Compressed Sensing Techniques for Decision Feedback Equalization of Sparse Wireless Channels

In this paper new efficient decision feedback equalization (DFE) schemes for channels with long and sparse impulse responses are proposed. It has been shown that under reasonable assumptions concerning the channel impulse response (CIR) coefficients, the feedforward (FF) and feedback (FB) filters may be also approximated by sparse filters. Either the sparsity of the CIR, or the sparsity of the DFE filters may be exploited to derive efficient implementations of the DFE. To this end, compressed sampling (CS) approaches, already successful in system identification settings, can significantly improve the performance of the non sparsity aware DFE. Building on basis pursuit and matching pursuit techniques new DFE schemes are proposed that exhibit considerable computational savings, increased performance properties and short training sequence requirements. To investigate the performance of the proposed schemes the restricted isometry property in the common DFE setup is also investigated.