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Advances in Space Research 49 (2012) 336–350

Attenuation prediction for fade mitigation using neural networkwith in situ learning algorithm

Bijoy Roy ⇑, Rajat Acharya, M.R. Sivaraman

SATCOM & Navigation Applications Area, Space Applications Centre, ISRO, Ahmedabad 380015, India

Received 5 January 2011; received in revised form 19 August 2011; accepted 12 October 2011Available online 20 October 2011

Abstract

Increasing demand of bandwidth in communication satellites has forced satellite links to be designed in Ku bands and above. But atthese frequencies, rain and other tropospheric elements result in large attenuation. To mitigate the tropospheric attenuation of micro-wave satellite signals above 10 GHz using any standard Fade Mitigation Technique (FMT), it is essential to have a priori knowledgeabout the level of attenuation. Hence, short-term rain attenuation prediction models play a key role in maintaining the link in whichnecessary compensation can be applied depending on the early information of attenuation. This paper presents a method of attenuationprediction using Adaptive Artificial Neural Network. Here In situ Learning Algorithm (ILA) has been used to enable the system to trackthe non-stationary nature of the attenuation. To validate this, Ku Band data, collected at three different sites in India have been used forthe purpose of prediction. The performance of the algorithm is determined through the estimation of prediction accuracy by comparingthe predicted values with the measured data. Results obtained using the mentioned technique shows considerably good accuracy even upto 20 s of prediction interval with acceptable ratio between the under and over predictions. The prediction performance is evaluated fordifferent prediction intervals. Furthermore the present model is also compared with the persistence model and the relative performance isquantified.� 2011 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Tropospheric propagation; Rain attenuation; Neural network; Adaptive learning; Fade mitigation

1. Introduction

1.1. Problem statement

The telecommunication market is experiencing an everincreasing demand of multimedia services by different endusers. Multimedia services require high data rate transmis-sion and to fulfil such needs, higher frequency bandwidthsare required. The presently popular satellite communicationradio frequency bands below 10 GHz being densely popu-lated, satellite communication channels, need to be shifted

0273-1177/$36.00 � 2011 COSPAR. Published by Elsevier Ltd. All rights rese

doi:10.1016/j.asr.2011.10.010

⇑ Corresponding author. Address: ACTD, ADCTG, SNAA, Bldg. No.24, Room No. 15, Space Applications Centre, ISRO, Ambawadi Vistar,Ahmedabad 380015, Gujarat, India. Tel.: +91 7926912415; fax: +917926915808.

E-mail address: bijoy_81@yahoo.co.in (B. Roy).

to the higher bands like Ku/Ka band (12–40 GHz), V band(40–75 GHz) or EHF band (30–300 GHz), to meet futuresatellite communication requirements. The atmosphericeffect of rain and other tropospheric elements increases withincreasing frequency. So the satellite signals above 10 GHzare severely attenuated by the tropospheric elements includ-ing rain. Unlike other regions, the effect is more severe intropical regions like India, where the rain is not only ofdiversified characteristics but also very high in both volumeand intensity. Therefore, the signals even in Ku band fre-quencies are severely attenuated. Attenuation more than10 dB has also been observed here in Ku band (Maitraet al., 2007). So, unlike the lower frequency bands, the satel-lite signals in both Ku and Ka bands are severely attenuatedmostly due to rain and also due to the other troposphericelements like clouds, gases, etc. This attenuation may some-times be so high that it may lead to satellite communication

rved.

B. Roy et al. / Advances in Space Research 49 (2012) 336–350 337

link failure unless properly compensated for. As it is notfeasible to provide adequate static link margin for this,proper Fade Mitigation Techniques (FMT) should beadopted during the period of large attenuation to maintainthe link in satellite communication systems. This is equallytrue for Ka band and as well as for Ku band as far as thetropical region is concerned.

Various standard FMTs are applied depending on theextent of attenuation (Castanet et al., 2002) and are usuallyactuated by a control system. These controllers have theability of detecting and predicting the actual level of totalattenuation in satellite link. Depending upon the predictedattenuation depth, the control system takes a decision andactivates a suitable FMT to compensate the probable loss.These controllers require a finite reaction time for activat-ing the mitigation technique. So, it should have the knowl-edge of the forthcoming attenuation in advance so that thecompensation may take place near simultaneously with thefade. Hence there is a requirement of having the predictionof level of attenuation a-priori that will use the attenuationvalue at time ‘t’ to get its possible value at any future time‘t + dt’. In making attenuation prediction for this purpose,any under-prediction will lead to an under-compensationof fade and may result in a loss of link-availability,whereas, over prediction of attenuation will lead to drain-age of power or resources. To avoid these drawbacks, itis necessary to predict the attenuation as accurately as pos-sible. This puts a hard bound on the prediction algorithmin terms of accuracy.

1.2. Related work

So far the work done on techniques for short term rainattenuation prediction can be broadly categorised intothree classes.

1.2.1. Statistical approach of prediction

Using statistical parameters of rain fade had been apopular method for prediction. Masseng and Bakken(1981) had proposed a dynamic stochastic model of rainattenuation. It was based on the lognormal stationarydistribution of rain attenuation along with a dynamic prop-erty of the model, using which the dynamic rain attenua-tion may be obtained. Results obtained analytically fromthe proposed model showed good correspondence withthe relevant experimental results. Later, Kastamonitiset al. (2003) proposed a model which takes an equi-weighted average of fade slopes over the past samplesand uses it for the prediction of the samples ahead. A sta-tistical approach was taken by van de Kamp (2003) wheretime series for Ku-band and V-band taken from the Olym-pus and ITALSAT satellites were used to generate theprobability of the next sample being at a certain attenua-tion level. A near real time fade prediction algorithm basedon the two sample model was presented by ONERA(Bolea-Alamanac et al., 2003; Van de Kamp, 2002a,b)and found to be performing better than the translation

and fade slope based prediction methods. However thismethod relies on two site-dependent parameters.

