Timothy N. Davidson, Zhi-Quan (Tom) Luo and K. Max Wong.
Design of orthogonal pulse shapes for communications
via semidefinite programming.
IEEE Transactions on Signal Processing,
48(5):1433-1445,
May 2000.
In digital communications, orthogonal pulse shapes are often used to represent message symbols for transmission through a channel. In this paper, 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. The formulation is used to design filters which achieve: a) the minimal bandwidth for a given filter length; b) the minimal filter length for a given bandwidth; or c) the maximal robustness to timing error for a given bandwidth and filter length. Bandwidth is measured either in spectral energy concentration terms or with respect to a spectral mask. The effectiveness of the method is demonstrated by the design of waveforms with substantially improved performance over the `chip' waveforms specified in recent standards for digital mobile telecommunications.
The paper is available as a pdf file
Some follow-up work that quantifies the trade-offs between orthogonality, robustness and bandwidth is available here.
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