz) 
CP type  Normal 
4.1 SID and timing detection
The residual timing error contributes to the phase rotation in the frequency domain which can be compensated using the pilot symbols.
4.2 Frequency offset estimation
4.3 CellID detection
4.4 Complexity analysis
Computational complexity
Algorithm  Multiplications  Additions  Example (multiplications) 

Module I  (70N ^{ D } + 60N ^{ D })λ  (70(N ^{ D }−1) + 60(N ^{ D }−1))λ  49920 
Module II  \(N^{D} N_{HF}^{D}\mu \)  \((N^{D}1) N_{HF}^{D}\mu \)  3686400 
CCSA  (70∗62μ + 60∗62μ)λ  (70∗61μ + 60∗61μ)λ  72540 
DC  \(N_{HF}^{D}N^{D}~+~L_{CP}*70~+~(70*62*3\mu)\)  \(N_{HF}^{D}(N^{D}1) + (L_{CP}1)*70 + (70*61\mu)\)  1277940 
MLA  NN _{ HF } μ  (N−1)N _{ HF } μ  943718400 
The computation complexities of different algorithms are also furnished in Table 2. The numericals presented in the table do not include the computations needed for FFT. λ, V, and μ are considered as 1, 16, and 3, respectively, for the examples provided in the table. But in CCSA and DC, the PSS search is done in frequency domain posing additional complexity due to the FFT operation. Module I is the least complex of all the algorithms presented which can be observed from the examples from the table.
5 Conclusions
A robust cell search procedure that consists of joint operation of two modules is proposed and studied based on the simulations. Both the modules estimate the timing and SID using crosscorrelation approach. Module I symbolbysymbol search technique which does not include the estimation of IFO is computationally less complex compared to that of module II. In module II, received signal is diagnosed over every sample to estimate timing and IFO jointly. IFO values are hypothesized over finite possibilities and detected based on the correlation with the PSS sequences. The cost of computations in module II is justified by its performance over module I. Efforts have been made to reduce the computation burden by operating over the decimated samples. The presented cell search operation gives the complete solution with perfect balance of performance and the computational complexity. Simulations have been carried out over the frequencyselective channels of different delay spreads confining to the LTE environment with 20 MHz BW.
Declarations
Acknowledgements
The authors would like to thank CCRAN project, Miety, Govt. of India for sponsoring this research work.
Authors’ contributions
MR is the main author of the current paper. MR and KK contributed to the conception and design of the study. SD contributed to the structuring and reviewing of the manuscript. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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