Introduction
The explosive growth of wireless communications is fast emerging with unbelievable data rates which primarily due to the phenomenal growth of cellular users around the world. The cell phone users globally account for nearly 3 billion and yet the handheld phone market segment is continually growing with great demand for one-stop communication applications like voice over internet protocol (VoIP), video and web-traffic. The 3GPPⁱ LTEⁱ (long term evolution), the newly evolving cellular wireless standard, aims to provide a new radio-access technology geared up to provide higher data rates, low latency, and greater spectral efficiency. The target peak data rates for downlink and uplink in the LTE system are set at 100Mbps and 50Mbps respectively with a 20MHz transmission bandwidth, correspondingly the peak spectral efficiencies ranging from 5-2.5bps/Hz. The LTE would provide solid network access through efficient network and spectrum management by dynamically allocating the bandwidth resources as per the users’ needs. Depending on the cell size and the number of users the LTE cellular air-interface can operate flexibly in any of the suitable transmission bandwidths 1.4MHz, 3MHz, 5MHz, 10MHz, 15MHz and 20MHz. This provides greater flexibility in spectrum utilization depending on the user equipment (UEⁱ) application. The spectral efficiency targets are designed to be achieved by employing advanced air-interface techniques such as single-carrier frequency division multiple access (SC-FDMA) in uplink, orthogonal frequency division multiple access (OFDMA) in downlink, and multiple-input multiple-output (MIMOⁱ) multi-antenna technologies. The LTE as the wireless cellular standard embraces internet protocol (IP) for all the applications with an ultimate goal of providing the best user experience in a fixed as well as mobility (~500kmph) situations. The challenging issues for LTE deployments will be the seamless integration of LTE with legacy network architectures that can provide smooth backward compatibility to legacy standards like GSM and CDMA. Currently, different wireless technologies (e.g., GSM, CDMA) are used throughout the world with variants ranging 1.5G to 2.5G, they will act as legacy fallbacks to LTE which is expected to be ratified by end of 2010 as the 4G cellular standard and network deployments are expected to start from 2011 and beyond.
In order to keep up the efficient network management the LTE UE continually measures the parameters of the current cell as well as the neighboring cells and makes a decision to camp on the strongest cell. The key parameters of the cell viz., master information block (MIB) and system information block (SIB) are measured for the intra-frequency and inter-frequency neighboring cells, they are tracked and uploaded to radio resource control (RRCⁱ) layer which makes control decisions on which cell the UE to camp. The control decisions include handing-off from E-UTRANⁱ FDD (frequency division duplex) mode to E-UTRAN FDD mode or from E-UTRAN FDD mode to E-UTRAN TDD (time division duplex) mode and vice versa. All these decisions are based on the measurements carried out by the cell searcher in UE receiver; therefore, the cell-searcher forms one of the important design topics of the LTE UE receiver chain. The article primarily focuses on the working of cell-selection, cell-reselection in RRC and cell-searcher in the physical layer baseband.

1. Cell-Selection and Re-Selection
After a UE has selected a PLMNⁱ (public land mobile network), the UE performs the cell selection procedure where the UE searches for a suitable cell. The cell selection process allows the UE to select a suitable cell where to camp on in order to access available services. In this process the UE can use stored information (Stored information cell selection) or not (Initial cell selection) for camping and accordingly acquires the MIB and SIB of cells that are broadcasted by the eNodeBs available within the cell reach [1]. Subsequently, the UE registers its presence in the tracking area, after which it can receive paging information which is used to notify UEs of incoming calls. The UE may establish an RRC [1] connection, for example to establish a call or to perform a tracking area update. When camped on a cell, the UE regularly verifies if there is a better cell available within the range, this process is termed as the Cell Reselection process [2]. When the UE obtains normal service with a valid Universal Subscriberⁱ Identity Module (USIMⁱ), the cell is termed as the Suitable cell. When the UE is in the Suitable cell status it get into the cell reselection process to fetch the best cell for camping on, during this process the UE maintains a list of cells which meet the S-quality criterion and will monitor regularly as the monitored cells, another list of neighboring cells that fall into a separate category such as Acceptable cell will be maintained as the list of detected cells. If the UE is unable to find a suitable cell, but manages to camp on a cell belonging to another PLMN, the cell is said to be an Acceptable cell and the UE enters a ‘limited service’ state in which it can only perform emergency calls. Some cells may indicate via their SIBs which cells are the Barred cells or Reserved cells. There is an Operator Service cell that provides normal service but is applicable only for UEs with special access rights.
The cell selection criterion is known as the S-criterion and is fulfilled when the cell selection receive level value satisfies the below equation [2].
Srxlev > 0 dB, where Srxlev is the Cell Selection RX level value (dB) and is calculated as Srxlev = Qrxlevmeas-(Qrxlevmin + Qrxlevminoffset) - Pcompensation

