2021 8th NAFOSTED Conference on Information and Computer Science (NICS) Prediction of Working Frequencies for Ionospheric Radio Links Nguyen Minh Giang Le Quy Don Technical University Hanoi, Viet Nam E-mail: giangnm@lqdtu.edu.vn Abstract — This paper presents method and calculation program to determine working frequency for high frequency radio links reflected one time from the ionosphere The calculation method takes into account the influence of ionospheric inhomogeneities on the characteristics of radio propagation Experimental results have shown that the calculation program based on presented method has high accuracy and fast calculation speed I INTRODUCTION Today, high frequency (HF) communication systems play important role in ensuring telecommunication for long distances besides other communication systems such as fiber optic lines, Viba, and satellite communication HF radio transmitters can transmit information over long distances up to several thousand kilometers with relatively small power due to the ability of HF radio waves to reflect one or many times in the ionosphere Therefore, improving the quality of HF communication systems is an important task The calculation process to build HF communication link requires determining diurnal variation of the Maximum usable Frequency (MUF) for that transmission line The MUF of ionospheric radio lines is the highest radio frequency that can be used for transmission between two points via reflection from the ionosphere at a specified time, independent of transmitter power When the working frequency is closer to the MUF value, the field strength of radio waves at the receiving point is greater, but if we choose the working frequency too close to the MUF, the signal at receiving point will be unstable because the ionosphere is a constantly changing environment and the MUF value also increases and decreases continuously according to that change Therefore, the optimum working frequency (OWF) is selected based on the value of MUF according to the empirical formula [1]: OWF = 0.85 MUF (1) There are many studies to develope method for calculating working frequency for ionospheric transmission link [2-3] However, these methods ignore the effect of ionospheric inhomogeneities on the propagation characteristics of radio waves There are also methods for calculating OWF based on constructing the trajectory of radio waves in the ionosphere using numerical integration method of ray equations [4-6] 978-1-6654-1001-4/21/$31.00 ©2021 IEEE However, these methods have complex algorithms and require long computation time Therefore, these methods are not suitable for quick calculation of working frequency for ionospheric radio links In this work, a simple method and calculation program that enable fast and highly accurate calculation of the OWF are presented The remainder of this paper is organized as follows: In Section II, a method for calculating working frequency for ionospheric radio links reflecting in horizontal homogeneous ionosphere is presented Section III describes method for determining working frequency of ionospheric radio links taking into account ionospheric inhomogeneities The calculation program based on presented method is included in Section IV Section V gives experimental validation of the calculation program Section VI is the generalization of the results obtained in this paper II CALCULATING WORKING FREQUENCY OF RADIO LINKS REFLECTING FROM THE HORIZONTAL HOMOGENEOUS IONOSPHERE To determine working frequency of ionospheric transmission line, it is necessary to predict parameters of the ionosphere at the time of transmission for a given location Currently, there are some popular semi-empirical models of the ionosphere, such as [7-8] that allow to calculate ionospheric parameters The input parameters for calculating by these models are: geographic coordinates of a location, time of day, date, the Wolf coefficient (W number) that characterizes the level of solar activity The semi-empirical models are based on many years of measurement by ionosonde stations In this paper, the model [7] is used because it satisfies two conditions simultaneously: it gives the calculated ionosphere parameters with allowed error, has fast computation time Using this model the parameters of the ionosphere can be calculated in real-time By using the ionosphere model [7], the following ionospheric parameters at the given point on the Earth can be determined: critical frequency of ionospheric layer, the height of layers E and F2, coefficient M(3000) for radio links with the length of 3000 km The coefficient M(3000) is defined as follows: 410 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) M 3000 f F2 MUF(3000) (2) tan Where f0 F2 is critical frequency of F2 layer at the midpoint of radio links; MUF(3000) is the maximum usable frequency for radio links with the length of 3000 km To determine the working frequency for ionospheric radio link reflected one time from the ionosphere, firstly the value MUF for this link needs