Sparse channel estimation for OFDM: Over-complete dictionaries and super-resolution

Wireless multipath channels can often be characterized as sparse, i.e., the number of significant paths is small even when the channel delay spread is large. This can be taken advantage of when estimating the unknown channel frequency response using pilot assisted modulation. Other work has largely focused on the greedy orthogonal matching pursuit (OMP) algorithm, using a dictionary based on an equivalent finite impulse response filter to model the channel. This is not necessarily realistic, as the physical nature of the channel is continuous in time, while the equivalent filter taps are based on baseband sampling. In this paper, we consider sparse channel estimation using a continuous time path-based channel model. This can be linked to the direction finding problem from the array processing literature and solved using the well-known root-MUSIC and ESPRIT algorithms, which have no formal time resolution. In addition, we show that a dictionary with finer time resolution considerably improves the performance of OMP and the related Basis Pursuit (BP) algorithm.