Timothy N. Davidson.
Efficient design of waveforms for robust pulse amplitude
modulation.
IEEE Transactions on Signal Processing,
49(12):3098-3111,
December 2001.
In this paper, a large and flexible set of computationally efficient algorithms is developed for the design of waveforms for pulse amplitude modulation which provide robust performance in the presence of uncertainties in the channel and noise models. Performance is measured either by a sensitivity function for threshold detection, or by the mean square error of the data estimate. For uncertainties which are modelled as being deterministically bounded, robustness is measured in terms of the worst-case performance, and for uncertainties which are modelled statistically, robustness is measured in terms of the average performance. The algorithms allow efficient evaluation of the inherent trade-offs between robustness, nominal performance and spectral occupation in waveform design, and are used to design `chip' waveforms with superior performance to those specified in recent standards for digital mobile telephony.
Some additional information on weighted robust designs appears in: T. N. Davidson, Z.-Q. Luo and K. M. Wong. Design of robust pulse shaping filters via semidefinite programming. In Proceedings of the Sixth Canadian Workshop on Information Theory, pp. 71-74, Kingston, Ontario, Canada, July 1999. (pdf file)
Some additional designs based on mean square error criteria appear in: T. N. Davidson, Efficient Design of Waveforms for Robust Pulse Amplitude Modulation using Mean Square Error Criteria. In Proceedings of the European Signal Processing Conference, pp. 365-368, Tampere, Finland, September 2000. (pdf file)
Some additional information on robust designs for statistically modelled channels appears in: T. N. Davidson, Efficient design of robust pulse shapes for communications using average performance criteria. In Proceedings of the 5th International Conference on Optimization: Techniques and Applications, Hong Kong, December 2001. (pdf file)
A Matlab m-file for the first example is available here.
The quantity denoted \hat{s}[k] in Figure 2 might not be a good approximation of s[k] and hence it ought to be denoted by a different symbol, say y[k]. Fortunately, this quantity is not used explicitly in the rest of the paper.
The solution to Problem 3 is also optimal for the case where the admissible set of $\Delta_Q$'s is the set of all square matrices whose Frobenius norm is less than v.
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