Constrained pulse shape synthesis for digital communications

The synthesis of optimal pulse shapes for digital data transmission over communication channels typically involves conflicting specifications. We consider the problem of finding a pulse satisfying some mandatory "hard" constraints while violating as little as possible the remaining "soft" constraints. The problem is formalized as that of minimizing a weighted sum of squared distances to the soft constraint sets over the intersection of the sets associated with the hard constraints. This constrained problem is analyzed and a numerical algorithm is proposed. Simulation results are presented.