Optimum Spectrum for QAM Perturbed by Timing and Phase Errors

An optimum spectrum is presented for a multilevel QAM system perturbed by timing error, phase error, and additive noise. We propose a double-jump spectrum (DJS) whose segment height is generally different from that of Franks' spectrum. The performance is analyzed with Gauss quadrature rules and a computer simulation. The results are compared to Franks' spectrum and the conventional cosine rolloff spectrum.