Effect of polynomial interpolations on the estimation performance of a frequency-selective Rayleigh channel in orthogonal frequency division multiplexing systems

In this paper, the authors provide an analytical expression of the mean square error (MSE) and the bit error rate (BER) lower bound of an orthogonal frequency division multiplexing signal transmission over a multipath Rayleigh channel considering estimation errors. For some pilot arrangements, an interpolation is required to perform the channel estimation. Owing to their low complexity, polynomial based interpolations are usually applied at the receiver, which induces estimation and signal errors. Based on a statistical analysis of these errors, the exact MSE expression of the channel estimation is provided. Furthermore, with a geometrical study of the constellation, an analytical BER limit is derived. For a given channel, it is shown that the errors are perfectly characterised by the interpolation method and the frequency gap between the pilot tones. All the steps of the analytical developments are validated through simulations. The proposed analysis then predicts the performance of the receiver, thus enabling the latter to a priori select the interpolation method with minimum complexity, according to a given channel and a BER target.