  Sparse structures are widely recognized and utilized in channel estimation.
Two typical mechanisms, namely proportionate updating (PU) and zero-attracting
(ZA) techniques, achieve better performance, but their computational complexity
are higher than non-sparse counterparts. In this paper, we propose a DCS
technique based on the recursive least squares (RLS) algorithm which can
simultaneously achieve improved performance and reduced computational
complexity. Specifically, we develop the sparse adaptive subspace
pursuit-improved RLS (SpAdSP-IRLS) algorithm by updating only the sparse
structure in the IRLS to track significant coefficients. The complexity of the
SpAdSP-IRLS algorithm is successfully reduced to
$\mathcal{O}(L^2+2L(s+1)+10s)$, compared with the order of
$\mathcal{O}(3L^2+4L)$ for the standard RLS. Here, $L$ represents the length of
the channel, and $s$ represents the size of the support set. Our experiments on
both synthetic and real data show the superiority of the proposed SpAdSP-IRLS,
even though only $s$ elements are updated in the channel estimation.
