  Maximum Likelihood (ML) algorithms, for the joint estimation of
synchronization impairments and channel in Multiple Input Multiple
Output-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system, are
investigated in this work. A system model that takes into account the effects
of carrier frequency offset, sampling frequency offset, symbol timing error,
and channel impulse response is formulated. Cram\'{e}r-Rao Lower Bounds for the
estimation of continuous parameters are derived, which show the coupling effect
among different impairments and the significance of the joint estimation. We
propose an ML algorithm for the estimation of synchronization impairments and
channel together, using grid search method. To reduce the complexity of the
joint grid search in ML algorithm, a Modified ML (MML) algorithm with multiple
one-dimensional searches is also proposed. Further, a Stage-wise ML (SML)
algorithm using existing algorithms, which estimate fewer number of parameters,
is also proposed. Performance of the estimation algorithms is studied through
numerical simulations and it is found that the proposed ML and MML algorithms
exhibit better performance than SML algorithm.
