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 , where , and a transmitter with an output amplitude constraint is evaluated. For any dispersive channel the maximum rate depends on 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 . It is shown that given any channel impulse response with rational Laplace transform, there exists an optimal set of inputs that are everywhere where 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 or , depending on the current message bit, is transmitted during each symbol interval, maximizes the data rate.