Performance Evolution in Satellite Communication Networks Along with Markovian Channel Prediction

Augmenting accurate prediction of channel attenuations can be of immense value in improving the quality of signals athigh frequency for satellite communication networks. Such prediction of weather related attenuation factors for the impendingweather conditions based on the weather data and the Markovian theory are the main object of this paper. The paper also describes anintelligent weather aware control system (IWACS) that is used to employ the predictions made from Markov model to maintainthe quality of service (QoS) in channels that are impacted by rain, gaseous, cloud, fog, and scintillation attenuations. Based onthat, a three dimensional relationship is proposed among estimated atmospheric attenuations, propagation angle, and predictedrainfall rate (RR pr ) at a given location and operational frequency. This novel method of predicting weather characteristicssupplies valuable data for mitigation planning, and subsequently for developing an algorithm to iteratively tune the IWACS byadaptively selecting appropriate channel frequency, modulation, coding, propagation angle, transmission power level, and datatransmission rate to improve the satellite's system performance. Some simulation results are presented to show the effectiveness of the proposedscheme.


Introduction
Recently, satellite based commun ication networks at high frequency bands have been rapidly expanding. These high frequencyoperations have enabled a wide variety of available and potentialapplicat ions and services including communicat ions, navigation,tele-med icine, remote sensing, distributed sensors networks,and wireless access to the internet. However, h igh frequencyoperations are prone to excessive digital transmissionerrors due to atmospheric attenuations [1]- [8].
Control systems attempt to minimize the effect ofattenua tionby adjusting the trans mission parameters and signal characterist ics .Ho wever, excit ing system rely on tot al attenuationin actuating the transmission control.Consequen tly, the control of t ransmission parameters have been less than the optimal as the detail knowledge o f occurrence probabilit ies ford ifferent impairments would have been miss ing . Kno wing expected impairments separately for different attenuation factors, more specifically the weather factors, would help us utilizethe most appropriate methods for mitigat ing impairments with mechanisms like up-link power contro l, adapt ive cod ing, antenna beam shap ing, ansite diversity [9], [10]. Therefore,improve quality of service (QoS) provisioning [11].
The major at mospheric and weather related factors in signalattenuation are rain fade, gaseous absorption, cloud attenuation,and tropospheric scintillat ion. A mong them, the rainattenuation (RA), also known as rain fade, is the dominantcause of signal impairment, especially at frequencies higherthan 10 GHz and small aperture antennas such as Very SmallAperture Terminal (VSAT) and Television Receive Only types(TVRO) [2], [12]- [17].
International Teleco mmunicat ion Un ion -Radioco mmun ications(ITU-R) maintains a la rge database for probability ofprecipitation and other parameters. It provides mathematicalequations and analytical approaches to estimate rainfall rate(RR) and different atmospheric attenuations around the worldfro m these data [18]. However, ITU-R techniques were developed in view of finding the average conditions and boundaryconditions, which are mo re useful for the design of controlsystem and less for the operation of those systems. Moreover,ITU-R techniques were developed at a time when the high frequencyoperations above Ku band, where losses become really significant,were not expected. Consequently, there was a greatroom to first improve the ITU-R techniques to maintain them accurateat higher frequency operations and second, to decouplethem fro m the fifteen years average data provided by ITUR.Instead, if we make ITU-R techniques work with real-t imeweather data, those techniques could help us achieve better operation,as they were helping us with the system design inthe past [13], [14], [17], and [19].
Some of the prior work in the area include [20], where RRis predicted by using weather radar reflection data instead ofground based measurement. Paper [21] presented a methodcalled two level Markov model to pred ict mu lti-path fading ofsignals. Authors of [22]presented a method for RA predictionwhich y ielded good results during low rain and low elevationangle. Authors in [24] presented fade duration prediction asa function of RA and frequency and used modelling of channelsto obtain signal attenuation due to clouds and precipitation.While [25] cited difficulty in approximating the lossesdue to limited availability of e xperimental data on clouds; [26]cited problem in developing accurate models due to ambiguityof cloud water content and cloud extent limits. In [10], authorspresent prediction models and analytical techniques fora range of operational parameters involving low-margin, lo welevation angle, inclined geosynchronous, and low earth orbitsystems. The paper estimated rain and scintillat ion whileassuming gaseous attenuations as constant. These techniqueshave helped to mature the control systems in satellite communicat ion.Due to new bandwidth and frequency requirements,the problems of attenuations due to various atmospheric factorshave come to receive increased level of prominence dueto increased operations at frequencies above 10 GHz. Theseproblems are articu lated very well by [2], [3], [7], and [12].
In our past research work, we demonstrated that a bettercontrol of satellite signal parameters resulting in improvedsystem performance could be achieved by taking into accountthe major weather related contributors of signal attenuationseparately [16]. In [5] we demonstrated how estimation of RR, aswell as attenuation due to rain, gas, cloud, fog, and scintillat ion,could be measured. The methodology yielded greateraccuracy in estimat ing the weather related attenuation. Totalattenuation as well as constituent weather attenuations werecalculated for any rainfall conditions and for any elevation angle.However, this methodology relied on historical data collected by ITU-Rthat provided average rainfall per year for locations throughoutthe world based on statistical data collected over a decade [6].During the research, we realized that the estimations wouldhave helped tune channel parameters in real-t ime had the real-t imemeasurements were used to gain a closer estimation of impendingweather conditions. The work reported in this paperwas inspired by that premise. As research thrusts were put to imp roveQoS on satellite based networks withthe use of intelligent prediction methods, the work presentedin this paper should be of significant interest to research anddevelopment co mmunity.This paper makes four major contributions towards imp rovingthe operation of satellite control systems and enhancing theperformance of satellite network systems. This is specificallytrue during severe weather condition and operat ions ofcommun icationc hannels above Ku band. The major contributionsof the work are: 1. Migrat ion of ITU-R techniques fro m the domain of the improvingdesign to the domain o f improving the operation, 2. Application of Markov theory in real-t ime predict ion ofweather and applying of those predictions in the forecastof atmospheric attenuation, 3. Imp rovement of ITU-R techniques in predicting rain, gas,cloud, fog, and scintillation attenuations mo re accuratelyat wide range of frequencies including Ka band and tomake them work at any propagation angle, and RRs, 4. An enhanced intelligent weather aware control system(IWACS) for achiev ing imp roved channel performance.
This paper is presented in five sections. Section 2 describesprediction of d ifferent weather attenuation factors based onMarkovian modelling of weather characteristics. Section 3 describescalculation of rain, gaseous, cloud, fog, and scintillationattenuations which will be used by IWACS in decision making. Section 4 presents simu lation environment and implementationof IWACS, results and discussions. Finally, weconclude this study in Section 5.

