Coded Sampling Bound - How Much Training is Needed for Iterative Semi-Blind Channel Estimation?

Coherent detection is commonly facilitated by means of pilot-aided channel estimation. While this approach offers a high estimation accuracy, the spectral and power efficiencies are reduced due to the pilot overhead. In the case that redundancy due to channel coding is not used for the purpose of channel estimation, the maximum pilot spacing for which a time-varying channel can be reconstructed without distortion is given by the Nyquist-Shannon sampling theorem. In this paper, it is shown that if channel coding is taken into account for channel estimation in an iterative fashion, the maximum spacing can be significantly extended, which results in an increased spectral efficiency. Towards this goal, a so-called coded sampling bound is derived. This semi-analytical bound is compared with the Nyquist-Shannon sampling theorem. The presented results indicate that the maximum pilot spacing can be arbitrarily large given a suitable channel code and code rate.