| Orthogonal frequency division multiplexing (OFDM) withstands multipath channel very well, and multiple-input multiple-output (MIMO) has very high transmission efficiency. Therefore, a MIMO system employing OFDM, denoted MIMO OFDM, is able to improve performance of the system and achieve high spectral efficiency. However, OFDM adopts orthogonal sub-carriers and the received signal of MIMO is a superposition of all of transmitted signals, which make the receiver of MIMO OFDM system more difficult. In this dissertation, we study different MIMO OFDM system with time domain and frequency domain training sequence. We deal with their synchronization, channel estimation and training sequence design problem.OFDM technology is very sensitive to synchronization error. First, we consider the time and frequency synchronization for MIMO OFDM system. Due to cyclic prefix, small symbol timing error does not result in inter-symbol-interference (ISI). But random symbol timing in different OFDM symbols not only adds the computation complexity of equalization but also degrades performance of the system. So MIMO OFDM systems require a robust and accurate symbol timing algorithm. Traditional ML method based on cyclic prefix has large MSE. In order to avoid this shortcoming, two improved algorithms are proposed: one is suite for slow fading channels; one is suite for fast fading channels. They distinguish integral ISI free region from ISI region instead of estimate one random sample in ISI free region of ML method, which significant degrade MSE. Because carrier frequency offset and sample timing offset destroy the orthogonality among subcarriers, seriously degrade system performance, and then MIMO OFDM systems need perfect carrier frequency and sample timing synchronization algorithms. For MIMO OFDM systems based on time domain training sequence, according to the carrier frequency offset (CFO) affects phase rotation between the two identical received training symbols in time domain, two correlations are used to get CFO estimation: First a small correlation span is used to get large estimation range, and then a large correlation span is used to make the estimation more precise. Sample timing error affects the number of samples in an OFDM symbol in time domain. We proposed a sample timing error algorithm reply on detection interval between different OFDM symbols. For MIMO OFDM systems based on frequency domain training sequence, we extended the CFO algorithm for SISO OFDM systems to MIMO OFDM systems, and proposed a sample timing error algorithm reply on detection phases of different pilots.Training sequence design affects transmission efficiency of MIMO OFDM systems, the performance of channel estimation also reply on it. In this dissertation, we do some research on time domain and frequency domain training sequence design of MIMO OFDM systems. Based on minimum mean square error, we found optimal time domain training sequences must have impulse-like autocorrelation and zero cross-correlation at least in maximum channel delay range. According to this criterion we proposed four optimal time domain training sequence design methods. We also found the number of optimal frequency domain training symbols at least is equal to the number of transmit antennas, and the sequences in same subcarriers for different antennas must be orthogonal.When estimating the channel state information for a transmitter-receiver pair of MIMO OFDM systems, the signals from other transmitter antennas become interference, which disturbs the accuracy of the estimation process. So channel estimation for MIMO OFDM systems becomes a challenge task. The paper proposed different channel estimation algorithms for frequency selective slow and fast fading channels. Considering the varying can be ignored in a long time for slow fading channel, we proposed adaptive filter channel estimation based on LMS and RLS algorithms. For fast fading channel, the channels need to be estimated real time. We proposed extended kalman algorithm to track time varying channel. The shortcoming of this method is low transmission efficiency, and then we proposed an extended kalman algorithm based on decision. Due to high computation complexity, we also proposed a time varying channel estimation method based on suboptimal time domain training sequence.
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