Akintunde A. Alonge

Characteristics of rainfall queues for rain attenuation studies over radio links at subtropical and equatorial Africa

Attenuation due to precipitation remains an important design factor in the future deployment of terrestrial and earth-space communication radio links. Largely, there are concerted efforts to understand the dynamics of precipitation in attenuation occurrence at subtropical, tropical, and equatorial region of Africa. In this deliberate approach, rainfall spikes pertaining to rain cells are conceptualized as distinct rain spike traffic over radio links, by applying queueing theory concepts. The queue distributions at Durban (29°52′S, 30°58′E) and Butare (2°36′S, 29°44′E)—respectively, of subtropical and equatorial climates—are investigated from distrometer measurements. The data sets at both sites are observed over four rain regimes: drizzle, widespread, shower, and thunderstorm. The queue parameters of service time and inter-arrival of rain spikes traffic at both regions are found to be Erlang-k distributed (Ek) and exponentially distributed (M), respectively. It is established that the appearance of rain rates over radio links invariably follows a First Come, First Served (FCFS), multi-server (s), infinite queue, and semi-Markovian process, designated as M/Ek/s/∞/FCFS discipline. Modeled queue parameters at both regions are found to vary significantly over different regimes. However, these queue parameters over the entire data set suggest similar queue patterns at both sites. More importantly, power law relationships describing other queue-related parameters are formulated. The paper concludes by demonstrating an application of queueing theory for rainfall synthesis. The proposed technique will provide an alternative method of estimating rain cell sizes and rain attenuation over satellite and terrestrial links.

Rainfall time series synthesis from queue scheduling of rain event fractals over radio links

Rainfall attenuation over wireless networks stems from random fluctuations in the natural process of arriving rainfall rates over radio links. This arrival process results in discernible rainfall traffic pattern which manifest as naturally-scheduled and queue-generated rain spikes. Hence, the phenomenon of rainfall process can be approached as a semi-Markovian queueing process, with event characteristics dependent on queue parameters. However, a constraint to this approach is the knowledge of the physical characteristics of queue-generated rain spikes. Therefore, this paper explores the probability theory and descriptive mathematics of rain spikes in rainfall processes. This investigation presents the synthesis of rainfall queue with rain spikes at subtropical and equatorial locations of Durban (29°52′S, 30°58′E) and Butare (2°36′S, 29°44′E) respectively. The resulting comparative analysis of rainfall distributions, using error analysis at both locations, reveals that queue-generated rainfall compares well with measured rainfall dataset. This suggests that the time-varying process of rainfall, though stochastic, can be synthesized via queue scheduling with the application of relevant queue parameters at any location.

Rainfall rate modeling for various rainfall types in South Africa

This paper models the rainfall rate in Durban (29° 97′S, 30°95′E), South Africa for four different rainfall classifications: drizzle, widespread, shower and thunderstorm. Twelve-months data obtained in 2009 via the Joss_Waldvogel disdrometer, gave a total of 729 independent rain events and 5,542,147 raindrops. The measured rain rate probability functions were compared with the Moupfouma model using 1-minute integration time. The maximum likelihood estimators were adopted for the parameters of two other statistical models, the lognormal and gamma models. The results show that gamma model had the closest performance for the various rain classifications under consideration.

Rainfall Microstructural Analysis for Microwave Link Networks: Comparison at Equatorial and Subtropical Africa

The quest to understand the variation of rainfall microstructures at subtropical and equatorial regions is vital to rain attenuation studies. In this study, point rainfall datasets obtained at Butare (2 - 36 0 S, 29 - 44 0 E) and Durban (29 - 52 0 S, 30 - 58 0 E), are compared at the re∞ectivity threshold of 38dBZ. Joss-Walvogel (JW) distrometer measurements collected from these two locations represent physical rainfall data from equatorial and subtropical climates respectively. The re∞ectivity threshold enables the classiflcation of rainfall datasets into stratiform and convective (S-C) precipitation regimes. These thresholds, Rth, at Durban and Butare are analysed based on three known rainfall microphysical parameters: rain rate, rainfall Drop Size Distribution (DSD) and radar re∞ectivity. The results from rain rate distributions at the both regions are similar for both stratiform and convective classes. However, the sampled DSDs indicate the dominance of larger rain droplets at Butare compared to observations at Durban, irrespective of the rain classes. In addition, it is found that the re∞ectivity distributions at both regions, under stratiform and convective conditions, are distinct in their probability proflles. The overall S-C analysis implied that the re∞ectivity and DSD proflles at both regions | result in signiflcant variation of predicted speciflc attenuation | at microwave and millimeter band. In comparison with other global locations, it is a-rmed that the S-C transition occurs globally at rain rates between 6mm/h and 13mm/h.

