Transmit signal design for optimal deconvolution

This paper solves the problem of designing successive transmit pulses to minimize the mean squared error of deconvolution in colored noise. The power spectral densities of the signal and noise are known a priori. In the special case of white noise, the analytical solution can be interpreted as the "water-filling" principle for the distribution of transmitted spectral energy. Numerical simulation of a simple example with exponentially correlated target signal and white noise illustrates the benefits of using adaptively designed transmit signals.