The Suggested Reciprocal Relationship between Maximum, Minimum and Optimum Usable Frequency Parameters Over Iraqi Zone

In this work, the relationship between the ionospheric parameters (Maximum Usable Frequency (MUF), Lowest Usable Frequency (LUF) and Optimum working Frequency (OWF)) has been studied for the ionosphere layer over the Iraqi zone. The capital Baghdad (44.42E, 33.32N) has been selected to represent the transmitter station and many other cities that spread over Iraqi region have represented as receiver stations. The REC533 communication model considered as one of the modern radio broadcasting version of ITU has been used to calculate the LUF parameter, while the MUF and OWF ionospheric parameters have been generated using ASAPS international communication model which represents one of the most advanced and accurate HF sky wave propagation models. The study has been conducted for the annual and seasonal time periods of the years (2009 and 2014) of the solar cycle 24. The results of the seasonal and annual tests have indicated that the interrelationship between the MUF and OWF with LUF was a fourth order polynomial equation, while the reciprocal relationship between the MUF and OWF was a simple relationship that could be represented by a linear regression equation. The reciprocal relationships between MUF, LUF and OWF parameters (present values) have shown a good fitting with the data generated using the international models (predicted values) and theoretical values calculated from the criterion equation.


Introduction:
The ionosphere is one of the Earth's atmosphere regions, which is expanded from about 60 to 1000 km. This region is formed by the interaction of solar radiation with uncharged particles from the upper part of the Earth's atmosphere by ions and electrons (1). The ionospheric layer depends on the electronic density, so this layer is sub-divided into four layers: Layer D (60 to 90 km), E and ES layers (90 to 140 km), F1 and F2 layers (140 to 420 km) and Topside layer (420 to 1000 km) (2).
The Maximum Usable Frequency (MUF), Optimum Workable Frequency (OWF) and Lowest Usable Frequency (LUF) are the ionospheric parameters; these parameters describe the acceptable operation frequencies of a radio service between given terminals. These parameters are affected by the primary factors influence (electron density of ionization), so these parameters will increase with higher ionization density and decrease with lower ionization density (3). The highest frequency that will reflect back to Earth by the ionized layers, the median value of (MUF) parameter is only 50% of the time (4). The (OWF) is defined as the best or "optimum" frequency to use at a given hour on a given circuit; it is possible to get value of the estimation of (OWF) by taking 85% of the (MUF) parameter. The (LUF) is defined as the lowest frequency that can be used in any radio communication between any two specified points at a particular angle of incidence. The median value of (LUF) parameter is 10% of the (MUF) parameter (5). The predicted values of (MUF, OWF and LUF) are constantly changing due to changes in ionospheric factors during the day, year and 11-year sunspot cycle. In addition, the values of the ionospheric parameter gradually change in the D, E, and F layers depending on the maximum electron density for each layer and the incidence angle of the emitted radio wave, as shown in Fig. 1 (6). In this is comparatively unaffected by the Earth's surface and might propagate signals over long distances (10).

HF International Communication Models:
In this project, the Advanced Stand Alone Prediction System (ASAPS) and Recommendation 533 (REC533) models have been selected as international models for the analysis of HF-links performance in the frequency range . The ASAPS international model that is considered as one of the most advanced and accurate HF sky wave propagation model has been adopted to determine the values of the MUF and OWF parameters, and the REC533 propagation prediction model could assess the reliability and compatibility between frequencies (3 -30 MHz). The propagation program was provided by Working Party 6A (WP6A) to the ITU in July 1993. This represents one of the modern radios broadcasting versions of ITU and recommended the entire world has been selected to obtain the LUF parameter between transmitter and receiver locations over studied area.

