Closed-Form Differential Hierarchical Demodulator of 2-source Hierarchical-MAC Channel

This letter addresses a problem of differential demodulation in a 2-source Hierarchical MAC (H-MAC) in the context of a Wireless Physical Layer Network Coded system with Hierarchical Decode and Forward strategy. We assume a parametric H-MAC with known attenuations but unknown phases. Component phases have generally strong impact on the resulting superposed constellation which poses high demands on the accuracy of their estimation. In this letter we propose multiple suboptimal closed-form differential demodulation methods which do not require explicit phase estimation and thus substantially simplify the receiver processing. We analyze and compare their performance. Particularly we measure the resulting hierarchical bit error rate for all proposed demodulation methods for different scenarios of a particular symbol alphabet and channel attenuation values. For comparison we include a reference scenario of a fully coherent demodulation.