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Due to complexity considerations, pulse-based modulations such as pulse position modulation (PPM) and on-off keying (OOK) are well suited for wireless sensor networks (WSNs) since they provide the possibility of carrier-less signaling and, more importantly, noncoherent reception bypassing channel estimation at the receiver. In this paper, we compare PPM and OOK in terms of their battery power efficiencies, using a nonlinear battery model, and under the same bandwidth occupancy, bandwidth efficiency and cutoff rate requirement. Cutoff rate is used as our comparison criterion because it leads to a tractable analysis that is often impossible through direct evaluation of random coding exponent or capacity. In addition, cutoff rate gives a universal expression for both coherent and noncoherent detection by simply setting various channel state information (CSI) qualities. Our system model integrates typical WSN transmission and reception modules with realistic nonlinear battery models. Circuit power consumption, dc-dc converter efficiency, and power amplifier efficiency are also taken into consideration. Our analytical results characterize the signal-to-noise ratio (SNR)-cutoff rate-CSI region where PPM is more power efficient than OOK, and vice versa. We provide an interpretation in terms of the transmission range and symbol set size. Numerical results are also provided to verify the analysis.