The energy efficiency of on-off keying with partial CSI and peak power constraints

It is well known that on-off keying (OOK) suffers from a 3 dB SNR penalty relative to BPSK for coded transmission over a Rayleigh fading channel with perfect receiver channel state information (CSI). Previously, the cutoff rate has been used to show that this 3 dB penalty can be partially recovered if the OOK transmission probability can be varied, with full recovery in the limit of vanishing rates. We extend these results to the case of imperfect CSI. We show that the maximum penalty with partial CSI is 4 dB, and that there is a range of rates and CSI quality for which the penalty is instead a gain. By further varying the transmission probability of the ´1´ bit in OOK, we show that the 3 dB penalty can be recovered for small rates, but not at larger rates. Finally, we consider the energy penalty for using OOK under a peak power constraint.