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Time variations of a doubly selective wireless channel and insufficient cyclic prefix (CP) length of an orthogonal frequency division multiplexing (OFDM) transmission system cause intercarrier interference (ICI) and interblock interference (IBI) as significant limitations. This paper investigates the problem of joint ICI and IBI mitigation in single-input multiple-output OFDM (SIMO-OFDM) systems. It is assumed, unlike most existing literature, that the channel delay spread is larger than the CP, and also the channel varies on each OFDM block. First, doubly selective channel is modelled using basis expansion model (BEM) and a closed-form expression for signal-to-interference-plus-noise ratio (SINR) is derived. Then, a time-domain equaliser is developed, which maximises the SINR for all subcarriers. Moreover, a frequency-domain equalisation approach is proposed which is based on the MSE minimisation per tone. A low-complexity implementation of the per-tone equaliser is also derived. An important feature of the proposed equalisers is that no bandwidth expansion or redundancy insertion is required except for the CP. Finally, complexity comparison and simulation results over Rayleigh fading channel are provided to illustrate the effectiveness of the proposed approaches. Since both equalisers are designed in the frequency domain, they provide significant interference cancellation.