Prediction of Channel Characteristics
This section describes the behaviour of RA at high frequency and proposes a method for better estimating channel attenuation in weather impacted satellite networks. The RA is co mputed, based on predicted rainfall rate (RR pr ), which itself is predicted by using Markov theory [27] along with ITU-R models and bi-linear interpolation [28], [29]. The method predicts RR at any location on earth, for a wide range of propagation angles and frequencies. The RR pr values are then used toadjust the control parameters and,therefore, help improve the QoS in communication channels.

The Rainfall Rate Predicti on
In this section, we present prediction of rainfall rate usingMarkov theory on the time series of weather data. For that reason, weather is considered a discrete random p rocess thatcan assume a set of fin ite states. Further, it is assumed that thechange from one state to another is a random discrete step withcertain transition probability (p), whose value is derived fro mstatistical properties of the system.

Classification of Rain
For the purpose of explaining to the reader the application ofMarkov modelling fo r p redicted rainfall rate, a specific locationis chosen where we divided rainfall rate ranges into five classes starting fro m zero mm/hr up to the highest rainfall rate asfollows: a. Class A: fro m zero up to but less than 1 mm/hr. b. Class B: fro m 1 up to but less than 4 mm/hr. c. Class C: fro m 4 up to but less than 8 mm/hr. d. Class D: fro m 8 up to but less than 14 mm/hr. e. Class E: values greater than 14 mm/hr. The discrete time interval chosen in this study was one hour. The reason being that environment should supplyweather data in one hour intervals. However, the method canbe applied for finer grain intervals given that weather data forshorter intervals are available. The approach in grouping total rain conditions into classifiedblocks has been depicted in Figure 1. This classificationin actual data provides the basis for the data required to applyMarkovian theory in the prediction of rainfall rate [8]. To make the classificat ion of rainfall rate to better reflectlocal statistical weather patterns, two parameters can be adjusted: a. Periodicity of rainfall rate: Instead of selecting one hourinterval, periodicity in minutes or hours could be used.The smaller the sampling period, the mo re instantaneouswill be the rainfall rate values especially when dealingwith rapidly changing weather conditions. b. Nu mber o f classes: Instead of five, the number of classes could be decreased or increased according to the variation of rainfall rate history for that location. More classes means more co mputational time with finer granularity of control.

