There is emerging interest in more detailed models for wireless shadowing, which may include nonconstant shadowing variance, non-lognormal shadowing, and, most importantly, correlation between paths; we focus on this last aspect. This paper offers a structured synthesis of the existing literature on autocorrelation and cross-correlation in wireless shadowing and attempts to fill existing gaps in the analysis of correlation models. We make a survey of these models and argue, as has previously been observed, that certain models are not mathematically feasible, which may lead to problems in simulations or analysis. We then state some theorems that test whether the models are positive semidefinite, which is the central necessary condition for feasibility, and evaluate the existing models accordingly. Additionally, we evaluate the models according to their physical plausibility, which leads us to choose one model among many as arguably the best one in existence so far. This paper should be useful as a guide on how to implement shadowing correlation in one's work, how to choose an appropriate correlation model, and how to modify existing models or create new models so that they fulfill mathematical feasibility.

/pdf/on-the-feasibility-of-wireless-shadowing-correlation-models-54vwmmg7ij.pdf

On the Feasibility of Wireless Shadowing Correlation Models

We derive an explicit model for the cross-correlation function of the shadowing components affecting the links between a mobile station and two base stations. This model includes both the autocorrelation model proposed in earlier work by Gudmenson in 1991 for the single component, and the cross-correlation early evidenced in the work by Graziano in 1978. The model is useful in analytical computations, e.g., of second order statistics of signal-to-interference ratio. The model can include the behavior of a time-variant cross-correlation at zero-time shift and of a non-homogeneous environment.

A general correlation model for shadow fading in mobile radio systems

Received signal power in mobile wireless communications is typically modeled as a product of three factors: distance-dependent average path loss law, variation in the local mean power (shadow fading), and small-scale fading. Of these three factors, the least investigated is the shadow fading, which is usually explained as a result of multiplication of large number of random attenuating factors in the radio channel. In this paper, the authors propose an additive model as an alternative physical basis for shadow fading within an "extended local area" where path loss is constant. Starting from a sum-of-sinusoids signal model, they show that under mild statistical assumptions on the powers of the sinusoids, the resulting signal power will have approximately Gaussian distribution in logarithmic scale. A cluster-based model for shadow fading emerges as a special instance of the general result. They present simulation and measurement results that support their theoretical findings. The new physical basis for shadow fading also provides insights into simulation and modeling of radio channels

/pdf/an-additive-model-as-a-physical-basis-for-shadow-fading-3o2g5d5x2q.pdf

An Additive Model as a Physical Basis for Shadow Fading

Millimeter-wave (mmWave) will be used for fifth-generation (5G) wireless systems. While many recent empirical studies have presented propagation characteristics at mmWave bands, macrodiversity and Coordinated Multipoint (CoMP) have not been carefully studied. This paper describes a large-scale mmWave base station diversity measurement campaign at 73 GHz in an urban microcell (UMi) in downtown, Brooklyn, NY, USA, and provides the first detailed analysis of CoMP and macrodiversity performance based on extensive measurements. The research employed nine different base station locations in a 200 m by 200 m area and considered 36 individual transmitter–receiver combinations for extensive co- and cross-polarized varying directional beam channel impulse response measurements. From the measured data, hypothesis testing with cross-validation shows that large-scale shadow fading of directional path loss at an RX from multiple base stations can be modeled as being independent. To consider life-like human blockage in CoMP and macrodiversity analysis, simulated human blockage traces are superimposed on the directional measurements to quantitatively show that a user that is served by multiple base stations undergoes dramatically less outage in the presence of rapid fading events, compared to a single serving base station. Moreover, the base station diversity measurements are used to determine the effectiveness of downlink precoding techniques for mmWave CoMP. While results show that the coordination can improve network performance by suppressing interference when it exists, nearly half of the 680 000 directional CoMP measurements (~43%) result in no interference for either user, meaning that macrodiversity alone may offer sufficient link and capacity improvement and that CoMP may not be necessary for interference coordination at mmWave when narrow directional beams are used.

/pdf/millimeter-wave-base-station-diversity-for-5g-coordinated-3xiogfel6w.pdf

Millimeter-Wave Base Station Diversity for 5G Coordinated Multipoint (CoMP) Applications

This paper considers the influence of the cross-correlated shadowing between base-stations on network level simulations. A method to generate correlated shadow fading processes is proposed, which makes it possible to study position dependent correlation models between multiple base stations (BS). The method has been used for static network level simulations with different synthetic correlation models, both angle-of-arrival- and distance-dependent, in order to study the C/I outage gain for different frequency reuse patterns and BS sectorizations.

Modelling cross-correlated shadowing in network simulations

Propagation measurements (performed at 900 MHz in a small cell urban environment) and simulations devoted to shadow fading analysis in a diversity context are presented. This work gives a more accurate understanding of the cross-correlation phenomena. It emerges that the cross-correlation coefficients may be quite high when the two stations see the mobile with the same azimuthal angle. In return, a complete decorrelation is often guaranteed when the mobile is between the two stations. The tables derived can be used either to pursue studies about macro-diversity or to investigate further the C/I statistical properties. The realistic model proposed is also of particularly interest in evaluating the performance of handover algorithms and in estimating the macro-diversity gain. For both cases, we present a model of the shadow fading processes, taking into account their different correlation characteristics. We apply this model to perform some simulations.

B. Guisnet

Papers

Measurements and modelisation of shadowing cross-correlations between two base-stations