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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 1, JANUARY 2006

Diversity Improvement Estimation From Rain Radar Databases Using Maximum Likelihood Estimation Kevin S. Paulson, Robert J. Watson, and Isa S. Usman

Abstract—This research examines route diversity as a fade mitigation technique in the presence of rain, for terrestrial microwave links. The improvement in availability due to diversity depends upon the complex spatio-temporal properties of rainfall. To produce a general model to predict the advantage due to route diversity it is necessary to be able to predict the correlation of rain attenuation on arbitrary pairs of microwave links. This is achieved by examination of a database of radar derived rain rate fields. Given a representative sample of rain field images, the joint rain attenuation statistics of arbitrary configurations of terrestrial links can be estimated. Existing rain field databases often yield very small numbers of high joint attenuation events. Consequently, estimates of the probability of joint high attenuation events derived from ratios of the number of occurrences can be highly inaccurate. This paper assumes that pairs of terrestrial microwave links have joint rain attenuation distributions that are bi-lognormally distributed. Four of the five distribution parameters can be estimated from ITU-R models. A maximum likelihood estimation (MLE) method is used to estimate the fifth parameter, i.e., the covariance or correlation. The predicted diversity statistics vary smoothly and yield plausible extrapolations into low probability situations. Index Terms—Availability, diversity methods, millimeter wave radio propagation meteorological factors.

I. INTRODUCTION

T

ERRESTRIAL microwave telecommunications links experience attenuation due to rain and this occasionally leads to outage. Traditionally, links are specified to have an outage period caused by rain fading not exceeding some small percentage of an average year, usually 0.01% or 0.1% of time, and the rain fade margin is built into the link budget by estimating the rain attenuation exceeded for this time. Many models exist to perform this calculation, e.g., COST235 [1], Rec. ITU-R P.530-10 [2] and Rec. ITU-R P.837-4 [5]. These models are adequate for individual links but provide only limited guidance on the performance of networks, e.g., Rec. ITU-R P.530-10 provides some guidance for more complex links such as multi-hop links and links utilising route diversity. Rec. ITU-R P.1410-2 [3] also provides some guidance for point-to-multipoint cellular systems. When a point in a network requires high availability, it is often more spectrum efficient to install multiple links to that

Manuscript received May 23, 2005; revised July 19, 2005. K. S. Paulson is with the Department of Engineering, University of Hull, Kingston Upon Hull, HU6 7RX, U.K. (e-mail: [email protected]). R. J. Watson and I. S. Usman are with the Department of Electronic and Electrical Engineering, University of Bath, Bath BA2 7AY, U.K. (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2005.861571

point rather than using higher transmit power on a single connection. The simplest case of diversity is a point connected to a network by two independent links. These links may operate at different frequencies and polarizations and will generally have different fade margins. In the case of route diversity, the links connect to two different points in the network and so operate along different paths. This scenario is primarily parameterized by the length, frequency, polarization and fade margin of each link and the azimuth angle between the two links where they converge at the point being serviced Other parameters include the link altitudes and inclinations, the integration time of fade measurements and many parameters describing the climate. A second scenario utilising route diversity is in cellular point-to-multipoint distribution systems, e.g., LMDS systems, Seidel [4]. These systems can be used to distribute telephony, TV and broadband access in dense urban areas. A user situated near the border of cells, will increase availability by linking to two or more base stations. Mesh systems, where nodes pass information between each other to extend network coverage, will generally have multiple routes between pairs of nodes and so are inherently route diverse. Route diversity increases availability, as when one link has failed due to rain attenuation the other may still be operational. The increase in availability is quantified using the diversity improvement (DI) or diversity gain (DG) factors, see Section V. The higher the correlation of rain attenuation on the two links, the lower the advantage from using diversity, as the failure of one link becomes an increasingly better predictor of the failure of the other link. This correlation is determined by the geometry of the link system and the spatial-temporal statistics of rain intensity. The development of DI models directly from link measurements is infeasible due to the large number of scenario parameters and the expense of setting-up and running each link combination. Spatial-temporal models of rain rate variation exists and have been applied to DI estimation, e.g., Paulson [7], [8], however the models have limited application as they do not describe rain no-rain boundaries and do not include important climatological parameters such as relative incidence of stratiform and convective rain. The method used in this paper is the examination of a database of rain radar measurements. Each rain radar measurement yields rain rate, averaged over a volume, at each point on a polar grid centered on the radar. The rain rate measurements can be converted into rain specific attenuation, , using Rec. ITU-R P.838-2. The instantaneous rain attenuation experienced on a terrestrial, microwave link may then be estimated

