  The resource constraints and accuracy requirements for Internet of Things
(IoT) memory chips need three-dimensional (3D) monolithic integrated circuits,
of which the increasing stack layers (currently more than 176) also cause
excessive energy consumption and increasing wire length. In this paper, a novel
3D wireless network on chips (3DWiNoCs) model transmitting signal directly to
the destination in arbitrary layer is proposed and characterized. However, due
to the the reflection and refraction characteristics in each layer, the complex
and diverse wireless paths in 3DWiNoC add great difficulty to the channel
characterization. To facilitate the modeling in massive layer NoC situation,
both boundary-less model boundary-constrained 3DWiNoC model are proposed, of
which the channel gain can be obtained by a computational efficient approximate
algorithm. These 3DWiNoC models with approximation algorithm can well
characterize the 3DWiNoC channel in aspect of complete reflection and
refraction characteristics, and avoid massive wired connections, high power
consumption of cross-layer communication and high-complexity of 3DWiNoC channel
characterization. Numerical results show that: 1) The difference rate between
the two models is lower than 0.001% (signal transmit through 20 layers); 2) the
channel gain decreases sharply if refract time increases; and 3) the
approximate algorithm can achieve an acceptable accuracy (error rate lower than
0.1%).
