Sequence designs for ultra-wideband impulse radio with optimal correlation properties

We formulate a combinatorial model of impulse radio sequences (IRSs) to study sequence or signal design for ultra-wideband (UWB) radio with unmodulated time hopping. Using this combinatorial model for IRSs, we develop necessary and sufficient conditions for the existence of IRSs. Several novel constructions for IRSs with optimal correlation properties are given. The constructions involve the Welch construction for Costas arrays, a quadratic polynomial construction over finite fields, recursive techniques for optical orthogonal codes, and combinatorial design techniques using perfect Mendelsohn designs (PMDs).