to be calculated C Because tan E tan sin sin E cos E cos tan E sin sin E A K B1 P (6) cos E cos From (6) and (3) we get the expression to calculate the value of MUF(D) From there, the value of OWF can be determined according to expression (1) Thus, the values of OWF(D) can be calculated according to the values M 3000 and f F at the midpoint of the transmission line These parameters are determined using ionospheric models [7-8] Hm E , from (5) we have: M 3000 M 3000 A1 (5) B III CALCULATING WORKING FREQUENCY OF IONOSPHERIC RADIO LINK TAKING INTO ACCOUNT IONOSPHERIC INHOMOGENEITIES Fig Calculation of OWF for radio links reflecting in the ionosphere To determine the value of MUF for any radio transmission line of length D, we suppose AB is a transmission line with the length of 3000 (km) and A1B1 is a transmission line of length D (km) with D 3000 km, these two transmission lines are arranged so that the midpoints of these paths coincide (Fig.1) With the above conditions, we can assume that radio ray travels from point A to point B with frequency f MUF(3000) and from point A1 to point B1 with frequency f MUF(D) will reflect at the same point C of the ionosphere Applying Secant law [9] to determine MUF(D ) for transmission line A1B1 we have: f F2 MUF D (3) cos The method for calculating OWF value in part does not take into account the inhomogeneities of the ionosphere Therefore, it can be supposed that the orthogonal projection of the reflection point of radio ray at the ionosphere on the earth surface is the midpoint of transmission line However, under inhomogeneity condition of the ionosphere, the reflection point of radio ray will deviate from the midpoint of the transmission line towards the higher critical frequency side [10] Considering the deviation of this reflection point will improve the accuracy in calculation of OWF The inclination angle of the reflective layer due to the difference in the height of the layer at the transmitter and receiver points can be calculated according to the figure below Where is inclination angle created by ray A1C with the vertical direction OC Two expressions (2) and (3) have the same value f F2 because it is calculated at the midpoint of two transmission lines To determine MUF(D) we need to calculate the angle According to Fig 1, we denote OA = OK = OB = RE, where RE is the length of earth radius 3000 AOC E (4) 2RE ACO E , A1CO , hm - is the reflected height of radio waves at reflecting layer F2 From Fig we can calculate: 411 hm hm1 Fig Inclination angle of of the reflective layer According to Fig 2, angle is calculated by expression: h h m1 tan( ) m (7) D0 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) Where h m1 and h m are the heights of reflection layer at points that equidistant from the midpoint of the transmission line We choose this distance to be 10 km If we call T is the angle of displacement of the reflected point from the midpoint of the transmission line, we have the following relationship [11] : T tan A 20 A cos A cos (8) Fig Calculation results by the developed program Then, the reflection angle of radio waves in the ionosphere taking into account the inhomogeneities of the ionosphere can be calculated by expression: tan Where A sin cos T A cos cos T (9) h0 D , RE 2R E h is the height of reflecting layer at the midpoint of transmission line Knowing angle , the value MUF can be calculated by (3), then OWF is defined by the expression (1) V EXPERIMENTAL VALIDATION OF THE DEVELOPED CALCULATION PROGRAM In order to verify the accuracy of the calculation method and developed program, experiments on two ionospheric radio links have been carried out The first experiment was conducted on a transmission line from Ky Anh (Ha Tinh) to Phu Ly (Ha Nam) The experiment was carried out in days, from September 16 to 17, 2020 The second experiment was conducted in days on transmission line from Ky Anh (Ha Tinh) to Son Tay (Hanoi) The experiment was carried out from November 25 to 26, 2020 IV DEVELOPING PROGRAM TO PREDICT WORKING FREQUENCIES OF IONOSPHERIC RADIO LINKS According to the presented method in the previous sections, the calculation program was built to calculate the working frequencies for ionospheric radio links Interface of the developed program is presented in Fig.3 Fig Locations of transmitter and receiver of two tested transmission lines Fig Interface of the developed program to predict working frequency of ionospheric radio link Input data for calculation include: geographic coordinates of the transmitting and receiving points, day; year; Wolf number W The values W for a given day can be obtained from [12] After entering all the input parameters, the program will calculate working frequency for each hour of a given day Calculation results are presented in the form of graph and table ( Fig 4) Locations of transmitter and receiver of two tested transmission lines are presented in Fig The parameters of the transceiver devices are the following: the power of the transceiver of 20 W, using single-sideband