Markov Model Implementation
I-Weight of Transition Probability Matrices: Different weights are assigned to each Markov state, zero order(present state), first order (previous state), and second order(previous to previous state), as defined in Markov Chaintheory. There exist no direct formulas for calculating theseweights and it needs iterative search involving trial and error.The weight values need to be validated over many sets of data.
The resulting weight vector is denoted as: where W(0), W(1), and W(2) represent weight assignedto present, previous, and previous to previous intervals,respectively, as shown in Figure 2. Each weight in (1)(1) has adifferent unique value and the largest value will belong to thepresent weight W(0) and so on for the other weights. Also,these weights are positive numbers and their summation isequal to one. This research came to conclude that there exista set of weight that work very well for all possible sets oftransition probability matrices describe below. In Markov Chain theory, the p robability of a discrete event to remain in state x is denoted as P(x). In this representation, independent chains without any memo ry of past state are called zero-order Markov Chains. The transition probability matrix of zero-order Markov Chaintheory [P 0 ] for the five presented classes is, thus, represented as follows: ]. P = P P P P P 0 Then the process consisting of a finite number o f states with known probabilities P(x, y) of transition fro m state y to state x is considered a first order Markov Chain [27], [30]- [31]. The t ransition probability matrix o f the first-order Markov Chain for the five classes is shown below in(3). These transitions are depicted in a pictorial form in Figure 3 and can be represented by: (3) Similarly, the transition probability matrix of the second-orderMarkov Chain theory P(z|xy) for the five classes is presentedin (4 The characteristics of these transition probability matricesare such that the entries for each column vectors in (2), (3), and (4) are positive numbers. The sum of the elements of eachrow in the matrices is one. The co lu mns represent probability vectors, which are the stochastic values for transition. The transition probabilit ies are dependent on statistical pattern of rain at a particular geography and climate.
Note that, m and nrepresent the number ofrows and columns, respectively.

Pred icted Rainfall Rate
The value of predicted rainfall rate for the immediately followingdiscrete time period is computed based on probability andweight co mbinations. These combinations present a specialmodule of weather predict ion of different weights assigned toeach transition probability matrix along with Markov Chain oforder φ, where φ is fin ite and equal to 2 in our case. Thus,the prediction of the future state is dependent on the present,previous, and previous to previous states and is independent of the other earlier states [8].
[P0]represents the rowcorresponding to the present state.
[P1] represents the row correspondingto the transition from the last state to the presentstate. [P2] represents the row corresponding to the transitionfro m the last-to-last to the last state and then to the presentstate. In our specific case, the m can be any value rangingfro m 1 to 5 and n can be any value ranging fro m 1 to 25 accordingto the previous and previous to previous weather state,respectively.
Also, PWs presented in (5)can be written in asimple mathematical form as: PW(u) = W(0).P 0 (u) + W(1).P 1 (m, u ) + W(2).P 2 (n, u). (2) Where u ranges from 1 to 5 and PW represents the probabilityweight values of the five existing classes (A, B, C, D, and E),thus: (3) Therefore, the predicted rainfall rate (RR pr ) will be belongingto the class that has the maximu m probability weight ofPW vector collected fro m (7). Figure 4 shows a demonstration for the effectiveness of ourmethod for predicting rainfall rate. At the beginning, we usedrandomly generated values of rainfall rate to determine theweights and probability matrix elements for our model [15].
These values were then tested against rainfall rate valuesthat were collected by Environment Canada for almost twomonth duration at SouthWest of King City using weather radarnear Toronto, Ontario, Canada. We applied our methodologyto predict the future state out of past states. The prediction dataobtained using our method and the measured rainfall data fro mEnvironment Canada are provided in Figure 4 and in Table 1.   Note thatonly small nu mbers of samples are presented in thetable to keep it readable and that the prediction matches closelywith the measured results.
We conclude that, the Markovian Chain has pro mising applicationin effectively predict ing the future weather result in statisticalterms. The results are astoundingly accurate. Therefore,our methodology for predict ing rainfall rate can be applied underdifferent weather conditions at any given location on earth.

