Sparsity Enhancement for Sparse Channel Estimation Using Non-orthogonal Basis

Compressed sensing framework can be employed to improve channel estimation and enhance spectral and/or energy efficiency for communication systems. To take advantage of compressed sensing, special basis are required to model a multipath fading channel with sparse channel coefficients. To apply compressed sensing method a set of orthogonal basis are required, where the coefficients meet the sparsity criteria. However, the orthogonality condition for the basis may be a limiting factor to improve the sparsity of the channel coefficients. In this paper we relax the orthogonality condition and use a dictionary learning algorithm such as K-SVD to find a set of new basis with sparse coefficients. Using this method results in a channel model with improved sparsity and better MSE performance for channel estimation. An OFDM system is considered over a sparse doubly-selective channel and the proposed method is investigated through simulation. The simulation results show that the enhanced channel sparsity achieved based on the proposed method, leads to improved channel estimation performance.