The orthogonal frequency-division multiplexing (OFDM) is a promising waveform for joint radar and communication systems. In this article, a unified approach is proposed to analyse both radar and communication robustness with respect to Doppler mismatch. The analytical study leads to an expression that links the radar performance to the communication one. The performance of a delay-Doppler radar is quantified by modelling the delay response of the OFDM radar with an appropriate random variable. Different delay filters are analysed, among which the Wiener filter. The analytical results are validated by simulations, they show that the radar system benefits from the Wiener filter, and the configurations where this filter outperforms the other ones are outlined.