Efficient design of waveforms for robust pulse amplitude modulation using mean square error criteria

The design of a pulse shaping filter which provides maximal robustness to an unknown frequency-selective channel is formulated as a convex optimization problem from which an optimal filter can be efficiently obtained. Robustness is measured by the worst-case mean square error of the data estimate over a class of deterministically bounded channels, and the optimization is subject to a constraint on the bandwidth of the filter. The design technique allows efficient exploration of design trade-offs between bandwidth, performance in an ideal channel and robustness to unknown channel distortion. It is used to design chip waveforms with superior performance to the waveform specified in a recent standard for digital mobile telephony.