  This paper proposes distributed adaptive algorithms based on the conjugate
gradient (CG) method and the diffusion strategy for parameter estimation over
sensor networks. We present sparsity-aware conventional and modified
distributed CG algorithms using $l_{1}$ and log-sum penalty functions. The
proposed sparsity-aware diffusion distributed CG algorithms have an improved
performance in terms of mean square deviation (MSD) and convergence as compared
with the consensus least-mean square (Diffusion-LMS) algorithm, the diffusion
CG algorithms and a close performance to the diffusion distributed recursive
least squares (Consensus-RLS) algorithm. Numerical results show that the
proposed algorithms are reliable and can be applied in several scenarios.
