# Time and Frequency Synchronisation in 4G OFDM Systems

- Adrian Langowski
^{1}Email author

**2009**:641292

https://doi.org/10.1155/2009/641292

© Adrian Langowski. 2009

**Received: **30 June 2008

**Accepted: **20 December 2008

**Published: **5 March 2009

## Abstract

This paper presents a complete synchronisation scheme of a baseband OFDM receiver for the currently designed 4G mobile communication system. Since the OFDM transmission is vulnerable to time and frequency offsets, accurate estimation of these parameters is one of the most important tasks of the OFDM receiver. In this paper, the design of a single OFDM synchronisation pilot symbol is introduced. The pilot is used for coarse timing offset and fractional frequency offset estimation. However, it can be applied for fine timing synchronisation and integer frequency offset estimation algorithms as well. A new timing metric that improves the performance of the coarse timing synchronisation is presented. Time domain synchronisation is completed after receiving this single OFDM pilot symbol. During the tracking phase, carrier frequency and sampling frequency offsets are tracked and corrected by means of the nondata-aided algorithm developed by the author. The proposed concept was tested by means of computer simulations, where the OFDM signal was transmitted over a multipath Rayleigh fading channel characterised by the WINNER channel models with Doppler shift and additive white Gaussian noise.

## 1. Introduction

*interblock interference*(IBI) and the frequency synchronisation error is one of the sources of

*intercarrier interference*(ICI). Thus, synchronisation is a crucial issue in an OFDM receiver design. It depends on the form of the OFDM transmission (whether it is continuous or has a bursty nature). In case of the WINNER MAC superframe structure shown in Figure 1 [2], synchronisation algorithms specific for packet or bursty transmission have to be applied.

Synchronisation is not fully obtained after the acquisition mode since the sampling frequency offset still remains uncompensated. The inaccuracy of the sampling clock frequency causes slow drift of the FFT window giving rise to ICI and subcarrier phase rotation. Both signal distortions, but not their sources, may be removed by a frequency-domain channel equaliser. However, the time shift of the FFT window builds up, and eventually the FFT window shifts beyond the orthogonality window of the OFDM symbol giving rise to IBI. Therefore, the sampling clock synchronisation, performed by a resampling algorithm, should also be implemented in the OFDM receiver.

A number of time and frequency synchronisation algorithms in the OFDM-based systems have already been proposed. The less complex but less accurate algorithms are based on the correlation of identical parts of the OFDM symbol. The correlation between the cyclic prefix and the corresponding end of the OFDM symbol, or between two identical halves of the synchronisation symbol, is applied in [3, 4], respectively. The use of pseudonoise sequence correlation properties was proposed in [5, 6]. Both solutions offer very accurate time and frequency offset estimates; however, the main disadvantage of both of them is their complexity.

The sampling frequency offset estimation has been investigated in many papers too. Since sampling period offset causes subcarrier phase rotation, some algorithms, like those introduced in [7, 8], estimate the phase change between the subcarriers of the OFDM symbol or between the same subcarriers of succeeding OFDM symbols (see the method described in [9]). A noncoherent solution, that is, without carrier phase estimates, was proposed in [10]. The drawback of that algorithm is its sensitivity to symbol timing synchronisation errors. Like the schemes shown in [7, 8], it requires pilot tones transmitted in every OFDM symbol, as it is done in the DVB-T system. Thus, such algorithms are not suitable for systems with pilot tones separated in time by data symbols, as it can be found in the WINNER system. The algorithm described in [9] is driven by data hard decisions made by the receiver, and it estimates and tracks the residual carrier frequency offset as well. That solution will be compared with the proposed algorithm in Section 7.2.

In this paper, fast and accurate timing and frequency synchronisation algorithms are proposed. The synchronisation is a two-stage process. First, coarse timing and fractional frequency offset synchronisation are performed. After detecting the transmitted signal, the carrier frequency and sampling frequency offsets are tracked during the tracking mode by a low-complex algorithm, which is immune to symbol timing offset estimation errors. The algorithm is designed for OFDM systems with a small pilot overhead, and it applies channel estimates already computed by the channel estimation block.

The paper is organised as follows. In Section 2, the system model is introduced. Section 3 contains the description of the acquisition mode algorithms. In Section 4, timing synchronisation errors are briefly characterised. Sections 5 and 6 contain the description of the decision-directed algorithm and the newly proposed algorithm in which channel transfer function estimates are used. Computer simulation results are presented and discussed in Section 7, and finally, the paper is concluded in Section 8.

## 2. System Model

where is the index of the OFDM symbol, is the frequency domain th modulated symbol, , and is the total number of subcarriers.

## 3. Data-Aided Correlation Scheme

### 3.1. Coarse Timing Synchronisation

*Downlink Synch*slot of the WINNER MAC superframe [2]. The first OFDM symbol of the

*Downlink Synch*is called the

*T-Pilot*and is dedicated to the synchronisation process. Two synchronisation symbol designs have been considered as possible

*T-Pilots*. Their time-domain structures are illustrated in Figure 3. The first one is used together with the original Schmidl and Cox algorithm [4], and the latter one is used with a modified version of the Schmidl and Cox algorithm proposed by the author. In order to generate OFDM symbols consisting of 2 and 8 identical elements, BPSK representation of the Gold sequence is transmitted on every second and eighth subcarrier of the OFDM symbol, respectively. If the Schmidl and Cox algorithm is applied together with the second candidate synchronisation symbol, the time metric plateau occurs after the first subsymbol. The problem is solved by multiplying the already generated time-domain OFDM symbol by the sign coefficients that are defined as

Detection of the maximum value of (4) ends the coarse timing synchronisation stage. However, fractional frequency estimation needs yet to be performed.

