Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic R\"ossler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure

Noncoherence of some lattices in Isom(Hn)

We prove noncoherence of certain families of lattices in the isometry group of the hyperbolic n-space for n greater than 3. For instance, every nonuniform arithmetic lattice in SO(n,1) is noncoherent, provided that n is at least 6.Comment: This is the version published by Geometry & Topology Monographs on 29 April 2008. V3: typographical correction

Low-complexity Noncoherent Iterative CPM Demodulator for FH Communication

In this paper, we investigate the noncoherent iterative demodulation of coded continuous phase modulation (CPM) in frequency hopped (FH) systems. In this field, one important problem is that the complexity of the optimal demodulator is prohibitive unless the number of symbols per hop duration is very small. To solve this problem, we propose a novel demodulator, which reduces the complexity by applying phase quantization and exploiting the phase rotational invariance property of CPM signals. As shown by computational complexity analysis and numerical results, the proposed demodulator approaches the performance of the optimal demodulator, and provides considerable performance improvement over the existing solutions with the same computational complexity

Low Complexity Noncoherent Iterative Detector for Continuous Phase Modulation Systems

This paper focuses on the noncoherent iterative detection of continuous phase modulation. A class of simplified receivers based on Principal-Component-Analysis (PCA) and Exponential-Window (EW) is developed. The proposed receiver is evaluated in terms of minimum achievable Euclidean distance, simulated bit error rate and achievable capacity. The performance of the proposed receiver is discussed in the context of mismatched receiver and the equivalent Euclidean distance is derived. Analysis and numerical results reveal that the proposed algorithm can approach the coherent performance and outperforms existing algorithm in terms of complexity and performance. It is shown that the proposed receiver can significantly reduce the detection complexity while the performance is comparable with existing algorithms