On an optimum algorithm for waveform synthesis and its applications to digital transmitters

This paper proves that the optimum algorithm for waveform synthesis of an analog waveform such that the quantisation noise over a band in frequency is minimised, is Viterbi decoding the analog waveform over the convolutional code generated by a band pass filter with the same passband. A novel application of waveform synthesis to design of efficient modulation systems is proposed, resulting in a completely digital transmitter with no analog stages required for modulation and upconversion. High speed applications of the proposed scheme require list decoder compatible filters of low constraint lengths. The paper proposes a design methodology for designing short list-decoder compatible filters by optimising their equivalent performance profiles (EPP) and analyses the performance of these encoders with varying list lengths. The paper also explains the transition phenomena observed in the performance of the encoders and derives a theoretical upper bound on the minimum number of list survivors to be retained to ensure negligible drop in the performance of the encoders.