Capacity and Reliability of Ionosphere Communication Channel Based on Multi-Carrier Modulation Technique and LUF-MUF Variation

Varuliantor DEAR, Annis SIRADJ MARDIANI, Nandang DEDI, Prayitno ABADI, Baud HARYO PRANANTO, ISKANDAR

Summary :

Low capacity and reliability are the challenges in the development of ionosphere communication channel systems. To overcome this problem, one promising and state-of-the-art method is applying a multi-carrier modulation technique. Currently, the use of multi-carrier modulation technique is using a single transmission frequency with a bandwidth is no more than 24 kHz in real-world implementation. However, based on the range of the minimum and maximum ionospheric plasma frequency values, which could be in the MHz range, the use of these values as the main bandwidth in multi-carrier modulation techniques can optimize the use of available channel capacity. In this paper, we propose a multi-carrier modulation technique in combination with a model variation of Lowest Usable Frequency (LUF) and Maximum Usable Frequency (MUF) values as the main bandwidth to optimize the use of available channel capacity while also maintaining its reliability by following the variation of the ionosphere plasma frequency. To analyze its capacity and reliability, we performed a numeric simulation using a LUF-MUF model based on Long Short Term-Memory (LSTM) and Advanced Stand Alone Prediction System (ASAPS) in Near Vertical Incidence Skywave (NVIS) propagation mode with the assumption of perfect synchronization between transmitter and receiver with no Doppler and no time offsets. The results show the achievement of the ergodic channel capacity varies for every hour of the day, with values in the range of 10 Mbps and 100 Mbps with 0 to 20 dB SNR. Meanwhile, the reliability of the system is in the range of 8% to 100% for every hour of one day based on two different Mode Reliability calculation scenarios. The results also show that channel capacity and system reliability optimization are determined by the accuracy of the LUF-MUF model.

• Publication: IEICE TRANSACTIONS on Communications Vol.E107-B No.4 pp.357-367
• Publication Date: 2024/04/01
• Online ISSN: 1745-1345
• DOI: 10.23919/transcom.2023EBP3122
• Type of Manuscript: PAPER
• Category: Antennas and Propagation

1.  Introduction

The main challenge of the ionospheric communication channel system is its low channel capacity and reliability. The low channel capacity is due to the multipath fading environment and the coherent bandwidth limitations [1], [2]. While the low-reliability main factor is caused by the boundary of the transmission frequency value, which follows the variation of the ionosphere plasma frequency [3]. To overcome the low capacity issue, a multi-carrier modulation technique such as Orthogonal Frequency Division Multiplexing (OFDM) is used as one of the solutions, with the purpose to avoid frequency selective fading [4]-[8]. To overcome the low reliability issue, a management frequency approach [9]-[11], along with the implementation of adaptive selection frequencies such as the Automatic Link Establishment (ALE) technique, employed in the system [12]-[14]. This technique enables the system to follow the variations in ionospheric plasma frequencies in order to guarantee the success of radio wave propagation from transmitter to receiver. Those approaches are known as the state-of-the-art methods in the development of the ionospheric communication channel system.

Currently, the use of a multi-carrier modulation technique in the ionosphere communication channel system uses a conventional main bandwidth which values are 3 kHz (narrowband HF) [15]-[19] and 24 kHz (wideband HF) [4], [20]-[22]. Meanwhile, the adaptive technique uses an analysis of data link quality from the sounding process to select a single frequency with a narrow bandwidth [23], [24]. Those combined approaches improve the reliability of the system by following the ionosphere plasma variation and increasing the channel capacity up to 9.6 kbps in the real-world implementation [25]. However, based on the range of minimum and maximum ionosphere frequency plasma values, which are in the range of MHz [3], [10], [26], the utilization of this frequency range as the main bandwidth of a multi-carrier modulation technique is quite promising. The utilization of the ionosphere frequency plasma range as the main bandwidth of the multi-carrier modulation technique could potentially optimize the use of available channel capacity while also maintaining its reliability. In this paper, we propose the multi-carrier modulation technique with a combination of the Lowest Usable Frequency (LUF) - Maximum Usable Frequency (MUF) variations in the ionosphere communication channel system and examine its capacity and reliability. The proposed system uses the variations of the LUF-MUF value from a model and uses it as the main bandwidth, where its maximum value could be more than 10 MHz. For the sub-carrier bandwidth, the bandwidth coherent value based on the International Telecommunication Union's (ITU) recommendation is used, where its value is in the range of kHz [27]. To analyze its capacity and reliability, we performed a numeric simulation using a LUF-MUF model based on Long Short-Term Memory (LSTM) and Advanced Stand Alone Prediction System (ASAPS) for Near Vertical Incidence Skywave (NVIS) propagation mode. To get a comprehensive explanation, the structure of this paper is presented as follows: In Sect. 2 we discuss the variation of the ionosphere and its channel capacity and reliability calculation. In Sect. 3, we explain the main concept of the multi-carrier modulation technique with a combination of LUF-MUF variation and its capacity and reliability analysis method. In Sect. 4, we show and discuss the numerical simulation result. In the last section, we conclude this paper.

