A mathematical theory of de‐integrating long‐time integrated rainfall and its application for predicting 1‐min rain rate statistics

To date, the methods devised for converting long‐term experimental probability distribution (pd), , of the rain rate ρ_T integrated in T min (T > > 1 min) to 1‐min pd, P_R(R), of the instantaneous rain rate R, are based on flawed T‐min data and, as such, are not based on fully reliable first principles. is not only an upward translated version of P_R(R) but also rotated clockwise and distorted. The current methods do not correct these errors. We propose and discuss a mathematical theory, which corrects these errors and thus de‐integrates T‐min experimental pds into the corresponding 1‐min pd, the input required by all rain attenuation prediction methods. The theory is based on simple first principles whose parameters are calibrated by means of a large and reliable rain‐rate data bank recorded in Spino d'Adda, a site held as an experimental laboratory and used for exploratory data analysis. We show that P_R(R) is modelled by four distinct functions in four disjoint ranges, and that this modelling is physically meaningful. We have tested the theory up to integration times of 12 h, with a large experimental data bank of 1‐min rain‐rate time series recorded in Gera Lario, Fucino, Rome, Prague, and Montreal, besides Spino d'Adda. Defined the fraction of rainy time in an average year, P_o (%), we have found that: (a) the modelling is very good up to 6 h; (b) in the range from about P_o to 0.001%, the error values are constant, with average error set at about ? 3% and RMS error less than 8% for T ≤ 120 min, less than about 9% for 120 < T ≤ 360 min. We have also applied the theory to rain‐rate time series provided by meteorological agencies with integration time T = 60 min (blind test) with excellent result. Copyright © 2011 John Wiley & Sons, Ltd.     

基于进化神经网络的地空路径雨衰减模型

雨衰减对工作在高频的地空通信链路稳定性具有很大影响。本文在考虑多个参数对雨衰减非线性影响的基础上,建立了基于进化神经网络的雨衰模型,并与ITU－R模型进行了比较。结果表明,利用本文提出的模型进行高频电波的预测具有更好的精度,可降低平均误差0.64dB,并减小标准偏差0.79bD,为雨衰减预测提供了一种新的方法。     

Characterization and modelling of time diversity statistics for satellite communications from 12 to 50 GHz

To compensate propagation impairments on Earth–space communication links, a specific fade mitigation technique to make up for rain propagation impairments is studied in this paper: the time diversity. This process consists in sending the information when the propagation channel allows to get it through. Here the time diversity technique is applied to different experimental attenuation time series collected in Europe: Spino d'Adda (Italy), Louvain‐la‐Neuve and Lessive (Belgium). These propagation measurements have been collected from 12 to 50 GHz and the performance of time diversity technique is assessed from the generation of time diversity statistics conditioned to the time delay. A prediction method of these statistics is also described. The proposed model relies on the time correlation of the attenuation time series. The model is validated and its accuracy analysed in terms of prediction error calculated using the different databases. Copyright © 2009 John Wiley & Sons, Ltd.     

A simple real‐time frequency scaling technique for rain attenuation and its performance

A new algorithm has been proposed for frequency scaling of rain attenuation. It uses the real‐time estimates of a spatial variation index in the rain rate profile suggested in simple atmospheric model (SAM) to obtain the scaled attenuation. Measured data are used to validate the algorithm which showed a typical accuracy of better than 2.5 dB for 95% confidence. The time profile of a model parameter derived from measured values has also been effectively utilized to envisage the rain cell movement, particularly for high elevation conditions. Simulated data with predefined rain rate profiles were also used for validations. The relative contributions of the model error and the measurement noise to the final error were obtained. The errors are attributed to the modelling mismatch and intermediate parameter estimation error. The estimation accuracy of the algorithm was found to worsen with reducing elevation. The overall error remains within 3 dB for 0.5 dB of measurement noise and up to lowest elevation of 30°. The simple approach of the model in conjunction with the adequate accuracy makes this algorithm a potential candidate to be used for real‐time open‐loop fade mitigation.     

