Models of HF Interference over Cyprus

Abstract

Interference from other users, due to the long-distance propagation of HF signals, causes spectral congestion, which is considered a primary detrimental effect on HF (3–30 MHz) communication systems. More than a year of HF electric field measurements from a calibrated monopole HF antenna collected by a dedicated measurement system installed in Cyprus have been used to compare neural networks and non-linear regression for the development of single-allocation congestion models in the HF spectrum. These models can be used to advise operators on typical interference spectral congestion levels and assist in the planning and management of frequency usage by assessing the interference level to alleviate spectral congestion in the HF band over Cyprus. The performance of these alternative modeling approaches is discussed in the context of their ability to successfully capture the diurnal variability of HF interference at a certain incident field strength threshold.

1. Introduction

Interference poses one of the most crucial operating challenges on HF (formally defined to extend from 3 to 30 MHz) communication systems as a result of the long-distance HF propagation characteristics. This becomes more severe during nighttime conditions due to the reduction of the operating range of HF frequencies within which HF systems can operate because of the absence of solar activity, which does not support a sufficient ionospheric ionization level. This limiting aspect during the evening hours is crucially challenging for HF military systems such as spread spectrum and NVIS (Near Vertical Incidence Skywave) which are in need of updated information on interference conditions. The temporal characteristics of HF interference are depicted by the systematic diurnal and seasonal variability features of HF spectral occupancy at a particular geographic location. This systematic behavior is due to the fact that users adjust their transmission schedules and frequencies in accordance with ionospheric variability. Various past experiments resulted in datasets that contributed to the investigation of this detrimental factor for specific types of users (e.g., broadcast users) and applications (e.g., OTHR, Over The Horizon Radar) [1,2]. Other HF spectral occupancy studies resulted in extended datasets on the basis of which congestion model specifications have been developed exploiting time-series and non-linear regression modeling approaches, as well as existing ionospheric models coupled with ray tracing [3,4,5]. One example of a long-term study is the HF spectral occupancy project at the University of Manchester, which has resulted in a twenty-year dataset of systematic HF interference measurements during stable daytime and nighttime ionospheric conditions from five monitoring sites over northern Europe. The outcome of this effort was a model specification known as the Laycock–Gott occupancy model [6]. Attempts have also been made, using other datasets, to apply neural networks (NN) to modeling the single allocation diurnal HF spectral occupancy [7], in the lower segment of the HF spectrum (4 MHz), focusing on groundwave users for long-term prediction [8] and short-term forecasting [9], with a focus on a single user type (broadcast users) [10], and for the entire HF spectrum [11].

This paper describes a comparison in the application of non-linear regression modeling similar to the Laycock–Gott approach and NN on a one-year dataset of electric field measurements received by a low-elevation angle antenna over Cyprus. These models provide a tool to quantitatively assess the expected HF spectral occupancy for a specific user type and frequency range over the eastern Mediterranean to enhance the capability of a HF communication system operator to evaluate the HF interference background under benign ionospheric conditions (i.e., under quiet geomagnetic activity). The dataset was collected by a dedicated HF monitoring system operating in Cyprus with a focus on the measurement and analysis of specific attributes expected to affect HF spectral congestion, such as antenna elevation angle, bandwidth, and azimuth [12]. The purpose of this study is to exploit more than a year of HF electric field measurements from the low-elevation calibrated monopole HF antenna to develop single-allocation HF spectral congestion models using neural networks and non-linear regression model specifications and compare these approaches.

2. Materials and Methods

The monitoring system is based on a R&S EM 510 digital wideband HF receiver connected to a switch that can select either the low- or high-elevation angle signal components of a R&S HE016 omnidirectional antenna (Figure 1). In this modeling study, the low-elevation angle dataset was used. The dataset was obtained by connecting the monopole HE016 antenna component to the antenna input of the R&S EM 510 measurement receiver using a 100-ms dwell time so that the full HF spectrum could be sampled in less than 30 min. By shifting a l kHz filter in 2 kHz increments in the frequency range of 1.606–30.000 MHz, we were able to determine the RMS field strength (in dBµV/m) in 14,198 channels corresponding to 95 ITU-defined frequency allocations for different user types in accordance with

Table 1. ITU HF frequency allocations.

