Eigen-based dictionary for ultra-wideband compressed sensing

In practice, sub-Nyquist rate sampling schemes are desirable in ultra-wideband (UWB) applications. Due to the fact that UWB signals are sparse in nature, compressed sensing (CS) is regarded as a promising technology which enables low rate sampling of UWB signals. In CS, a crucial issue is to find the best dictionary which statistically achieves the sparsest representation of the target signals. This is because that the number of measurements (sampling rate) required by CS to reconstruct the original signals is proportional to the sparseness. In this paper, we propose an eigen-based dictionary for CS-based UWB channel estimation and signal detection, where the eigenvectors of the covariance matrix of the UWB channel are used as the elements of the dictionary. For ease of implementation, the generalized rotation matrix, instead of the Gaussian random matrix, is employed as measurement matrix and orthogonal matching pursuit (OMP) algorithm is employed to reconstruct original UWB signals. Simulation results over realistic channels show that the proposed dictionary outperforms conventional dictionaries.