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In this paper, we consider a general cooperative wireless sensor network (WSN) and the problem of channel estimation. We develop a matrix-based set-membership normalized least mean squares (SM-NLMS) algorithm 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. The proposed SM-NLMS channel estimation method requires the setting of a bound for appropriate performance. However, an inappropriate and fixed error bound will result in overbounding and underbounding problems which degrade the performance significantly. Therefore, we present and incorporate an error bound function into the SM-NLMS 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, reduced complexity and robustness to the time-varying environment and different signal-to-noise ratio (SNR) values.