The Values of Weights and Transition Probabilities
The values of the weight matrix as defined in (1) and the transitionprobabilities as defined in (2), (3), and (4)were obtainedthrough an extensive exercise of iterative adjustments and theirtest of valid ity on rainfall rate data. At the end, the study notonly revealed a set of workable values but they also revealed the following behaviours: 1-For a g iven set of transition probabilit ies, there is a correspondingweight that gives the best prediction of rainfallrate in Markov Chain theory.
2-Studies done over actual rain data revealed that the fivestates model developed here gives extremely reliab le predictionof rain with the following values of weights (W's)are: The full set of values could be obtained by contacting theauthors.
3-When rain rate classification as done in Sect ion 2.1.1 isaltered to better suite different locations on earth, the coefficientsmentioned above will change. However, thevalues listed here will give good starting values for theiterative process of finding the new values. Notice that, the weights and the transition probability matricesvalues are selected init ially based on the statistical investigationof historical field of data collected over several years. Wediscovered that the coefficient of the matrices and the weightsremain relatively stable alt-hough weather conditions vary significantly.Nevertheless, ome severe weather conditions notrecorded by the data analysed for this research could requiresomeadjustments.
Note that, we acknowledge the dependence of Markoviantheory in stochastic assumptions and the potential errors in estimat ingthe weights and the coefficients of transition probability matrices. This is denoted especially for the fact that themethod assumes stationary weather within one discrete timeperiod; its prediction is nothing more than a practical appro ximation.Nevertheless, the test on the fields' data demonstratedhighly respectable results, yielding prediction values to containlow relative percentage error of (≤9.9%) for the presentedfifteen hundred hours for rainfall rate.

Migrating ITU-R Model from the Design Domain to the Operational Domai n
ITU-R technique for estimating environmental attenuations based on weather data collected over a decade and a half has served us well in system design because it is able to provide average and boundary conditions that a communicat ion system would be subjected to. ITU-R provides not only the geographic parameters of a location, such as the height above the sea level and the average rain height as shown in Figure 5,but also the weather factors like probability of precipitation and mathematicalformu la for estimating rainfall rate, and subsequentlyestimatingsignal attenuation due to rain, gas, cloud, fog, andscintillat ion. The knowledge of the attenuation servesuseful purpose in optimizing the design by find ing the best combination of frequency, modulation,coding, and othertransmission and reception parameters for a given location in relative to other locations. The research work reported in this paper stemmed fro mknowing that if these techniques were to be extended to estimatethe attenuations in a real-time environment, they wouldhave greatly served in the purpose of operating those designedsystems optimally by allowing selecting proper combination of controllable parameters. Therefore, the ITU-R methodologywas studied and extended to solve the problem of adapting thecontrol systems with instantaneous variations of weather attenuation.
We propose the use of Markov theory in estimat ingthe weather condition for the immed iately following timeperiodbased on the real-time data of immed iately precedingperiods and the statistical probability of state changes. Subsequentexperiments demonstrated that the inclusion of Markovianpredict ion technique and its resulting data as an input to ITU-Rtechniques resulted in real-time prediction of weather attenuations.
The next enhancement made in ITU-R techniques was estimatingattenuation as a function of rainfall rate, propagationangle, and operational frequencies so that they hold true evenunder high frequency operation above Ku band. The outcomeof these changes was that they yielded highly accurate estimationof RR and then that of rain, gaseous, fog, cloud, andscintillationattenuations. Such evolution in the ability to predict weather attenuation in real-t ime had direct consequencein improving the real-time control by enhancing theability toselect the signal parameters.
The follo wing are the key benefits achieved by the proposedtechnique: 1. Better estimation of attenuation including high frequencyoperations.
2. Real-time estimat ion of RR. The prediction of RR ismade by viewing the weather data fro m a moving windowof fixed time intervals and the impending rainfall rate isestimated based on current rate, previous rate, and previousto previous rate.
3. Calcu lation of attenuations based on the real-t ime estimationof RR.
4. Real-time signal adaptation to weather variation by selectingappropriate channel parameters.