Code	Primary Users	Frequency (MHz)	Code	Primary Users	Frequency (MHz)
1	FIXED/MOBILE	1.606–1.810	49	FIXED/MOBILE	13.800–14.000
2	AMATEUR	1.810–1.850	50	AMATEUR	14.000–14.350
3	FIXED/MOBILE	1.850–2.045	51	FIXED/MOBILE	14.350–15.000
4	FIXED/MOBILE	2.045–2.300	52	AEROMOBILE	15.000–15.100
5	FXD./MOB./BCST.	2.300–2.500	53	BROADCAST	15.100–15.600
6	FIXED/MOBILE	2.500–2.850	54	FIXED	15.600–16.000
7	AEROMOBILE	2.850–3.155	55	FIXED	16.000–16.360
8	FIXED/MOBILE	3.155–3.200	56	MARITIME/MOB.	16.360–16.860
9	FXD./MOB./BCST.	3.200–3.400	57	MARITIME/MOB.	16.860–17.410
10	AEROMOBILE	3.400–3.500	58	FIXED	17.410–17.550
11	FXD./MOB./AMTR.	3.500–3.800	59	BROADCAST	17.550–17.900
12	FIXED/MOBILE	3.800–3.900	60	AEROMOBILE	17.900–18.030
13	AEROMOBILE	3.900–3.950	61	FIXED	18.030–18.068
14	FIXED/BCST.	3.950–4.000	62	AMATEUR	18.068–18.168
15	MARITIME/MOB.	4.000–4.438	63	FIXED/MOBILE	18.168–18.780
16	FIXED/MOBILE	4.438–4.650	64	MARITIME/MOB.	18.780–18.900
17	AEROMOBILE	4.650–4.750	65	FIXED	18.900–19.300
18	FXD./MOB./BCST.	4.750–5.060	66	FIXED	19.300–19.680
19	FIXED/MOBILE	5.060–5.480	67	MAR/MOB.	19.680–19.800
20	AEROMOBILE	5.480–5.730	68	FIXED	19.800–20.000
21	FIXED/MOBILE	5.730–5.950	69	FIXED/MOBILE	20.000–20.500
22	BROADCAST	5.950–6.200	70	FIXED/MOBILE	20.500–21.000
23	MARITIME/MOB.	6.200–6.525	71	AMATEUR	21.000–21.450
24	AEROMOBILE	6.525–6.765	72	BROADCAST	21.450–21.870
25	FIXED/MOBILE	6.765–7.000	73	AEROMOBILE	21.870–22.000
26	AMATEUR	7.000–7.100	74	MAR/MOB.	22.000–22.400
27	BROADCAST	7.100–7.300	75	MAR/MOB.	22.400–22.855
28	FIXED/MOBILE	7.300–7.800	76	FIXED	22.855–23.000
29	FIXED/MOBILE	7.800–8.195	77	FIXED/MOBILE	23.000–23.200
30	MARITIME/MOB.	8.195–8.500	78	AEROMOBILE	23.200–23.350
31	MARITIME/MOB.	8.500–8.815	79	FIXED/MOBILE	23.350–24.000
32	AEROMOBILE	8.815–9.040	80	FIXED/MOBILE	24.000–24.500
33	FIXED	9.040–9.500	81	FIXED/MOBILE	24.500–24.890
34	BROADCAST	9.500–9.900	82	AMATEUR	24.890–25.000
35	FIXED	9.900–10.000	83	MAR/MOB.	25.000–25.210
36	AEROMOBILE	10.000–10.100	84	FIXED/MOBILE	25.210–25.550
37	FIXED/AMATEUR	10.100–10.150	85	RAD/ASTR	25.550–25.670
38	FIXED/MOBILE	10.150–10.600	86	BROADCAST	25.670–26.100
39	FIXED/MOBILE	10.600–11.175	87	MAR/MOB.	26.100–26.175
40	AEROMOBILE	11.175–11.400	88	FIXED/MOBILE	26.175–26.500
41	FIXED	11.400–11.650	89	FIXED/MOBILE	26.500–27.000
42	BROADCAST	11.650–12.050	90	FIXED/MOBILE	27.000–27.500
43	FIXED	12.050–12.230	91	FXD./MOB./METR.	27.500–28.000
44	MARITIME/MOB.	12.230–12.730	92	AMATEUR	28.000–28.500
45	MARITIME/MOB.	12.730–13.200	93	AMATEUR	28.500–29.000
46	AEROMOBILE	13.200–13.360	94	AMATEUR	29.000–29.700
47	FIXED/MOBILE	13.360–13.600	95	FIXED/MOBILE	29.700–30.000
48	BROADCAST	13.600–13.800

