# Models of HF Interference over Cyprus
## 3 Model Specification and Performance  
The following parameters proved to be the most significant in terms of their influence on HF spectral occupancy over Cyprus according to the measurements obtained during the duration of the project and the subsequent analysis:  
1. Field strength;
2. Frequency;
3. Type of user;
4. Season (day of year);
5. Time of day. By definition, measured and fitted congestion must always lie within the fixed bounds of 0-1, so as to be interpreted as a ratio. However, since regression coefficients can in principle assume any real value, it is possible for a model to yield fitted congestion values outside this range. In order to overcome this deficiency, we may consider the alternative of transforming measured congestion values prior to modeling. In this way, we ensure that the fitted values will always lie within the meaningful interval from 0 to 1. A suitable nonlinear link function, called the logit transform, is used in accordance with the Laycock  
Figure 7: Correlation coefficient for signal strength measurements received in the same 1 kHz channel by low- and high-elevation HE016 antenna components plotted across the HF band. Gott framework [14]. The logit transform, which restricts transformed congestion within the range from 0 to 1, is:  
\[\ln\frac{Q}{1-Q}=\mu(X)=a+bX, \tag{1}\]  
therefore, the inverse logit function is:  
\[Q=\frac{e^{\mu(X)}}{1+e^{\mu(X)}}, \tag{2}\]  
the link function relates the linear predictor or model index function given by \(\mu(X)\) to the response variable \(Q\). Further on, \(\mu(X)\) will be denoted as y for simplicity. The logit transform exhibits a relatively linear behavior for values of Q in the range \(0.15<Q<0.85\), corresponding to values of y in the range \(-1.75<y<1.75\). When fitting a model index function to measured congestion values, the greatest sensitivity is in the linear region of the transform. Outside the linear region, large variation in the model index function will translate into large or small congestion values. The final model equation developed for diurnal variation of HF spectral occupancy over Cyprus is given below:  
\[Q_{k}=\frac{e^{y_{k}}}{1+e^{y_{k}}} \tag{3}\]  
\[\begin{array}{ll}y_{k}\,=\,A&+\,B20\,\log\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\  
(than required) have a limited ability to represent functions that map the inputs to the desired output. In fact, bigger (than required) networks may result in overfitting of the dataset, which corresponds to non-representative attributes and degrades the performance of the neural network in terms of generalization. The number of hidden layers and the associated number of neurons in each layer are determined experimentally. Five hidden neurons were initially used for each allocation. The optimum number of hidden neurons was determined by forward selection due to the difference in complexity and occupancy characteristics in each allocation. More specifically, for each allocation, an initial trial was made with five hidden neurons, followed by consecutive trials with the number of neurons increased by five until the performance of the trained network on the test data showed a significant improvement. Each network was trained using the Levenberg-Marquardt backpropagation algorithm with the MATLAB neural network toolbox based on early stopping on a validation set including 20% of the values for each allocation. Levenberg-Marquardt was applied as the training algorithm based on its speed in training moderate-sized feed-forward networks. There was no consideration of overfitting since the number of free parameters in the networks was very small compared to the number of examples used for their training. All inputs to the networks were normalized by setting the mean value of each input to zero and its standard deviation to one. Note that all congestion values from each measurement session were treated as a group so that there was no temporal correlation between the examples in the 60% training and 20% test parts.