The authors consider the distributed estimation of a random vector signal in a power constraint Wireless Sensor Network (WSN) that follows a Multiple-Input and Multiple-Output (MIMO) coherent multiple access channel model. They design linear coding matrices based on Linear Minimum Mean-Square Error (LMMSE) fusion rule that accommodates spatial correlated data. They obtain a closed-form solution that follows a water-filling strategy. They also derive a lower bound to this model. Simulation results show that when the data is more correlated, the distortion in terms of Mean-Square Error (MSE) degrades.