Energy required to transmit a signal is approximately proportional to d
α, where d is the distance and
is the
attenuation factor or
path loss exponent, which depends on the transmission medium. When
α = 2 (which is the optimal case), transmitting a signal half the distance requires one fourth of the energy and if there is a node in the middle willing spend another fourth of its energy for the second half, data would be transmitted for half of the energy than through a direct transmission - a fact that follows directly from the
inverse square law of physics.
