Efficient evaluation of trade-offs in waveform design for robust pulse amplitude modulation

The design of a pulse shaping filter which provides maximal robustness to an unknown frequency-selective channel has previously been formulated as a convex optimization problem from which an optimal filter can be efficiently obtained. Robustness was measured by the worst-case 'peak' intersymbol interference over a class of deterministically bounded channels, and the optimization was subject to a constraint on the bandwidth of the filter. The purpose of the present paper is to show that the design trade-offs between bandwidth, performance in an ideal channel and robustness to unknown channel distortion can be efficiently evaluated using this convex optimization problem. In the design examples, these trade-offs are used to select chip waveforms with superior performance to those specified in standards for digital mobile telephony.