The UE shall measure the RSRP level of the serving cell and evaluate the cell selection criterion S for the serving cell at least every DRX (discontinuous reception) cycle. The UE shall filter the RSRP measurements of the serving cell using at least 2 measurements where the two measurements shall be spaced by, at least DRX cycle/2. If the UE has evaluated in Nserv consecutive DRX cycles that the serving cell does not fulfill the cell selection criterion S, the UE shall initiate the measurements of all neighbor cells indicated by the serving cell, regardless of the measurement rules currently limiting UE measurement activities. If the UE in RRC_IDLE has not found any new suitable cell based on searches and measurements using the intra-frequency, inter-frequency and inter-RATⁱ information indicated in the system information for 10 s, the UE shall initiate cell selection procedures for the selected PLMN [2]. After this 10 s period a UE in RRC_IDLE state is considered to be "out of service area". UE shall perform the cell re-selection with minimum interruption in monitoring downlink channels for paging reception. At intra-frequency and inter-frequency cell re-selection, the UE shall monitor the downlink of serving cell for paging reception until the UE is capable to start monitoring downlink channels of the target intra-frequency and inter-frequency cell for paging reception. The interruption time shall not exceed TSI-EUTRAⁱ + 50 ms. TSI-EUTRA is the time required for receiving all the relevant system information data according to the reception procedure and the RRC procedure delay of system information blocks defined in for a E-UTRAN cell. For a UE supporting E-UTRA measurements in RRC_IDLE state, the UE shall be capable of monitoring a total of at least 8 carrier frequency layers, which includes serving layer, comprising of any allowed combination of radio access technologies (RAT).
The UE does the cell reselection criteria estimation for intra-frequency, inter-frequency and inter-RAT cell reselection as defined in [2] at least every DRX cycle. One DRX Cycle time can vary from 0.04sec 2.56 seconds depending on the evaluation period and measurement criterion. When a non zero-value of Treselection is used, the UE shall only perform reselection on an evaluation which occurs simultaneously to, or later than the expiry of the Treselection timer.
All parameters except for Qrxlevmeas are provided via system information. The Qrxlevmeas is the measured value of the cell’s reference signal received power (RSRP) expressed in dBm. The RSRP is calculated by averaging the squared values of the cell-specific reference signals (RS) received at the UE. The UE estimates the RS positions in the OFDMA symbol based on the cell-identity information [3] and extracts the resource elements corresponding to the RS positions and estimates the Qrxlevmeas. The Qrxlevmin is the minimum required receive power level (dBm) in the cell and is signaled as Q-RxLevMin by higher layers as part of the System Information Block Type 1 (SIB Type 1). Qrxlevmin is calculated based on the value provided within the information element, the typical value in dBm is -115dBm [4] Qrxlevmin for UTRA neighbour and -140dBm [4] for present cell. Qrxlevminoffset is an offset to Qrxlevmin that is only taken into account as a result of a periodic search for a higher priority PLMN while camped normally in a Visitor PLMN (VPLMNⁱ). This offset is based on the information element provided within the SIB Type1, taking integer values between (1…8) also multiplied by a factor of 2 in dB. This gives a wider range by keeping the number of bit transmitting this information. The offset is defined to avoid “ping-pong” between different PLMNs. If it is not available then Qrxlevminoffset is assumed to be 0 dB.
Pcompensation = max(PEMAX – PUMAX ,0) (dB)
Pcompensation is a maximum function as shown in the equation above. Whatever parameter is higher, (PEMAX-PUMAX) or 0 is the value used for Pcompensation. PEMAX [dBm] is Maximum TX power level an UE may use when transmitting on the uplink in the cell (dBm),
whereas PUMAX (dBm) is the maximum transmit power of an UE according to the power class the UE belongs to. At the moment only one power class is defined for LTE, which corresponds to Power Class 3 in WCDMA that specifies +23 dBm. PEMAX is defined by higher layers and corresponds to the parameter P-MAX defined in [11]. Based on this relationship, PEMAX can take values between -30 to +33 dBm. The P-MAX information element (IE) is part of SIB Type 1 as well as in the RadioResourceConfigCommon IE, which is part of the SIB Type 2.
In a real network a UE will receive several cells perhaps from different network operators. The UE only knows after reading the SIB Type 1 if this cell belongs to its operator’s network (PLMN5 Identity). First the UE will look for the strongest cell per carrier, then for the PLMN identity by decoding the SIB Type 1 to decide if this PLMN is a suitable identity. Afterwards it will compute the S criterion and decide whether it is a suitable cell or not. All the SIB information is transmitted through PDSCH (physical downlink shared channel) regularly with a predefined periodicity, where as MIB is transmitted in subframe #0 of every radio frame in FDD. Figure 1shows the interaction between cell-searcher and the RRC cell reselection modules where several measurements w.r.t. existing and neighboring cells made in cell-searcher are uploaded to RRC for decision making on the appropriate cell to camp on or remain in the connected mode for the present cell or switch to idle mode.

