Third generation partnership project (3GPP) has developed long-term 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 down-link (DL) and 50 Mbps in up-link (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. Single-carrier frequency division multiplexing (SC-FDM) is adopted in UL to reduce the peak to average power ratio (PAPR). A cyclic prefix (CP) is inserted in every OFDM and SC-FDM 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 time-frequency 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 sub-carrier in an OFDM symbol.
The dedicated channel for synchronization in LTE is divided into two parts, namely, primary synchronization channel (PSCH) and secondary synchronization channel (SSCH). The signals transmitted on PSCH are primary synchronization sequence (PSS) which carry sector ID (SID), and the signals on SSCH are secondary synchronization sequence (SSS) which carry group ID (GID). The cell ID is obtained by combining the IDs on PSS and SSS as given by
$$\mathrm{cell ID}~=~3*\text{GID} + \text{SID}. $$
In order to successfully detect the cell ID, UE has to extract SID and GID from both the synchronization channels. There are 504 distinct cell IDs available in LTE, which are grouped into 168 distinct groups identified by GID. All the groups contain three identical SIDs. GID ∈ {0, 1, 2 …,167} is carried by SSS, and SID ∈ {0, 1, 2} is carried by PSS.
Two OFDM symbols for each of PSCH and SSCH are transmitted in every frame with a separation of 5 ms. PSS present in the two symbols convey the same message, i.e., SID. To differentiate the first and second half of a frame, SSS present in two symbols are not identical; however, they convey same information. The goal of the synchronization procedure is to align to the frame boundaries of corresponding BS. The cell search and synchronization process will be complete if the UE performs the following operations successfully.
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
The synchronization signals are placed in the center 1.08 MHz of the bandwidth which corresponds to 72 subcarriers of the OFDM symbol. Primary synchronization sequence is constructed from one of the three length-63 Zadoff-Chu (ZC) sequences in the frequency domain, with the center element punctured to avoid transmission on DC subcarrier [
3]. Three PSS sequences are used in LTE, corresponding to the three SIDs. The sequence
S
M
used for the PSS are generated from ZC sequence with selected roots
u = {25,29,34} and is given by
$$S_{M}(k) = e^{\frac{-juk(k+1)}{63}}; \text{where~} k = {0,1,..,62} \text{~and~} M = {0, 1, 2} $$
where
M is the SID. Similar to PSS, secondary sequence is also positioned in the centre 62 REs nullifying the DC subcarrier. The SSS is also a frequency domain sequence, which is an interleaved concatenation of two length-31 m-sequences. The two sequences are named as even sequence and odd sequence. Both even and odd sequences are scrambled with an m-sequence whose cyclic shift value depends on sector ID. The odd sequence is further scrambled by an m-sequence with cyclic shift value determined by even sequence. The combination of cyclic shifts of even sequence and odd sequence corresponds to the GID [
3]. The synchronization signals are chosen based on their correlation properties and frequency offset sensitivity. The low sensitivity to frequency offsets by the signals helps in reducing the burden of synchronization on the devices. Without loss of generality, all the neighboring BSs are assumed to have distinct cell IDs. However, there are only three possible SIDs. So, there is a high probability that neighbouring BSs also possess same SID. The identification of cell-ID is confirmed by accurately decoding the broadcast channel. UE is expected to achieve a miss detection probability equal to 1% at −6 dB SNR for broadcast channel [
1].
The accurate synchronization in both time and frequency domains is gaining importance in the wake of new trends like carrier aggregation, HetNets, and coordinated multi-point [
4]. Cell search and synchronization is a basic operation and a much power-consuming 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 auto-correlation 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 self-correlation 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 high-speed 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 module-I 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 cross-correlation 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 CP-based 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.
CP-based 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 cross-correlation with the PSS sequence over multiple integer CFO hypotheses. The residual offsets of CFO and timing are compensated using SSS and cell-specific 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.