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This paper studies the problem of frequency-and time-selective (doubly selective) channel estimation in full-duplex multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. In particular, the maximum-likelihood (ML) principle is employed to formulate a pilot-aided channel estimation algorithm. To reduce the number of doubly selective channel parameters to be estimated, various basis expansion models (BEMs) are used as fitting parametric models. The use of BEMs enables an increase in the system spectral efficiency since estimating a reduced number of channel parameters entails a reduction in used pilot overhead. This paper provides analytical and empirical results of the BEM-based channel estimation accuracy. Several mean square error (MSE) results show that the discrete prolate spheroidal (DPS) or Karhuen Loeve (KL) basis functions would be a suitable choice …