Figure-1 Cell selection, reselection communication to cell-searcher in physical layer

The cell-searcher does the following measurements and communicates to RRC as well as to different modules in medium access control (MACⁱ) and physical (PHY) layer.

o MIB parameters estimation:
 NID cell
 Bandwidth
 Number of antennas at eNodeB
 CP Normal or Extended
 PHICH Duration (normal or extended)
 Cell-Specific RS
o Measured Parameters of the cell
 RSRP
 RSSI (received signal strength indicator obtained from RF when performing RF carriers scanning)
 SNR (signal to noise ratio)

2. Cell-Searcher
One of the most crucial design issues in LTE is the initial cell search and timing and frequency synchronization. When an UE is powered on, it has to first synchronize itself with the eNodeB frame timings. Furthermore, it has to identify the cell and gather all the relevant system information before registering on to it. LTE downlink physical layer uses OFDMA. Since OFDM based systems are very sensitive to symbol timing errors, it is very important to determine the correct symbol starting position before executing other tasks, such as frequency synchronization, channel estimation, etc. Unlike the previous standards, LTE is fully IP based. All the relevant cell specific system information are transmitted as physical downlink broadcast channel (PBCH) within the physical layer. To be able to extract the information, the UE must identify the frame boundary and identify the cell ID. The cell searcher module initially performs the cell parameters estimation by processing PSS, SSS and PBCH.
To aid in the process of frame synchronization and identification of cell, the latest LTE specifies two synchronization signals: the primary synchronization signal (PSS) and the secondary synchronization signal (SSS). The PSS is one of the three Zadoff-Chu (ZC) sequences which are transmitted using the central 62 subcarriers twice within a radio frame. The SSS is a binary sequence of +1's and -1's, which is transmitted by the same subcarriers twice within a radio frame. LTE specifies 504 unique physical layer cell identities. The physical layer cell identities are grouped into 168 unique physical layer cell identity groups, each group containing three unique identities. The detection of the PSS provides the cell ID within a group, denoted as , and the detection of SSS provides the group ID, denoted as .
In the literature, there are many time and frequency synchronization algorithms for OFDM based systems [2, 3, 4]. However there are very few known algorithms for the current specification of the LTE. Tsai et al [5] present some design considerations for the synchronization signals in LTE. . Manolakis et al [6] present a cell search procedure where both the PSS and SSS are detected in the frequency domain using correlation based approaches. In this paper we propose a cell search and time synchronization algorithm which is different from the one in [6]. Our time synchronization procedure consists of essentially two steps: coarse symbol timing estimation using the cyclic prefix (CP) structure of a radio frame, fine timing estimation using the primary and secondary synchronization signals. The coarse timing is estimated using the well-known MMSE approach [7]. We detect the PSS and SSS around the coarse estimates for this purpose. The identification of the PSS and SSS also provides us the physical layer cell ID.
Unlike the approach in [6], we detect the PSS in the time–domain so that the FFT operation is avoided. The detection of SSS follows the same line as in [6], but with several changes. First of all, we estimate and equalize the channel at the SSS using the detected PSS. Second, we determine the CP (normal or extended) from the absolute value of the correlation during the index detection of the first interleaving sequence. Third, the second interleaving sequence index is searched around the first index instead of searching over the entire range.

