Sparse channel estimation including the impact of the transceiver filters with application to OFDM

Traditionally, the dictionary matrices used in sparse wireless channel estimation have been based on the discrete Fourier transform, following the assumption that the channel frequency response (CFR) can be approximated as a linear combination of a small number of multipath components, each one being contributed by a specific propagation path. In practical communication systems, however, the channel response experienced by the receiver includes additional effects to those induced by the propagation channel. This composite channel embodies, in particular, the impact of the transmit (shaping) and receive (demodulation) filters. Hence, the assumption of the CFR being sparse in the canonical Fourier dictionary may no longer hold. In this work, we derive a signal model and subsequently a novel dictionary matrix for sparse estimation that account for the impact of transceiver filters. Numerical results obtained in an OFDM transmission scenario demonstrate the superior accuracy of a sparse estimator that uses our proposed dictionary rather than the classical Fourier dictionary, and its robustness against a mismatch in the assumed transmit filter characteristics.