1.2.2. Regression based predictor

Regression is another sought out technique for shortterm models. Dossi (1990) proposed a technique where heused a first order linear regression to calculate the fadeslope over previous n samples with an offset added to biasin favour of the most recent sample. Among the relativelyrecent studies, Gremont et al. (1999) developed and com-pared two predictive fade detection algorithms with fixedand variable detection margins for different outage proba-bilities. Prediction is done based on ARMA equation andthe margins were obtained in real time from the statisticsof the prediction error with a moving window. The latterwas found to be more efficient and has lower fixed excessmargin requirement. De Montera et al. (2008) implementeda switching Auto Regressive Integrated Moving Average/Generalized Autoregressive Conditional Heteroscedasticity(ARIMA/GARCH) model for short term fade prediction.This model not only predicted the attenuation level, butalso the conditional error distribution.

1.2.3. Artificial Neural Network (ANN) method

ANN has been extensively used to predict troposphericimpairment. It was used for long term prediction of rainattenuation by Yang et al. (2000). The results show thatapplying the ANN model decreased the mean predictionerror and the RMS error compared to CCIR model. Maly-gin et al. (2002) implemented ANN technique to mitigatesignal fading using a controller, for a VSAT link in whichneural network architecture was deployed for the decisionmaking block of the controller. The controller ultimatelyled to activate adaptive modulation as a fade countermea-sure. Barthes et al. (2006) developed a neural networkmodel for the separation of atmospheric effects onattenuation. Ibrahim (2007) predicted rain attenuation interrestrial point-to-point line of sight links at 97 GHz withANN and results were in very good agreement with exper-imental data. Similarly De Montera et al. (2008) in theirswitching ARIMA/GARCH model deployed ANN to sep-arate the attenuation effects due to gases, clouds and rain,before going for frequency scaling of attenuation fromdownlink frequency to uplink frequency.

Adaptive form of the neural network has been popularlyused in prediction. Chambers and Otung (2005) proposedan ADAptive LInear NEuron (ADALINE) approach toshort term prediction. A single linear neuron with anetwork input of a tapped delay line of three elements wasused. It was demonstrated that in case of fade predictionaccuracy, adaptive filtering methods surpass slope-averag-ing models. More over the ADALINE neural network witha Least-Mean-Square (LMS) recursive weight estimationmethod performed better than an ARMA model with aRecursive Least-Squares (RLS) method.

Later Chambers and Otung (2008) investigated the per-formance of three short term predictors ARMA, statistical

338 B. Roy et al. / Advances in Space Research 49 (2012) 336–350

and ADALINE. They proposed a hybrid predictor com-bining both the ARMA and ADALINE algorithm, basedon current error performance. The hybrid is found to bedependent to some extent on geographical climate or eleva-tion angle.

1.3. Novelty of the current work

The statistical nature of the attenuation is non-station-ary. So, in this paper an artificial neural network with ‘In

situ learning technique’ (Haykin, 1994), which can adaptitself with changing features of the parameters, has beenused for temporal prediction. By the virtue of this speciallearning feature the system learns recurrently from theinput samples, tracking the inherent non stationary fea-tures at real time and thus no initial training of the networkis required. Due to this property, the model may be usedfor different kind of climatic zone rain conditions, as wellas, for varying frequencies and elevations without alteringthe model configuration. The input data to the network isonly attenuation value after removal of scintillation andhigh frequency random components.

Out of all works available to the authors in open litera-ture, the adaptive linear neuron approach by Chambersand Otung (2005) is the closest to this work. But, comparedto the adaptive model proposed by Chambers and Otung,which is linear and with only single level of neuron, thismodel has both linear and nonlinear modules. The pipe-lined recurrent network used here is comprised of two sep-arate modules of juxtaposed non-linear NN subsystems.The linear subsystem is a tapped delay filter with four taps.The non-linear modules being recurrent in nature can carrythe history and modify its weights according to the non-stationary features of the input parameters, which the sys-tem learns from the oncoming input samples. So thechanges in the rain parameters attributing to the attenua-tion, like rain rate, rain slope, etc. as well as the signalparameters like the frequency and elevation angle are welltraced by this predictor due to its in situ learning feature.Hence the model automatically gets tuned to track the var-iation in attenuation due to these parameters and in a wayits performance is independent of them. So, this model canbe used universally without prior training to any conditionand region. This is the novelty of the current work. To val-idate this special feature and to assess the performance, themodel is tested with measured data from different sites hav-ing different system configuration. The results are describedin the subsequent sections.

2. Methodology

2.1. Input data used

We obtained attenuation data in Ku Band, collected atthree different locations in India namely Kolkata at Insti-tute of Radio Physics and Electronics (INRAPHEL),Kharagpur at Indian Institute of Technology (IIT) and

Hassan at Master Control Facility (MCF) for testing ourmethodology. The details of the sites and correspondingsatellites from which the attenuation data are collected isgiven in Table 1. The duration of events taken up for studyare also mentioned in the table. At all the sites the data iscollected at the sampling interval of 5 s.

