For single-carrier systems with frequency domain equalization, decision feedback
equalization (DFE) performs better than linear equalization and has much lower
computational complexity than sequence maximum likelihood detection. The main challenge in
DFE is the feedback symbol selection rule. In this paper, we give a theoretical framework
for a simple, sparsity based thresholding algorithm. We feed back multiple symbols in each
iteration, so the algorithm converges fast and has a low computational cost. We show how
the initial solution can be obtained via convex relaxation instead of linear equalization,
and illustrate the impact that the choice of the initial solution has on the bit error rate
performance of our algorithm. The algorithm is applicable in several existing wireless
communication systems (SC-FDMA, MC-CDMA, MIMO-OFDM). Numerical results illustrate
significant performance improvement in terms of bit error rate compared to the MMSE
solution.