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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. Cramér-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.

Joint estimation of the random impairments, phase noise (PHN) and channel, in orthogonal frequency division multiplexing (OFDM) system is investigated in this study. Bayesian Cramér-Rao lower bounds (BCRLBs) for the joint estimation of PHN and channel are derived, and are compared with the corresponding standard CRLB, which shows the significance of joint estimator in a Bayesian framework. The authors propose maximum a posteriori algorithms for the estimation of PHN and channel, utilising their statistical knowledge which is known a priori. 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 BCRLB. Nomenclature Upper case bold italic letters denote matrices and lower case bold italic letters denote column vectors.