Abstract We show that there is a measure-preserving system $(X,\mathscr {B}, \mu , T)$ together with functions $F_0, F_1, F_2 \in L^{\infty }(\mu )$ such the correlation sequence $C_{F_0, F_2}(n) = \int _X F_0 \cdot T^n F_1 T^{2n} \, d\mu $ not an approximate integral combination of $2$ -step nilsequences.

Introduction: The exploitation of temporal and spatial diversity can significantly improve communication quality and associated system performance in a rich-scattering wireless environment. This has been demonstrated through proposals for space-time coded modulations over multiple-input multiple-output (MIMO) radio channels which are understood to be very beneficial for high data-rate systems, ...

In Code Division Multiple Access (CDMA) systems all users transmit in the same bandwidth simultaneously. Communication systems following this concept are "spread spectrum systems''. In this transmission technique, the frequency spectrum of a data-signal is spread using a code uncorrelated with that signal. As a result the bandwidth occupancy is much higher then required. The codes used for spre...

The paper develops an approximate semi-analytical solution for the computation of third statistical cross-moments modal responses in a stochastic dynamic analysis. These moments would require heavy twofold numerical integration general context but are drastically simplified proposed formulation by taking advantage assumed distinctness between low characteristic frequency loading and natural fre...