The design of useful signaling alphabets in a burst-noise environment is treated as a discrete signal-design problem. A binary alphabet with minimum Gabor bandwidth is formulated as a discrete optimization problem to illustrate the design philosophy. The solution is obtained by using an eigenvalue approach. This technique is extended to the design of signals in a burst-noise environment where the burst is simulated by the removal of samples. Higher order alphabets are constructed for specific sample sizes and their performance evaluated.

In this paper, signal design in a burst-noise environment is considered. Two distinct approaches are presented, each resulting in a class of signals for which the trade-off between signal bandwidth and immunity to large-amplitude bursts is shown. In the first approach the design is treated as an optimization problem subject to energy and endpoint constraints in a fixed time interval, and a uniform probability distribution of the location of the burst within the interval. The second approach considers signal design as a two-player differential game, where design flexibliity is obtained through the second player's choice of an initial value in the resulting differential equation. Performance curves for signals designed by using both methods are compared. It is shown how the first design procedure is easily extended toM-ary alphabets, thus obtaining the full advantage of the proposed technique.