modulation (SSB) and dipole antenna with horizontal configuration Experiments were carried out at different hours of the day Working frequency for each hour calculated by the proposed program Fig shows the calculation results of working frequencies for radio links Ky Anh - Phu Ly and Ky Anh - Son Tay in graphic form 412 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) At night time, the HF communication quality is worse than in day time This phenomenon can be explained by the reason that at night time radio energy is absorbed more strongly by the ionosphere than during the day, especially in rainy, windy and foggy weather conditions Using the program allows determining the working frequency for each communication session with the calculation time less than 10 seconds From the experimental results, it can be seen that the presented calculation method and algorithm have high accuracy and fast calculation time Using the developed program can improve the performance of HF communication systems VI CONCLUSION This paper presented a simple method for determining working frequency of ionospheric transmission lines with considering the influence of ionospheric inhomogeneities Based on the presented method, a calculation program was built to predict working frequency of ionospheric radio links Experimental results have shown that the developed program gives high accuracy of calculating working frequency for ionospheric transmission lines REFERENCES Fig Calculated working frequency for ionospheric transmission lines from Ky Anh to Phu Ly on 13 September 2020 (a) and from Ky Anh to Son Tay on 25 November 2020 (b) In the first experiment, we conducted 18 communication sessions, at each session one frequency calculated by the program is used In the second experiment, we conducted 37 communication sessions, at each communication session we used one main frequency calculated by the program and additional frequencies, with values higher and lower than 0.5 MHz relative to the main frequency In case the main frequency does not work, each additional frequency will be tested in turn To evaluate the accuracy of the calculation method, we calculate the probability of successful communication, denoted by X The value of X is determined by the expression: N X 100% M Where N is the total number of hours that communication by ionospheric radio waves on that link is possible, M is the total testing hours on that link From two experiments, the following results are obtained: in the first experiment, the probability of successful communication by ionospheric radio links is 78% with 14/18 successful communication sessions In the second experiment for the transmission line from Ha Tinh to Son Tay, the probability of successful communication is 92 % with 34/37 successful communication sessions [1] A.A Kulykovsky Handbook on the theoretical foundations of radio electronics –M : Energy, 1977.- 505 p [2] A.A Vasenina, “Prediction of the maximum usable frequencies of HF radio lines based on vertical sounding of the ionosphere,” Scientific Bulletin of NSTU, No (2014), pp 79 - 88 [3] ITU-R methods of basic MUF, operational MUF and ray-path prediction, International Telecommunication Union, 2008, ITU-R, Recommendation P.l240-1 [4] Penzin, M., Ilyin, N.V., Ponomarchuk, S (2017), “ Advanced model of HF radio waves propagation based on normal wave method,” 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), pp.1291-1297 [5] Sazhin V.I Computer simulation of radio wave propagation in the regular ionosphere Irkutsk: Publishing house ISU - 1993, 40 p [6].Levy M Parabolic Equation Methods for Electromagnetic Wave Propagation The Institution of Electrical Engineers; London, UK: 2000 [7] A simple HF propagation method for MUF and field strength: Document CCIR 6/288 – CCIR XVI-th Plenary Assembly – Dubrovnik, 1986 – 34 p [8] D Bilitza, “ IRI the International Standard for the Ionosphere,” Adv Radio Sci., №16 (2018), pp.1-11 [9] Davies, K Ionospheric radio London, United Kingdom: The Institution of Engineering and Technology, 1990 – 580 p [10] Agarushev A.I, Agarushev V.I., Prediction of long-range propagation characteristics of radio waves in the inhomogeneous ionosphere, Irkutsk: Irkutsk branch of MSTU GA,2018 [11] Agarushev A I., Shortwave radio communication systems with multipath suppression: monograph, Irkutsk: ISTU, 2009 160 p [12] http://meteo-dv.ru/geospace/AverageMonthW 413 ... PREDICT WORKING FREQUENCIES OF IONOSPHERIC RADIO LINKS According to the presented method in the previous sections, the calculation program was built to calculate the working frequencies for ionospheric. .. Calculation of OWF for radio links reflecting in the ionosphere To determine the value of MUF for any radio transmission line of length D, we suppose AB is a transmission line with the length of 3000... usable frequency for radio links with the length of 3000 km To determine the working frequency for ionospheric radio link reflected one time from the ionosphere, firstly the value MUF for this link