2.  Theoretical Background

2.1  Variation of Ionosphere Channel

As a radio wave propagation medium in the High Frequency (HF) radio spectrum, the earth's ionosphere is formed by the electrons which resulted from atmosphere ionization at 60 to 2000 km altitudes. The formation of the ionosphere layers is determined by the space weather dynamics with the main source is solar activity radiation [28]. The dynamic formation of the ionosphere layer causes the frequency of radio waves that can propagate in the ionosphere layer to vary in time and place [3]. Variations of the radio wave frequency values that can be reflected by the ionosphere layer could refer to the critical frequency value of the ionospheric F layer (\(f_{o}F2\)) which has daily, seasonal, and solar cycle activity variations [28]. For application in ionospheric channel communication, the \(f_{o}F2\) value can be converted into the lower limit and upper limit of reflected frequency, namely the Lowest Usable Frequency (LUF) and Maximum Usable Frequency (MUF). Therefore, to guarantee the propagation of radio waves from transmitter to receiver, the transmission frequency values should be selected between the LUF and MUF values.

The calculation of LUF and MUF is based on the geometry of the transmitter and receiver locations and is expressed by the equation as follows:

\[\begin{equation*} MUF = \alpha . f_{o}F2 \tag{1} \end{equation*}\]

and

\[\begin{equation*} LUF = \alpha . f_{min} \tag{2} \end{equation*}\]

with \(\alpha\) is the geometry factors of transmitter and receiver locations which could be expressed using equations:

\[\begin{equation*} \alpha = \frac{\sqrt{{h^2}+{d^2}}}{h} \tag{3} \end{equation*}\]

\(h\) is the height of the ionosphere layers, and \(d\) is the distance between the transmitter and receiver. For Near Vertical Incidence Skywave (NVIS) propagation mode, where the distance of transmitter and receiver is less than 300 km, the value of \(\alpha\) is equal to 1. The values of LUF and MUF directly follow the \(f_{min}\) and \(f_{o}F2\) values [29], [30].

2.2  Channel Capacity

Besides being known as a channel that has temporal and spatial variations, the ionosphere's physical properties also cause radio wave propagation from the transmitter to the receiver to experience more than one path, known as a multipath channel. As a multipath fading channel, ionospheric channel capacity can be calculated by the following equation:

\[\begin{equation*} C= \int_{-\infty}^\infty B \log_{2} (1 + \gamma) p(\gamma)d\gamma \tag{4} \end{equation*}\]

where \(C\) is the capacity in units of bits per second (bps). \(B\) is the coherent bandwidth (Hz), \(\gamma\) is the signal to noise ratio (SNR) value, and \(p(\gamma)\) is the probability density function (pdf) of the SNR value, which follows the variation of the channel realization gain value. The channel capacity in the above equation is called the ergodic capacity, as it is known as a random process. For the upper limit of the channel capacity, the calculation using the Additive White Gaussian Noise (AWGN) channel could be used, which is expressed in the equation as follows:

\[\begin{equation*} C= B \log_{2} (1 + \overline{\gamma}) \tag{5} \end{equation*}\]

with \(\overline{\gamma}\) is the average of SNR. For the calculation of the total channel capacity using a multi-carrier modulation technique where each sub-channel is independent and identically distributed (i.i.d), the total ergodic capacity of the system could be expressed as follows:

\[\begin{equation*} C_{tot}= \Sigma_{k=1}^K B \log_{2} (1 + \gamma_{k})p(\gamma_{k}) \tag{6} \end{equation*}\]

with

\[\begin{equation*} \gamma_{k}= \frac{|g_{k}|^2 P_{k}}{N_{k}B_{k}} \tag{7} \end{equation*}\]

\(g\) is the realization of the channel gain for each of the \(k\) sub-carriers, \(P\) is the transmitted power, \(N\) is the noise spectral density, and \(B\) is the sub-carrier bandwidth with its values below the coherent bandwidth of the channel.

In addition to ergodic capacity, the calculation of multipath fading channel capacity can be expressed by outage capacity. Outage capacity is the probability of transmission failure based on specified criteria, such as minimum SNR. Outage capacity is expressed using the equation as follows:

\[\begin{equation*} C_{outage}= P_{r}(\log_{2}(1+\gamma)< r) \tag{8} \end{equation*}\]

where \(Pr(.)\) is the probability function and \(r\) is the minimum data rate threshold with an acceptable error value. Outage capacity also has meaning as a measure of system reliability.

