In wireless communications, a delay due to the propagation distance in proportion to the length of the optical path may occur. Generally, in a cellular system including a base station and a terminal station, the base station may become a master to control the synchronization of a plurality of terminal stations. The terminal station may transmit a signal so that the signal reaches to the base station at a timing which is determined by the base station. If an error with respect to a synchronization of timing occurs, interference with other stations may occur.
Specifically, a multiple access system like Time Division Multiple Access (TDMA) system is configured by some units, each length of the unit corresponds to a transmission period, the unit being called such as “a frame” or “a slot”. If a timing error is large, a station may transmit a signal beyond its allowed transmission period, across a plurality of frames or slots. An overlap with the transmission period of other stations may cause interference at the other stations. In addition, in the multiple access system using Cyclic Prefix (CP), like Orthogonal Frequency Division Multiple Access (OFDMA), if the timing error exceeds Cyclic Prefix (CP), orthogonality characteristics may be lost. Thus, the station may not be able to separate the signals caused by some stations, into a signal corresponding to each station.
As a method for establishing synchronization between a base station and a terminal station, for example, in the system of Worldwide Interoperability for Microwave Access (WiMAX), Long Term Evolution (LTE) or IEEE802.22, a terminal station transmits a signal, called a ranging code or a random access preamble, to a base station for establishing synchronization. Thereafter, the base station detects a timing error based at least in part on the signal, then the base station notifies the terminal station of the timing adjusting value or the offset value (differential value) from the predetermined timing, them the terminal station performs a timing adjustment to establish synchronization. In this scheme, the terminology “ranging” means an adjusting process for a transmission power, a frequency or transmission timing at the terminal station, based at least in part on a location of the terminal station, in an initial stage of establishing communication between the base station and the terminal station.
In the system using Orthogonal Frequency Division Multiplexing Modulation (OFDM Modulation), a terminal station transmits a signal in the time domain as a symbol for a ranging. Here, the signal in the time domain is generated by OFDM Modulation (Inverse Fast Fourier Transform (IFFT)), under subcarrier modulation of a random code. As to a method for detecting timing offset in the base station, there is a method utilizing a correlation of an output from an OFDM demodulator (Fast Fourier Transform (FFT)) and a code. When a timing offset between the actual timing of a received signal and the timing which is assumed by the base station is occurred, a phase difference is generated between subcarriers after the FFT output. The phase difference increases in proportion to the frequency difference. Using this characteristic, there is a method for detecting a timing offset based at least in part on the difference between the subcarrier interval and the phase rotation amount.
For example, in the case of OFDM system where a size of FFT is prescribed for 2048 points, such as IEEE802.22, the subcarrier having the longest period consists of 2,048 samples as one period. Therefore, when one (1) sample of timing offset occurs, phase rotation of 2π/2048 radians occurs. Similarly, in the subcarrier which is adjacent to the subcarrier having the longest period, the phase rotation of 2×2π/2048 radians occurs. That is, when comparing the amount of phase rotation between subcarrier adjacent each other, there is the phase difference of 2π/2048 radians. Since a ranging subcarrier (subcarrier for ranging signal) is allocated at every ten (10) subcarriers in IEEE802.22, there is the phase difference of 10×2π/2048 radians in the relationship between subcarriers away 10 subcarriers. Therefore, when the phase difference between the ranging subcarriers for the output after FFT is φ radians, a timing offset can be calculated by the following formula (1).
                    Offset        =                              2048            ⁢            φ                                2            ⁢                          π              ⨯              10                                                          formula        ⁢                                  ⁢                  (          1          )                    