Railway satellite channel at Ku band and above: Composite dynamic modeling for the design of fade mitigation techniques

Past studies on the railway satellite channel (RSC) at Ku band and above consider exclusively the attenuation coming from the metal power arches (PAs) along the railway route, producing significant though deterministic periodical fast fading. Nevertheless, limited attention has been given to model tropospheric effects on the RSC. The present paper takes a more comprehensive view of the RSC by introducing a novel stochastic dynamic model of rain fading in mobile satellite systems on top of the diffraction because of PAs. The proposed approach builds upon well‐established research on rain attenuation time series synthesizers employing stochastic differential equations. It is shown that this propagation tool may provide significant aid, in general, in mobile satellite system simulations and in the design of fade mitigation techniques (FMTs), particularly aiming at the railway scenario. The tool enables the generation of fade events, fade duration statistics, rain attenuation power spectrum and predicting the necessary FMT control loop margin. This is particularly useful for the RSC because most of the proposed FMTs focusing on PAs are not appropriate for compensating atmospheric fading. Copyright © 2011 John Wiley & Sons, Ltd.     

Space communications with variable elevation angle faded by rain: Radio links to the Sun–Earth first Lagrangian point L1

How rain attenuation affects space links with variable elevation angles is not yet fully researched. The aim of this paper is to investigate this topic by simulating rain attenuation at K_a Band, in slant paths with variable elevation angles, with the Synthetic Storm Technique (SST), in links connected with spacecrafts at the Sun–Earth first Lagrangian point L₁, viewed from Spino d'Adda (Italy), Tampa (Florida), White Sands (New Mexico). The input to the SST is a large database of time series of 1‐min rain rate recorded on site, 10 years in Spino d'Adda, 4 years at Tampa and White Sands. After recalling known results on the elevation angle of the Sun (i.e. L₁), θ_s (°), seen from latitude λ (°), I report what seems to be a new result: the mode of the probability density function of θ_s in a year, in the range 0 ≤ λ ≤ 90° ? ε (Earth axis tilt angle ε = 23.44°), coincides with the peak angle found at the day of the Winter solstice at the site, a result valid also for other planets, once their tilt angle is used. Compared to the complementary probability distribution function (pdf) of rain attenuation calculated for a geostationary (GEO) link (fixed elevation angle), the pdf to L₁ depends on the rain‐rate pdf during the contact time with L₁, according to the local climate. I show that, to obtain a good and easier estimate of the rain attenuation pdf in L₁ links, we can consider a GEO link with elevation angle equal to the mean angle and rain rate pdf, both during the contact time, and that the mode angle gives an upper bound to the rain attenuation pdf in the sites considered. Copyright © 2015 John Wiley & Sons, Ltd.     

Raindrop size distribution using method of moments for terrestrial and satellite communication applications in Singapore

As communication services using higher frequencies are growing rapidly in the tropics, there is an increasing need for a finer model to predict the attenuation due to rain. The raindrop size distribution (DSD) is one of the major sources of error in any prediction model, mainly because of its variability in both space and time. The DSD parameters are computed from distrometer data that are classified into stratiform and convective types using S-band radar data. The method of moments is employed to estimate the parameters of lognormal DSD. The modeled DSD parameters are optimized by examining the root mean square (RMS) error and the average probability ratio (APR) in estimation of the rain rate, rain attenuation, and radar reflectivity factor simultaneously. The proposed model gives maximum (close to unity) APR and minimum RMS error when compared to any other set of DSD parameters.     

Performance Investigation of Space‐Time Block Coded Multicarrier DS‐CDMA in Time‐Varying Channels

In this letter, we evaluate the system performance of a space‐time block coded (STBC) multicarrier (MC) DS‐CDMA system over a time selective fading channel, with imperfect channel knowledge. The average bit error rate impairment due to imperfect channel information is investigated by taking into account the effect of the STBC position. We consider two schemes: STBC after spreading and STBC before spreading in the MC DS‐CDMA system. In the scheme with STBC after spreading, STBC is performed at the chip level; in the scheme with STBC before spreading, STBC is performed at the symbol level. We found that these two schemes have various channel estimation errors, and that the system with STBC before spreading is more sensitive to channel estimation than the system with STBC after spreading. Furthermore, derived results prove that a high spreading factor (SF) in the MC DS‐CDMA system with STBC before spreading leads to high channel estimation error, whereas for a system with STBC after spreading this statement is not true.     