2.3  Reliability of Ionosphere Communication System

To calculate the reliability of the ionospheric channel communication system, there are six types of reliability levels stated by the International Telecommunication Union (ITU) [31], namely: Mode Reliability, Circuit Reliability, Reception Reliability, Path Reliability, Communication Reliability, and Service Reliability. Mode Reliability (MR) is the basic level of ionospheric communication system reliability according to the limitations of the transmission frequency that could propagate in the skywave mode. In simple terms, the non-zero value of the Mode Reliability level is determined by the selection of the transmission frequency value in the range of LUF - MUF values. The Circuit Reliability is a calculation of communication circuit reliability based on the performance of a selected transmission frequency, such as the minimum SNR value limit. The Circuit Reliability calculation also includes the Mode Reliability calculation and is used as a basis for calculating the reliability level of a communication circuit, which is known as the Basic Circuit Reliability (BCR). For digital modulation, the BCR calculation is expressed by the equation as follows:

\[\begin{equation*} BCR(\%)= R_{SN}.R_{T}.R_{F} \tag{9} \end{equation*}\]

where \(R_{SN}\) is the probability of achieving the SNR minimum (\(SN_{o}\)). \(R_{T}\) s the probability that the required time spread at a level of \(-10\) dB relative to the peak signal amplitude is not exceeded. \(R_{F}\) is the probability that the required frequency dispersion at a level of \(-10\) dB relative to the peak signal amplitude is not exceeded. To calculate \(R_{SN}\), there are two equations that could be selected based on the condition, which are:

\[\begin{equation*} \begin{split} R_{SN} & = 130 - 80 / [1 + (SN_{m} - SN_{o})/D_{l} ] & \text{for } SN_{m} \geq SN_{o} \\ & = 80/[ 1 + (SN_{o}-SN_{m})/D_{u}]-30 & \text{for } SN_{m} < SN_{o} \\ \end{split} \tag{10} \end{equation*}\]

with \(SN_{m}\) is the monthly median SNR value. \(D_{u}\) and \(D_{l}\) are the upper decile and lower decile deviation of monthly median SNR values, respectively. For calculating \(R_{T}\), there are equations that are also based on two different conditions, which are:

\[\begin{equation*} \begin{split} R_{T} & = 130 - 80 / [1 + (T_{o} - T_{m})/D_{Tu} ] & \text{for } T_{m} \leq T_{o} \\ & = 80/[ 1 + (T_{m}-T_{o})/D_{Tl}]-30 & \text{for } T_{m} > T_{o} \\ \end{split} \tag{11} \end{equation*}\]

with \(T_{m}\) is the monthly median time spread, \(D_{Tu}\) and \(D_{Tl}\) are the lower decile and upper decile deviation of monthly median time spread values, respectively. For calculating \(R_{F}\), the equations based on two conditions that could be used are:

\[\begin{equation*} \begin{split} R_{F} & = 130 - 80 / [1 + (F_{o} - F_{m})/D_{Fu} ] & \text{for } F_{m} \leq F_{o} \\ & = 80/[ 1 + (F_{m}-F_{o})/D_{Fl}]-30 & \text{for } F_{m} > F_{o} \\ \end{split} \tag{12} \end{equation*}\]

where \(F_{m}\) is the monthly median frequency dispersion,\(D_{Fu}\) and \(D_{Fl}\) are the upper decile and lower decile deviation of monthly median frequency dispersion values, respectively.

The \(SN_{m}\), \(R_{T}\), and \(R_{F}\) values could be obtained from ionospheric physical models such as VOACAP [32]. While the upper and lower decile values for those parameters could be selected from the ITU document [31]. To determine the \(SNo\) value, the BER curve as a function of SNR could be used based on the accepted minimum BER value.

For communication circuits that use more than one transmission frequency, the calculation of reliability is done using Basic Reception Reliability (BRR) which is expressed by the equation as follows:

\[\begin{equation*} BRR(\%)= 100[1- \prod_{k = 1}^{K} (1-\frac{BCR(f_{k})}{100}) ] \tag{13} \end{equation*}\]

with \(BCR(f_{k}\)) is the basic circuit reliability of each carrier frequency.

3.  Multi-Carrier Modulation with LUF-MUF Variation

The basic form of multi-carrier modulation is dividing the data stream into multiple sub-streams that are transmitted over different orthogonal subchannels centered at different sub-carrier frequencies [33]. In this study, the proposed block diagram of the multi-carrier modulation technique with a combination of LUF-MUF variations in the ionosphere channel communication system is shown in Fig. 1. The data stream transmission is divided into an independent number of \(K\) sub-carriers, which are determined by the variations of LUF-MUF and Bandwidth coherent (\(B_{c}\)) values. The values of LUF-MUF and \(B_{c}\) are known on the transmitter and receiver sides.

