## 1 Introduction

[2] Developing and applying millimeter wave (MMW)-band wireless systems, for example, multiple input multiple output communication technologies, are hot research areas in future wireless system investigation, because of the many advantages of the MMW system compared to lower frequencies, such as higher capacity, narrower beam, smaller size of terminal, stronger antijamming capability, better electromagnetic compatibility, more easily miniaturizing installation, smaller size of antenna, etc. [*Gong*, 2008; *Xiong*, 2000; *Xie*, 1990; *Xu*, 2003]. One important aspect of designing the wireless system is the investigation of radio wave propagation characteristics (such as refraction, reflection, scattering, attenuation, phase shifting, depolarization, scintillation, duct, and additional noise), when radio wave propagates through various environments [*Ishimaru*, 1977; *Gong*, 2008; *Sizun*, 2003; *Xiong*, 2000; *Xie*, 1990; *Xu*, 2003; *Verma et al*., 1989]. The propagation effects, which are more serious at MMW frequencies, directly influence system performance. Those effects restrict the further development of MMW technologies [*Ishimaru*, 1977; *Gong*, 2008; *Sizun*, 2003; *Marie Edith Gimonet et al*., 2002; *Xiong*, 2000; *Xie*, 1990; *Xu*, 2003; *Verma et al*., 1989].

[3] One principal technical difficulty for MMW technology is to evaluate and mitigate the attenuation induced by troposphere propagation environments, like rain, cloud, snow, fog, sand, and storm. Among those, rain-induced attenuation is the most severe attenuation [*Ishimaru*, 1977; *Gong*, 2008; *Sizun*, 2003; *Xiong*, 2000; *Xie*, 1990; *Xu*, 2003; *Verma et al*., 1989]. Rain-induced attenuation can be dozens, even hundreds of decibels. Usually, the attenuation will be more severe at higher frequency. For example, the rainfall, which can induce an inconspicuous effect for C bands, may cause interruption on systems working at K_{u} and K_{a} bands [*Xiong*, 2000; *Xie*, 1990; *Zhao*, 2001].

[4] Power reserve technology is one of the most important approaches adopted to mitigate rain-induced fade, which mitigates deep fade by a fixed power margin. A fixed power margin is needed for power reserve technology to mitigate rain-induced fade. The fixed power margin is decided by the results of long-term statistical characteristics of rain-induced attenuation. Many models, which can obtain long-term statistical characteristics, have been proposed: Improved Assis-Einloft Model [*Costa*, 1983], Australian Model [*Flavin*, 1996], Brazil Model [*Pontes*, 1992], Bryant Model [*Bryant et al*., 2001], Crane Global Model [*Crane*, 1978, 1980], Crane Two Components Model [*Crane*, 1982, 1996], EXCELL Model [*Capsoni et al*., 1987a, 1987b], Garcia Model [*García-López et al*., 1988; *García and Peirò*, 1983], ITU-R Model [*ITU-R P*.*618-10*, 2009], Karasawa Model [*Karasawa and Matsudo*, 1990; *Karasawa and Matsudo*, 1991], Leitao-Watson Model [*Leitão and Watson*, 1986], Matricciani Model [*Matricciani*, 1991, 1993], Misme-Waldteufel Model [*Misme and Waldteufel*, 1980], SAM Model [*Stutzman and Dishman*, 1982, 1984], Svjatogor Model [*Svjatogor*, 1985] (all these models mentioned above are also summarized and discussed by *Ioan Chisalita et al*. [2002]), DAH Model [*Dissanayake et al*., 1997], Manning Model [*Manning*, 1986] (the DAH model and Manning model are also summarized and discussed by *Ippolito* [1999]), UK Model [*Doc*. *3 M*/*134*, 2005; *Doc*. *3 M*/*28*, 2003], Japan Model [*Karasawa*, 1989], and China Model [*Zhao*, 2001].

[5] While applying power reserve technology, a very large power margin is needed at any time because of the high-level attenuation at higher MMW frequencies. However, the high-level attenuation is a sparse case, because rainfall, especially heavy rain, is a relatively sparse event in time and space. Therefore, one obvious drawback of power reserve technology is the waste of power. For example, the rain rate in Beijing, China, for 0.01% of an average year is about 42 mm/h. The predicted attenuation for 0.01% of an average year using the International Telecommunication Union-Radio (ITU-R) model [*ITU-R P*.*618-10*, 2009] is approximately 50 dB, under the following link conditions: 35 GHz frequency, circular polarization state, and 35° link elevation. The fixed power margin of 50 dB must be reserved whenever to ensure the communication reliability of 99.99%, but the fixed power margin is only needed for a small part of an average year. Moreover, the large power can interfere with other wireless systems; it can increase the loading of power-supply system of spacecraft, for example satellites.