2.2. Pre-processing of data

The attenuation is obtained from the difference of theinstantaneous measured power recorded by the receiverfrom an ad-hoc reference level representing the clear skycondition. That is a constant value of the signal power, isremoved from the received power to obtain the said attenu-ation. This constant value has been preset a-priori andobtained from the average value of a large numbers of sam-ples of the received signal under no-rain condition. Thus,truly, the obtained attenuation is a relative measurementof the signal power from a fixed pre-defined level. Any vari-ation in the true no-rain level from this fixed reference level isreflected in this case as a variation in the attenuation and istaken care by ANN. However, the prediction added to thisfixed level gives the predicted value of the total signal level.

So apart from the very slowly varying component due tothis variation in the clear-sky level the temporal variationof attenuation thus obtained is composed of two compo-nents, a slow variation which is mostly due to the rain gen-erated attenuation and a fast variation, generally due toscintillations and other high frequency random noise. Toanalyse the contribution of various frequency componentsto the total attenuation the power spectra of signal fluctu-ations during a number of events are observed. Fig. 1shows the spectral density of signal attenuation for twotypical events measured at Kolkata. At lower frequencies,the variations are constituted by true rain attenuation com-ponents. Hence, they are dependent upon the variations inthe individual rain events, which are intrinsically slow.Hence they are different for different events. While, thehigher frequency components, being the manifestations ofthe rapid random fluctuations and noise, they are statisti-cally equal in every event and independent of the constitut-ing rain variations. Hence, they are observed to becongruent and similar for the two events shown in the plot.

The variation in signal due to rain attenuation can bemodelled through proper algorithm but the signal fluctua-tion generated due to high frequency components cannotbe predicted by the model. As the variation due to high fre-quency random component is imposed over the slow vari-ation due to rain, it is required to be removed from thetotal signal before predicting, in order to make proper pre-diction of the slow varying rain attenuation.

The high frequency variation may be removed from themeasured attenuation, thus making the time series smooth.This can be done by considering a moving window of fixedwidth with measured samples within it constituting a leastsquare linear fit of attenuation values. Here, to find thesmoothed value of the nth instant in a causal way, all pre-

Fig. 1. Spectral density of signal attenuation.

Fig. 2. Methodology for smoothening of data.

Table 1Station and data detail over which proposed prediction model is verified.

Sr. no. Station Station location Satellite Satellite location Elevation angle Observation time Frequency (GHz)

1 INRAPHEL, Kolkata 22�34’ N 88�29’ E NSS-6 95�E 63� July–Aug. 2004 11.1722 IIT, Kharagpur 22�32’ N 88�31’ E INSAT 4CR 74�E 59� Sep.-2009 11.6993 MCF, Hassan 13�00’ N 76�05’ E INSAT 3B 83�E 73� Sep.-2004 11.544

B. Roy et al. / Advances in Space Research 49 (2012) 336–350 339

vious samples up to 1 m is taken and a linear curve isobtained using least square fit. The curve value at the lastsample, i.e. at the nth instant, vs

N is considered as thesmoothed value at that instant. To obtain the smoothedvalue at the next sample instant, i.e. (n + 1)th instant,vs

Nþ1 the same procedure is followed while the windowshifts by one sample. In this way, the smoothing process,using samples of previous instances only, remains causal.As a fixed order curve is required to be generated only, itis also convenient for use in real time. It is required to benoted that, as at every sample instant, as the window shiftsby one sample step, the oldest data from the previous win-dow is excluded and the latest measured data is included.Hence the slope is accordingly modified at every samplinginstant. So, although the window is of fixed width of 1 minterval, the slope changes with every sampling step. Themethodology of the smoothing process is explained inFig. 2.

The total attenuation, smoothed attenuation and thehigh frequency random components separated from datafor three different stations are shown in Fig. 3.

Using the proposed algorithm of the ANN Technique,the prediction is done for the smoothed attenuation. Thedetails of prediction algorithm are given in Sections 2.3to 2.5. The predicted attenuation will differ from the origi-nal smoothed attenuation due to the prediction error of theANN technique. The prediction is carried out for three dif-ferent intervals of 5, 10 and 20 s.

The prediction error is then analysed to obtain its statis-tical nature. Once the distribution of prediction error isacquired, suitable margin is derived from it and is addedto the predicted value of attenuation in order to compen-sate the prediction error and to eliminate any under predic-tion. The details are given in Sections 3.1 and 3.2. In thisway modified predicted value of smoothed rain attenuationis obtained.

2.3. Basic principles of adaptive neural network with in situ

learning

Rain attenuation varies in a very complex manner withthe rain intensity and as well as the elements like the loca-tion, elevation angle, polarization, etc. in addition to itsnatural variation with frequency. In the Indian tropicalregion, where the rain features are conspicuous and diver-sified, the rain characteristics show considerable variationsover time and space. The attenuation at any fixed locationalso shows large statistical variations. So, for prediction ofthe attenuation, it is required that the NN must adapt tosuch statistical variations by learning from the incomingtime series, along with simultaneous prediction. Real timerecurrent network are suitable for this kind of predictionas they can adapt to such statistical variations by learningfrom the incoming time series, along with simultaneousprediction process. But the number of neurons required isoften very large which increases the computation complex-ity. Use of a pipelined structure can alternatively serve therequirement of large numbers of neurons for this purpose.Such an adaptive predictor consists of a non-linear subsys-tem followed by a linear one. The non-linear subsystem is apipelined recurrent network with a number of modules. Itrecurrently holds the history and identifies the changes inparameters from the oncoming samples. Consequently, itmodifies its weights to accommodate the non-stationaryfeatures of the input parameters and hence in situ learning

Fig. 3. Total attenuation, smoothed variation and the high frequency random components for locations at (a) INRAPHEL, (b) IIT and (c) MCF.