Fig. 1  Block diagram of the proposed ionosphere communication system using the multi-carrier modulation technique and LUF-MUF variations. Variations of LUF-MUF values and bandwidth coherence determine the number of sub-carriers and are known by the transmitter and receiver for optimization of available capacity usage along with reliability.

The LUF and MUF values could be obtained from physics models such as the International Reference of Ionosphere (IRI) [34], the Advanced Stand-Alone Prediction System (ASAPS) [35], and NeQuick [36] that available for public uses. Those models are empirical models that were built using different methods but have a similar number of input variables, namely: location, time, and conditions of solar activity. In practice, more than one input variable could make the system more complex. Therefore, in addition to these empirical models, a method that is currently developing and has the potential to be used practically is a machine learning-based model [37]-[39]. The machine learning model could utilize a single variable of time series data. Therefore, the LUF-MUF model based on machine learning is simpler to practically apply in the proposed system. In this study, the LSTM machine learning model was used for the analysis beside the empirical physic model namely ASAPS.

The LUF-MUF values determine the main bandwidth, with a value in the range of MHz. To roughly determine the number of sub-carriers of the proposed system, the main bandwidth is divided by the Bandwidth coherent (\(B_{c}\)) as spacing sub-carrier frequency to avoid frequency selective fading. The \(B_{c}\) value is in the range of kHz and can be obtained from the delay spread value recommended by ITU [27] or from the channel sounding system as part of the channel estimation process [40], [41]. In this study, the \(B_{c}\) value is 2 kHz refers to the ITU delay spread value in quite ionosphere conditions, and is known by the transmitter and receiver. To calculate the total channel capacity, the equation that could be used is expressed as follows:

\[\begin{equation*} C_{tot}= \Sigma_{k=1}^K B_{k} \log_{2} (1 + \frac{|g_{k}|^2 P_{k}}{N_{k}B_{k}}) \tag{14} \end{equation*}\]

where \(P_{k}\) is the transmit power, \(g_{k}\) is the channel gain, \(B_{k}\) is the sub-carrier bandwidth following the \(Bc\) value, and \(N_{k}\) is the noise spectral density values of each independent \(k\) sub-carrier. The number of \(K\) sub-carriers are determine using the following equations:

\[\begin{equation*} K_{i}= \frac{MUF_{i}-LUF_{i}}{B_{c}} \tag{15} \end{equation*}\]

where \(MUF-LUF\) is the value of the maximum-lowest usable frequency values as a function of time \(i\), and \(B_{c}\) is the coherent bandwidth value. In this calculation, the maximum number of sub-carriers is assumed without using guard band frequency and the system has perfect synchronization between transmitter and receiver with no Doppler, and no time offsets.

To calculate the reliability of the proposed system, the Basic Circuit Reliability (BCR) is used according to Eq. (9). However, because the ground truth of LUF-MUF determines the success of each sub-carrier frequency transmission in the BCR calculation, the Mode Reliability (MR) calculation should be conducted first. If the sub-carrier transmission frequency is outside the actual LUF-MUF range, then the transmission of radio waves from the transmitter to the receiver cannot be realized perfectly due to some sub-carrier frequencies not being reflected by the ionosphere [3], which inherently causes the BCR values for those frequencies to be zero. To calculate the Mode Reliability of the proposed multi-carrier technique, there are two scenarios that can be used, namely:

• Scenario \(\#\)1. Transmission fails completely if one or more of the sub-carriers cannot be realized, and
• Scenario \(\#\)2. Transmission can still be realized with some degree of reliability, even if some sub-carriers cannot be realized.

For the Scenario \(\#\)1, the Mode Reliability (MR) calculation for multi-carrier transmission could be expressed as follows:

\[\begin{eqnarray*} &&\!\!\!\!\! MR(\%)=\frac{1}{M} \Sigma_{m=1}^M P(LUF;MUF)_{m}.100\nonumber\\ &&\!\!\!\!\! P(LUF;MUF)_{m}= \begin{cases} 1, & \text{if } LUF_{pred} \geq LUF_{act} \\ & \cap MUF_{pred} \leqslant MUF_{act} \\ 0, & \text{otherwise} \end{cases}\nonumber\\ &&\!\!\!\!\! \tag{16} \end{eqnarray*}\]

where MR is the Mode Reliability in the \(M\) period time, \(LUF_{pred}\) and \(MUF_{pred}\) are the LUF and MUF from the model, and \(LUF_{act}\) and \(MUF_{act}\) are the actual values of LUF and MUF from observation. MR values that achieve 100\(\%\) show that in periods of \(M\), the system is reliable due to all sub-carrier transmissions being able to propagate in the ionosphere channel. However, if the MR value is less than 100\(\%\), then the system is not reliable at the period of \(M\) because one or more sub-carrier transmissions are not able to propagate in the ionosphere channel. The \(M\) period time could represent the period of an hour in one day or the period of a day in one month.

