Optimal training design for channel estimation in inhomogeneous distributed sensor networks

This paper investigates the optimal training design for channel estimation in an inhomogeneous distributed sensor network, which is used to estimate a unknown parameter. The training design includes the power allocated for each sensor and the power scheduling between training pilots and sensor observations. In addition to the total power constraint on all the sensors, we introduce individual power constraint for each sensor, which reflects the practical scenario where all sensors are separated from one another. Since the final average mean square error (MSE) depends on the unknown parameter, a lower bound of the MSE is derived to compensate the channel estimation error (CEE). The Multilevel and “cave” waterfilling type solutions are proposed for the optimal training design to minimize the lower bound MSE, with only the sum power constraint and both the sum and individual power constraints, respectively. Simulation results demonstrate the performance of the proposed training design.