Performance of optimum and suboptimum OFDM‐CPM receivers over multipath fading channels

A class of orthogonal frequency division multiplexing‐continuous phase modulation (OFDM‐CPM) signals is introduced in which binary data sequence is mapped to complex symbols using the concept of correlated phase states of a CPM signal. Canonical optimum and suboptimum multiple‐symbol‐observation OFDM‐CPM receivers are derived. Multipath channel with AWGN is assumed. The receivers are analyzed for bit error rate (BER) performance in terms of high‐ and low‐SNR bounds. These bounds are illustrated as a function of parameter h, time delay and attenuation level. It is shown that OFDM‐CPM systems, with h=0.5,0.25 and an observation interval length of two symbols, can outperform conventional OFDM‐PSK system for a two‐ray multipath model. Copyright © 2005 John Wiley & Sons, Ltd.     

A method to achieve clear‐sky data‐volume download in satellite links affected by tropospheric attenuation

For data downloading from satellites, the traditional approach of considering the complementary probability distribution, P(A_trop) of the total tropospheric attenuation A_trop (dB), at a frequency, polarization, and elevation angle, may be too pessimistic, and it may lead to large overdesign. If the data volume downloaded in a given observation time T_obs (a day, a week, a month, etc.), with a constant probability of symbol error, is more valuable than the instantaneous symbol, or bit rate (as it may be the case in Earth resources observation or in other services that allow long delays in communicating data), another approach can avoid overdesign, namely the various adaptive coding and modulation techniques. We study a particular time integral of A_trop(t): (i) to define the average efficiency of a radio channel faded by the troposphere and (ii) to design a method that can theoretically achieve the same volume of data downloaded in clear‐sky conditions (no troposphere), even if the radio link is faded by the troposphere. The average efficiency and its bounds can be calculated from the complementary probability distribution of A_trop(t). We explicitly apply the theory to radio links faded by rain, by using the experimental rain‐attenuation time series measured with satellite ITALSAT in a 37.8° slant path, at 18.7, 39.6, and 49.5 GHz at Spino d'Adda (Italy), and to those simulated with the synthetic storm technique. Based on the average efficiency, we define the method that can achieve in T_obs, theoretically, the same data volume as in clear sky, directly applicable to quadrature phase‐shift keying, multiple phase‐shift keying, and Shannon capacity theorem. The method requires a fixed increase in power margin, and bandwidth, compared with clear‐sky conditions, and delivers an average symbol rate equal to the maximum symbol rate obtainable when A_trop(t) = 0. The method can also be used in terrestrial links at any frequency. We compare its theoretical performance with the traditional adaptive coding and modulation techniques and show that, even theoretically, these techniques cannot achieve unitary efficiency as, on the contrary, the novel method can do. Copyright © 2015 John Wiley & Sons, Ltd.     

Channel estimation algorithms for cooperative spectrum sensing in amplify‐and‐forward cooperative system

In amplify‐and‐forward (AF)‐based cooperative spectrum sensing system, the bit‐error‐rate (BER) performance and detection probability will decrease because of the existence of channel estimation error. In this paper, the influence of channel estimation error on system performance is firstly deduced, and then, linear minimum mean‐square error (LMMSE) channel estimation algorithm with filtering delay time‐domain windowing (LMMSE‐filtering‐DTW) technique and modified singular value decomposition‐based LMMSE algorithm are proposed to improve the channel estimation performance for code division multiple access system and orthogonal frequency division multiplexing system in AF cooperative scenario, respectively. Simulation results verify the effectiveness of the two proposed channel estimation algorithms in cooperative spectrum sensing, and when E_b/ N₀ is bigger than 20 dB, given the required false alarm probability smaller than 15%, the difference of detection probability between the channel obtained using the proposed channel estimation algorithms and the ideal channel is less than 2.5%, respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

Recursive maximum likelihood estimation of time‐varying carrier frequency offset for orthogonal frequency‐division multiplexing systems