3. LTE Downlink Frame Structure
LTE specifies two types of radio frame structures [8]: Type 1 (also called Frequency Division Duplex or FDD) and Type 2 (also called Time Division Duplex or TDD). Both structures are specified over a frame timing of 10 msec. Each radio frame consists of 20 slots numbered from 0 to 19 and one slot duration is 0.5 m second. Alternatively, a radio frame consists of 10 subframes each subframe spanning two slots or 1 msec. Each slot consists of 7 OFDM symbols or 6 OFDM symbols depending on whether the cyclic prefix is of type normal or extended, respectively. In the frequency domain, the signal in each slot is described by a resource grid of subcarriers. 12 subcarriers make a resource block (RBⁱ). The subcarriers have a spacing of 15 KHz, thus each RB spans 180 KHz in the frequency domain. RBs consist of resource elements, each element corresponding to one subcarrier in the frequency domain and one OFDM symbol in the time domain. The LTE radio frame structure in time and frequency domains is shown in Fig. 1. Corresponding to the subcarrier spacing of 15KHz, the OFDM symbol interval is selected to be msec. This makes all the subcarriers orthogonal over this time duration. Each OFDM symbol consists of 2048 samples. Thus the sampling period is sec. A slot therefore consists of 15360 samples, a subframe consists of 30720 samples, and a frame consists of 307200 samples. The additional number of samples in a slot other than the samples for the OFDM symbols account for the CP, as shown in Fig. 2.

Fig. 1: LTE downlink frame structure

Fig. 2: Slot structure for normal CP
4. Primary Synchronization Signal
The PSS sequence in LTE downlink is one of three Zadoff-Chu sequences. Each ZC corresponds to one of three physical layer cell IDs in a group. The PSS is sent over the central 6 RBs. Out of the 72 subcarriers only the central 62 subcarriers are used. The remaining 10 subcarriers are kept reserved. The PSS is sent every 5 milliseconds, twice in a radio frame. In the case of FDD, the PSS is sent in the last OFDM symbol of every 1st and 11th slot of a frame (refer to Fig. 3). In the case of TDD, the PSS is sent in the 3rd symbol of every 3rd and 13th slot of a frame. The generation and mapping of the Zadoff-Chu sequence to the resource elements are specified in sections 6.11.1.1 and 6.11.1.2 of [1]. The PSS sequence is given by

where denotes the root index. The physical cell ID within a group is denoted by . The root index is equal to 25, 29, and 34 corresponding to values 0, 1, and 2 respectively [9].

5. Secondary Synchronization Signal
The SSS is also sent over the central 6 RBs. Like the PSS, only 62 subcarriers are used, the remaining 10 subcarriers are kept reserved. In the case of FDD, the SSS is sent in the symbol immediately preceding the symbol carrying PSS. In the case of TDD, the SSS is sent 3 symbols earlier than the PSS symbol. Unlike the PSS, the SSS is a binary sequence which is a interleaving of two length-31 binary sequences. The sequence is scrambled with another sequence which is generated using . The generation of SSS and the mapping to resource elements are specified in section 6.11.2.1 and 6.11.2.2 of [1].

