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In this paper, we consider a general cooperative wireless sensor network (WSN) and the problem of channel estimation. A matrix-based set-membership recursive least squares (RLS) algorithm called BEACON is developed for the estimation of the complex channel parameters in order to reduce the computational complexity significantly and extend the lifetime of the WSN by reducing its power consumption. Then, we present and incorporate an error bound function into the BEACON channel estimation method which can adjust the error bound automatically with the update of the channel estimates. Computer simulations show good performance of our proposed algorithms in terms of convergence speed and steady state mean square error, reduced complexity and robustness to the time-varying environment and different signal-to-noise ratio (SNR) values.