A recursive maximum likelihood carrier frequency offset (CFO) estimator is proposed in this work, where redundancy information contained in the cyclic prefix of multiple consecutive orthogonal frequency‐division multiplexing (OFDM) symbols is exploited in an efficient recursive fashion. Because the estimator is based on multiple OFDM symbols, the time‐varying CFO must be considered. We investigate the effect of time‐varying CFO on the performance of the estimator and the trade‐off between fast tracking ability and low estimation variance. We show that, without channel noise, the mean squared error (MSE) of estimation due to CFO estimation variation increases approximately quadratically with n, where n is the number of OFDM symbols used for CFO estimation (estimation window size), whereas the MSE due to channel noise decreases proportionally to 1/n (approximately) if the CFO is constant. A closed‐form expression of the optimal estimation window size (approximately) is derived by minimizing the MSE caused by both time‐varying CFO and channel noise. For wireless systems with time‐varying rate of change for CFO, the proposed estimator can be implemented adaptively. In addition, typical optimal estimation window sizes for WiMAX, DVB‐SH and MediaFLO systems are evaluated as an example. Copyright © 2011 John Wiley & Sons, Ltd.     

The Prediction of Rain-Induced Attenuation in MM Wave Band by Rain Medium System Model

While the millimeter radio wave propagates through rainfall, it will be attenuated heavily due to assimilation and scattering of rain. It is imperative to establish a simple and effective model to predict the rain-induced attenuation. In this paper, the rainfall is taken as a random system that can attenuate the radio wave. The transfer function matrix model is selected to be the random system model. Using experiment rain attenuation data at different rain rate, the correlation entropy and residue error of the system is obtained by system identification method. On the basis of correlation entropy and residue error, we can determine the order of the predication system. At last, the predication model that can forecast heavy rain attenuation by small rain attenuation is gotten by applying the least square method. The comparison shows that the discrepancy between the predication result of the obtained model and the experiment rain attenuation data is relatively minor.     

基于非平稳时序ARIMA模型的W频段雨衰预测

针对目前绝大多数雨衰预测模型仅验证到55 GHz,而经过验证的W频段预测模型相对较少,且存在模型表述复杂度高、计算量大的问题,该文提出一种结构简单、计算量小的实时预测方法。该方法基于ARIMA模型,利用非平稳雨衰时序中相邻时序间的相关性建立预测模型,对初始序列进行平稳性检验,通过差分变换将非平稳序列转化为平稳序列,并对平稳化后的时间序列进行参数估计及诊断检验,将传统非线性预测转化为线性预测。并先将该ARIMA(1,1,6)模型在不同极化方式、预测间隔和时序个数的条件下进行比较,然后分别与ITU-R, Silva Mello模型在垂直极化、预测间隔0.10 GHz,时序个数50的条件下进行比较,最后使用ARIMA(1,1,6)模型进行预测,并对照预测序列与仿真序列的吻合度。结果表明,ARIMA模型与ITU-R, Silva Mello模型所得结果预测误差不超过10-3 ,且衰减变化趋势基本相同,预测序列与仿真序列间吻合度较高,说明该方法可用于W频段雨衰预测,且预测精度高,模型表述简单。     

Turbo equalization of doubly selective channels

In this paper, turbo equalization for transmission over doubly selective channels is proposed. The maximum a posteriori probability (MAP) algorithm is used for channel detection as well as for channel decoding. The detection/decoding constituents can exchange soft information in an iterative manner resulting in the so‐called turbo equalization. The time‐varying multi‐path fading channel is modeled using the basis expansion model (BEM). In this BEM, the time‐varying channel is viewed as a bank of time‐invariant finite impulse response filters, and the time variation is captured by means of time‐varying complex exponential basis functions. Therefore, the time‐varying transition tables that characterize the time‐varying channel can also follow a similar BEM. The complexity of the MAP channel detector is rather prohibitive for practical applications. This motivates the search for lower‐complexity soft‐output channel detectors. For this purpose, soft‐output linear minimum‐mean square error (LMMSE)‐based channel detectors are proposed for single carrier as well as for multi‐carrier systems. With the use of Gaussian approximation, expressions for the a posteriori and extrinsic log‐likelihood ratios have been derived. The performance of the proposed turbo equalization schemes are evaluated using numerical simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Prediction model of time diversity using Japan rain radar data

