If anyone know a literature available that justify, how much minimum transmission amplification energy is required for a node to transmit data at certain distance. So, accordingly, networks amplification energy can be set.
First of all to calculate the transmission power you need to know the propagation model adapted to your application. Once you fixed your propagation model, you can extract the relation between the power of transmission Ptx and the power received Pr by a receiver (which is a function of the distance and also the parameters of the area of interest).
Based on the communication standards and the modulation technique you are using, you can express Pr in terms of the error probability and SNR.
Furthermore, based on the expression obtained based on the propagation model, you can express Ptx in terms of Pr.
Finally, you can express the energy needed to transmit a single bit for a specific distance which is expressed as follow:
Etx_bit=((1+alpha)*Ptx+Pct)*R
where R is the bit rate, and Pct is the power consumed by radio model circuitry.
The answer to your question is dependent on many things, not the distance only. In addition to the distance, it also heavily dependent on the RF frequency band, the propagation condition, the Tx/Rx techniques, and so on. For instance, regarding the propagation condition, is it used in-door or out-door ? Is there a line of sight (LOS) propagation path, or no LOS path at all ? Is the Tx/Rx in fixed location or in moving ? Talking about the RF frequency band, for instance, if it is working in the millimeter wave band (e.g. 60-GHz band), there is a significant extra power loss in the air. Regarding to the used techniques, what kind of modulation scheme is used ? Is there any error correction coding technique used ? These things greatly affect the answer to your question. Good luck.