340 B. Roy et al. / Advances in Space Research 49 (2012) 336–350

is achieved. The linear part consists of a tapped delay filter.The non-linear part provides an approximate predictionwhich is later fine tuned by the linear subsystem. Herethe pipelined recurrent network used in the non-linear sub-system is composed of two modules, Module-1 and Mod-ule-2 as shown in Fig. 4. The linear subsystem as shownin Fig. 5 is a tapped delay filter with four taps. We first dis-cuss, in general terms, the building blocks of the AdaptiveRecurrent Neural Network.

2.4. Non-linear recurrent neural network

The present section will describe the basic principle ofthe adaptive recurrent non-linear NN. Fig. 4 shows thearchitecture of the same which consists of a pipelinedrecurrent structure. As per the figure, it is made up oftwo modules, viz. Module-1 and Module-2, juxtaposed ina manner such that the output of Module-2 is used as aninput to Module-1. Both of the modules carry a single neu-ron with synaptic weights at each individual input and witha nonlinear activation function. Each module of the net-work receives two sets of attenuation values as input.

One set consists of four most recent past samples of mea-sured attenuation and the other of predicted attenuation.Since the variations in the influencing factors controllingthe attenuation are already included in the history pro-vided, they are not supplied individually as separate inputs.

The inputs are the samples of attenuation obtained atdefinite and distinct sampling instants. For convenience,the time instant just before the sampled value of time ‘t’is obtained will be denoted as (t)� and that just afterobtaining the sampled value as (t)+. We also denote thevalue of a variable n present at any node in the time inter-val (t � 1)+ to (t)� as n(t � 1).

The system should predict the attenuation of the instantt, i.e. A(t), lying in the time interval between instant(t � 1)+ to instant (t)�. At this instant of (t � 1)+, an arrayof four most recent measured attenuation values forms thefirst set of input to Module-1 which is represented as vectorX1(t � 1) given by:

X1ðt � 1Þ ¼ ½Aðt � 1Þ;Aðt � 2Þ;Aðt � 3Þ;Aðt � 4Þ�T

¼ Aðt � 1� jjj ¼ 0; 1; 2; 3Þ; ð1aÞ

Fig. 4. Architecture of the non-linear part of the adaptive recurrent network.

Fig. 5. Architecture of the linear part of the adaptive recurrent network.

B. Roy et al. / Advances in Space Research 49 (2012) 336–350 341

where A(s) is the measured value of attenuation at the in-stant s.

For Module-2 the corresponding input is a delayed ver-sion of the input in Module-1. So, at the present instant of(t � 1)+ this input is X2(t � 1), given by:

X2ðt � 1Þ ¼ Aðt � 2Þ;Aðt � 3Þ;Aðt � 4Þ;Aðt � 5Þ½ �T

¼ Aðt � 1� jjj ¼ 1; 2; 3; 4Þ¼ Z�1fX1ðt � 2Þg� �

: ð1bÞ

Similar set of predicted attenuation input are providedto Module-1 and Module-2 in addition to the set of mea-sured attenuation. At the instant (t � 1)+, the latest infor-mation to the input of Module-2 is that of theattenuation at (t � 2) and its output predicts the value ofthe attenuation at the next instant, i.e. A(t � 1). At thisinstant the set of predicted input to Module-1 is the arrayof four most recent attenuation values predicted by Mod-ule-2. This can be represented by vector Y1(t � 1) and givenas

Y 1ðt � 1Þ ¼ ½A2ðt � 1Þ; A2ðt � 2Þ; A2ðt � 3Þ; A2ðt � 4Þ�¼ A2ðt � 1� jjj ¼ 0; 1; 2; 3Þ;

where, Ak(s) is the predicted value of the attenuation byModule-k for instant s.

A delayed version of this input forms the correspondingpredicted input to Module-2. So, at this instant of (t � 1)+

this input is Y2(t � 1) and is given by:

Y 2ðt � 1Þ ¼ ½A2ðt � 2Þ; A2ðt � 3Þ; A2ðt � 4Þ; A2ðt � 5Þ�¼ A2ðt � 1� jjj ¼ 1; 2; 3; 4Þ¼ ½Z�1fY 2ðt � 2Þg�:

Therefore, the general expression for the input to Module-kat instant s can be represented as

I kðsÞ ¼ ½XkðsÞ; YkðsÞ�;where

XkðsÞ ¼ Aðs� ½k � 1� � jjj ¼ 0; 1; 2; 3Þ and Y kðsÞ¼ Akðs� ½k � 1� � jjj ¼ 0; 1; 2; 3Þ:

Each input is multiplied with the corresponding synapticweights. At first, these weights are kept identical and dur-ing the learning process they subsequently alter themselves.These weighted inputs are added together and provided asthe total input to the respective neuron. So, the total inputvk (t � 1) to the neuron in the kth module at this instant is;

vkðt � 1Þ ¼ wkðt � 1Þ � I kðt � 1Þ ¼ wkðt � 1Þ � ½Xkðt � 1Þ;Y kðt � 1Þ� ¼ 3

Xj¼0

fwk;jðt � 1ÞAkðt � 1� j� ½k � 1�Þg

þ fwk;jþ4ðt � 1ÞAkðt � 1� j� ½k � 1�Þg k ¼ 1; 2;

ð2Þ

where, wk(s) = [wk,0 wk,1 wk,2 � � � wk,7]|s is the input synapticweight vector for the neuron in module k at instant s.

