This paper studies the channel estimation and equalisation of orthogonal frequency-division multiplexing (OFDM) systems over doubly selective channels. We consider practical channel estimation schemes based on basis expansion model (BEM) and clustered pilots. We investigate the influence of the parameters of the channel estimation scheme, including the dimensionality of the BEM basis and bandwidth chosen for the frequency-domain (FD) channel matrix. We address the performance degradation of linear and nonlinear equalisation due to imperfect channel estimation and study the usage of regularisation to enhance the performance. The numerical results show that regularisation can effectively enhance the detection performance.