The effects of rain attenuation on communication systems will become more pronounced in future satellite communication systems, especially with the planned use of the 21‐GHz band or higher‐frequency bands. Diversity techniques provide a solution to mitigate rain attenuation effects. This study proposes a time diversity technique, one such technique that is likely to demonstrate high effectiveness. To model the system, rainfall rate statistics are necessary, and reliability is improved as the amount of statistical data increases. This paper derives the cumulative distribution of the rainfall rate across Japan over 4 years using rain radar data from the automated meteorological data acquisition system and ground‐based rain radar network and evaluates the rainfall rate at 23 observation points across Japan. We carry out a performance evaluation for all locations within Japan to confirm the efficiency of the time diversity method. Finally, we propose prediction model of the time diversity gain for Japan and other significant parameter which is time correlation of rainfall rate that was found from the time diversity results for further investigation. Copyright © 2016 John Wiley & Sons, Ltd.     

Near‐optimum short‐term fade prediction on satellite links at Ka and V‐bands

Several short‐term predictors of rain attenuation are implemented and tested using data recorded from a satellite link in Southern England, and a comparison is made in terms of the root‐mean‐square error and the cumulative distribution of under‐predictions. A hybrid of an autoregressive moving average and adaptive linear element predictor is created that makes use of Gauss–Newton and gradient direction coefficient updates and exhibits the best prediction error performance of all prediction methods in the majority of cases. Copyright © 2007 John Wiley & Sons, Ltd.     

Total CNIDR degradation during rain fade conditions of a dual polarized satellite link suffering from double adjacent satellite interference

Atmospheric impairments have a significant influence on the performance of modern satellite communication networks, working at Ku, Ka and potentially Q/V frequency bands. Both differential rain attenuation from an adjacent satellite system, operating at the same frequency range, and cross‐polarization phenomena on dual polarized satellite systems due to rain and ice crystals, induce a further aggravation on the already limited signal‐to‐noise‐plus‐total‐interference ratio (CNIDR), due to the frequency and orbital congestion of today's global communication satellite constellation. In the present paper, a new statistical methodology, towards the modelling of CNIDR under rain fade conditions, is proposed to include interference effects by two adjacent satellites, incorporating the impact of correlated fading channels (spatial rainfall inhomogeneity) of multiple slant paths. The method is based on a convective raincell model and the lognormal assumption for both the point rain‐rate statistics and the slant‐path rain attenuation. The obtained numerical results indicate the significant impact of the second interfering satellite on the aggravation of total interference effects. Some simple mathematical formulas for the prediction of the CNIDR, based on the derived theoretical results, and demonstrating the influence of various link parameters on the total link availability statistics, are also presented. Copyright © 2009 John Wiley & Sons, Ltd.     

The Study of Rain Specific Attenuation for the Prediction of Satellite Propagation in Malaysia

Specific attenuation is the fundamental quantity in the calculation of rain attenuation for terrestrial path and slant paths representing as rain attenuation per unit distance (dB/km). Specific attenuation is an important element in developing the predicted rain attenuation model. This paper deals with the empirical determination of the power law coefficients which allow calculating the specific attenuation in dB/km from the knowledge of the rain rate in mm/h. The main purpose of the paper is to obtain the coefficients of k and α of power law relationship between specific attenuation. Three years (from 1st January 2006 until 31st December 2008) rain gauge and beacon data taken from USM, Nibong Tebal have been used to do the empirical procedure analysis of rain specific attenuation. The data presented are semi-empirical in nature. A year-to-year variation of the coefficients has been indicated and the empirical measured data was compared with ITU-R provided regression coefficient. The result indicated that the USM empirical measured data was significantly vary from ITU-R predicted value. Hence, ITU-R recommendation for regression coefficients of rain specific attenuation is not suitable for predicting rain attenuation at Malaysia.