Calculation of Rain, Gaseous, Cloud,Fog, and Scintillation Attenuations
In this paper, a new relat ionship model is proposed for estimatingvarious weather attenuations as a function of propagationangle, RR pr , and frequency, for any derived geographic locationof ground terminals. This model results in three dimensionalgraphs which relates the attenuation, RR pr , and propagationangle for a selected operational frequency, which may be anyvalue fro m 0 to 55 GHz. RA is the single greatest weatherdependent signal attenuation factor, which occurs in satellitenetworks largely due to signal absorption and scattering of incomingsignal. Fortunately rain forms only in the tropospherethat extends around sixteen kilo meters fro m sea level wh ilethe satellites are located in geostationary orbit at 35,800 kmabove earth [6]. Therefore, exposing signal to rain attenuationonly during a small portion of its transmission path as shownin Figure 6.
Nevertheless as the frequency increase the losses increaseas shown in Table 2[32]- [35]. Even heavy rainfall of 10 cm/hrseems to cause a small attenuation of 0.05 dB/km with RF signalsat 2.4 GHz. The Ku band attenuation for the same rain fall,however, is approximately nine times that of C-band, andthus very substantial for it to be ignored [36], [37]. Therefore,estimating different atmospheric attenuations at regional or indiv idualsites is important for improving control ofsatellite channel parameters especially when h igher transmissionfrequencies are adopted to achieve greater transmissionrate through communication channels.  In this section a new technique for estimating channel attenuationsis presented. This technique, estimates constituentcontributors of total attenuation separately and extends it togive good approximat ions for a wide range of signal frequencies,propagation angle, and RR pr . The technique uses ITU-Rcoefficients as shown in Figure 5 wh ile estimating the attenuationat grid locations in a weather collection map that was used by ITU-R. Incases where the location of concern does not fall on the grid, ab i-linear interpolat ion technique is then used to get the parameters [5] , [13].
Most of the formulas and variables presented in this sectionare direct evolutions from the ITU-R method with notify modifications and enhanced presentation for different weather parameters. We implemented these formulas and variablesto handle real-time data of the present one hour window and used the Markovian predict ion that was presented earlier with proposed values of the matrices components to predict the data for the following period.
This section is devoted first, to predict constituent contributorsof channel attenuation separately due to different weather variants,and then, to determine the total attenuation due to all of thefactors combined. Also, included in this section is the technique for calculatingthe signal to noise ratio (SNR) based onthese attenuations.

Calculating Rain Attenuation (RA)
The RA, represented as (A r ), is predicted by using a set offunctions and solving them for d ifferent satellite-location dependentvalues. The values of RA are calcu lated as a functionof frequency (f) and predicted rain fall rate (RR pr ). The foundationalwork of this technique and its variab les are explainedin [5], [14] and [38].
The key destination of this technique is that we start with anattenuation value at a known frequency (f n ), and then estimatethe attenuation at one increment higher frequency (f n+1 ).Then using the attenuation at (f n+1 ), we find attenuation at(f n+2 ), and so on. That is, once RA is known at any lowerfrequency, we will be able to compute RA at a higher frequency andcontinue the process until the maximu m desiredfrequency is reached.
This iterative calculation is made using the following threeequations. Equation (12) establishes the relationship betweenRA and RR pr (see [13], [19]for full description).
Thesecond equation (13) establishes relationship between an intermed iatevariable H with a known value of RA at a knownfrequency (f n ). Then the next equation (14)calcu lates RA atthe next frequency (f n+1 ). Th is process is iterat ively repeateduntil RA reaches the desired frequency.
The RA for different frequencies and RR pr values can beobtained from [13]: Where A r (θ,RR pr ) represents RA for a given value of RR pr ,and propagation angle θ, as shown in Figure 7. As a reference,the variab les L E , φ, and γ R are described in [13].
This method also has an added advantage by providinghigh CPU efficiency since we do not have to repeat the entirecalculat ion for each frequency ending with similar resultsto that for existing ITU-R. It is achieved by eliminating the accumu lated errorwhen co mpared to that of existing appro ximated ITU-Rsolution [13].
The predicted values of RA at any desired location, for differentpropagation angles, RR pr , and channel frequency, are important determinants in channel qualities. Ho wever, in orderto control the satellite channels efficiently, we also need to factorother parameters like gaseous, cloud, fog, and scintillat ionattenuations as described below.

Calculating Gaseous Attenuation
In this section, an analytical method for estimat ing gaseousattenuation has been presented. This has been an extension ofthe methodology presented in ITU-R P. 676. The slant pathattenuation depends on various meteorological conditions createdby the distribution of temperature, pressure, and humidityalong the transmission path. Thus, the effective path lengthvaries with location, month of the year, height of the stationabove the sea level, and propagation angle. The gaseous attenuationis calculated using the following steps:  i Where ph: pressure (hPa), r ph =ph=1013,r t = 288/ (273 + t), ρ water-vapour density (g/ m 3 ),f: frequency (GHz), and t: mean temperature values(°C), can be obtained from ITU-R P. 1510 when noadequate temperature data is available.
3. Equ ivalent Path Length for the Dry A ir: The equivalent height of the dry air is given by: Notice that water vapour has resonance of (22.235 GHz), (183.31 GHz), and (325.1 GHz)respectively and that attenuation changes with theamount of water vapour in the atmosphere.
The above method calculates slant path attenuation for watervapour that relies on the knowledge of the profile of watervapourpressure (or density) along the attenuation path.
This section proposes a method to obtain the path attenuationbased on surface meteorological data using the cosecant lawfor a given propagation angle and RR pr as: and dB,and θ ≤5°. Thus, the estimated gaseous values are computedat any desired location, for all ranges of propagation angle andRR pr , and for any frequency as shown in Figure 8.

