On the random dynamics of Volterra quadratic operators

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex Sm-1. We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system almost surely converge to one of the vertices of the simplex Sm-1, implying the survival of only one species. We also show that the minimal random point attractor of the system equals the set of all vertices. The convergence proof relies on a martingale-type limit theorem, which we prove in the appendix.DFG, GSC 14, Berlin Mathematical Schoo

Nonlinear digital pre-distortion of transmitter components

We present a linear and nonlinear digital predistortion (DPD) tailored to the components of an optical transmitter. The DPD concept uses nonlinear models of the transmitter devices, which are obtained from direct component measurements. While the digital-to-analog converter and driver amplifier are modeled jointly by a Volterra series, the modulator is modeled independently as a Wiener system. This allows for block-wise compensation of the modulator by a Hammerstein system and a pre-distortion of the electrical components by a second Volterra series. In simulations and extensive experiments, the performance of our approach for nonlinear DPD is compared to an equivalent linear solution as well as to a configuration without any digital pre-distortion. The experiments were performed using M-ary quadrature-amplitude modulation (MQAM) formats ranging from 16-QAM to 128-QAM at a symbol rate of 32 GBd. It is shown that DPD improves the required optical signal-to-noise ratio at a bit error ratio of 2???10-2 by at least 1.2 dB. Nonlinear DPD outperforms linear DPD by an additional 0.9 dB and 2.7 dB for higher-order modulation formats such as 64-QAM and 128-QAM, respectively

Nonlinear digital pre-distortion of transmitter components

We present a linear and nonlinear digital predistortion (DPD) tailored to the components of an optical transmitter. The DPD concept uses nonlinear models of the transmitter devices, which are obtained from direct component measurements. While the digital-to-analog converter and driver amplifier are modeled jointly by a Volterra series, the modulator is modeled independently as a Wiener system. This allows for block-wise compensation of the modulator by a Hammerstein system and a pre-distortion of the electrical components by a second Volterra series. In simulations and extensive experiments, the performance of our approach for nonlinear DPD is compared to an equivalent linear solution as well as to a configuration without any digital pre-distortion. The experiments were performed using M-ary quadrature-amplitude modulation (MQAM) formats ranging from 16-QAM to 128-QAM at a symbol rate of 32 GBd. It is shown that DPD improves the required optical signal-to-noise ratio at a bit error ratio of 2???10-2 by at least 1.2 dB. Nonlinear DPD outperforms linear DPD by an additional 0.9 dB and 2.7 dB for higher-order modulation formats such as 64-QAM and 128-QAM, respectively