Fig. 3: PSS and SSS with Type 1 (FDD) frame
6. Detection of reference sequences in time-domain
In the LTE, the PSS is a ZC sequence in the frequency domain, distributed over the central 62 subcarriers. The corresponding OFDM signal in the time domain is the inverse FFT of not only the ZC sequence coefficients, but also resource element values in other subcarriers outside the central 6 RBs. The time domain OFDM signal is therefore not a ZC sequence. Furthermore, the ZC sequence used as PSS has length 62. The IFFT size used in OFDMA is 2048 so as to accommodate the maximum bandwidth of 20 MHz. Even if we reserve all other subcarriers except the central 62 subcarriers, the time domain OFDM symbol is not a ZC sequence. Therefore, to detect a ZC sequence in the time domain, we need to use the equivalent time-domain representations.
Consider a vector of samples in the time domain. Let us denote it by . In order to check if contains the ZC sequence , we would first apply the FFT on , extract the coefficients corresponding to central 62 subcarriers, and then correlate them with . The absolute value of the correlation can be written as , where denotes the Discrete Fourier Transform (DFT) matrix of order , and is a rectangular matrix of size 62x2048 for extracting only the coefficients corresponding to central 62 subcarriers. The above term can be rewritten as , where denotes the IFFT of after padding zeros. Thus the ZC sequence can be equivalently represented by the length- reference sequence .
The ZC sequences have constant amplitude value of 1. Thus when a ZC sequence is multiplied by its complex conjugate element-wise, we get 1 at all 62 subcarriers. If we pad zeros to , then the resulting product sequence will look as in Fig. 4. The IFFT of this sequence is easy to compute. Ignoring the scale factor, we get the IFFT as

This can be simplified as

Now element-wise multiplication in the frequency domain results in circular convolution in the time domain. Because of the CP structure and the symmetry of the ZC sequences, we can show that the circular convolution is the same as the correlation. What follows is that, in the case of an identity channel, that is, a channel without any additive noise and with unity impulse response, the correlation of a reference sequence with the PSS symbol in time-domain will have the same value as the above formula (with a scale factor) if the PSS is the corresponding ZC sequence. At earlier samples, up to the beginning of the CP, the correlation will be given by the above formula exactly. However, at later samples, part of the input vector will overlap with the CP of the next OFDM symbol. Therefore the above formula will only represent an approximation within a few sample locations. Fig. 5 confirms this observation where we compare the above formula with the actual correlation computed for an identity channel.

Fig. 4: ZC sequence multiplied with its complex conjugate and padded with zeros

Fig. 5: Correlation between IFFT of zero-padded PSS ZC sequence and input time domain signal.
When the channel has multipaths with additive noise, the correlation computation as before will lead to a convolution with the above function with some additive noise. If the channel impulse response length is relatively much smaller compared to the main lobe width, then the peak of the correlation will be around the peak of the function computed above, which happens at the beginning of the OFDM symbol carrying the PSS.

7. Time Synchronization and Cell search Method
The proposed time synchronization consists of two steps: (1) Coarse symbol time estimation, and (2) Fine timing estimation. Fig. 6 shows the sequence of steps followed and the outputs at the different stages.

Fig. 6: Time synchronization overview
8. Coarse symbol time estimation
The symbol boundaries are estimated using the CP structure of the LTE downlink radio frame. The received data is shifted by 2048 samples (OFDM symbol length) and is multiplied with the original data element-wise after being complex-conjugated. Then the mean squared error (MSE) metric [7] is calculated over a sliding window of 144 samples (normal CP length for all symbols except the 1st symbol in the case of FDD). The minimum value of the MSE metric over each non-overlapping segment of 2048 samples is assumed to be the starting sample of the cyclic prefix (CP) preceding a symbol. The detailed steps are given in the following and the procedure is illustrated in Fig. 7.
Step 1: Shift the received data to left by 2048 samples:

where denotes the received samples from RF and denotes its length.
Step 2: Compute MSE metric over a window of 144 samples:

Step 3: Minimize MSE over each segment of 2048 samples:

where denotes the starting sample index of the CP for the th symbol.
Step 4: Get symbol timing estimate by adding the CP length:
,
where denotes the starting sample of the th symbol.

Fig. 7: Coarse estimation of symbol boundaries
9. Fine time estimation
The fine timing estimation starts with the detection of PSS. This provides us the cell ID within a group ( ) and 5 milliseconds timing synchronization. This is followed by the channel estimation at the subcarriers carrying the PSS and then the detection of SSS after channel equalization. This gives us the group ID of the cell ( ) and, thus the unique cell ID ( ), frame synchronization, and the CP type (normal or extended).

