  Wireless OFDM channels can be approximated by a time varying filter with
sparse time domain taps. Recent achievements in sparse signal processing such
as compressed sensing have facilitated the use of sparsity in estimation, which
improves the performance significantly. The problem of these sparse-based
methods is the need for a stable transformation matrix which is not fulfilled
in the current transmission setups. To assist the analog filtering at the
receiver, the transmitter leaves some of the subcarriers at both edges of the
bandwidth unused which results in an ill-conditioned DFT submatrix. To overcome
this difficulty we propose Adaptive Thresholding for Sparse Signal Detection
(ATSSD). Simulation results confirm that the proposed method works well in
time-invariant and specially time-varying channels where other methods may not
work as well.