Test and Result:
The years of 2009 and 2014 have been adopted to be a time period of study, because the selected years represent a beginning and peak of the solar cycle 24. The monthly sunspot numbers for the selected years are shown in Table 1   The spherical geodesic parameters Path Length and Bearing (transmitter to receiver (Tx to Rx) and vice versa (Rx to Tx)) have been calculated for all the selected receiver stations distributed over the studied zone. The values of the calculated geodesic parameter and the geographical location coordinates (longitude and latitude) have been illustrated in Table 2:- In this research the international communication model "ASAPS" has been used to calculate the dataset of the MUF and OWF parameters, while the dataset of the LUF parameter has been determined using the "REC533" international communication model. The behavior of MUF, LUF and OWF parameters have been studied statistically by analyzing the generated dataset from the ASAPS and REC533 models for annual and seasonal time periods for the selected years .
The seasonal ionospheric parameter variation has been investigated for four seasons. Table 3, illustrates sample of the seasonal and annual statistical analysis results of MUF, OWF and LUF parameters resulted from the execution of the picked international models for the link (Baghdad -Zurbatia). Table 3. Samples of statistical analysis of MUF, OWF and LUF parameters for the adopted years to the link (Baghdad-zurbatia).
The seasonal and annual variations of the ionospheric parameters have been performed for the selected receiver stations over Iraqi zone.   The analytical study of the generated dataset for the ionospheric parameters (MUF, LUF and OWF) has been conducted to examine the probability of getting a reciprocated correlation between these parameters. In order to investigate the correlation between the selected parameters, the study has been made for the annual and seasonal time periods of the adopted study years. The results of the analytical study showed that the correlation between ionospheric parameters can be expressed by a polynomial relationship, so the proposed reciprocal correlation equations between the tested parameters could be expressed as follows: ……… 1 Y = a o + a 1 x 1 + a 2 x 2 + ⋯ + a 5 x 5 ……… 2 So, the suggested reciprocal correlation equations can be expressed by the following set of equations: The reciprocal correlation between MUF, OWF and LUF parameters have been determined for the annual and seasonal times of the years 2009 and 2014. Based on the results of the statistical analytical study, the equation of reciprocal correlation turned out to be a polynomial equation of the Fourth Order. Table 4 shows sample of correlation coefficients (ao, a1, a2, a3 and a4) and the correlation parameter (R 2 ) of the yearly and seasonal periods of the presumed years. According to the results obtained from the statistical analysis and depending on the values of the reciprocal correlations between (LUF and MUF), (LUF and OWF) parameters, it can be noticed that there is a weak correlation between these sets of parameters. Therefore, the reciprocal correlations between these sets are not going to be considered in this work. The data of the OWF and MUF parameters have been calculated for the years 2009 and 2014 using the suggested reciprocal correlation equations (eq. 3 -6) based on the correlation coefficients (ao, a1, a2, a3 and a4) that have been shown in Table ( Table 5.   The correlated relationships between ionospheric parameters have been conducted. The seasonal and annual tests for the correlation between these parameters showed that the reciprocal correlation between MUF and OWF can be represented by a linear regression equation, while the reciprocal correlations between (MUF and LUF), (OWF and LUF) are a polynomial which represented by a fourth order polynomial equation (Quadratic Polynomial Equation). The correlation coefficients shown in Table 4 illustrate that the suggested reciprocal equations can give a good fit between these parameters standing on the values of (R 2 ).

Comparison between Present, Predicted and theoretical value of the OWF parameter for the link (Baghdad -Ajlan) of the annual time of the years 2009 and 2014
Tables 5, 6, 7, 8, and 9 show a comparison between theoretical, predicted and present annual and seasonal correlation values of (MUF and OWF) for a sample link of (Baghdad-Ajlan) for the years 2009 and 2014. The results generated from the suggested correlation equations show a good fitting with the other results. Bröms M. et al. (13) noted the good agreement between oblique and vertical sounder data and the linear relationship between variations of MUF and LUF for F2-layer. Also, Aqeel Z. Aziz et al. (6), illustrated that the results of an analytical study for the behavior of (MUF and OWF) parameters over Iraqi territory showed a good fitting between the predicted values (suggested mathematical model) and theoretical values that calculated using ICEPAC, REC533 and VOACAP models. Depending on the values of the MSE, it can be noticed that the values generated using the suggested reciprocal correlation equation comparing with the values calculated from the international model were closer than those values calculated using the theoretical criterion equation. The presented Tables show that the correlation between the two parameters is good, where it gives generally mean square error (MSE) within the average value of (0.011-0.544).

Conclusions:
The behavior of MUF, LUF and OWF ionospheric parameters studied for the years (2009 and 2014) of the solar cycle 24 over Iraqi region shows a stabilized and regular variation for the annual time of selected years. The results of the seasonal analytical study for the behavior of MUF, LUF and OWF parameters over Iraqi zone show a wide variation in the behavior of these parameters. The variation in the summer time (2009) shows more variation than in (2014) that due to the influence of the solar activity on the structure of ionosphere layer. The correlation between MUF and OWF parameters is simple, and can be expressed by linear regression. The reciprocal correlation between MUF, OWF with LUF parameters are polynomial and can be expressed by a fourth order