The integration of Multiple Input Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) techniques has become a preferred solution for the high rate wireless technologies due to its high spectral efficiency, robustness to frequency selective fading, increased diversity gain, and enhanced system capacity. The main drawback of OFDM-based systems is their susceptibility to impairments such as Carrier Frequency Offset (CFO), Sampling Frequency Offset (SFO), Symbol Timing Error (STE), Phase Noise (PHN), and fading channel. These impairments, if not properly estimated and compensated, degrade the performance of the OFDM-based systems In this thesis, a system model for MIMO-OFDM that takes into account the effects of all these impairments is formulated. Using this system model, we de-rive Cramer-Rao Lower Bounds (CRLBs) for the joint estimation of deterministic impairments in MIMO-OFDM system, which show the coupling effect among different impairments and the significance of the joint estimation. Also, Bayesian CRLBs for the joint estimation of random impairments in OFDM system are derived. Similarly, we derive Hybrid CRLBs for the joint estimation of random and deterministic impairments in OFDM system, which show the significance of using Bayesian approach in estimation. Further, we investigate different algorithms for the joint estimation of all impairments in OFDM-based system. Maximum Likelihood (ML) algorithms and its low complexity variants, for the joint estimation of CFO, SFO, STE, and channel in MIMO-OFDM system, are proposed. We propose a low complexity ML algorithm which uses Compressed Sensing (CS) based channel estimation method in a sparse fading sce-nario, where the received samples used for estimation are less than that required for a Least Squares (LS) or Maximum a posteriori (MAP) based estimation. Also, we propose MAP algorithms for the joint estimation of the random impairments, PHN and channel, utilizing their statistical knowledge which is known a priori. Joint estimation algorithms for SFO and channel in OFDM system, using Bayesian framework, are also proposed in this thesis. The performance of the estimation methods is studied through simulations and numerical results show that the performance of the proposed algorithms is better than existing algorithms and is closer to the derived CRLBs.