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PAULSON et al.: DIVERSITY IMPROVEMENT ESTIMATION FROM RAIN RADAR DATABASES USING MAXIMUM LIKELIHOOD ESTIMATION

by pseudo-integration of the rain specific attenuation along the link [10]. Radar images may be used to estimate the instantaneous, joint rain attenuation experienced by arbitrary configurations of links lying within the imaged area. By translating and rotating the link network within the geographical limits of the measured rain fields, a large number of joint link attenuations can be derived. If a large database of radar images is an unbiased sample of the rain field population experienced by a region, then the sample of joint attenuations may be used to estimate the joint attenuation distribution. Although the number of network simulations may be very large, the accuracy of derived probabilities is limited by the number of rain events measured. Even for a large database, there may be a small number of specific classes of event, e.g., stratiform or convective, sufficiently intense to cause outage. Databases of radar images have been constructed to provide adequate sampling statistics for individual link attenuation events exceeded 0.01% of the time, e.g., the CRIE database (see Section II) and ExCell [12]. However, for the diversity cases of most interest where the link attenuation correlation is low, the number of extreme joint attenuation events is unlikely to be adequate for probability estimation. Two independent links would experience their 0.01% exceeded rain attenuation only 0.000 001% of the time. Even for an individual link, there are likely to be no measured events yielding extreme link attenuations with average annual occurrences less than 0.001% of time. This paper assumes that pairs of links have joint attenuation distributions that are bi-lognormally distributed. The five parameters of the bi-lognormal distribution can be estimated using all the joint attenuation data, not just the extreme values. This yields DI models and link attenuation models that vary smoothly and plausibly to low percentages of time. II. THE CHILBOLTON RADAR INTERFERENCE EXPERIMENT (CRIE) The CRIE was a two year rain measurement campaign between 1987–1989, designed primarily for development and testing of rain scatter interference models as part of the COST 210 project [13]. It aimed to record an unbiased sample of the rain events occurring near Chilbolton, in the south of England, latitude 51 9 North, longitude 1 26 West. Rain fields were scanned using the Chilbolton Advanced Meteorological Radar, CAMRa, a 25 m steerable antenna equipped with a 3 GHz, doppler-polarization radar. The climate in the region is temperate maritime with an average annual rain rate exceeded 0.01% of the time of approximately 30 mm/hr. For the two-year period the radar was operated on a 28 day duty cycle. A set of near-horizontal (PPI) and vertical (RHI) radar scan were recorded in a 10 min cycle for 9 out of the 28 days. If no rain was detected (defined by a measured radar reflectivity greater than 25 dBZ) the data was discarded and this was recorded by the operator. The days of operation were chosen well in advance and with no reference to weather forecasts. The PPI scans were acquired with an elevation of 1.5 and covered an area approximately 50 in azimuth centered south west of the radar. As the scan rate of the radar is 1 /s it took less than 1 min to complete a PPI scan. Hence, the scan duration

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Fig. 1. Annual rain rate exceedance distributions derived from radar and measured by co-sited rain gauge. These are compared with Rec. ITU-R P.837-1 zones E and F, and the Rec. ITU-R P.837-2 prediction for Chilbolton.

is well within the 20–30 min duration for the lifetime of a rain event [14] and each scan represents a good snapshot of the rain field before any significant structural change has taken place. The resulting database contains 3199 scan sets, and 30 590 records of no-rain. It has been used for angular diversity and path length reduction factor studies, see Goddard and Thurai [9], [10], and Tan and Pedersen [11]. Each scan set contains a PPI and several RHI scans measuring horizontal and vertically and . polarized radar reflectivity, Data were collected between the ranges of 4.8 km and 158 km from the radar and averaged over 300 m intervals. For this paper, only the data between 20 and 40 km are used. This is to avoid sample volumes being within the freezing level and to limit differences in volume averaging due to beam spreading. This yields 68 reflectivity measurements along each ray. The beam width is 0.25 yielding 210 rays in each scan. Each set of PPI scans have been range corrected, calibrated, and correction made for absorption by atmospheric gasses. Reflectivities below the noise floor of 10 dBZ were assigned zero rain rates. Negative values of differential reflectivity, , are assumed to be due to nonliquid hydrometeors or anomalous propagation and are eliminated from the dataset. The rain-hail algorithm of Leitao and Watson [15] has been used to eliminate other data points where nonliquid hydrometeors may have influenced reflectivities. Finally, dual polarization reflectivity data was transformed into rain rate fields, see Usman [16]. Fig. 1 illustrates the estimated radar rain rate distribution compared with rain gauge statistics at the same site [10]. Also included are statistics from Rec. ITU-R P. 837-1 for the U.K. (using now obsolete ITU-R rain zones) and P. 837-2 for Chilbolton (using ITU-R rain maps). Zone E and Rec. P.837-2 are both known to underestimate the average annual 0.01% exceeded rain rate for Chilbolton by 20%. Over the range of exceedance probabilities down to 0.01%, the rain gauge and radar estimated rain rate distribution are largely consistent. Below this probability the radar derived rain rate distribution looks plausible suggesting that the effects of nonliquid hydrometeors has largely been removed.

