On Optimal Signal Sets for Digital Communications with Finite Precision and Amplitude Constraints

M. Honig, S. Boyd, B. Gopinath, and E. Rantapaa

IEEE Transactions on Communications, 39(2):249-255, February 1991. Conference paper appeared in Proceedings of the IEEE Globecom Conference, Tokyo, pp.248-253, November 1987.

The maximum data rate that can be reliably communicated given a linear, time-invariant, dispersive channel, a receiver that samples the channel output to within an accuracy of pm d, where dgeq 0, and a transmitter with an output amplitude constraint is evaluated. For any dispersive channel the maximum rate depends on d and is finite. The transmitted waveforms must be designed so that two channel outputs associated with two distinct transmitted signals are separated in amplitude at a particular time by d. It is shown that given any channel impulse response with rational Laplace transform, there exists an optimal set of inputs that are pm A everywhere where A is the maximum allowable amplitude. Furthermore, in any finite time interval, each input changes sign a finite number of times. 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.