  M-ary On-Off Frequency-Shift-Keying (OOFSK) is a digital modulation format in
which M-ary FSK signaling is overlaid on On/Off keying. This paper investigates
the potential of this modulation format in the context of wideband fading
channels. First it is assumed that the receiver uses energy detection for the
reception of OOFSK signals. Capacity expressions are obtained for the cases in
which the receiver has perfect and imperfect fading side information. 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
a PAR limitation, it is extremely power inefficient to operate in the very low
SNR regime. On the other hand, if there is only a peak power limitation, it is
demonstrated that power efficiency improves as one operates with smaller SNR
and vanishing duty factor. Also studied are the capacity improvements that
accrue when the receiver can track phase shifts in the channel or if the
received signal has a specular component. To take advantage of those features,
the phase of the modulation is also allowed to carry information.