Calculating Cl oud and Fog Attenuati ons
Cloud and fog can be described as a collection of sma ller raindroplets, or alternatively, as different interactions from rain asthe water droplet size in fog and cloud is smaller than thewavelength of 3 GHz signals.
The cloud and fog attenuations(A cf ) can be expressed in terms of RR pr and propagationangle for a specific frequency and temperature valuest k (Kelvin), through the following series of equations, culminating into equation (37).
where t k : Temperature (Kelvin) ε 2 = 3.51, ε 1 = 5.48, density,along a cross section of 1 m 2 fro m surface to topof clouds for a given site. The L v is provided fro m ITU-R for the predicted probability of precipitation (pr) based on RR pr .Refer to [5] to obtain the relation between pr and RR pr . In allpredicted situations the value of pr is normally found to be in the range of 0.0001 to 0.5. These attenuations are presentedas a function of θ and RR pr at a station in King City has beenshown in Figure 9.

Calculating of Scintillati onAttenuati on
The cumulat ive distribution of tropospheric scintillat ion isbased on monthly or longer average ambient temperature.Th is distribution reflects the specific climate condition of thesite [5], [39]. In satellite co mmunicat ions, scintillat ion attenuationresults from rapid variations in the signal's amp litude andphase due to changes in the refractive index of the earth's atmosphere.A general technique for predicting this attenuationas a function of RR pr and propagation angle that is greaterthan 4° is given here.
(47) The estimated scintillat ion attenuation calculated by using(45) on ITU-R data resulted in a set of A s (θ, RR pr ) valuesin relat ion to propagation angle, RR pr , frequency, and locationas shown in Figure 10.
Given these four attenuations, the total weather attenuationA W (θ,RR pr ), can be calculated fro m [5], [8], and [13]: The results with the available measurement data for all latitudesfor the prediction of wide RR pr ranges and propagationangle are shown in Figure 7, Figure 8, Figure 9, Figure 10, and Figure 11.The second component of attenuation is caused by freespace [36,37]. We call the loss that occurs in free space freespace attenuation. The free space attenuation, A 0 (f), is obtained as follo ws: A 0 (f) = (4.π.d/λ) 2 , (49) Whered is the distance between transmitter and receiver andthe wavelength λ = c/f. It would be significant to note that afree space is space with nothing at all in it.
This phenomenondoes not exist in the known universe but interstellar space isa good approximation. The most important four features offree space are its uniformity everywhere, absence of electricalcharge, no current flowing through it, and its infinite extent inall d irections [40], [41].
That we have obtained atmospheric attenuation and freespace loss, the total attenuation (A t ) can be calculated fro mthe following relation: Where A t (θ, RR pr ) is the total attenuation, A W (θ, RR pr ) isthe atmospheric attenuation described in (48)(48), and A 0 (f) isthe free space loss described in (49).
A three dimensional relat ionship for these attenuations withrespect to propagation angle and RR pr is presented in Figure 12.
These attenuations, for systems running at frequencies above10 GHz-especially those operating with low propagationangles and/or margins, must be considered along with the effectof multip le sources of simultaneous occurring.
This method provides a useful general tool for scaling atmosphericattenuations according to these parameters. Also, ithelps to provide designers with a perceptib le v iew of approximateddifferent attenuation values that can be computed at anydesired location, for differentfrequencies, and for wide rangesof RR pr and propagation angles.The outcome becomes a key factor in diagnosing, adjustingand improving satellite signal power, modulat ion and codingschemes, monitored and controlled altogether by a powerfuland efficient intelligent-based attenuation countermeasure system.
We found that practically the prediction of total attenuationobtained in this way is respectable approximation. The totalattenuation is used to calculate SNR, wh ich is then used bythe IWACS in determin ing channel quality and subsequentlyadjusting satellite propagation parameters as described in thenext section.