The output of kth module at any instant (t � 1)+ is givenby:

ykðt � 1Þ ¼ f fvkðt � 1Þg ¼ Akðt � ½k � 1�Þ: ð3ÞHere, ‘f’ is the activation function for that module. In thepresent model, a log-sigmoid activation function is usedin both the modules and is defined as

f ðxÞ ¼ 1=f1þ expð�xÞg: ð4ÞAt this instant, the out put y1 (t � 1) from Module-1 is thepredicted value of attenuation of instant t, i.e. bA1ðtÞ. Thisprediction is then passed on to the linear section for further

342 B. Roy et al. / Advances in Space Research 49 (2012) 336–350

tuning of the prediction values in the way as discussed laterin the Section 2.5.

Let us now, discuss the process by which the non-linearmodel tunes itself for the next prediction. At instant (t)+,the true measurement of the variable A(t) is available.Hence at first, the error of the non-linear prediction atthe output of each module is calculated from the differencein the predicted and the measured values. So,

ekðtÞ ¼ Aðt � ½k � 1�Þ � ykðt � 1Þ; ð5Þ

where, k is the module number and yk(t � 1) is the value ofattenuation predicted by the kth module at instant (t � 1)+.

After every sampling and before the next predictionweight matrices are modified using the error signals. Mod-ification of weights are done in the way to minimize thecost function given by,

EðtÞ ¼ k1fe2ðtÞg2 þ k0fe1ðtÞg2; ð6Þ

where k is an exponential forgetting factor that lies in therange 0 < k < 1. A very low value of k is used when thesamples are highly uncorrelated and hence the last set ofdata has very low significance in prediction at the currentinstant. Whereas, a very high k is attributed for cases whenthe samples are highly correlated over time and hence lastset of data has a very significance in predicting at the cur-rent instant. Here as the attenuation correlation over timeassumes a moderate value, a moderate value of k = 0.5 hasbeen taken here for forgetting factor.

The weights get modified after every sampling instant sby an amount Dwk(s). The method of modification isdescribed in Haykin (1994) and is carried out in the follow-ing manner. The weights of Module-1 only influence theerror e1. Therefore,

Dw1ðtÞ ¼ 2k0le1ðtÞf 01I1ðt � 1Þ: ð7Þ

But, the weights of Module-2 affect both e1 and e2. So,

Dw2ðtÞ ¼ 2k1le2ðtÞf 02I2ðt � 1Þ þ 2k0le1ðtÞf 01f 02I2ðt � 1Þ: ð8Þ

Here, l is the learning factor of the network and f 0k is thederivative of the activation function f of module ‘k’. Themagnitude of the learning factor determines the rapiditywith which the system converges. But keeping a very high va-lue of this parameter may result in oscillation of the output.Here, we have empirically selected the value of l, such thatthe output does not show any oscillation and at the sametime it is considerably high for obtaining quick convergence.

Using the causality relation, we have assumed that theweights of instant ‘s � 1’ are not affected by the weightsof instant ‘s’. Thus the modified weight for the next instantwill be,

wkðtÞ ¼ wkðt � 1Þ þ DwkðtÞ: ð9Þ

For the recurrent pipe line network used in this work, theforgetting factor k is set to 0.5 and the learning factor to0.1.

Once the weights are modified at instant (t)+ the systemis then tuned for the next prediction. At this instant (t)+,

the input data is shifted in such a way that now the inputto the modules are

IkðtÞ ¼ ½Aðt � ½k � 1� � jjj ¼ 0; 1; 2; 3Þ; Aðt � ½k � 1� � jjj¼ 0; 1; 2; 3Þ�:

The output of Module-1 is y1(t) which is the predicted va-lue of attenuation of instant (t + 1), i.e. A (t + 1).

After each prediction of the nonlinear modules, the finalpredicted output y1 is passed to the linear part of thesystem.

2.5. The linear tapped delay filter

The output of the recurrent network forms the input tothe tapped delay filter. Here at the instant (t � 1)+, theinput vector Y(t � 1) is constituted by the most recent fourpredicted values at the output of Module-1 of the non-lin-ear section. So,

Yðt � 1Þ ¼ ½y1ðt � 1Þ; y1ðt � 2Þ; y1ðt � 3Þ; y1ðt � 4Þ�¼ ½A1ðtÞ; A1ðt � 1Þ; A1ðt � 2Þ; A1ðt � 3Þ�: ð10Þ

Each element of the input vector is first multiplied with cor-responding element of tapping weight vector w(t � 1) = [w0 w1 w2 w3]|t � 1 and then added to predict thevalue of A (t). So, the predicted value of A (t), i.e. A (t), pre-dicted by the linear part at instant ‘(t � 1)+’ is given byp(t � 1), where,

pðt � 1Þ ¼ wðt � 1ÞYðt � 1Þ ¼ AðtÞ: ð11Þ

Fig. 5 represents a schematic of the linear network used inthe prediction process, showing the inputs, output and thetap delays. The tapped delay filter used in this work con-sists of four taps.

At the next instant, t, when the value of A(t) is mea-sured, the error at the out put of the linear filter is calcu-lated as

elðtÞ ¼ AðtÞ � pðt � 1Þ ¼ AðtÞ � AðtÞ: ð12Þ

Weights are modified with the error value using the LeastMean Square (LMS) technique. The LMS algorithm mini-mizes an instantaneous estimate of the overall cost functionE ¼ 1=2

Pe2

l , at any specific iteration ‘n’. This is unlike thesteepest descent method that minimizes the sum of thesquares of errors integrated over all previous iterations ofthe algorithm up to and including iteration n. So, ifDw(t) is the corresponding change in the weight vector,the new weights become

wðtÞ ¼ wðt � 1Þ þ DwðtÞ: ð13Þ

This new weight is used with the corresponding input Y (t)for the purpose of predicting p(t) = A (t + 1). The pipelinedrecurrent network does a global minimisation of the errorand thus the first level of prediction is achieved. Whereasthe tapped delay filter gives a fine-tuning to the predictedvalue with the virtue of local minimisation (Haykin,

B. Roy et al. / Advances in Space Research 49 (2012) 336–350 343

1994). The final output at instant ‘t’, i.e. the prediction ofthe attenuation value A (t + 1), is obtained as p(t) at theoutput of the linear section.

