The impact of hard-decision detection on the energy efficiency of phase and frequency modulation

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.