The terahertz band is an unlicensed frequency range that is expected to be exploited in the near future for many different types of communications, including wireless communication in nano-scale sensor networks. However, as terahertz band is the resonance frequency of many molecules, communication in this band is severely affected by molecular absorption noise and attenuation. In this paper, we consider a nano-scale terahertz sensor network (TSN) where the chemical composition of the medium varies over time causing absorption for different frequency regions at different times. We propose frequency hopping as a means to overcome the problem of dynamic molecular absorption in composition varying channels. We formulate the frequency selection problem as a Markov Decision Process (MDP), which allows us to adjust the rate of frequency switching for the nano sensors because resource constrained TSN nodes may not be able to switch frequency rapidly. We show that, compared to nonhopping channel selection, frequency hopping can significantly improve capacity and bit error rate when nano sensors have severe power constraints. We propose practically realizable offline policies that obviate the need for observing the channel states, yet perform close to the MDP-based solutions.

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