. Each l kHz channel was defined as occupied at a particular field strength threshold (from −20 to 45 dBµV/m in 5 dBµV/m steps) if the signal RMS value determined over the 100 ms observation period exceeded the corresponding calibration threshold set at the receiver’s input. The fraction of such channels across each user allocation then defines the congestion, Q for the particular field strength threshold, and allocation using the particular antenna (Figure 2) [13]. The HF spectrum is divided by the International Telecommunications Union (ITU) into frequency allocations for 9 different user types to account for the fact that there is an international agreement that defines its utilization. Interference characteristics for distinct types of users exhibit significant differences; therefore, the dataset was divided into 95 ITU-defined frequency allocations for different user types in accordance with Table 1. This is because different user types employ different transmission powers, bandwidths, modulation schemes, and operating procedures. ITU rules and guidelines dictate that transmissions in the HF spectrum must adhere to specific operating frequency ranges from designated frequency assignments, with the frequency assignment selected on the basis of several aspects such as average propagation conditions, expected attenuation due to D-layer absorption, atmospheric noise background, and last but not least, anticipated spectral occupancy levels emanating from local groundwave or long-distance skywave signal transmissions.

Figure 3 depicts measured field strength measurements received from the monopole antenna over a frequency range of 5.060–5.480 MHz, which corresponds to a fixed/mobile allocation 19 (Table 1). The bar chart in Figure 3b below illustrates occupied channels with black bars at a threshold of 20 dBµV/m on top of a white background, which corresponds to unoccupied channels.

Full HF spectra of signal strength measurements at midnight (00:00 LT), early morning (06:00 LT), noon (12:00 LT), and late afternoon (18:00 LT) are shown in Figure 4. At midnight, due to the absence of solar radiation, the ionization of the F layer is at its minimum, and therefore the maximum usable frequency (MUF), which dictates the range of HF frequencies that can be supported for skywave propagation, is also at its minimum. Consequently, HF users must occupy the lower end of the HF band, causing increased spectral occupancy.

At early morning (06:00 LT), as the solar radiation increases, the MUF (that is, the critical frequency of the F2 layer multiplied by an MUF factor, which is a function of the link distance) increases, which encourages some of the users to migrate to the middle range of the HF spectrum (15–20 MHz), as shown in Figure 4b, to exploit the available spectrum. The MUF is the highest frequency that can establish communication for a link of a certain distance with a probability of 50% of the time, and it is calculated by multiplying the critical frequency of the F2 layer (foF2) by an MUF factor that is a function of the link distance.

At noon (12:00 LT), the absorption of HF skywave signals as they pass through the lower ionospheric layer (D-layer) in the lower HF band causes users to shift to the upper segment of the HF band (>20 MHz). Due to maximum ionization, the MUF peaks at noon, and as a result, the higher HF band (i.e., 12–30 MHz) becomes congested, as shown in Figure 4c.

At 18:00 LT, the ionization decreases, and subsequently, users migrate back to the lower frequencies, resulting in higher occupancy, as demonstrated in Figure 4d.

Figure 5 depicts the 24 h variation of occupancy in the HF spectrum for interference signals exceeding a threshold of 20 μV/m, which is in accordance with the temporal signal characteristics manifested in Figure 4. At noon, most HF interference signals appear in the middle of the HF band, whereas during the evening hours, HF spectral occupancy increases in the lower segments of the HF band. This is attributed to the decrease in solar radiation, which limits ionospheric ionization and, subsequently, supports HF signal propagation at higher frequencies. The HF spectral occupancy increase during nighttime is exacerbated by co-channel interference, which becomes more pronounced as a consequence of stronger skywave HF signals propagating for longer distances due to the disappearance of the D-layer absorption in the absence of solar radiation. These variability features enable the usage of a limited range of HF frequencies, causing an increase in occupancy levels within available allocations. These conditions become even more severe during low solar activity periods when the range of usable operating frequencies is limited, further causing higher spectral occupancy levels.

