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In this paper, we consider a general cooperative wireless sensor network (WSN) with multiple hops and the problem of channel estimation. Two matrix-based set-membership (SM) algorithms are developed for the estimation of complex matrix channel parameters. The main goal is to significantly reduce the computational complexity, compared with existing channel estimators, and extend the lifetime of the WSN by reducing its power consumption. The first proposed algorithm is the SM normalized least mean squares (SM-NLMS) algorithm. The second is the SM recursive least squares (RLS) algorithm called BEACON. Then, we present and incorporate an error bound function into the two channel estimation methods, which can automatically adjust the error bound with the update of the channel estimates. Steady-state analysis in the output mean-square error (MSE) is presented, and closed-form formulas for the excess MSE and the probability of update in each recursion are provided. Computer simulations show good performance of our proposed algorithms in terms of convergence speed, steady-state mean square error, and bit error rate (BER) and demonstrate reduced complexity and robustness against time-varying environments and different signal-to-noise ratio (SNR) values.
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