  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.
