Smart grid system state measurement estimation over wireless channels

The transmission of delay sensitive smart grid system state measurements over wireless channels is considered. In the system under consideration, remote sensors obtain noisy state measurements and send these measurements over wireless channels to the control center. Our goal is to design transmission schemes that minimize a weighted sum of the square errors of the state measurements estimates. Due to the delay sensitive nature of the state measurements, low complexity memoryless coding and decoding strategies are considered. Optimal power allocation strategy, both over the fading state and over the measurements, are derived. It is shown that if there is only one measurement, the optimal power allocation strategy is a modified version of the well-known water-filling solution: sticky water-filling solution. For the general case, if the observation matrix is a diagonal matrix, the optimal power allocation over time is still sticky water-filling solution. The optimal power allocation over the state measurements is simply to put all available power to the most important measurement according to a criteria to be specified in the paper. For the general observation matrix, an asymptotically optimal power allocation scheme is presented.