In this paper, the authors consider a general cooperative Wireless Sensor Network (WSN) with multiple hops and the problem of channel estimation. Two matrix-based set-membership algorithms are developed for the estimation of the complex matrix channel parameters. The main goal is to reduce the computational complexity significantly as compared with existing channel estimators and extend the lifetime of the WSN by reducing its power consumption. The first proposed algorithm is the Set-Membership Normalized Least Mean Squares (SM-NLMS) algorithm. The second is the set-membership Recursive Least Squares (RLS) algorithm called BEACON. Then, they present and incorporate an error bound function into the two channel estimation methods which can adjust the error bound automatically with the update of the channel estimates.