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III. LINK RAIN ATTENUATION STATISTICS It has been observed that link rain attenuation is a stochastic process with a marginal distribution that is well approximated by a lognormal [17], [18]. Correspondingly, to a similarly good approximation, the joint distribution of rain attenuation on two links may be assumed to be bi-lognormally distributed. A lognormal distribution is parameterized by its mean and variables are joint lognormally distributed then variance. If the -vectors of simultaneous variable samples are multi-lognormally distributed and this distribution is parameterized by means and covariances. For multidimensional distributions of link rain attenuations, these parameters (the means and covariances) completely determine the cumulative joint distribution, while all links experience rain fade. The diversity advantage for any subset of the links, for any choice of fade margins, may be calculated directly from this distribution and a factor allowing for partial coverage of the network. The mean and variance of rain attenuation for an individual link can easily be estimated from existing information sources such as Rec. ITU-R P.530-10. However, the correlation/covariance of link rain attenuation for arbitrary pairs of links is largely unavailable. The correlation of link attenuation depends upon the spatial extent and variability of rain fields, and therefore on the relative occurrence of stratiform rain and convective rain within a given region. An explicit parameter that defines this relative occurrence is the rain thunderstorm ratio. Several investigations have shown that the variation of this ratio over a climatic region is weak [19]–[22]. Therefore, link correlation values are expected to be correlation valid over a large geographical area. A. The Statistics of Rain Attenuation Let be the link rain attenuation process while some part of the link experiences rain, and be the log rain attenuation process. Let the mean and variance of be and , respectively. If the rain attenuation is assumed to be lognormally distributed then the probability density function (PDF) for link attenuation is (1) is the probability of no rain attenuation, where is a normal PDF with mean and variance , and . has weight unity when and is The delta function zero elsewhere. This first term is due to periods without rain when the link experiences no rain attenuation. The second term is the lognormal distribution of attenuation when the link experiences rain. For two or more links the situation is complicated by the situations where not all links experience rain attenuation simultaneously. The joint attenuation PDF for two links may be written

(2)

is the probability of no rain attenuation on either link where is the probability that only link experiences rain while , has attenuation. The two-parameter delta function, weight unity when both parameters equal zero. The four terms correspond to periods when neither link experiences rain, only link one experiences rain, only link two experiences rain, and is the joint bivariate both links experience rain. normal PDF where , is the vector of means , i.e. and is the covariance matrix

(3) The second term in (2) is the distribution of rain fade on link 1 while link 2 experiences no fade and the normal distribution parameters are the mean and variance of log attenuation on link . 1 conditional on and exceeding their reThe joint probability of spective fade margins, and , respectively, is

(4)

IV. ESTIMATION OF LOGNORMAL PARAMETERS Given a sample of realizations of a lognormal variable, the mean and variance can be estimated directly from the moments of the sample. However, this approach is not applicable to the determination of means and covariances of link rain attenuation due to censoring and error in the samples. CAMRa estimates of rain rate become inaccurate below 1 mm/hr due to noise in the radar reflectivity measurement. Estimates of high rain rates are similarly inaccurate due to quantization of radar reflectivity. Similarly, estimates of link rain attenuation derived from CAMRa measured rain fields become increasingly unreliable at attenuations below that associated with 1 mm/hr rain rate along the link. The method chosen to estimate the mean and covariances needs to be robust in the presence of variable error across the sample range and adaptable to censorship of the sample, i.e., below some attenuation threshold the measurements may not be known although it may be known how many there are. In this paper we use maximum likelihood estimation (MLE) which is consistent and unbiased in the estimates of the parameters of the bivariate distribution of log attenuation. The parameter estimates are based on direct analysis of all the sample values, to maximize a likelihood function. The likelihood function is proportional to the probability of observing the measured dataset, given an underlying, parameterized PDF. The framework of the method allows it to be applied to unreliable or corrupt samples. In censored measurement regions, only the number of values is used in the likelihood function. , the Consider the random normal variable natural logarithm of rain attenuation, which is only accurately measurable within certain limits. In the univariate case and respectively. the left and right cutoff points are


