We consider distributed estimation of a random vector signal in a power constraint wireless sensor network (WSN) that follows multiple-input and multiple-output (MIMO) coherent multiple access channel model. We design linear coding matrices based on linear minimum mean squared error (LMMSE) fusion rule that accommodates correlated sources. We obtain a closed-form solution that follows water-filling strategy. We also derive a lower bound distortion to this model. Simulation results show that when the sources are more correlated, the distortion in terms of mean squared error (MSE) degrades. By taking into account the effects of correlation, observation, and channel matrices, the proposed method performs better than equal power method.