The HF spectral occupancy variation in the lower HF spectrum frequencies is exactly opposite in comparison to the upper portion of the band. In the lower portion of the HF band, occupancy peaks during the evening hours since allocations follow the 24 h pattern of circuit LUF (Lowest Usable Frequency). The LUF is the lowest frequency that can provide the necessary Signal-to-Noise ratio (S/N) to ensure the minimum requirement of service for a certain link. It is highly correlated with absorption (due to D-layer ionization), which is inversely proportional to the square of the carrier frequency.

The 24 h variation profile for allocations in the upper HF spectrum is the inverse of that of allocations in the lower portion of the band, as it is also characterized by significant diurnal variation, albeit with interference levels that peak during the daytime hours. Typical diurnal variation profiles for allocations in the lower and upper HF bands are shown in Figure 6a,b, respectively.

Although the primary purpose of HF skywave propagation is long-range communication, short-range communication is also possible through near vertical incidence skywave (NVIS) HF propagation. According to NVIS, transmitted waves at high-elevation angles are reflected by the ionosphere to facilitate umbrella-like coverage. NVIS is suitable when ground-wave communication is not possible due to terrain-imposed limitations, such as in the case of Cyprus, for which NVIS communication is particularly important. The typical frequency range for NVIS is 2–10 MHz. To investigate the effect of congestion on such NVIS links, we also collected a high-elevation dataset obtained by the turnstile component of the HE016 antenna. We then calculated the correlation coefficient for all 1 kHz channels plotted as a function of frequency across the entire HF spectrum in the range of 1.606–30.000 MHz for 280 days from our dataset, for which we collected the same number of measurements for each of the 1 kHz channels. The corresponding plot is shown in Figure 7. From this plot, we can observe that the correlation coefficient exhibits a notable variation across the HF spectrum between the low and high antenna components of the HE016 array, which indicates there is a considerable difference in the signals received with the two antenna components. As a result, only the low-elevation dataset received by the monopole antenna component was incorporated in the present modeling study.

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:

• Field strength;
• Frequency;
• Type of user;
• Season (day of year);
• 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–Gott framework [14]. The logit transform, which restricts transformed congestion within the range from 0 to 1, is:

$$\ln \frac{Q}{1-Q}=\mu (X)=a+bX,$$

(1)

therefore, the inverse logit function is:

$$Q=\frac{e^{\mu (X)}}{1+e^{\mu (X)}},$$

(2)

the link function relates the linear predictor or model index function given by μ(X) to the response variable Q. Further on, μ(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:

$${\mathrm{Q}}_{\mathrm{k}}=\frac{{\mathrm{e}}^{y_{\mathrm{k}}}}{1+{\mathrm{e}}^{y_{\mathrm{k}}}}$$

(3)

$$\begin{array}{ll}{y}_k\hspace{0.17em}=\hspace{0.17em}\mathrm{A}& +\hspace{0.17em}\mathrm{B}20\log {\hspace{0.17em}}_{10}\hspace{0.17em}(E)\hspace{0.17em}\\ & +\hspace{0.17em}{C}_1\cos \hspace{0.17em}\left({\theta }_D\right)\hspace{0.17em}+\hspace{0.17em}{C}_2\hspace{0.17em}\cos \hspace{0.17em}\left(2{\theta }_D\right)\hspace{0.17em}+C_3\hspace{0.17em}\sin \hspace{0.17em}\left({\theta }_D\right)+C_4\hspace{0.17em}\sin \hspace{0.17em}\left(2{\theta }_D\right)\\ & +\hspace{0.17em}{D}_1\cos \hspace{0.17em}\left({\theta }_H\right)\hspace{0.17em}+\hspace{0.17em}{D}_2\hspace{0.17em}\cos \hspace{0.17em}\left(2{\theta }_H\right)\hspace{0.17em}+D_3\hspace{0.17em}\sin \hspace{0.17em}\left({\theta }_H\right)+D_4\hspace{0.17em}\sin \hspace{0.17em}\left(2{\theta }_H\right)\end{array}$$

E         Field strength threshold, 1–100 µV/m.