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If a measurement is censored, i.e., the only information yielded is that it is greater than , then the likeliby measurement hood of this measurement is (9)

Fig. 2.

and the contribution of such measurement to the likelihood . function is Extending the method to the bivariate case is achieved by replacing the PDF integrals in (6) and (9) with two dimensional integrals over the two variables. The probability of falling in one to , requires integration to of the censored regions, on at least one of the variables, similar to (9). measurements Consider the observational set where are made in feature region , with corresponding likelihood , for . The total likelihood function can be written

Feature space for censored, joint rain attenuation measurements.

Let us define a new, censored random variable , such that . In the bivariate case a second is introduced with cutoff points are and random variable . The censored observations become

(5) The feature space for the censored observations is illustrated in Fig. 2. This can be regarded as the union of nine disjoint regions; in which the observations are uncensored on both variates, and on which the observations the four regions , , are censored on one variate, and the regions , , , and in which the observations are censored on both variates. The MLE of the parameters, where the correlation is defined by , is given by maximizing, with respect to , a likelihood function . The likelihood function is defined as the log probability of measuring the observed data. In the univariate case, the probais bility of making an observation

(10) The approximation is valid when the absolute errors are same for all the measurements and small relative to the standard deviations. Calculation of the MLE parameter set requires max. In general, need not have a unique maximization of imum. However, in this application, a good first approximation is available from the moments of the uncensored data. In all cases, Nelder-Mead optimization yielded the same maximum when all initial parameters were varied by 50%. An extended discussion on the framework can be found in various sources, in particular [23], [24]. Fig. 3 shows the variation of the correlation estimates derived using the MLE method for links with angular separations betweens 0 and 180 and lengths between 1 km and 9 km. The correlation exhibits symmetry about 180 . Varying the link frequency in the range 20 to 50 GHz, and hence changing the power-law relation between rain rate and specific attenuation, has no significant affect on link correlation. V. ESTIMATION OF THE DIVERSITY IMPROVEMENT FACTOR

(6)

The approximation is valid when the absolute error is small relative to the standard deviation. The probability of making a number of independent observations is the product of the individual probabilities, i.e.

The diversity improvement factor is defined in Rec. ITU-R P.530-10 as: , where is the probability of is the probability outage in the original (reference) link and of outage using the diverse network. If the reference link, Link is greater than then 1, operates until the attenuation . Using the same notation for a two-link system, the diversity improvement can be written (11)

(7) and the likelihood function is (8)

The numerator and denominator of this expression may be estimated using (1) and (2) respectively once the parameters are known, i.e.

(12)

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Figs. 3. Correlation of rain attenuation on pairs of microwave links, derived from the CRIE database using MLE. (a) Pairs of links of equal length, i.e., 1, 3, 5, 7, and 9 km from top to bottom. (b) Pairs links with unequal length as shown.

For the current application, the numerator, , is estimated directly from the radar-derived marginal distribution for the individual distribution, (1). The univariate lognormal distribution is fitted using the MLE method. The numerator may be written

(13) The first term in the numerator yields the probability of outage on the primary link while the second link is unaffected by rain. For small networks with diameters less than a few kilometers, this term will be negligible and can be omitted. This yields a formulation using only the joint distribution (14) However, intense convective storms with diameters of 5 to 10 km are important contributors to outages on short links and the chance of such storms affecting a subset of links in a network greatly increases as the diameter increases. For widely separated links, for example in the case of site diversity, the first term of the numerator can dominate, Crane and Horng Chung [25]. An alternative diversity quality factor is diversity gain (DG). It provides a measure of the reduction in the fade margin or an increase in the signal power due to diversity. DG is defined as the difference (in decibels), between the attenuation experienced by the reference link and diversity link system, exceeded at a cer, i.e. tain percentage of time, t% or availability, (15) and are the attenuations exceeded of In (15), the time on the reference link and diversity link system respectively. The attenuation experienced by the diversity system is defined as the minimum of the simultaneous attenuations expe-

