The Impact of Quantization on the Energy Efficiency of Phase and Frequency Modulation

The impact of quantization on the energy efficiency of phase and frequency modulation is investigated. Transmission over the additive white Gaussian noise (AWGN) channel, and coherent and noncoherent fading channels is considered. It is assumed that the receiver quantizes the received signals by performing hard-decision detection. Closed-form expressions for the first and second derivatives of the phase-shift keying (PSK) capacity at zero signalto-noise ratio (SNR) are obtained. The spectral-efficiency/bit-energy tradeoff in the low-SNR regime is analyzed by finding the wideband slope and the bit energy required at zero spectral efficiency. The performance loss incurred by quantization and channel fading is quantified. Practical design guidelines are drawn from the information-theoretic analysis. The energy efficiencies of M -ary orthogonal frequency-shift keying (FSK) and on-off frequency-shift keying (OOFSK) are studied. It is shown that for fixed M and duty cycle, bit energy requirements grow without bound as SNR vanishes. The minimum bit energy values are numerically obtained for different values of M and the duty cycle. Requirements to approach the minimum bit energy of −1.59 dB are identified.