Revisiting the Lognormal Modelling of Shadowing Effects during Wireless Communications by Means of the α-μ/α-μ Composite Distribution

Properly modeling the shadowing effects during wireless transmissions is crucial to perform the network quality assessment. From a mathematical point of view, using composite distributions allows one to combine both fast fading and slow fading stochastic phenomena. Numerous statistical distributions have been used to account for the fast fading effects. On the other hand, even though several studies indicate the adequacy of the Lognormal distributon (LNd) as a shadowing model, they also reveal this distribution renders some analytic tractability issues. Past works include the combination of Rayleigh and Weibull distributions with LNd. Due to the difficulty inherent to obtaining closed form expressions for the probability density functions involved, other authors approximated LNd as a Gamma distribution, creating Nakagami-m/Gamma and Rayleigh/Gamma composite distributions. In order to better mimic the LNd, approximations using the inverse Gamma and the inverse Nakagami-m distributions have also been considered. Although all these alternatives were discussed, it is still an open question how to effectively use the LNd in the compound models and still get closed-form results. We present a novel understanding on how the α-μ distribution can be reduced to a LNd by a limiting procedure, overcoming the analytic intractability inherent to Lognormal fading processes. Interestingly, new closed-form and series representations for the PDF and CDF of the composite distributions are derived. We build computational codes to evaluate all the expression hereby derived as well as model real field trial results by the equations developed. The accuracy of the codes and of the model are remarkable.

Illuminating Time: The Visibility of Temporality in Prehistory

Using the astronomical animation software of Stellarium, this chapter will demonstrate how time was ‘staged’ by prehistoric people at particular periods during the solar and lunar years. It will show how they ‘choreographed’ night- and day-lighting and landscape shadowing effects, along with the appearance and travels of other celestial phenomena in relation to the monuments and their horizons. It was this staging of natural lighting through illumination, brightness, luminescence, shine, gleams, glows, glare, and small points of light, and the opposites of all of these, that enabled their concepts of time to be experienced, shared, and acknowledged by prehistoric peoples.

Cluster wakes impact on a far-distant offshore wind farm's power

Our aim with this paper was the analysis of the influence of offshore cluster wakes on the power of a far-distant wind farm. We measured cluster wakes with long-range Doppler light detection and ranging (lidar) and satellite synthetic aperture radar (SAR) in different atmospheric stabilities and analysed their impact on the 400 MW offshore wind farm Global Tech I in the German North Sea using supervisory control and data acquisition (SCADA) power data. Our results showed clear wind speed deficits that can be related to the wakes of wind farm clusters up to 55 km upstream in stable and weakly unstable stratified boundary layers resulting in a clear reduction in power production. We discussed the influence of cluster wakes on the power production of a far-distant wind farm, cluster wake characteristics and methods for cluster wake monitoring. In conclusion, we proved the existence of wake shadowing effects with resulting power losses up to 55 km downstream and encouraged further investigations on far-reaching wake shadowing effects for optimized areal planning and reduced uncertainties in offshore wind power resource assessment.

Earth's shadowing effects by computer algebra

The short-periodic perturbations of orbits of an artificial satellite due to the radiation pressure during one orbital period are influenced by Earth's shadow. For the semi-analytical theories it is necessary to calculate great number of coefficients. Using computer algebra we have computed them for some of applicable semi-analytical theories.