For the Scenario \(\#\)2, where reliability is still realized even though there are several sub-carriers that fail to propagate in the ionosphere channel, the calculation of the Mode Reliability can be expressed by the equation:

\[\begin{equation*} \begin{array}{@{}l@{}} \displaystyle MR(\%)=\frac{\Sigma_{k=1}^K P(f_{k})}{(\frac{MUF-LUF}{B_{c}})}.100 \\[4mm] P(f_{k})= \begin{cases} 1, & \text{if } LUF \leqslant f_{k} \leqslant MUF \\ 0, & \text{otherwise} \end{cases} \end{array} \tag{17} \end{equation*}\]

where \(B_{c}\) is the coherent bandwidth value which determines the number of sub-carriers from the main bandwidth. LUF-MUF is the actual value from the observation, and \(P(f_{k})\) is the probability of each \(k\) sub-carrier frequency, which is in the range of the LUF-MUF from the model. In this scenario, even though one or more sub-carrier transmissions cannot be realized due to the ionospheric channel not supporting the propagation from the transmitter to the receiver, the system still has some degree of reliability.

4.  Numerical Simulation Results

In this section we evaluate the ergodic capacity and reliability of the proposed system using numeric simulation. The simulation was done by sending a number of random message bits to each of the independent sub-carrier channels as shown in the block diagram of Fig. 1 and evaluating the achieved capacity and reliability. Parameter that used in the simulation are shown in Table 1, with assumption perfect synchronization between transmitter and receiver with no Doppler, and no time offsets which are source of Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI). The sub-carrier frequencies are determined from the range of LUF-MUF values, which resulted from a model. For LUF-MUF models, we use the ASAPS and LSTM models. The ASAPS model is provided in the public domain and could be used openly, with its prediction performance already reported in [42]-[44]. However, for the LSTM model, we designed its architecture and tested its performance.

Table 1  Simulation parameter values.

4.1  LSTM Model Performance

Long short-term memory (LSTM) is an artificial neural network that has a feedback connection and thus can be classified as a recurrent neural network (RNN) [45]. LSTM has been shown to outperform traditional RNNs on numerous temporal processing tasks [46]. These temporal processing tasks include the processing of multivariate time-series data to perform predictions on future values. In this research, LSTM is used to predict the LUF-MUF values with the architecture of the LSTM model presented in Fig. 2.

Fig. 2  Architecture of the LSTM model to predict the LUF-MUF values.

The model of LSTM consists of three LSTM layers and one fully connected layer, with inputs in the form of \(f_{min}\) and \(f_{o}F2\) data set values. The data set was obtained from Ionosonde in Pontianak, and the period of data for the LSTM training and fitting process is December 2022. The output of the LSTM model is the prediction of the \(f_{min}\) and \(f_{o}F2\) values, and its performance is evaluated based on the actual \(f_{min}\) and \(f_{o}F2\) values from Ionosonde Pontianak in January 2023. The \(f_{min}\) and \(f_{o}F2\) prediction values are equivalent to the LUF-MUF values for determining the main bandwidth of the proposed system. The method of the LSTM model is open-loop forecasting, where the recent observation data is reused for the future prediction process.

The prediction results of the LSTM model for the parameters \(f_{min}\) and \(f_{o}F2\) as LUF-MUF equivalent values are presented in Fig. 3. Comparison of the predicted results of the LSTM model with the actual values shows that the root mean square error (RMSE) value is 0.55502 for the \(f_{min}\) parameter. As for the parameter \(f_{o}F2\), the RMSE value has reached 0.56099. The RMSE value of \(f_{min}\) and \(f_{o}F2\) that reaches 0.5 MHz will have a significant impact on the utilization of available channels and the level of system reliability. For instance, using a 2 kHz bandwidth of subcarriers based on ITU delay spread recommendations values [27], the 0.5 MHz error prediction value lower than the actual could make around 250 subcarriers not used effectively. Meanwhile, the 0.5 MHz error prediction value higher than the actual could make around 250 subcarriers impossible to realize, which influenced the reliability of the system. Figure 4 shows the statistical analysis of the performance of the LSTM model. The correlation between the predicted results and the actual parameter \(f_{min}\) is 0.89. As for the parameter \(f_{o}F2\), the correlation is 0.905. The error distribution of \(f_{min}\) has a mean 0.02247 and a standard deviation 0.53438. While the distribution of errors resulting from the prediction of \(f_{o}F2\) has a mean value \(-0.13771\) and a standard deviation of 0.54536.

Fig. 3  Comparison between predicted values output from the LSTM model and actual values for (a) \(f_{min}\) and (b) \(f_{o}F2\) in January 2023. The vertical axis is frequency, and the horizontal axis is the sequence of the predicted data set number.

Fig. 4  Performance of LSTM model for (a) \(f_{min}\) and (b) \(f_{o}F2\) prediction values.

