Efficient design of waveforms for robust pulse amplitude modulation

In this paper, a large and flexible set of computationally efficient algorithms is developed for the design of waveforms for pulse amplitude modulation that 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 that are modeled as being deterministically bounded, robustness is measured in terms of the worst-case performance, and for uncertainties that are modeled statistically, robustness is measured in terms of the average performance. The algorithms allow efficient evaluation of the inherent tradeoffs 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.