142 IEEE COMMUNICATIONS LETTERS, VOL. 3, NO. 5, MAY 1999 Fade Slope Statistics for Three 12-GHz Satellite Beacon Links in Brazil E. Couto de Miranda, M. S. Pontes, and L. A. R. da Silva Mello Abstract— Fade slope is defined as the rate of increase or decrease of attenuation over time. In this letter the possible corre- lation between the statistics of fade slope values and attenuation levels is investigated. Results show a direct positive correlation between the mean values of fade slope and the attenuation levels. The distributions of fade slope values present a degree of skewness toward the negative values that makes the curves depart from the Gaussian distribution observed by other authors. I. INTRODUCTION AND EXPERIMENTAL SETUP F ADE slope is defined as the derivative of the attenuation time series. In essence, it gives the rate of increase or decrease of the attenuation in time. This information is very important in the design of fade countermeasures based on adaptive power control. It has been suggested that fade slope values have a direct correlation with attenuation level and rainfall rate [1]. For slant path propagation, the correlation with rainfall rate may not be significant, unless for sites with elevation angles close to 90 . Therefore, in this paper only correlations with attenuation levels are investigated. Statistical analysis of fade slope values include basic descriptive statistics for the worst season, nonparametric estimation of fade slope distribution and the relationship between the cumulative distri- bution of the absolute value of fade slope and the attenuation. The three experimental links are located in the cities of Bel´ em, Recife, and Rio de Janeiro (at approximately 1 ,8 , and 23 of latitude south, respectively). The sites locations allow a comparison between the behavior of the fade slope in equatorial (Bel´ em) and tropical (Recife and Rio de Janeiro) Brazil. The measurements periods were April 1996–March 1997 for Bel´ em, December 1996–November 1997 for Recife and September 1995–August 1996 for Rio de Janeiro. The receiver antennas are pointed toward Intelsat 705, located at 50 W. The beacon frequency is 11.452 GHz and it is clockwise circularly polarized. The beacon signal has a narrow bandwidth due to the lack of modulation. Since all the energy is contained close to the center frequency, the receiver was built with a narrow bandwidth, thus reducing the noise. The dynamic range of the receivers is in excess of 30 dB, being large enough to allow the observation of severe attenuation events. A tipping bucket raingauge with 0.1-mm capacity and 1-min integration time is placed near the antennas. The Manuscript received December 17, 1998. The associate editors coordinating the review of this letter and approving it for publication was Prof. M. D. Zoltowski. The authors are with the Centre for Telecommunication Studies, Pontifical Catholic University of Rio de Janeiro, G´ avea, Rio de Janeiro, RJ 22453-900, Brazil (e-mail: erasmus@cetAc.puc-rio.br). Publisher Item Identifier S 1051-1089(99)04408-7. TABLE I TOP TO BOTTOM OF EACH CELL:VALUES OF MEAN,STANDARD DEVIATION, SKEWNESS, AND KURTOSIS FOR EACH ATTENUATION THRESHOLD data are sampled at 1 Hz and stored in a computer for posterior downloading. High-frequency noise is reduced by the analysis software, which performs the smoothing of the data by averaging over 2 s, thus reducing the sampling rate from 1 to 0.5 Hz. This sampling and logging computer is called Data Acquisition Unit (DAU). The DAU is designed for remote operation, allowing the deployment of several satellite beacon receiver units throughout the country for a more widespread coverage of different radioclimatic areas. Data are preprocessed to eliminate spurious effects that could masquerade the results, such as power cuts causing gaps on the received power being recorded. This paper also aims at increasing the available database of rainfall induced attenuation in southern latitudes. II. RESULTS A. Descriptive Statistics Table I presents the descriptive statistics for the fade slope values obtained from the three sites, choosing the worst season for attenuation. The choice of a limited period for the statistics of fade slope follow not only the specifications of the ITU-R 1 , but is also in agreement with works by other authors such as Nackoney and Davidson [5] and Mauri et al. [6]. The threshold 1 ITU-R Recommendation 579-5. 1051–1089/99$10.00  1999 IEEE