θ_D      2.π.day/365, day = 0, 1 ... 365.

θ_H      2.π.hour/24, hour = 0, 1 … 23.

A, B, C, and D Model coefficients to be estimated from data.

During the process of developing occupancy models, in the algorithm used by the program, the iterative equations have the same form as the normal equations used in the least squares regression, except that a weighted least squares method is used, in which each response variable is weighted by its variance. Thus, the estimation procedure for the model parameters is commonly referred to as iterative weighted least squares regression. When fitting a model to data, it is important to exclude insignificant explanatory variables from the final model specification. Stepwise regression was used to achieve this task, although all the parameters were shown to be significant in almost all the allocations.

The neural network models were trained to predict allocation congestion using the threshold, cosθ_D, sinθ_D, cos2θ_D, sin2θ_D, cosθ_H, sinθ_H, cos2θ_H, and sin2θ_H parameters (the same parameters used in the non-linear regression models). Neural networks are composed of neurons (with multiple input and output connections that mimic the role of biological neurons) and one-directional connections that enable the activation between neurons. Each one-directional connection is assigned a certain weight based on the intensity of the connection. These weights represent the processing capacity of the neural network, which is acquired through their adjustment so that the output will gradually approximate a desired output during training. The two major aspects of neural network development are the selection of an appropriate architecture and the training algorithm that will be applied during the learning process. The architecture is characterized by the number of neurons and how they are interconnected. The neural networks developed were feed-forward, fully connected, two-layer networks with nine input neurons and one output neuron. In the case of feed-forward neural networks, units are arranged in layers with connections only between two adjacent layers, such that a unit in a layer can send a signal only to any of the units in the next layer through an activation function. Hidden and output neurons had logistic sigmoid activation functions since their output ranges from 0 to 1 and matches the congestion range, so that no transformation of the neural network outputs was required. The architecture selection for a given dataset is critical since smaller datasets (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 back-propagation 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. In fact, the examples were randomized before each experiment, and the predictions obtained were then mapped back to their original order.

The performance of the developed models was evaluated based on the Root Mean Squared Error (RMSE) and the Correlation Coefficient (CC) between the predicted and actual congestion values. Both RMSE and CC quantify how well a model fits a dataset. However, the RMSE indicates how well a model can predict in absolute terms, while the CC indicates how well a model can predict in relative terms. The profiles of the CC, RMSE, and CC variation across the spectrum reflect a distinctive pattern that is characterized by the superior performance of the NN approach, as shown in Figure 8 and Figure 9. This is indicated by the fact that the CC for NN models is equal to or higher (this is mostly evident for allocations <40) than the CC for the non-linear regression models for most of the allocations, with the exception of allocations in the range of 64–80. With respect to the RMSE profile, we can observe that RMSE is notably low for both model approaches for allocations in the range of 50–70. This can be attributed to the fact that most of the congestion values for higher incident field thresholds for these allocations are zero due to the lack of ionospheric propagation support at these frequency allocations. This implies that diurnal and seasonal variations appearing at the lowest threshold will not appear at higher thresholds, and therefore the models will tend to saturate at these thresholds. The higher frequency allocations are actually also used for groundwave transmissions, and this is reflected in the higher RMSE values for allocations 80–95.

Examples of model fits for indicative days are shown in Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14, distributed across the HF spectrum. These plots show that both approaches can express the 24 h interference variation with reasonable accuracy and capture the dynamic variability during a 24 h day interval across the HF spectrum.

4. Conclusions

Non-linear regression and NN approaches have been applied and compared with respect to their ability to encapsulate the diurnal and seasonal variation of HF spectral occupancy for various types of users in the HF spectrum to augment the existing procedures for HF frequency assignments based only on propagation conditions. NN models demonstrate a relatively superior performance based on the Correlation Coefficient of measured versus predicted values for the majority of frequency allocations, although the Root Mean Squared Error performance between the two approaches for most allocations across the HF spectrum is comparable. The dataset on which the models were developed corresponds to a medium-to-high solar activity period (2022). Continuation of the measurement campaign for a number of years will enable the introduction of the sunspot number (the primary indicator of solar activity) as an additional parameter in these models, extending their applicability in the context of frequency planning for HF users and operators over the eastern Mediterranean.