rienced by the convergent links. Both DI and DG may be calculated from the joint fade pdf. However, DI is more directly calculable as it is a ratio of probabilities. The calculation of DG requires numerical inversion of the analytic PDF. To illustrate the methods, twelve route diversity scenarios have been investigated. Three pairs of link lengths are considered: 2 and 2 Km, 4 and 7 Km, and 8 and 8 Km. For each pair of link lengths, four angular separations are considered 30 , 45 , 90 and 180 . Figs. 4–6 illustrate the diversity gain and diversity improvement, predicted by (12), using distribution parameters extracted from the CRIE database using the MLE method. Also plotted are the DI and DG calculated using probabilities derived from the number of occurrences of joint attenuations in the CRIE database. For illustration, the balanced diversity case is considered; where each link has a fade margin that yields the same availability, i.e., 99.99%. For the DG graphs, Figs. 4(a), 5(a), and 6(a), the probability of outage is given. For the DI graphs Figs. 4(b), 5(b), and 6(b), the reference link fade margin is given. The symbols are advantage based on probabilities derived from number of occurrences while lines use the MLE probability distributions. Diversity factors calculated directly from the frequency of joint attenuations can be seen to be erratic and nonmonotonic. These errors are due to the very low number of events used to estimate joint event probabilities. The DI and DG calculated by the method proposed in this paper are smooth, monotonic and plausible down to low probability levels. VI. CONCLUSION A method has been developed for predicting diversity improvement and diversity gain on arbitrary networks of terrestrial microwave links, from databases of rain radar data. Joint link rain attenuation is assumed to have a multi-lognormal distribution. The distribution parameters are estimated using a method based on MLE. This method uses all the data, is robust in the presence of measurement error, and naturally caters for censored data. The resulting predictive model smoothly extrapolates into regions of low probability in a plausible way.


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Figs. 4(a), 5(a), and 6(a) diversity gain and (b) diversity improvement for pairs of links of length. Fig. 4: 2 and 2 Km; Fig.5: 4 and 7 Km; Fig.6: 8 and 8 Km. Four angular separations are considered 30 , 45 , 90 , and 180 .

Although the current method relies on accessing a rain radar database, the authors are using the method to investigate empirical relationships between link correlation and primary link parameters, e.g., length and angular separation. A predictive

model of the correlation of link rain attenuation would remove the need to use the radar data and allow diversity improvement and gain to be calculated from ITU-R models of individual link fade distributions.