4.2  Ergodic Channel Capacity

Figure 5(a) shows the results of calculating the ergodic capacity and upper limit (upper bound) of channel capacity on January 1, 2022, based on the main bandwidth values of the LUF-MUF ASAPS and LSTM models with SNR values between 1 and 20 dB. From the figure, it can be seen that the ergodic channel capacity varies every hour, with values ranging from 10 Mbps to 100 Mbps. This achieved ergodic capacity value is higher than the existing achieved capacity, which is 9.6 kbps [25].

Fig. 5  Comparison of ergodic capacity using the ASAPS and LSTM models on January 1, 2023, with (a) variations of SNR 1 to 20 dB and (b) SNR 20 dB. The achieved ergodic capacity values are in the range of \(10^{6}\) to \(10^{8}\) bps, while the conventional method is below \(10^{3}\) bps [25].

In Fig. 5(b), it can be seen specifically the calculation of the ergodic capacity of the channel with 20 dB SNR of two model LUF-MUF. The channel ergodic capacity using the ASAPS model shows that the minimum ergodic capacity occurs at 23 Universal Time (UT), or 6 Local Time (LT; UT+7) with a value \(5.8\cdot 10^{7}\) bps. Meanwhile, the maximum capacity is at 12 UT or 19 LT, with values up to \(1,58\cdot 10^{8}\) bps. The minimum ergodic capacity using the LSTM is \(6.6\cdot 10^{8}\) bps and occurs at 22 UT or 05 LT. The maximum ergodic capacity of the LSTM model occurs at 15 UT or 22 LT with values up to \(1.56\cdot 10^{8}\) bps.

Figure 6 depicts a comparison of ergodic channel capacity between the ASAPS model, LSTM model, and the actual values on January 1, 2023. Figure 6(a) shows the calculation of ergodic channel capacity for SNR values between 1 and 20 dB. While Fig. 6(b) shows the ergodic channel capacity with 20 dB SNR. Based on the figure, it can be seen the difference between the ergodic channel capacity value of the model and the actual value. The calculation of ergodic channel capacity using models can be higher or lower than the actual ergodic channel capacity values. This condition depends on the comparison between the LUF-MUF values of the model and the actual LUF-MUF values, which determine the main bandwidth value. When the predicted main bandwidth value from the model is lower than the actual main bandwidth (an underestimate), there is still available ergodic channel capacity that can be realized. However, when the predicted main bandwidth from the model is higher than the actual main bandwidth (an overestimate), some ergodic channel capacity cannot be realized, which affects the system's reliability.

Fig. 6  Calculation of the ergodic capacity based on the main bandwidth variations from the ASAPS model, LSTM model, and actual main bandwidth on January 1, 2023, with (a) variations of SNR from 1 to 20 dB and (b) SNR 20 dB.

In Fig. 6(b), the actual ergodic capacity in the 23 UT to 00 UT, or 06 LT to 07 LT, is lower than the ergodic capacity of the ASAPS and LSTM models. This condition occurs due to the lower values of the actual main bandwidth compared to the predicted main bandwidth values from the ASAPS and LSTM models. The ASAPS and LSTM models exhibited limitations in accurately predicting the lower values of actual \(f_{min}\) and \(f_{o}F2\), consequently leading to higher main bandwidth and ergodic capacity when compared to the actual values. The inability of the ASAPS and LSTM models to predict the \(f_{min}\) and \(f_{o}F2\) could be attributed to the “sudden change” of the \(f_{min}\) and \(f_{o}F2\) trend values in those periods of time. Around 23 UT-00 UT, or 06-07 at local time, the sun begins to rise (sunrise). The formation of the ionosphere layers in this period changes from the dominant recombination process to the dominant ionization process as the radiation from the sun starts [47]. The trends of the \(f_{min}\) and \(f_{o}F2\) values start to increase as the solar radiation increases, which is opposite to the previous trends. In addition to these conditions, the rate of the ionization process in the D layer, which determines the \(f_{min}\) values, is different from the rate of the ionization process in the F layer, which determines the \(f_{o}F2\) value [48]. The \(f_{min}\) values increase faster than the \(f_{o}F2\) values, which makes the actual main bandwidth lower compared to the previous values. These “sudden trend changes” could not be correctly predicted by the ASAPS and LSTM models, which resulted in a lower actual ergodic capacity value.

In Fig. 7, the calculation of ergodic channel capacity as a function of SNR for every hour on January 1, 2023, using the actual LUF-MUF value is presented. From the calculation results, it can be seen that the highest capacity occurs at 13 UT (20 LT) and the lowest capacity at 00 UT (07 LT). When the SNR is 0 dB, the difference in capacity between the minimum and maximum is 10 Mbps. Meanwhile, at 20 dB SNR, the difference reaches 100 Mbps.

