Performance Analysis of Hierarchical Decision Aided 2-Source BPSK H-MAC CSE with Feed-Back Gradient Solver for WPNC Networks

The paper addresses a problem of channel phase estimation in a 2-source Hierarchical MAC channel in a Wireless Physical Layer Coded (WPNC) system with Hierarchical Decode and Forward strategy. We assume a non-pilot based estimator, a pilot based one would require orthogonal pilot signal resources which are not available in a WPNC system. In such a system, the receiving relay node does not have the individual source data available and the only data related estimator aid is a many-to-one network coded data function. We analyze the properties of the estimator metric and the performance of the estimator with a feed-back gradient solver. Particularly we analyze: (1) mean square error (MSE) performance including its relation to Cramer-Rao Lower Bound (CRLB), and (2) we analyze properties of ambiguity modes of the estimator.