Compressed Sensing for Denoising in Adaptive System Identification
  We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter approach the compressed version of the sparse system instead of the original system. To this end, we use random filter structure at the transmitter to form the measurement matrix according to the CS framework. The original sparse system can be reconstructed by the conventional recovery algorithms. As a result, the denoising property of CS can be deployed in the proposed method at the recovery stage. The experiments indicate significant performance improvement of proposed method compared to the conventional LMS method which directly identifies the sparse system. Furthermore, at low levels of sparsity, our method outperforms a specialized identification algorithm that promotes sparsity. 
Seyed Hossein Hosseini and Mahrokh G. Shayesteh
cs.IT math.IT