Fig. 7  Ergodic channel capacity based on the actual bandwidth value of the ionosphere channel on January 1, 2023

In Fig. 8, the outage capacity with a minimum SNR value between 1 and 5 dB is presented as a general calculation of the reliability level of communication systems in the Rayleigh distributed channel. It can be seen that an increase in the SNR minimum or threshold value is followed by an increase in the outage capacity. If the SNR value on the receiving side increases and the minimum SNR value remains constant, the outage capacity value decreases.

Fig. 8  Outage capacity with minimum SNR (\(SN_{o}\)) from 1 to 5 dB.

4.3  Reliability

Figure 9 shows the calculation of the Mode Reliability for each day in January 2023 with the first scenario based on Eq. (16). The \(M\) period of this Mode Reliability calculation is for each day in one month. From Fig. 9, it can be seen that the Mode Reliability using the LUF-MUF value from the ASAPS model in January 2023 is in the range of 10\(\%\) to 79\(\%\), and the Mode Reliability using the LSTM model is in the range of 8\(\%\) to 79\(\%\). The lowest value of Mode Reliability in the ASAPS model is 10\(\%\), which occurs on January 11, while the highest value of Mode Reliability is 79\(\%\) and occurs on January 19. The lowest value of Mode Reliability of the LSTM model is 8\(\%\) and occurs on January 31, while the highest value of Mode Reliability is 79\(\%\) and occurs on January 24, 2023.

Fig. 9  Mode reliability calculation result for each day in January 2023 using Scenario \(\#\)1.

To get a more detailed explanation of calculation results from Mode Reliability values using Scenario \(\#\)1, which is given in Fig. 9, a good example of comparative data between the LUF-MUF model values and the actual LUF-MUF values from observation over one day, namely January 6, 2023, is presented in Fig. 10. It can be seen that on January 6, 2023, between 11 and 22 UT, the LUF and MUF values of the ASAPS model are between the actual LUF-MUF values. This condition is considered reliable because the range of subcarrier frequencies that were selected in the transmission system could be realized. Different conditions occurred between 6 UT and 11 UT. The LUF-MUF value of the ASAPS model is outside the range of the actual LUF-MUF values, where the LUF model is lower than the actual LUF. Therefore, the system is considered unreliable because all the selected subcarrier frequencies could not be fully realized. At different time periods, namely 0 UT to 1 UT, it can be seen that the predicted LUF value of the ASAPS model is within the range of actual LUF-MUF values. However, the predicted MUF value is outside the range of actual LUF-MUF values, which is considered to be an unreliable system. This condition explains why the ASAPS Mode Reliability value reached 68\(\%\) on January 6, 2022, as shown in Fig. 9. Similar to the ASAPS model, some of the predicted LUF and MUF values from the LSTM models are within the range of the actual LUF-MUF values, which occurred between 16 and 22 UT, and are considered reliable. Meanwhile, the predicted LUF and MUF values between 6 UT and 10 UT were outside the range of the actual LUF-MUF values, which caused the system to be considered unreliable.

Fig. 10  Comparison of actual LUF-MUF values with results from (a) ASAPS, and (b) LSTM models on 6th January 2023.

In Fig. 11, the Mode Reliability calculation result using the first scenario for every hour of every day in January 2023 based on Eq. (16) is presented. The \(M\) period of this Mode Reliability calculation is for each hour in one day. The blue color represents a system considered unreliable, while the yellow color represents a system considered reliable. In every hour of the day, if the LUF-MUF from the model is within the range of the actual LUF-MUF, the system is considered reliable at that hour. However, if some values of the LUF-MUF from the model were outside the actual LUF-MUF, the system is considered not reliable at that hour due to the fact that one or more of the sub-carriers could not be realized. From the figure, it can be seen that the dominant reliable system occurs from 17 UT to 23 UT, which is at night in local time. The dominance of a reliable system at night can be attributed to the very low \(f_{min}\) value parameter due to the disappearance of the D layer during nighttime [49]. With the disappearance of the D ionosphere layer, the determination of the main bandwidth only depends on the accuracy of the MUF value prediction.

Fig. 11  Mode reliability for each hour in January 2023 using Scenario \(\#\)1. The yellow box color indicates the system is reliable. While the blue box color indicates the unreliability of the system, The white color with ‘No Available Data (ND)’ marks shows the unavailable MR calculation results due to the unavailable data of the actual LUF-MUF.

