A wavelet-based approach to channel estimation

We present a new wavelet-based approach to channel estimation with a training sequence. The training sequence is constructed with scaling functions which are associated to compactly supported orthonormal wavelets. By sampling the received signal in a proper manner, we can acquire the projection of channel impulse response onto the subspace spanned by the scaling functions, which allows a simple yet accurate channel estimation. In contrast to most of the existing methods that treat a channel response as a discrete time (symbol-spaced or fractional-symbol-spaced) function, our approach instead estimates it as a bandlimited continuous function, which is a more natural formulation. A theoretical analysis for the estimation error is provided in Appendix. The computation complexity is shown to be on the order of O(K), where K is the number of data samples we obtain from received signals. Furthermore, our approach can be easily modified to be robust to severe channel conditions such as very low SNR (signal-to-noise ratio) or a large delay spread. Two applications are considered. Simulation results demonstrate its good performance.