[6] Space diversity technology is another main approach to mitigate rain-induced fade. It is based on the spatially uncorrelated character of rain-induced attenuation affecting different links whose Earth stations are located in different regions. While applying space diversity technology, it is necessary to build two or more Earth stations in different regions, which surely increase the investment of human and financial resources. As mentioned, rainfall, especially heavy rain, seldom occurs, so the resources will be wasted for most of an average year.

[7] The fixed power margin for power reserve technology and the investment of human and financial resources for space diversity technology can be seen as a waste for most of an average year. Thus, adaptive fade mitigation technologies, such as adaptive power control (APC) technology, are proposed [*de Montera1 et al*., 2008]. APC technology is different from power reserve technology. APC is able to increase transmitted power to a specific level, only when the specific rain-induced attenuation is predicted. Therefore, real-time dynamic characteristics of rain-induced attenuation are the urgent needs for APC to predict and trace the real-time changing of rain-induced attenuation [*Burgueno et al*., 1990; *de Montera1 et al*., 2008; *Willis et al*., 2006].

[8] In recent years, some models and methods for forecasting or investigating dynamic rain-induced attenuation have been proposed, including a linear regression model [*Dossi*, 1990; *de Montera1 et al*., 2008], a first-order stochastic equation [*Manning*, 1990, 1991], a Markov-chain method [*Castanet et al*., 2003; *Fiebig*, 2002; *van de Kamp*, 2003], an adaptive linear filter [*Grémont et al*., 1999], a neural network [*Chambers and Otung*, 2005; *Mallet et al*., 2006], a model based on the fade slope [*Van de Kamp*, 2002], a switching ARIMA process with generalized autoregressive conditional heteroscedasticity (ARCH) errors [*de Montera1 et al*., 2008], the first- and second-order statistics properties of rain attenuation time series [*Burgueno et al*., 1990; *Baldotra and Hudiara*, 2004; *Matricciani*, 1994; *de Montera1 et al*., 2008; *Willis et al*., 2006; *van de Kamp*, 2003]. In previous publications, the approaches, which are based on data measured in the specific countries or areas, are restricted by their invariable parameters. Some of them merely offer the statistical characteristics of specific measured attenuation time series, or just an idea on how to obtain the statistical characteristics of attenuation time series. Admittedly, those publications indeed prompt related studies on forecasting dynamic rain-induced attenuation.

[9] It is well known that rain-induced attenuation is dependent not only on the determinate factors like link elevation angle, operating frequency, etc., but also on some random factors like rain rate, rainfall type, the shape and size distributions of the raindrops, the space distribution of rainfall rate, etc. Therefore, the result seems not satisfactory if one attempts to self-forecast by applying the statistical characteristics and invariable parameters obtained with a certain measured attenuation time series. Therefore, it is not possible to accurately obtain the change of attenuation at different times during rainfall events in other countries or areas, while applying these statistical characteristics and invariable parameters. The predicted results are not perfect using the ARIMA model with constant parameters, even in the self-forecasting case, an example of this case will be shown in section 2 of this paper. Therefore, the models and methods proposed in previous publications cannot predict accurately enough the next-time attenuation during an on-going rainfall event for an APC system to adjust transmitted power in real time, at the aim of mitigating rain-induced fade. Thus, a practical model or method, adaptive to particular rainstorms, for forecasting real-time dynamic rain-induced attenuation is urgent. It should be able to predict accurately the next-time attenuation based on current or past attenuation during an on-going rainfall event.

[10] In this paper, the novel and practical modified genetic algorithm (MGA)-autoregressive integrated moving average (ARIMA) model for forecasting real-time dynamic rain-induced attenuation has been established by introducing genetic algorithm (GA) ideas into the ARIMA model, with the data measured in Xi'an, China. The model is able to avoid the aforementioned problems, although the data measured in Xi'an, China is used to establish the model. In fact, while applying this model to forecast the attenuation during an on-going rainfall event, the parameters used by the ARIMA model are completely renewed and optimized in real time. The MGA calculates these parameters based on a parameter database, which will be discussed in section 3. It can be found in section 3 that a parameter database with *m* groups of parameters can give 2* ^{m}* groups of new parameters, and with the process of duplication, overlap, and mutation, new parameters will be generated. It has been proved that this model is adaptive and intelligent, and has the potential possibility to be employed in engineering for any country or area, with MGA generating the optimized parameters of the ARIMA(1,1,7) model.

[11] This paper has given the parameter database of the ARIMA(1,1,7) model based on the data measured in Xi'an, China. However, the proposed model shall be more applicable if more parameters based on attenuation data measured in diverse regions are included in the parameter database. Thus, the methods to establish the parameter databases in other countries or areas are recommended in section 5. The methods are feasible and convenient to obtain the databases in other countries or areas.