Figure 12 is the second scenario Mode Reliability calculation result, which shows the hourly variations of MR values on each day in January 2023 for the ASAPS and LSTM models. For each hour in a day, there are no zero values for MR, which indicates the total failure of transmission. However, there are a number of hours for which the MR value cannot be calculated due to the unavailability of the actual LUF-MUF, which are on the 5th, 11th, 12th, 17th, and 21st. The unavailable MR calculation values are shown in a white color box with the ‘No Available Data (ND)’ mark. Based on the calculations, the Mode Reliability of the LSTM model shows a high value for each day from 12 UT to 20 UT, which reaches up to 100\(\%\). As for the ASAPS model, the highest value of Mode Reliability is in the range of 13 UT to 16 UT. The 100\(\%\) value of Mode Reliability indicates that all sub-carrier transmissions based on the range of LUF and MUF model values are acceptable because the ionosphere layer is able to support the propagation. The Mode Reliability value that is less than 100\(\%\) indicates that a number of sub-carrier transmissions fail due to being outside the range of the actual MUF-LUF value. Fluctuations in the Mode Reliability level indicate that transmission from each sub-carrier for every hour of the day cannot be fully realized. There are several sub-carrier transmissions experiencing problems as the LUF and MUF model values do not match the actual LUF and MUF values. The lowest value of the second scenario Mode Reliability calculation for both ASAPS and LSTM models is in the range of 40\(\%\).

Fig. 12  Mode Reliability for each hour in January 2023 using Scenario \(\#\)2. The MR values are presented in color. The white color with ‘No Available Data (ND)' marks shows the unavailable MR calculation results due to the unavailable data of the actual LUF-MUF.

The calculation of Mode Reliability in Fig. 12 shows the reliability fluctuations of the selected sub-carriers based on the realization of available sub-carriers. For each subcarrier frequency that can be used, the BCR value can be calculated using equation (9) with monthly SNR (\(SN_{m}\)) values based on the VOACAP prediction model (Fig. 13(a)), \(SN_{o}\) values based on the BER versus SNR curve using BPSK modulation (Fig. 13(b)) for BER values of \(10^{-3}\), and \(D_{l}\) values based on the ITU table (ITU, 1999). Using Eq. (9), the BCR value for a single sub-carrier frequency is \(130 - 80/[1 + (50 - 24)/8].1.1= 111.1765\%\) or 100\(\%\). Because the \(SN_{m}\) value presented in Fig. 13(a) is quite uniform over the range of LUF-MUF values, this value can also be used as a representation of the BCR value for all sub-carrier frequencies, which is 100\(\%\). This result also affects the calculation of the BRR value using Eq. (13) with a 100\(\%\) reliability. Even though the BRR value is 100\(\%\), it should be noted that this value is limited by the selection of the sub-carrier frequency in the range of the actual LUF-MUF value only. The LUF-MUF values from the model can be different from the actual LUF-MUF values. Therefore, the optimization of channel capacity and reliability in this system is determined by the accuracy factor of the LUF-MUF value model, whose function is the determination of the main bandwidth value.

Fig. 13  (a) Monthly SNR prediction from the VOACAP model, and (b) BER versus SNR curve for BPSK modulation in Rayleigh distributed channel. The \(SN_{o}\) values can be determined based on acceptable BER values.

5.  Conclusion

The multi-carrier modulation technique, combined with LUF-MUF variation, is a promising method for improving the channel capacity while also maintaining the reliability of the ionospheric communication channel system. This method uses variations of LUF-MUF prediction values from a model as the main bandwidth and a Bandwidth coherent \(B_c\) value as the subcarrier bandwidth. Numeric simulation using the ASAPS and LSTM models for the LUF-MUF values shows the achieved ergodic channel capacity varies in a range of 10 Mbps to 100 Mbps with SNR 0 to 20 dB. While the reliability level of the system using two scenarios of Mode Reliability calculation shows the values are in the range of 8\(\%\) and 100\(\%\) for every hour of the day. The simulation was conducted in Near Vertical Incidence Skywave (NVIS) propagation mode over the Pontianak region in January 2023 with the assumption of perfect synchronization, no Doppler, and no time offsets. The result also shows that the optimization of capacity and reliability were determined by the accuracy level of LUF-MUF models. If the model predicts lower LUF-MUF range values than the actual, the reliability level is maximized, but several of the available subcarrier bandwidths are not utilized. However, if the model predicts a higher LUF-MUF range value than the actual, the utilization of all the available subcarrier bandwidth is maximized, but sacrificing the reliability level to be low due to some of the sub-carrier transmissions cannot be realized.

Acknowledgments

We would like to express our sincere gratitude to our supervisor, Professor Adit Kurniawan, for his valuable guidance and support throughout the research process. This work was supported by the Research Organization for Aeronautics and Space in DIPA 2023 for Space Research Center.

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Authors

Varuliantor DEAR
  Institute Technology Bandung,National Research and Innovation Agency

Annis SIRADJ MARDIANI
  National Research and Innovation Agency

Nandang DEDI
  National Research and Innovation Agency

Prayitno ABADI
  National Research and Innovation Agency,Telkom University

Baud HARYO PRANANTO
  Institute Technology Bandung

Keyword

ionosphere communication channel,  capacity,  reliability,  multi-carrier,  LUF,  MUF