10. PSS detection
The PSS is detected in the time domain. The coarse symbol timing provided by the previous step is used as an initialization in the PSS detection. Corresponding to the three ZC sequences, we pre-compute three reference sequences in the time domain whose FFTs produce the respective ZC sequence values at the designated 62 subcarriers and 0’s at other subcarriers. These three time domain sequences are correlated with blocks of 2048 input samples each block starting within a threshold interval from the coarse estimate. If the maximum value of the correlation within this interval is greater than a preset threshold, then the corresponding OFDM symbol timing is noted and the corresponding symbol is assumed to contain the PSS corresponding to the maximizing reference sequence. The index of the correlation maximizing reference sequence provides us . The detailed steps of the PSS detection process are as follows:
Step 1: Pre-compute the IFFT of ZC sequences after padding zeros. Corresponding to the ZC sequence in the frequency domain, let us denote the reference sequence in the time-domain by .
Step 2: Extract an OFDM symbol length vector starting within 10 samples from the coarse estimate:

Step 3: Find the correlation between the block and each reference sequence :
,
Where ‘h’ denotes complex conjugate transpose.
Step 4: Find the maximum correlation coefficient over the interval and compare with a preset threshold. If the value is larger than the threshold, then the symbol timing and the cell ID are known. Otherwise, move to the next coarse estimate and jump to step 2:

Where denotes the maximum value of the correlation with an identity channel, and denotes the starting sample index of the PSS symbol.
Step 5: Estimate the channel frequency response at the 62 subcarriers carrying the PSS after applying FFT:
,
Where denotes the FFT of the detected PSS symbol at the kth subcarrier. The overall detection process is shown in the Fig. 8.

Fig. 8: PSS detection procedure
11. SSS detection
We assume the FDD frame structure in this paper. In this case, the SSS is transmitted by the same subcarriers as those of PSS in the immediately preceding symbol. Therefore we can assume that these channel parameters remain the same for the SSS subcarriers as well. Unlike the PSS, the SSS is a binary sequence of +1’s and -1’s formed after the interleaving of two sequences which depend on two parameters and [1]. These two parameters are derived from the group ID of the cell ( ). Furthermore, these two sequences are scrambled with two binary sequences which depend on . Therefore the detection algorithm proceeds by first deriving the scrambling sequences, then finding the values of and , and then finally computing the value of by a simple table look-up procedure. The detailed steps of the detection process are given as follows:
Step 1: Extract the symbol immediately preceding the PSS symbol. Since the CP length is not yet known, extract two symbols at two CP lengths. Apply partial FFT to each symbol to extract only the 62 subcarriers carrying the SSS.
Step2. Equalize each of these two vectors by dividing by the channel frequency response estimated earlier using the PSS. Remove the imaginary parts of the coefficients and then quantize the real values to +1 or -1 depending on whether they are positive or negative. Let the two vectors be denoted by and .
Step 3. Generate two scrambling sequences and using . Divide the even coefficients of the equalized vectors and by to get two estimates of .
Step4. Generate the reference sequence and circularly correlate it with the two estimates of . Compare the maximum correlations for the two sequences. If yields higher correlation value, we say that the CP is of type ‘normal’, otherwise the CP is of type ‘extended’. The circular shift corresponding to the maximum value gives us the estimate of .
Step 5. Generate the reference sequence , and then using the estimated value of , generate the scrambling sequence . If the CP is normal, divide the odd numbered coefficients of by the product sequence to get an estimate of the sequence . Otherwise, divide the odd numbered coefficients of for the same purpose.
Step 6. Correlate the estimated sequence circularly with the reference sequence . The circular shift yielding the maximum correlation value within from the estimate is an estimate of . If , then the slot containing the SSS has index 0 (subframe number 0), else it has index 10 (subframe number 5). In the latter case, swap the values of and .
Step 7. Using the and values, compute the group ID from Table 6.11.2.1-1 [1]. Then compute the absolute cell ID as . Based on the slot number, compute the starting sample of the frame. The various steps of the detection process are shown in Fig. 9.

