Performance limitation in random sinusoidal signal estimation

This paper studies the performance limitations of an LTI SISO discrete-time system in estimating a type of random input signal from its output signal. The input signal under consideration is a random sinusoidal signal. The estimation performance is measured by the energy of certain averaged error between the output of the estimator and the signal under estimation. Our purpose is to find the fundamental limit of the best attainable estimation performance under any estimator structure and parameters, in terms of the characteristics of the given system as well as the signal under estimation. It is shown that the fundamental limit depends on the interaction between the signal under estimation and the nonminimum phase zeros of the system. Moreover, this result is extended to optimal prediction and smoothing problems.