Channel estimation: unified view of optimal performance and pilot sequences

Abstract

Channel estimation is of paramount importance in most communication systems in order to maximize data rate. In modern systems, the possibly large number of transmit/receive antennas and subcarriers makes this task difficult. Several parametric models, either linear or nonlinear, have thus been proposed to ease channel estimation by reducing the dimension of the estimation problem. In this paper, the problem of estimating an object of interest parameterized according to a model, based on noisy complex linear observations is studied. The Cramér-Rao bound (CRB) for this general problem is given, highlighting its key dependency on the introduced variation space. Then, identifiability conditions are given, and the minimal value of the CRB, as well as a general strategy to build minimal length power constrained observation matrices are determined. The results are finally illustrated in a general wideband MIMO context. They allow to retrieve well known previous results, but also to exhibit minimal length optimal pilot sequences in a simple nonlinear physical model setting. Note that the results of this paper are general and could perfectly be used in other applications as well.