3. Results and discussion

With the above methodology, short term prediction ofsmoothed attenuation was performed over a number ofevents at three different stations. Two basic characteristicsof the prediction algorithm are explored. Firstly the modelshould provide minimum numbers of under prediction ofattenuation to avoid any loss of lock and secondly the overpredictions should be such that the excess power predictedfor compensation, over the actual exact amount requiredjust to counterbalance the attenuation, is optimal. In thefollowing sub-sections results of the prediction model arepresented to evaluate its performance against above twocharacteristics. Further to observe the variation in perfor-mance with changing prediction interval, the prediction isdone for 5, 10 and 20 s intervals.

The performance of the proposed model is also com-pared with an existing short term prediction model. Here‘persistence model’ has been considered for comparison

Fig. 6. Predicted and observed smoothed attenuation with 5 s prediction inter

and all above mentioned criteria are also verified for thesame.

A term has been defined to quantify the relative perfor-mance of the proposed model to the persistence model. Thedetailed comparison and inferences drawn from the resultsare discussed in the following sub-sections.

3.1. Prediction of smoothed rain attenuation

At first step the model estimation accuracy is observedduring predicting the smoothed attenuation value of agiven event. The ANN-ILA based prediction plot ofsmoothed attenuation for the selected three events, fromthree different sites are shown in Fig. 6. Here predictionis carried out at every 5 s interval. Both observed smoothedattenuation and the predictions are shown. Similar predic-tion plots for 10 and 20 s prediction interval are given inFigs. 7 and 8, respectively.

As observed from the plots, the ANN requires few initialsamples for convergence. The required numbers of suchsamples are different for different events. Once the conver-gence is obtained, the subsequent samples are well trackedand the prediction error reduces. The deviation of pre-dicted value from the observed value is found to increase

val, for three different locations at (a) INRAPHEL, (b) IIT and (c) MCF.

Fig. 7. Predicted and observed smoothed attenuation with 10 s prediction interval, for three different locations at (a) INRAPHEL, (b) IIT and (c) MCF.

344 B. Roy et al. / Advances in Space Research 49 (2012) 336–350

on increasing the prediction interval. In certain cases theprediction is found to overshoot and undershoot withsharp changes in slopes. Besides, typically, the errors werefound to be proportional to the absolute value of the atten-uation. So instead of absolute error, the relative predictionerrors were analysed.

The relative prediction error er, is defined as

er ¼ ðeo � epÞ=eo; ð14Þ

where eo is the observed attenuation and ep is the predictedattenuation.The PDF of the collective relative predictionerror for all the stations are shown in Fig. 9. The stationwise relative error statistics for three different predictionintervals is given in Table 2.

Observing the mean values of relative error in Table 2,it can be inferred that for 5 s prediction interval, predic-tion is fairly unbiased at INRAPHEL (Kolkata) and IIT(Kharagpur) but performance deteriorates at MCF (Has-san). On increasing the prediction interval to 10 and 20 sthe performance remains consistent at INRAPHEL andIIT, while it continues to deteriorate at MCF. The stan-dard deviation values for 5 s prediction interval indicatethat the predictor has consistent confidence on relative

prediction error at all the three stations. With increasingthe prediction interval an increase in standard deviationis observed.

The relative error probability distributions shown inFig. 9 are Gaussian like but with a longer tail. The longertail of the distribution curve arises due to large predictionerror at instants when the attenuation slope changesabruptly. At these points the model adapts to the changeafter a small latency period.

As discussed earlier two main feature of the model per-formance to be observed are the excess power lost per stepdue to over prediction and the percent of under predictionfor best conditions, both of the parameters should as lowas possible. The product of these two parameters namedas Performance-index ‘g’, quantifies the performance interms of the desired objective. So, lower this product betteris the performance. Hence, it is defined as

g ¼ Loss per stepðdBÞ �Under Prediction Percentage:

ð15Þ

To quantify the advantage of the proposed ANN modelover any other model taken as reference, we define a term‘Relative Performance Index (RPI)’ as below

Fig. 8. Predicted and observed smoothed attenuation with 20 s prediction interval, for three different locations at (a) INRAPHEL, (b) IIT and (c) MCF.

B. Roy et al. / Advances in Space Research 49 (2012) 336–350 345

RPI ¼ 10 � log10ðgReference Model=gANN-ILA ModelÞ: ð16Þ

The value of this term is indicative of the advantage ob-tained by using the proposed model over any referencemodel. RPI increases where the proposed ANN model per-forms better than the reference one. The persistence modelis taken as reference in our case. This definition is consis-tent for all cases except for conditions where any of theconstituting components turns trivial, when the RPI be-comes undefined. These three parameters, viz. the LossPer Step (LPS), Under Prediction Percentage (UPP) andthe Performance index (g) for these two models are pre-sented in Table 3, for different prediction interval and atall the three locations. As the prediction interval is in-creased the g increases slowly showing that the model per-formance deteriorates gradually with increase in predictioninterval. The same parameters for the persistence modelhave also been given in the Table 3 for comparison. Thepersistence model assumes that the observed value of atten-uation at the instant ‘t’ will prevail up to time ‘t + 1’. So thepredicted attenuation at time‘t + 1’ is nothing but mea-sured attenuation on time ‘t’ or A (t + 1) = A (t). The

RPI value given in Table 3 is observed to increase with in-crease in prediction interval, which means that the relativeperformance of proposed ANN model gets better than thepersistence model with increasing prediction interval.

