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Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) is a familiar modern wireless broadband technology due to its resistance against multipath fading, high data transmission rate, and spectral efficiency. This technology delivers dependable communication as well as a large range of coverage. The precise recovery of Channel State Information (CSI) and synchronization among the receiver and transmitter are two major challenges for MIMO-OFDM systems. Several estimate procedures, like blind, pilot-aided, and semi-blind channel estimating, are used to recover channel state information. Yet, those systems have several flaws that cause them to perform poorly. Hence, this paper describes the basic introduction of the Channel Estimation (CE) process in the MIMO-OFDM system. The main goal of this survey is to study analyzing and categorizing the channel estimation algorithms, and simulation tools in different contributions. Further, the performance analysis with different performance metrics from diverse contributions is pointed out. Thus, this review article presents a detailed overview of the various channel estimation schemes that have been exploited in the OFDM channel to enhance the estimation of the CSI in the MIMO-OFDM systems. This work presents and discusses the relevant comparative results and computational complexity for all of these CE systems. Furthermore, there is a list of open study directions for further exploration. [ABSTRACT FROM AUTHOR]