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In this article, timing synchronization in OFDM is attained with the help of Zadoff–Chu sequence as a training symbol. An algorithm based on the cross-correlation property of fractional Fourier transform (FRFT) is proposed to generate a new timing metric. In this algorithm, cross correlation of received signal and Z–Chu sequence is taken at the receiver side in FRFT domain. The mathematical analysis of proposed estimator has been done and the variance of timing metric is obtained under the effect of AWGN channel. The simulation result shows that the variance of timing metric decreases as signal to noise ratio increases. The mean and MSE of the timing offset is simulated under HYPERLAN indoor channel (type-A). The proposed estimation method has been compared with existing methods and established as a better method to combat timing offset.

In the LTE system, Zadoff---Chu (ZC) sequence is used for the generation and detection of physical random access channel (PRACH) preamble sequence. The key step of PRACH baseband signal generation is to perform a discrete Fourier transform (DFT) of ZC sequence, which is characterized by the root index u and a rotation factor p. On-line computation according to the DFT formula is adopted in traditional algorithm, which has high computational complexity and is hard to meet the real-time requirement of LTE system. In this paper, it is mainly to improve the calculation of rotation factor p in DFT formula. Based on theoretical analysis of the ZC sequence DFT property, the symmetry property and recurrence relations of its rotation factor p are derived. Hence, a small amount of the rotation factors p in a ZC sequence can be calculated off-line and stored in memory firstly. And then all the other rotation factors can be obtained by looking up the table and some simple computations. As a result, the improved ZC sequence DFT can be achieved with less computational effort at a little expense of memory space.

Recently, Long Term Evolution Advanced (LTE-A) has been widely deployed for the fourth generation wireless communication system due to its high spectral utilization and throughput performance compared with the other systems. LTE-A adopts the Primary Synchronization Signal (PSS), which is generated from the frequency-domain Zadoff---Chu sequence to complete the synchronization and cell search at the receiver. Rather than the full cross-correlation search of the conventional synchronization method, in this paper, we propose a blind and low-complexity synchronization method that utilizes the time-domain symmetric property of PSS sequence. Results show that the proposed method can predict the arrival time and frequency offset of the received signal precisely and has the low-complexity advantage.

For the uplink in the long-term evolution (LTE) systems, the physical random access channel (PRACH) adopts Zadoff–Chu (ZC) sequences as preamble sequences, and each user can choose a unique cyclic shift for user identification. In high-mobility scenario, the Doppler frequency shift raises up the false alarm probability by inducing the correlation peak offsetting at the receiver side. Traditional detection method utilizes multiple search windows for searching the potential uplink users. When the Doppler frequency shift is larger than the subcarrier spacing, the energy of correlation peak leaks outside the search window and increases the false alarm probability. In this paper, we present a novel design for PRACH preamble sequence for high-speed railway scenario. Through numerical observation, we find out that the offset of the correlation peaks only depends on the initial root sequence number and the length of ZC sequences. Therefore, the root number of ZC sequences should be carefully designed to generate a preamble sequence to fight against the Doppler frequency shift. Consequently, those offsets of the correlation peaks are concentrated within a single search window, resulting in lower complexity of detection and lower probability of false alarm for random access in LTE uplink.