Relating Total Attenuation wi th Signal to Noise Ratio (SNR)
SNR is a measure of signal strength for satellite signal relativeto attenuations and background noise, usually measuredin decibels (dB) [41]. The signal energy (E s ) to noise powerspectral density (N 0 ) per symbol is calculated fro m the knowledgethat E s = C .T s = C = R s , where C is signal power,Ts is symbol duration, and R s transmission rate.
T (effective noise temperature) = T a + T r (52) Where T a is noise temperature o f the antenna as represented in Table 3, and T r (noise temperature of the receiver) = (10 Nr/10 -1) . 290.(53) In the above equation the Noise Figure (N r ) for a low-noiseamplifier is found to be in the range of 0.7 to 2 dB. The aboveequations can now be combined as: Where Pt an d Pr are t rans mitter and receiv er po wer, and G t and G r are ant enna g ain at trans mitt er and receiv er sides respect ively.Therefore, It shou ld be no ted th at th e SNR est imat ion o f (54) willbe optimi zed by the v irtue o f hav ing bett er estimat ion of A t thro ugh (56).

Simulation Environment and Implementation
The mathemat ical solution for finding any weather attenuationand utilizing that informat ion to improve signal qualityin satellite networks were tested in a simulated system namedIWACS. The system monitors channel qualities and appliescounter measures, which involves controlling of power, frequency,propagation angle, modulation, coding, and data rate.
The outcome is the evolution in signal fidelity, especiallyabove 10 GHz, through reduction in digital transmission errors.
In this section, the architecture of the IWACS is briefly mentioned. Details are avoided because the material presentedin earlier section has been the main focus of this article.
The IWACS was simu lated in Mat lab simulat ions version7.10.0 running on i7 -2630QM, 2.00 GHz CPU and6.00 GB RAM. A special module was written to read weatherdata fro m Environment Canada supplied in aspecially formattedtext stream and converted into a three hour sliding windowof moving weather data always proceeding the present mo ment.
Software modules were written to extract propagation related parameters shown in Figure 5 for the location fro m ITURsupplied data. Algorithm for predicting the RR based onMarkov theory with fixed-duration weather data was written. Also, the IWACS used heuristic algorith ms that emp loyedfield inputs in problem solving, learning and discovery.The system adhered to formalized knowledge represent ations chemes practiced in the industry, and mach ine learning techniques,to reach optimal decisionin dealing with d ifferent atmosphericconditions [5], [8], [16], [42 ], and [43].The key feature of the IWACS is that it adjusts to signalvariations with a fast response time. In acco mplishing this, theemployed technique used feedback of SNR values fro m thereceiv ing end of the channel and uses that knowledge to mit igatefuture weather attenuations, thus preventing them fro mactually manifest in the channels. This proactive approachto the adjustment of signal characteristics is what makes thesystem meet end-to-end QoS requirements.The core architecture of the IWACS is shown in Figure 13,where it may be noted that it consists of four control blocks,the first control b lock, the second control block, the third controlblock, and the fourth control block, a feedback loop andcounter iteration, along with a special module called decisionsupport system (DSS). This figure illus-trates the Interrelation-shipsof various blocks involved in tuning propagation characteristicsof a commun ication The first control block collects vital data like propagationangle, frame size, frequency, transmit signal power, andweather data. Based on these data, it computes atmosphericattenuation and SNR for the following time period. Th is iswhere the bulk of the techniques exp lained in earlier sections areemp loyed.
The second control block co mpares the differences betweenthe estimated SNR and the minimu m SNR values sought tomaintain a desired level of QoS, usually set by system's designersbased on experience. These comparisons lead to oneof three d ifferent possible outcomes {A, B, o r C} as shown in Figure 13. The first outcome {A}, is for estimated SNR valuessmaller than the threshold level. In this case the DSS willdecide to increase transmit power up to a maximu m limit of -30 dB (0 dBm). The second outcome {B, is where estimatedSNR values equal to or exceed the threshold level. TheDSSwill be satisfied and will ju mp to the last block. The thirdoutcome {C}, is for estimated SNR smaller than the thresholdlevel even after increasing the transmit power to its maximu mvalue. The DSS will go to the next b lock for selecting a co mbinationof transmission characteristics.
In the third control block, based on adjusted SNR value,the DSS will opt for the adjustment of other parameters suchas data rate, frequency, modulation, and coding values. If thethreshold level value can be reached by using any of the differentvariable co mbinations, then the DSS will decide to moveto the last block for the final decision. This block emp loysan aid similar to Tab le 4 in making these decisions, which areprepared based on field experience and expert suggestions. The fourth control block interacts with the remote end ofthe channel and determines the current SNR. It then feeds thecurrent SNR value to the input block so that the system's realtimestate is appropriately monitored. This in turn helps toiteratively adjust the channel state.
In case a satisfactory SNR is not achieved through differentcombinations, the control system goes back to first controlblock through feedback and counter iteration block to re-adjustthe parameters (as exp lained earlier) andcomes to re-wo rk withthe tables according to DSS decision, until a satisfactory valueis reached at which theprocedure will stop. In case significantimprovement is not achieved, the system will abandon the processafter a set number of iterations and gives a warning tothe operator. Whereas, the number of iteration can be set bysystem's designers based on the specific location.
The SNR and other measured parameters are fed to the DSS block to help make the decision to maintain QoSandsatisfy SLAs. The DSS and its network optimization blocksare depicted in Figure 14.
The periodically-co mputed attenuationkeeps updating the knowledge input to the DSS, which is constructed from specific classes of algorith ms that takesexperiential decision inputs from the user so that they couldbe factored in decision-making activit ies. Typical informat ionthat a DSS might gather and present would be: a-Accessing current informat ion assets such as knowledgebase, satellite parameters, and triggering of periodicquery b-Maintaining the database of different comb inations ofchannel parameters known to give acceptable system performance.The other blocks can then find the right combinationswith the aid of DSS.
Thus, the IWACS min imizes the attenuation effect andmaximizes the channel robustness and efficiency by improvingSNR. Such improvement in turn imp roves QoS. The ability tobetter predict rain attenuation for different weather conditionsand operational frequencies makes the quest for imp roved QoSa reality.