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ACKNOWLEDGMENT The authors would like to acknowledge the support of D. Eden and D. Bacon, previously of Ofcom; the staff of Chilbolton who acquired the radar data; and other members of the CCLRC Radio Communications Research Unit for their helpful contributions. REFERENCES [1] Radiowave Propagation Effects on Next Generation Fixed Services Terrestrial Telecommunications Systems, URL http://europa.eu.int, 1996. [2] Propagation Data and Prediction Methods Required for the Design of Terrestrial Line-of-Sight Systems, ITU-R (2001), Recommendation ITU-R P.530-10. [3] Propagation Data and Prediction Methods Required for the Design of Terrestrial Broadband Millimetric Radio Access Systems Operating in a Frequency Range of About 20–50 GHz, ITU-R (2003), Recommendation ITU-R P.1410-2. [4] S. Y. Seidel, “Propagation and Radio Planning at 28 Ghz for LMDS, LMDS Tutorial,” Understanding LMDS Technologies, Jul. 15, 1996. [5] Characteristics of Precipitation for Propagation Modeling, TU-R (2003), Recommendation ITU-R P.837-4. [6] Specific Attenuation Model for Rain for Use in Prediction Methods, ITU-R (2003), Recommendation ITU-R P.838-2. [7] K. Paulson, “A spatial-temporal model of rain rate random fields,” Radio Sci., vol. 37, pp. 21–28, 2002. , “Prediction of diversity statistics on terrestrial microwave links,” [8] Radio Sci., vol. 38, p. 1047, 2003. [9] J. W. F. Goddard and M. Thurai, Modeling of Attenuation Due to Rain on Terrestrial Paths Using Chilbolton Radar Data: NRPP Research Note Rutherford Appleton Laboratory, 1996. [10] J. W. F. Goddard and M. Thurai, “Radar derived path reduction factors for terrestrial systems,” in Proc. Inst. Elect. Eng. 10th Int. Conf. Antennas and Propagation, vol. 436, Edinburgh, U.K., 1997, p. xxxiii+553+396. [11] J. Tan and L. Pedersen, “Study of simultaneous coverage and route diversity improvement under rainy periods for LMDS systems at 42 GHz,” in Proc. Millenium Conf. Antennas and Propagation, AP2000, Davos, Switzerland, Ap. 9–14, 2000. [12] C. Capsoni, F. Fedi, C. Magistroni, A. Paraboni, and A. Pawlina, “Data and theory for a new model of the horizontal structure of rain cells for propagation applications,” Radio Sci., vol. 22, no. 3, pp. 395–404, 1987. [13] COST210, “Influence of the atmosphere on interference between radio communications systems at frequencies above 1 GHz,”, EUR 13407 EN 1991. [14] I. Zawadzki, “Statistical properties of precipitation patterns,” J. Appl. Meteorology, vol. 12, pp. 459–472, 1973. [15] M. J. Leitao and P. A. Watson, “Application of dual linearly polarized radar data to prediction of microwave path attenuation at 10–30 GHz,” Radio Sci., vol. 19, pp. 209–221, 1984. [16] I. S. Usman, “Development of point to multipoint models for availability and fade mitigation in the millimeter wave frequency range,” Ph.D. dissertation, University of Bath, Bath, U.K., 2005. [17] S. H. Lin, “Statistical behavior of rain attenuation,” Bell Syst. Tech. J., vol. 52, pp. 557–581, 1973. [18] F. M. Galante, “Statistical evaluation of rain fades and fade durations at 11 GHz in the European region [satellite links],” in Proc. Inst. Elect. Eng. Int. Conf. Satellite Communication Systems Technology, London, U.K., 1975, pp. 302–307. [19] C. Ito and Y. Hosoya, “The thunderstorm ratio as a regional climatic parameter: Its effects on different integration time conversion rain attenuation, site diversity and rain depolarization,” in Proc. 27th URSI General Assembly, Maastricht, Netherlands, 2002, p. 4. [20] P. L. Rice and N. R. Holmberg, “Cumulative time statistics of surface point rainfall rates,” IEEE Trans. Commun., vol. COM 21, pp. 1131–1136, 1973. [21] E. J. Dutton and H. T. Dougherty, “Year-to-year variability of rainfall for microwave applications in the U.S.A.,” IEEE Trans. Commun., vol. COM 27, pp. 829–832, 1979.

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Kevin S. Paulson received the B.Sc. degree in physics and the M.Sc. degree in atmospheric physics from the University of Auckland, New Zealand, and the Ph.D. degree in applied mathematics from Oxford Brookes University, Oxford, U.K., for work in medical electrical impedance tomography. From 1998 to 2004, he led research into terrestrial radio telecommunications in the Radio Communications Research Group of Rutherford Appleton Laboratory, U.K. His primary research interest is the mitigation of rain fading across radio networks. He initiated the Research Council funded Rainmap network coordinating research into the broad-scale modeling of rain for engineering applications. Currently he is a Lecturer in Telecommunications at the University of Hull, U.K.

Robert J. Watson was born in England, U.K., on June 23, 1971. He received the B.Eng. and Ph.D. degrees in electronic engineering from the Department of Electronic Systems Engineering, University of Essex, Colchester, U.K., in 1992 and 1996 respectively. He was a Senior Research Officer in the Departments of Mathematics and Electronic Systems Engineering, at the University of Essex, from 1995 to 1998, where he was involved in number of projects including space-borne rain-radar studies, Doppler and polarization diversity weather radar studies and rainfall rate estimation from dual-frequency microwave links. In October 1998, he joined the Telecommunications, Space and Radio research group in the Department of Electronic and Electrical Engineering, University of Bath, Bath, U.K., as a Lecturer. He has consulted widely for industry in the area of radio propagation and radar systems. His current research interests include tropospheric radio-wave propagation on terrestrial and earth-space links and atmospheric science remote sensing. Dr Watson is currently the Secretary and Representative to the U.K. International Union of Radio Science (URSI) Commission F (Wave propagation and Remote Sensing).

Isa S. Usman was born in London, U.K., on June 24 1976. He received the M.Eng. degree in electrical and electronic engineering from the University of Bath, Bath, U.K., in 2000. Upon graduation, he was sponsored by the Rutherford Appleton Laboratory, near Oxford, to perform Ph.D. research as a student of Bath. His research involved the investigation of mitigation techniques to optimize the performance of terrestrial links in the presence of rain. He has made contributions to EMBRACE and Cost 280 projects of the European Community.