  The central design challenge in next generation wireless systems is to have
these systems operate at high bandwidths and provide high data rates while
being cognizant of the energy consumption levels especially in mobile
applications. Since communicating at very high data rates prohibits obtaining
high bit resolutions from the analog-to-digital (A/D) converters, analysis of
the energy efficiency under the assumption of hard-decision detection is called
for to accurately predict the performance levels. In this paper, transmission
over the additive white Gaussian noise (AWGN) channel, and coherent and
noncoherent fading channels is considered, and the impact of hard-decision
detection on the energy efficiency of phase and frequency modulations is
investigated. Energy efficiency is analyzed by studying the capacity of these
modulation schemes and the energy required to send one bit of information
reliably in the low signal-to-noise ratio (SNR) regime. The capacity of
hard-decision-detected phase and frequency modulations is characterized at low
SNR levels through closed-form expressions for the first and second derivatives
of the capacity at zero SNR. Subsequently, bit energy requirements in the
low-SNR regime are identified. The increases in the bit energy incurred by
hard-decision detection and channel fading are quantified. Moreover, practical
design guidelines for the selection of the constellation size are drawn from
the analysis of the spectral efficiency--bit energy tradeoff.
