In this study, the authors propose to use the cubic convolution interpolation function with a free variable to generate a class of constant-coefficient interpolation functions. The interpolations functions can be applied to an orthogonal frequency-division multiplexing-based receiver for channel estimation. For a given channel, different interpolation functions from the class have different bit error rates (BERs). Therefore by using a search algorithm, a better interpolation function is chosen with the aid of a performance indicator, such as the estimated mean-squared error (EMSE). Although the uneven distribution of pilots in the IEEE 802.16e system prohibits direct utilisation of the cubic interpolation function, a simple approach has been proposed to solve this problem. The proposed method is validated in the IEEE 802.16e downlink system by Monte Carlo simulation. The simulation results also confirm that channels with different statistical properties should use different interpolation functions. In addition to the Monte Carlo simulation, we also analyse the BER of the proposed approach. We find that the BERs based on the analytical evaluation and on the simulation closely match each other. Finally, it is shown that the EMSE is an acceptable performance indicator for medium-to-high signal-to-noise ratio.