In this paper, we propose the mitigating scheme to reduce the effects of phase noise in multi-input multi-output-orthogonal frequency division multiplexing system with independent oscillator in each RF chain. Our proposed schemes consist of two stages; channel estimation stage and data decoding stage. In the first stage, we propose the channel estimation algorithm based on maximum a posteriori (MAP) estimator and a method of selecting the training sequence for channel estimation and we provide the mathematical analysis of our proposed scheme. In the second stage, MAP estimators are used to jointly estimate phase noise at TX and RX and detect data symbols. For analysis of mean square error (MSE) performances, we derive Bayesian Cramėr-Rao bound for multi-parameter estimation problem in each stage. At the end of this paper, we demonstrate from our simulation results that our mathematical analysis is accurate and the proposed algorithm improves the bit-error-rate performance and MSE performance compared with existing schemes.