Robust pulse amplitude modulation via semidefinite programming

The design of the waveform for a pulse amplitude modulation scheme is formulated as a convex semidefinite programme (SDP), from which a globally optimal solution can be found using highly efficient interior point methods. The SDP is used to design a waveform which provides maximal robustness to timing error subject to a constraint on its duration and a relative spectral mask constraint on the transmitted signal. As an example we design a waveform with substantially improved performance over the 'chip' waveform in the IS95 standard for code division multiple access mobile telephony.