Results
The system, built on the foundation of the above mentionedprincip les, was found to deliver noteworthy improvements inthe performance of satellite networks.
The system monitored the SNR atthe receiving end of the channels, compared it with a threshold,and searched for a blend of available power, frequency,propagation angle, coding, transmission rate, and modulationin response to predicted channel attenuation. It then attemptedto maintain a desired level of SNR as shown in Figure 12, Figure 13, Figure 14, Figure 15, andFigure 16. Such maintenance required the aid of anexpanded form of Table 4 for selecting the right comb inationof propagation parameters. Figure 15 and Figure16 co mpare the SNR before and afterthe techniques discussed in this paper are put to usefor making improved system performance. These figures representcases when SNR fell between (-39 ~-16) dB,and transmit power fro m (-100 ~ -88) dB befo re intelligentdecision mechanism was turned on. The improvementsmade in SNR and transmit power level were significant afterthe IWACS was allowed to operate under the same conditions.The SNR imp roved to (5 ~ 27) dB and the transmit powerlevel ranged fro m (-63 ~-51) dB.Both cases were subjectedto identical weather conditions where total attenuationdue to weather rangedfrom (215 ~ 225) dB for a frequencyof 20 GHz at 40 degree propagation angle. Note that the systemwas able to bring the upper limit of transmit power to lessthan the maximu m allowed of -30 dB. Any time this limitis reached, signal parameters are re-adjusted to prevent uncontrolledsignal transmission as shown in Figure  16and Tab le 4. Itshould be noted that the improvements in channel performancemade by the scheme are significant.

Conclusions
Precip itation, gaseous formation, cloud, fog, and scintillat ioncause attenuation of satellite signals. These attenuationsbecome especially pro minent at frequencies above Ku band.Such attenuation makes it difficu lt to provide agreed upon QoSby satellite networks unless special mitigation measures aredevised to counter weather effects. Such control systems couldbe optimized to its most effective status if we had the bestpossible techniques for predicting channel attenuation due toweather related factors.This paper presents a technique forpredicting channel attenuation based on real-time weather dataand the use of the Markov theory. The results thus obtained, arefound to be able to make significant improvement over thetechniques known thus far. This technique positively contributesto QoS maintenance by allo wing for better tuning andadaptation of signal propagation parameters such as frequency,power, propagation angle, modulation, coding, and transmissionrate with changing weather conditions. The paper also introducesa three dimensional relat ionship model between attenuation, propagation angle, and RR pr with an imp lication that for a given atmospheric condition, the signal attenuationcould be predicted with much imp roved accuracy thanthe techniques known to us. An IWACS, wh ich controls modulation, coding, transmission power, frequency, propagationangle, and transmission rate to improve channel robustness, isbriefly described. It is believed that the technique presentedhere can be of significant interested to research and developmentcommun ity interest in improving the throughput of satellitenetworks.