ON OPTIMUM SIGNAL SETS FOR DIGITAL COMMUNICATIONS WITH FINITE PRECISION AND AMPLITUDE CONSTRAINTS.

Given a time-invariant linear dispersive channel, a receiver with a finite-precision A/D (analog-to-digital) converter, and a transmitter with an output amplitude constraint, the question of what is the maximum achievable communication rate is considered. For any dispersive channel the maximum rate is finite even without additive noise. The related question of what is the minimum time it takes for the receiver to distinguish one out of N possible transmitted messages is also examined. The transmitted waveforms must be designed so that at some time instant two channel outputs associated with two distinct transmitted signals are separated in amplitude by some distance d greater than 0, representing the receiver precision. It is shown that given any impulse response, there exists an optimal set of inputs that are plus or minus A everywhere, where A is the maximum allowable amplitude. If the channel impulse response is a single decaying exponential, it is shown that simple binary signaling, in which A or -A, depending on the current message bit, is transmitted during each symbol interval, maximizes the data rate.