Orthogonal frequency division multiplexing (OFDM), which is a kind of frequency division multiplexing, has many applications for data transmission because of its several merits as following. OFDM shows high spectral efficiency because of the orthogonality between the overlapped adjacent frequency bins called subchannels or subcarriers whose bandwidth are very narrow, and the symbol period of the OFDM modulated signal, which is generally propotional to the number of the subcarriers, is considerably long compared to single carrier schemes. So, OFDM is robust against the impulse noise and need comparatively simple equalization scheme.
OFDM needs symbol timming synchronization called frame synchronizaton in order to extract the data exactly from the symbol. OFDM, however, has some problem in synchronization because it is composed of a lot of subcarriers and so we can not use the conventional synchronization scheme like the phase locked loop, square law device, etc., which is used for single carrier modulation. In OFDM systems, the symbol timming error i.e., the frame synchronization offset results in phase errors of every subcarriers and so increases the symbol error rate during QAM decoding like single carrier modulation. So, if we can compute the offset by examining the every subcarrier's phase error, it can be used as a measure for frame synchronism and we can, furthermore, decrease the symbol error rate due to the synchronization alignment error by compensating the offset. In most OFDM systems, after initial acquisition, fine frame synchronism is usually maintained using several subcarriers as pilot tones. This results in lower channel efficiency, and degraded system performance when the pilot channels are impaired by several interferences.
In this thesis, we proposed a method to estimate the frame synchronization offset for orthogonal frequency division multiplexing(OFDM) frame alignment without resort to pilot tones. We first derive the probability density functions of the phase errors of every subcarriers after detection in the receiver which occur due to the frame synchronization offset and the Gaussian noise, and we show that the probability density functions can be approximated to the Gaussian density function. On the basis of these facts, we derived a decision-directed maximum-likelihood estimation of frame synchronization offset. We applied the proposed scheme to the 4-QAM and 16-QAM systems, and could confirm the excellency of the performance by computer simulation. The accuracy of the estimator is less than 0.01 sample point in the case of 4-QAM when signal to noise ratio is 10 dB, and this method can only be used where the frame synchronization offset is so small that decision errors do not occur. Therefore this scheme can be classified as fine synchronization method.
We also developed an algorithm for the initial synchronithm. There are many situations where the initial time synchronisation is needed. The OFDM systems, for example, need the initial frame synchronisation for initial acquisition. Typical method for performing the initial time synchronisation is to use a correlation detector which needs to repeat a calculation at every sampling time when new data are received and needs the interpolation. We propose a new method using the OFDM data frame which need only one computational process if we have any data of proper time interval. We propose a method to establish the initial time synchronism by estimating the synchronisation offset in frequency domain using orthogonal frequency division multiplexing(OFDM) signals. We use the 4-QAM signal as the modulation scheme for every subcarrier. A maximum-likelihood estimation of the initial time synchronisation offset is derived, and the performance of the proposed scheme is confirmed by computer simulation. The scheme can be used not only for the initial frame synchronisation of OFDM system but also for any other systems which need the initial time synchronisation. In this thesis we also developed the coarse synchronization method which can be used when the frame synchronization offset is so large that the fine synchronization method can not be applied because of the symbol decision errors. We know that the decision errors occur more frequently at the high subcarrier bins. So we developed an algorithm by which we can reject them and we established a detection method of the frame offset using the valid subcarriers by the maximum-likelihood estimation method. Finally, we developed some methods, in the appendixes, by which we can estimate the signal to noise ratio even though there is a large synchronization offset, and we can judge the reliability of the frame synchronization offset estimate.
