Power efficiency of joint frequency-phase modulation in the low-SNR regime over noncoherent Rician channels

Transmission of information over noncoherent Rician fading channels using M-ary orthogonal on/off FSK (OOFSK) signaling with phase modulation is considered. The capacity of this signaling scheme is obtained both for finite M and as M tends to infinity. Power efficiency is investigated when the transmitter is subject to a peak-to-average power ratio (PAR) limitation or a peak power limitation. It is shown that, under PAR limitation, in contrast to average power limited systems, the minimum bit energy is not always achieved at zero spectral efficiency. It is concluded that, in these cases, operating at very low spectral efficiency should be avoided. On the other hand, it is demonstrated that if there is only a peak power limitation, power efficiency improves as one operates with smaller SNR and vanishing duty factor.