Numerical evaluation of QAM self-noise spectra for fourth-power law clock recovery

A method for numerically evaluating the self-noise spectra for fourth-power law clock recovery for a quadrature amplitude modulation (QAM) receiver is described. Numerical values are obtained for quadrature phase shift keying (QPSK), 16 QAM, 64 QAM, and 256 QAM systems. Two conclusions are drawn from these results: (1) the quadrature spectrum manifests a dip at the zero frequency for the QPSK case only, and (2) the ratio of the inphase or quadrature self-noise power to the power of the desired recovered clock is not a monotonic function of the excess bandwidth factor. However, the zero excess bandwidth factor is close to the best choice for all orders of QAM modulation.<>