Abstract
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.
Highlights
This paper focuses on the channel state estimation (CSE) problem in parametrized Hierarchical MAC
We focus on a special case of both sources having BPSK alphabets As = {±1}, i.e., s A (c A ) = 2c A − 1, constellation mappers s A (c A) ∈ {0, 1}, and for s B
We use the fact that the source constellation mappers s A (c A ), s B (c B ) are one-to-one functions, and both of them are from the PSK class of alphabets |s A | = |s B | = 1
Summary
Wireless Physical Layer Network Coding (WPNC) is a PHY layer concept for communications in dense radio networks with highly interacting signals. Information 2019, 10, 40 source nodes) channel parametrization becomes of paramount importance, since (apart of significant performance consequences) it affects the overall structure of the hierarchical (soft-output) demodulator (H-SODEM). It affects the shape of H-constellation which is a highly complicated nonlinear function of the relative fading. This problem becomes even more significant in the randomly time-variant fading channels, where traditional pilot based approaches have limited applicability. Thorough additional details can be found in [1]
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