This paper focuses on the channel state estimation (CSE) problem in parametrized Hierarchical MAC (H-MAC) stage in Wireless Physical Layer Network Coding (WPNC) networks with Hierarchical Decode and Forward (HDF) relay strategy. We derive a non-pilot based H-MAC channel phase estimator for 2 BPSK alphabet sources. The CSE is aided only by the knowledge of H-data decisions. At HDF relay, there is no information on individual source symbols available. The estimator is obtained by a marginalization over the hierarchical dispersion. The estimator uses a gradient additive update solver and the indicator function (gradient) is derived in exact closed form and in approximations for low and high SNR. We analyze the properties of the equivalent solver model, particularly the equivalent gradient detector characteristics and its main stable domain properties, and also the detector gain and equivalent noise properties under a variety of channel parameterization scenarios.
Full/Half Duplex Cooperative NOMA Under Imperfect Successive Interference Cancellation and Channel State Estimation Errors