Fig. 9: SSS detection procedure
12. Experimental Results
The proposed synchronization scheme was implemented in the LTE downlink physical layer at the receiver side at 20 MHz bandwidth. The transmitted radio frame was of Type 1 (FDD) at normal CP. The total number of Resource Blocks and subcarriers were 100 and 1200 respectively. The IFFT size was 2048, thus the sampling period was 1/(15x2048) msec, (i.e., 32.55 microsec) and there were 2048 samples per OFDM symbol. We simulated the channel with different additive white Gaussian noise levels (SNR=10 dB, 20 dB, and 30 dB) and with different number of multipaths (1 to 5). The multipath channel was simulated using the channel model given in [10]. For each number of multipaths, we simulated 100 channels at each SNR. At each instance, we selected the transmitting cell ID randomly within 0 and 503. We considered only one transmitting antenna. Since the PSS and SSS are transmitted from the same antenna ports, we expect similar performances in the case of two or 4 transmitting antennas as well.
Fig. 10 shows the MSE metric computed during the coarse timing estimation over one slot duration. In this particular instance, we used a channel having 5 multipaths with AWGN corresponding to 30 dB. As we can see, there are seven dips corresponding to seven symbols. Furthermore, these dips are not as sharp as they appear. When we look closely, we see that the MSE metric decrease and increase around the minimum location are gradual (Fig. 11). This is expected since the sliding window moves by one sample at a time in our case.

Fig.10 MSE metric computed over one slot duration

Fig 11. MSE metric around a symbol boundary
Fig. 12 shows the correlation computed with the three ZC sequences in the time domain around the coarse estimate for the PSS symbol. In this particular case, the cell ID was 134, thus the actual ZC sequence transmitted as PSS corresponds to . As we can see, the correct ZC sequence produces the highest peak and is above the threshold.

Fig. 12: Absolute value of the correlation with time-domain ZC sequences around the PSS symbol.
We estimated the starting sample of the frame and computed the offset from the true starting sample. Fig. 13, Fig. 14, and Fig. 15 display the percentage of occurrences of different offsets at SNR 10 dB, 20 dB, and 30 dB respectively. The different colors stand for different channel filter lengths, or equivalently different number of multipaths. For each case, we realized 100 channels and computed the percentage offsets over these channels. First of all, we notice the offsets are limited to a few samples only. As the number of multipaths increases, the offset may increase slightly. However, the proposed algorithm is able to detect the starting sample correctly at majority of occasions. The small amount of offset can be corrected in a subsequent step. As another observation, we note that as the additive channel noise is decreased, the detection performance generally improves. We observed that, in all the cases, the detected cell ID was identical to the true cell ID.

13. Conclusions
In this paper, we have presented a new cell search and symbol time synchronization method for LTE. The method first coarsely estimates the symbol beginning using the CP structure of the LTE downlink frame. Then the symbol containing the primary synchronization signal is detected by correlating the three Zadoff-Chu sequences in the time domain with blocks of samples around the coarse estimates. The detection of secondary synchronization signal then follows after the channel estimation and equalization. Simulations with different channel conditions demonstrate that the proposed algorithm is quite robust in identifying the cell ID. The timing estimate is correct up to an offset of a few samples, which can be corrected in a following step.
The presented algorithm is the first part of the initial cell search and synchronization procedure. This will be followed by the extraction and decoding of PBCH channel. The PBCH channel contains all cell specific system information such as the cell ID, CP, frame type, bandwidth, etc. The detected cell ID can be confirmed during the PBCH decoding process.
The main factor in the initial cell search and synchronization is the required time. The UE should be able to detect the cell quickly and register on to the eNodeB. Considering a real scenario, a given UE is very unlikely to move to a completely new cell every time it is switched on. Instead of considering all possible cell IDs, it can first search over a small list of cell IDs used in the recent past. This can decrease the correlation computation time during the PSS and SSS detection to some extent. Further improvements can be made by simplifying the correlation computation, decreasing the search window size about the coarse estimate, etc.

Fig. 13: Frame boundary detection performance at SNR equal to 10 dB. is the number of multipaths.

Fig. 14: Frame boundary detection performance at SNR equal to 20 dB. is the number of multipaths.

Fig. 15: Frame boundary detection performance at SNR equal to 30 dB. is the number of multipaths.

14. References
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[2] 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); 3GPP TS 36.304 V9.0.0 (2009-09) User Equipment (UE) procedures in idle mode
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