  Due to the unique characteristics of sensor devices, finding the
energy-efficient modulation with a low-complexity implementation (refereed to
as green modulation) poses significant challenges in the physical layer design
of Wireless Sensor Networks (WSNs). Toward this goal, we present an in-depth
analysis on the energy efficiency of various modulation schemes using realistic
models in the IEEE 802.15.4 standard to find the optimum distance-based scheme
in a WSN over Rayleigh and Rician fading channels with path-loss. We describe a
proactive system model according to a flexible duty-cycling mechanism utilized
in practical sensor apparatus. The present analysis includes the effect of the
channel bandwidth and the active mode duration on the energy consumption of
popular modulation designs. Path-loss exponent and DC-DC converter efficiency
are also taken into consideration. In considering the energy efficiency and
complexity, it is demonstrated that among various sinusoidal carrier-based
modulations, the optimized Non-Coherent M-ary Frequency Shift Keying (NC-MFSK)
is the most energy-efficient scheme in sparse WSNs for each value of the
path-loss exponent, where the optimization is performed over the modulation
parameters. In addition, we show that the On-Off Keying (OOK) displays a
significant energy saving as compared to the optimized NC-MFSK in dense WSNs
with small values of path-loss exponent.