Rainfall rate prediction based on artificial neural networks for rain fade mitigation over earth-satellite link

In this paper, we present a model for rainfall rate prediction 30 seconds ahead of time using an artificial neural network. The resultant predicted rainfall rate can then be used in determining an appropriate fade counter-measure, for instance, digital modulation scheme ahead of time, to keep the bit error rate (BER) on the link within acceptable levels to allow constant flow of data on the link during a rain event. The approach used in this paper is pattern recognition technique that considers historical rainfall rate patterns over Durban (29.8587°S, 31.0218°E). The resultant prediction model is found to predict an immediate future rain rate when given three adjacent historical rain rates. For our model validation, error analysis via root mean square (RMSE) technique on our prediction model results show that resultant errors lie within acceptable values at different rain events within different rainfall regimes.

60GHz millimeter-wave radio in South Africa: Link design feasibility and prospects

The need to deliver efficient wireless services has spurred many network providers to access higher frequency bands on the millimetre-wave (mm-wave) platform which caters for larger system bandwidth and throughputs. This option offers networks the benefits of increased carrier flexibility and robust channel capacity, for many user applications, which are currently in high demand. The 60 GHz band is currently among the millimeter radio bands with high global appeal because of its capacity to provide multigigabit wireless solutions, for both outdoor and indoor applications. However, in many African countries, technological specifications required to initiate widespread deployment of this wireless technology is almost non-existent. Therefore, this paper will foray into some technical aspects concerning the future deployment of the 60 GHz wireless radio technology in South Africa. The major attenuation sources militating against the application of this frequency for seamless outdoor signal communication are mainly of two kinds: atmospheric and inclement weather conditions due to precipitation. With the deployment of this technology almost in the offing at urban areas, there is need to ascertain key infrastructural components required for link design of base stations at selected areas of South Africa. This will address fundamental radio resource issues pertaining to power levels, minimum link distances, network adaptability and transmission issues. In this paper, the overall fade margin required to deploy outdoor 60 GHz Line-of-Sight (LoS) radio systems in South Africa is investigated at ten urban sites under clear air and precipitation conditions. It is found that the role played by system antennas, alongside the peripheral receiving amplifier circuits, may hold the key to improving achievable signal levels, especially during intense events of precipitation.

Time series rainfall spike modelling from Markov chains and queueing theory approach for rainfall attenuation over terrestrial and earth-space radio wave propagation in Jimma, Ethiopia

Rainfall attenuation over radio wave propagation originates from the stochastic turbulence of rainfall intensity on wireless networks, especially at higher operating frequencies. Basically, three parameters characterize a stochastic process of rainfall: rainfall spike, rainfall rate regimes and the sojourn time of a rainfall spike in each rain rate regime. In this paper, the characteristics of rainfall spikes are investigated as a randomly varying in four rainfall rate states in Jimma, Ethiopia using Markov chain model and queueing theory approach. From the first model the spikes transition probability matrix among regimes is determined and found to be ergodic and, applying the second approach the sojourns time distribution of spike is modelled and the result shows Erlang-K probability distribution not the common exponential distribution for all regimes with very minimum fitting errors.

Temporal characterization of rainfall time series analysis for wireless networks

Estimation analysis for rainfall time series can be applied as a technique in improving dynamic rain fade countermeasures. In this study, the nth-powered sine function is considered in analyzing the time series patterns in Durban, South Africa. With an assumed exponent factor, n = 2 and width factor, β = 0.9, the proposed function is seen as an appropriate envelope with Root Mean Square (RMS) error ranging between 13% and 30%. The Fast Fourier Transform (FFT) and Power Spectral Density (PSD) show that the frequency components of the measured rainfall residues compare well with those of the proposed function. At simulated microwave frequencies of 12 GHz, the function is seen to mask and track the fluctuating rainfall specific attenuation patterns at our site.