### 3.2. Fractional Frequency Estimation

*A*is equal to (assuming every subcarrier of every pilot symbol is used), so is the maximum frequency offset which can be estimated. It can be observed that there are a number of available frequency offset estimates due to repetitive nature of the synchronisation symbol. The correct estimates are computed within the window starting from the end of the third subsymbol

*A*and ending at the end of the last subsymbol. This implies that the frequency offset estimation quality can be improved by averaging the estimates computed during the window , that is,

where is the cyclic prefix length. The use of the offset equal to in averaging aims to compensate the influence of the symbol timing estimation error on the computed frequency offset.

## 4. Postacquisition Synchronisation Errors

where , , is an attenuation caused by both offsets, and is the Gaussian noise sample.

The sampling period offset affects the OFDM signal in two ways. First, it rotates data symbols. Second, since accumulated sampling period offset is not constant during the OFDM symbol but increases from sample to sample, it disturbs the orthogonality of the subcarriers giving rise to intercarrier interference. However, for small offsets the second phenomenon and the attenuation are negligible, and they will not be considered in this work.

## 5. Decision-Directed Algorithm

where
and
are CFO and SPO loop filters coefficients, respectively. The sampling period offset estimate controls the *interpolator/decimator* block that corrects the offset. The carrier frequency offset is used for correcting the phase of the time samples of the received OFDM signal. The drawback of this algorithm is that the CFO estimate does not take into consideration the influence of SPO that can be significant during the initialisation of the algorithm.

## 6. Proposed Algorithm

### 6.1. CFO and SPO Estimation

*m*th channel. Instead of using an

*interpolator/decimator*block, the proposed scheme corrects the subcarrier phases. This implies that the intercarrier interference remains unchanged, however, the receiver is simpler and cheaper. Another consequence of this solution is that the FFT window drift during one OFDM symbol is estimated instead of the exact sampling period offset. After substituting (13) into (14) and modifying the intermediate result, the phase-difference-dependent , assuming , is defined as

### 6.2. DPLL

*digital phase-locked loop*(DPLL) filters whose block diagram is presented in Figure 5. Coefficients and are the proportional and integral coefficients, respectively. The transfer function of the DPLL is [14]

From the sampling frequency offset loop output the integer and fractional part of the accumulated sampling period error are extracted. The integer part is used for correcting the FFT window while the fractional part is used for correcting the subcarriers phase.

### 6.3. Channel Estimation

*Zero Force*(ZF) channel estimator was applied to obtain the initial channel estimate [16]:

*mean square error*(MSE) [17]

where is the coefficient dependent on transmitted symbols power and is constant during the transmission. The channel coefficients are updated every received OFDM symbol. The author would like to stress that the channel estimation algorithm is not an integral part of the carrier frequency and sampling frequency offset estimation algorithm and other channel estimation algorithms can be applied as well.

## 7. Simulation Results

WINNER signal parameters.

Base Coverage Urban | Microcellular | Indoor | |
---|---|---|---|

Carrier frequency | 3.95 GHz DL | 3.95 GHz | 3.95 GHz |

Signal bandwidth | 2 × 45 MHz | 89.84 GHz | 89.84 GHz |

Subcarrier distance | 39062.5 Hz | 48828.125 Hz | 48828.125 Hz |

Used subcarriers | 1152 | 1840 | 1840 |

2048 | 2048 | 2048 | |

256 | 200 | 200 | |

Channel models | C2 | B1 | A1 |

Max velocity | 19.44 m/s | 19.44 m/s | 1.39 m/s |

Packet langth | 192 | 192 | 192 |

### 7.1. Acquisition

If the frequency offset is larger than four times subcarrier distance, an integer frequency offset estimation algorithm, like the one described in [19] or [20], is required.

### 7.2. Tracking

DPLL loops parameters.

Channel model | Algorithm | SFO DPLL | CFO DPLL | ||
---|---|---|---|---|---|

A1 | DD | 0.20 | 0.20 | 0.40 | 0.50 |

proposed | 0.30 | 0.20 | 0.40 | 0.50 | |

B1 | DD | 0.30 | 0.20 | 0.40 | 0.50 |

proposed | 0.35 | 0.20 | 0.50 | 0.30 | |

C2 | DD | 0.23 | 0.44 | 0.40 | 0.50 |

proposed | 0.23 | 0.44 | 0.30 | 0.50 |

## 8. Conclusions

In this paper, link-level synchronisation algorithms designed for the OFDM-based proposal for 4G system developed in the WINNER project have been introduced. A new time metric and pilot symbol design for coarse timing synchronisation, as well as new carrier and sampling frequency offset estimation algorithms, were proposed. The algorithms were tested in three different transmission scenarios. Simulation results showed that on the basis of only one OFDM symbol, the algorithms, at the cost of moderate complexity, gave accurate time and frequency offset estimates. The carrier and sampling frequency offset estimation and tracking algorithm, based on the channel estimates, is suitable for transmission systems with low pilot overhead. Simulation results showed that for low SNR, the proposed algorithm works better than the decision-directed solution.

## Authors’ Affiliations

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