For 5 s prediction interval it can be seen from Table 3that performance index (g) has lower value for persistencethan ANN model at all the sites. This means that the over-all performance of the persistence model is better than theANN model at prediction interval of 5 s. During 10 s inter-val, value of g for both the models is comparable atINRAPHEL and MCF, while at IIT it is higher for persis-tence. Considering 20 s prediction interval, at all the sitesthe persistence model gives very high value of figure ofmerit than the proposed ANN model. The variation of gwith prediction interval suggests that persistence modelperforms better than proposed model at lower predictioninterval. But as the prediction interval increases, the perfor-mance of the proposed ANN model improved compared tothat of persistence. At the higher intervals of 20 s the pro-posed ANN model gives better results than persistence.The better performance of the proposed ANN model overpersistence at 20 s makes it useful for prediction applica-

Table 2Station wise relative prediction error statistics at different prediction intervals.

Station Average relative error Standard deviation of relative error Relative error value for 95% containment

5 s 10 s 20 s 5 s 10 s 20 s 5 s 10 s 20 s

INRAPHEL 0.001 �0.004 �0.008 0.107 0.128 0.159 0.148 0.171 0.194IIT 0.006 0.011 0.012 0.100 0.116 0.144 0.175 0.199 0.215MCF �0.029 �0.037 �0.060 0.154 0.176 0.208 0.173 0.209 0.216

Fig. 9. Relative prediction error probability distribution for three different locations at (a) INRAPHEL, (b) IIT and (c) MCF.

346 B. Roy et al. / Advances in Space Research 49 (2012) 336–350

tion at such prediction intervals. Therefore at 20 s predic-tion interval the performance of the proposed ANN andpersistence models are compared under different predictionerror compensation techniques. This is discussed in nextsection.

3.2. Compensation of prediction error

The prediction error may lead to either under predictionor over prediction. As the control loop in a FMT activatesthe suitable mitigation technique depending on the pre-

dicted fade, any over prediction will result in drainage ofresources, while the under prediction may lead to loss oflink. So ideally the predictor should predict the attenuationwith no under-prediction and with minimum over-predic-tion, as well.

The next issue is reducing the number of under predic-tions. In order to design our predictor such that it onlyhas 5% chance of under-prediction, we find the value ofthe relative error in the distribution that accommodates95% of the errors and leaves only 5% of the total errorbeyond it in the error distribution tail. The corresponding

Table 3Event wise power loss per step, percent of under prediction, performance index and relative performance index for 5, 10 and 20 s prediction interval.

Stations Performance parameters Prediction interval

5 s 10 s 20 s

ANN-ILA Persistence ANN-ILA Persistence ANN-ILA Persistence

INRAPHEL LPS (dB) 0.046 0.038 0.051 0.072 0.058 0.130UPP 59.424 48.715 61.247 47.520 63.954 47.412g (dB) 2.717 1.852 3.115 3.414 3.712 6.160RPI(dB) �1.665 0.398 2.200

IIT LPS (dB) 0.188 0.146 0.216 0.295 0.242 0.481UPP 54.326 50.000 61.157 53.414 59.130 50.000g (dB) 10.183 7.317 13.198 15.768 14.279 24.045RPI(dB) �1.435 0.773 2.263

MCF LPS (dB) 0.081 0.069 0.117 0.119 0.169 0.219UPP 47.256 49.288 46.455 47.516 48.708 47.955g (dB) 3.816 3.400 5.414 5.672 8.216 10.478RPI(dB) �0.501 0.202 1.056

B. Roy et al. / Advances in Space Research 49 (2012) 336–350 347

error values are already given in Table 2. It is observedhere for a definite prediction interval the value is consis-tent for all the stations considered. This forms the basisof the prediction error compensation technique used hereand discussed in this section. From this table we candeduce that for prediction interval of 20 s, 95% of the

Fig. 10. Predicted and observed attenuation after appending the bound f

relative errors remain below 0.25, irrespective of thelocation.

The required compensation may be done by adding suitablemargin to the predicted value in two different approaches asdescribed below. The performance after each approach is eval-uated for both ANN-ILA and persistence model.

or three different locations at (a) INRAPHEL, (b) IIT and (c) MCF.

Table 4Event wise power loss per step, percent of under prediction, performance index and relative performance index with and without power margins at 20 sprediction interval for ANN and persistence models.

Stations Performance parameters Without margin With estimated margin With quantized margin

ANN-ILA Persistence ANN-ILA Persistence ANN-ILA Persistence

INRAPHEL LPS (dB) 0.058 0.130 0.304 0.357 0.803 0.855UPP 63.954 47.412 0.581 6.452 0.000 2.151g (dB) 3.712 6.160 0.177 2.301 0.000 1.839RPI(dB) 2.200 11.139 Undefined

IIT LPS (dB) 0.242 0.481 1.230 1.339 1.760 1.840UPP 59.130 50.000 2.609 4.918 1.739 4.098g (dB) 14.279 24.045 3.209 6.583 3.061 7.540RPI(dB) 2.263 3.121 3.915

MCF LPS (dB) 0.169 0.219 0.742 0.749 1.193 1.182UPP 48.708 47.955 3.579 7.435 0.596 1.301g (dB) 8.216 10.478 2.657 5.569 0.712 1.538RPI(dB) 1.056 3.214 3.345

