Motions in vehicular ad hoc networks (VANETs) cause Doppler Frequency Shifts (DFSs) which are described by frequency dispersions in the received signals. Although the VANETs channels are perturbed by noise sources such as multipath delay spread, shadowing and interference, a DFS due to the high speed vehicular mobility is a major cause of high bit-error rates (BER). Schemes for estimating and compensating DFSs in VANETs with medium to high speed mobility have been reported in the recent literature. However, significant computational complexity with some methods configured in MIMO-OFDM systems has rendered them non-attractive in full-scale deployment of high speed VANETs. The research question that remains unanswered is what scheme can be proposed to estimate and compensate for the DFS at a reduced computational complexity when MIMO-OFDM systems and high speed mobility conditions are considered? This paper answers this question by proposing a pilot-assisted DFS estimator and compensator based on the general complex exponential basis expansion matrix (BEM) modelling. The proposed method realizes a low computational complexity DFS estimator and compensator in the linear order of the Fast Fourier Transform (FFT) size as compared to the DFS uncompensated MIMO-OFDM systems whose computational complexity has been noted to be in a quadratic order of the FFT size. Numerical results indicate that the proposed BEM method demonstrates a better BER performance than the conventional approaches under the same MIMO configurations for moderately high vehicular speeds. ACM CCS (2012) Classification: Networks → Network algorithms → Basis expansion modelling algorithms → Network design and planning algorithms Networks → Network types → Ad hoc networks → Mobile ad hoc networks → Vehicular ad hoc networks Networks → Network performance evaluation → Network simulations Keywords: basis expansion matrix modelling (BEM), doppler frequency shifts (DFS), inter carrier interference (ICI), multiple input multiple output (MIMO) systems, orthogonal frequency division multiplex (OFDM) systems, signal to noise ratio (SNR), vehicular ad hoc networks (VANETs)