Sequential design of experiments for a rayleigh inverse scattering problem

We consider the problem of imaging a Rayleigh scattering medium using an array of sensors. We study the effect of noise on the estimation of Rayleigh scatterer reflection powers by setting up a sequential design of experiments. We derive an expression for the mean squared error for estimating the scatterer reflection powers. We keep the transmitted spatial waveforms fixed and find the optimal energy allocation strategy that minimizes this error under a fixed energy constraint. We show that this sequential design approach performs better than a single step experiment. Closed-form expressions for the optimal transmission scheme and the minimum mean squared error are provided