In this thesis, we consider two problems in multiple antenna system. First, we propose the data-aided frequency offset estimator in multiple transmit and receive antenna system which operates in frequency flat fading channel. The estimator is based on maximum likelihood criterion and does not require channel information. By adding a constraint that the training sequence is represented as the repetition of Hadamard code, we make the complexity of estimator much lower. Secondly, we consider the effect of channel estimation error and propose the modified V-BLAST (Vertical Bell Laboratories Layered Space Time) detection algorithm. In the proposed algorithm, we replace the nulling vector of general V-BLAST with the new nulling vector which reduces the effect of channel errors. With simulations, we test the performances of the proposed algorithms.