Properties of ambiguity functions for weighted pulse trains with Oppermann sequences

In this paper, we consider properties of the auto-ambiguity and cross-ambiguity functions of weighted pulse trains with Oppermann sequences. Several properties are examined and proved which in turn allows for reducing the design space for optimization of a particular design. The insights gained from these properties are consolidated in a formal framework leading to procedures that can be used for a more structured waveform design. Numerical examples are provided to illustrate the relationship between sequence parameters and performance characteristics