Orthogonal pulse shape design via semidefinite programming

In digital communications, orthogonal pulse shapes are often used to represent message symbols for transmission through a channel. The design of such pulse shapes is formulated as a convex semidefinite programming problem, from which a globally optimal pulse shape can be efficiently found using interior point methods. The formulation is used to design filters which achieve the minimal bandwidth for a given filter length, and the minimal filter length for a given bandwidth. The effectiveness of the method is demonstrated by the design of waveforms with substantially improved performance over the 'chip' waveforms specified in the standards for digital mobile telecommunications.