Massive MIMO is considered as one of the promising technologies that can meet the growing demands of 5G communications. It has the potential to provide substantial enhancements in both link reliability and data throughput of the system. In order to achieve the advantages of massive MIMO, the base station requires accurate channel impulse response (CIR) for each transmit-receive link. Most existing works consider the frequency selective (FS) channels with slow time-variations. However, high mobility communications have been incorporated as an essential part of the 5G communications. Therefore, there is need to develop new channel estimation methods for communication over channels which are both FS and time-selective or doubly selective (DS). DS channel estimation is extremely challenging because the parameters to be estimated are numerous. In this thesis, the DS channel estimation for Massive MIMO-OFDM systems is discussed. In contrast to the existing literature, it is assumed that the channel varies within each OFDM block. The DS channel is modeled using basis expansion model (BEM). By using BEM, the number of parameters to be estimated is considerably decreased. Estimating BEM coefficients using linear estimators, itself, still needs transmitting substantial number of pilots which is not suitable in terms of users sum rate. On the other hand, it is known that most wireless channels can be modeled as discrete multipath channels with large delay spread and very few significant paths. This results in sparse CIR and sparse BEM coefficients. In this thesis, novel methods are proposed to estimate the BEM coefficients using compressed sensing (CS) and block CS recovery tools. The simulation results show that the proposed CS- and block-CS-based fewer number of pilots. Key Words: Massive MIMO , OFDM, Doubly Selective Channel, Compressed Sensing, Channel Estimation