## 1 Introduction
Various existing models in the literature exploit the spatial correlation structure of the shadowing field, without taking into account the temporal variability [10; 11; 12; 13], while others that include the temporal evolution consider it solely a result of user's mobility, by transforming the spatial correlation to temporal, without really addressing the temporal evolution of the field, mainly caused by obstruction movement in the vicinity of the receiver [14; 15; 16]. This is especially important in indoor environments [17], when line of sight (LOS) is disturbed, as several studies indicate, see [18; 19] and the references therein. Similar results, although less intense, are expected for distributed indoor-outdoor and/or densely populated urban networks [18]. However in these models, shadowing correlation and cross-correlation for different locations and base stations are not taken into account. Whereas autocorrelation of shadowing refers to the case of one base transmitter, cross-correlation refers to the correlated shadowing of signals from different base stations. This statistical behavior of differently originated signals is of great importance for the design of cellular wireless networks, interference studies, handover algorithms, cooperative diversity schemes, etc. The correlation phenomenon is present in outdoor [20], as well as in indoor environments [21; 22; 23]. Moreover even links without a common node, if closely located, exhibit shadowing correlation [23; 24]. In [25] a stochastic differential equation (SDE) is introduced for shadowing dynamic modeling, able to capture the random attenuation variations with respect to time, but without considering shadowing cross-correlations from different base stations, either. Moreover some publications from the application of correlated shadowing phenomena in relaying architectures and cooperative networks are [26; 27; 28; 29; 30; 31] and on stochastic differential equations are [32; 33]. Up to now, in the literature there are not analytical dynamic statistical channel models for the large scale fading that could be used for the evaluation of complex wireless network architectures. Therefore there is a strong motivation to develop a theoretical model with parameters that can be adopted to experimental measurements. In this paper, a novel dynamic shadowing model (channel model framework) is proposed, able to deal with the temporal evolution of the propagation environment and also incorporate the spatial correlation structure, by considering any type of correlation exhibited by different radio links, including auto-correlation and cross-correlation. The model assumes the lognormal distribution for shadowing fading, incorporating all important statistical parameters, as validated from experimental studies. While being consistent with existing shadowing literature and published results, it captures every important aspect of shadowing modeling in a single framework. It is based on a system of stochastic differential equations (SDEs), and its solid mathematical framework permits the calculation of important statistical parameters, while keeping complexity and computational cost to accepted levels. The model can be used for the effective design and simulation of fixed and mobile wireless systems. In this paper there novel analytical results are also presented concerning average outage durations (AOD), level crossing rates (LCR) and hand-offs, based on the proposed probabilistic structure of shadowing and the method of multi-dimensional level crossings. The strengths of the proposed approach are the employment and the usage of many theoretical models in order to develop a consolidated space-time dynamic model for large scale fading. The components of the model are well accepted and have been proved theoretically. The weakness of the approach is that it needs experimental verification. To the authors' best knowledge there are not specific measurements in the literature to validate the proposed modeling.