348 B. Roy et al. / Advances in Space Research 49 (2012) 336–350

3.2.1. Addition of fixed relative error bound to predicted

attenuation

As per the values obtained in Table 2 and the inferencedrawn in Section 3.1, 95% of the possible prediction errorsremain bound within a fixed relative margin which is 0.25for 20 s interval of predictions. This forms the basis foradding a multiple of predicted attenuation to the predictedvalue to compensate the prediction error. Thus in the firstmethod, with 20 s prediction interval, an absolute compen-sation value is added to the prediction at every instantwhich is 0.25% of the predicted value of that instant. Hereit is worthy to note that the distribution of the relativeerrors were obtained by normalising the prediction errorswith the true values of attenuation from which the marginto be added was set. Whereas, during compensating theprediction error, this bound value is multiplied with thepredicted value instead. This may lead to prediction errorat certain instants in spite of bound addition. The additionof the bound is supposed to accommodate 95% of all pos-sible prediction errors and minimize the under predictionsto 5%, irrespective of location. Fig. 10 shows the effect ofadding bound to the predicted attenuation value and thecomparison of the predicted value with actual attenuation,for 20 s prediction interval. The effect of margin addition toprediction performance of the proposed ANN and persis-tence model is provided and compared in Table 4. It givesthe value of power loss per step, percent of under predic-tions and performance index without and with additionof margin. For all calculations first 9 samples are ignoredfor each event, since steady-state performance is of greaterinterest. The RPI value of the proposed ANN model overthe persistence one is also provided in Table 4.

It is seen that the addition of bound to ANN predictedattenuation value satisfactorily covered the attenuation.The power margin appended has become useful in over-coming the under prediction of attenuation even duringthe steep rise in the attenuation. But this also leads toexcess power drainage due to over prediction at certaintime. The decrease in performance index suggests that all

together the prediction performance has been improved.It is because the extent to which under prediction isreduced is more than the extent to which power loss hasincreased.

In the case of persistence model improvement of predic-tion performance on addition of power margin is evidentfrom decrease in the performance index value. But whencompared to corresponding values for the proposedANN model the performance index in persistence case ismuch greater than those of the proposed model. Hence afurther advantage is obtained in proposed model as com-pared to persistence one on appending the power margin.This point is also evident from Fig. 11, showing variationof the power loss by step function of the under predictionfor different kind of margins on proposed ANN and persis-tence models.

3.2.2. Quantisation of predicted value after adding fixed

relative error bound

In a FMT control loop used in all pragmatic systems, itis impractical to add compensation which is varying in acontinuous manner. So, typically it does the attenuationcompensation by adding margins in pre-defined quantainstead. Therefore, in the second approach, we set the inte-gral values of attenuation as our discrete quantum levels ofmargin. So, instead of adding the exact values of the sum ofthe prediction and the prediction error compensation, thisvalue is first raised to its nearest integer ceiling to achievethe quantum level. This level is then taken as the total mar-gin for attenuation compensation. Here, similar to the firstmethod the prediction error compensation is derived bymultiplying the relative error bound with the predictedvalue. The implication of this modification is shown inthe last block of Table 4. The power loss per step is calcu-lated for each event and the percent of under predictions isalso recorded. It is evident from Table 4 that there is a fur-ther decrease in the percent of under prediction but evi-dently at the same time power loss per step shows asimultaneous increase. But again the decrease in perfor-

Fig. 11. Power loss as a step function of the under prediction for different kind of margins on ANN and persistence models at three different locations viz.(a) INRAPHEL, (b) IIT and (c) MCF.

B. Roy et al. / Advances in Space Research 49 (2012) 336–350 349

mance index reflects further improvement in prediction effi-ciency. Again as observed in earlier case, the improvementin the model performance, on applying quantised margin,is more pronounced in ANN model than its persistencecounter part.

This fact is well supported by the values of RPI for theproposed ANN model and presented in Table 4. It givesthe variation of model advantage for proposed model forprediction without any margin and with two differentapproaches for adding margins for all the sites. Theincreasing value of RPI suggests that degree of improve-ment in model performance is more for ANN-ILA thanpersistence, when similar power margins are applied.

4. Conclusions

The proposed Adaptive Artificial Neural Networkdeveloped in this paper with ILA has shown quite signifi-cant accuracy while predicting the short term attenuationvalues with the limited Ku band data obtained from threestations at INRAPHEL (Kolkata), IIT (Kharagpur) and

MCF (Hassan). It has been found that the accuracy deteri-orates with prediction interval but remains bound withinan acceptable range. When compared with the persistencemodel, it is found to perform better at higher predictionintervals. The model even over-performs the persistencemodel when equivalent compensations are added to eachof them.

The main limitation of this method is that it is presentlypredicting the slowly varying attenuation and the scintilla-tion effect is not predicted. So, for complete prediction nec-essary in a FMT control loop, it is required to addprovision in the model to predict the probable scintillationeffect. Another concern of the existing model is the consid-erable power lost per step when fixed margin are added tocompensate prediction error. As a further study the modelcan be modified by adding a variable margin to the pre-dicted value in an adaptive manner to reduce the excessover bound leading to drainage of recourses. This will alsoeventually help in judiciously managing the mitigationresources by the mitigation control loop. It has beenplanned to extend this study for Ka band signals.

350 B. Roy et al. / Advances in Space Research 49 (2012) 336–350

Acknowledgements

We extend our heartfelt gratitude to INRAPHEL-Uni-versity of Calcutta, IIT-Kharagpur and MCF-Hassan forproviding the attenuation data for Ku band.

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