Novel UWB pulse shaping using prolate spheroidal wave functions

In this paper novel prolate spheroidal wave functions are proposed as pulse shapes for use in impulse radio (ultra-wideband) communications. These classes of functions yields orthogonal pulses and have a constant pulse width regardless of the pulse order. This is an important property since it eliminates inter-symbol interference. An M-ary communications system is considered that employs these pulses, and the generation of these pulses using the eigenfunction form of a self-adjoint operator is proposed. It is also shown that these pulses are suitable for use in pulse position modulation (PPM) ultra wideband (UWB) communication systems.