Cutoff rate optimal binary inputs with imperfect CSI

We use the cutoff rate to study the optimal binary input distributions for the Rayleigh flat-fading channel with imperfect receiver channel state information (CSI). First, we evaluate the cutoff rate and analyze the optimal binary input as a function of the CSI quality and receiver SNR. Next, we study the limiting distributions - BPSK and on-off keying (OOK) - and derive an analytic design rule that allows adaptive switching between these two as the receiver CSI changes. We establish the virtues of a modulation scheme that employs only these limiting distributions, rather than the full spectrum of binary inputs. Finally, we use our results to design an adaptive modulation scheme for pilot symbol assisted modulation systems. We show that switching between just BPSK and equiprobable-OOK is nearly optimal for moderate to large SNR, and that switching between BPSK and generalized-OOK is nearly optimal for all SNR