Design of orthogonal pulse shapes for communications via semidefinite programming

Timothy N. Davidson, Zhi Quan Luo, Kon Max Wong

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


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 that achieve a) the minimal bandwidth for a given filter length; b) the minimal filter length for a given bandwidth; 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.

Original languageEnglish (US)
Pages (from-to)1433-1445
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - May 2000

Bibliographical note

Funding Information:
Manuscript received March 18, 1999; revised October 14, 1999. This work was supported by a research grant from Natural Sciences and Engineering Research Council of Canada and a grant from Telecommunications Research Institute of Ontario (TRIO). The associate editor coordinating the review of this paper and approving it for publication was Dr. Alle-Jan van der Veen.


  • Code division multiaccess
  • Multirate fir digital filters
  • Optimization methods
  • Pulse amplitude modulation
  • Signal design


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