To further improve the short-term forecasting ability of the critical frequency of the ionosphere F2 layer (foF2), a sample entropy optimized deep learning long-short-term memory (LSTM) forecasting model based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is proposed. The ICEEMDAN-LSTM model uses the foF2 hour-level time series data of Dourbes station from 2009 to 2019 for training and verification and realizes a single-step high-precision foF2 time series forecast. Through the statistical analysis of the observation of foF2 parameters and the forecast results of the model, the ICEEMDAN-LSTM model can predict foF2 parameters well during the geomagnetic calm and storm periods. Moreover, the proposed model outperforms others in predicting foF2 time series under diurnal and seasonal variation. In the high solar activity year, the RMSE, RRMSE, MAE, and R ² evaluation indexes of the ICEEMDAN-LSTM model are 0.19MHz, 4.33%, 0.13MHz, and 0.99, respectively, and they are 0.22MHz, 5.54%, 0.14MHz, and 0.95 in the low solar activity year. The ICEEMDAN-LSTM has the highest forecast accuracy in different solar activity years and is almost unaffected by solar activity. Meanwhile, the prediction performance of ICEEMDAN-LSTM is also verified by observatories in other regions, with high forecasting accuracy. The above shows that the ICEEMDAN-LSTM model has good applicability and usability, and the forecast accuracy of foF2 short-term forecasting can be improved further.

To further improve the quantitative forecasting ability of high-frequency (HF) communication frequency, we propose a maximum usable frequency (MUF) adaptive forecasting method. This method has four new features: 1) The Volterra filter is introduced to this method, which is easy to implement due to the simple structure. 2) This method can forecast M(3000)F2 based on past measurements without using any previous or forecast data of geomagnetic and solar activity parameters. 3) The spatial characteristics of the M(3000)F2 can be obtained by the improved reconstruction method based on geomagnetic coordinates. 4)The high prediction accuracy can be obtained by the training data set on the 27-day (one solar rotation period). Through the statistical analysis of the measurements and predictions, the results show that the forecast values are in good agreement consistent with the measurement during the geomagnetic quiet or the disturbance periods. This method is proven to have good adaptability and usability and has a further performance improvement compared with ITU and long-term forecast models. And the root-mean-square error of MUF forecasts decreased by 1.9MHz and 0.9MHz on average, and the relative root-mean-square error decreased by 12.6% and 2.9% on average.

To achieve accurate forecasting of the peak height of the ionospheric F2 layer (hmF2), we propose a hybrid deep learning model of improved seagull optimization algorithm (ISOA) optimized long short‐term memory (LSTM) model based on a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) theory. The hybrid model decomposes the hmF2 time data into multiple subsequences through CEEMDAN and reconstructs the subsequences by sample entropy and correlation coefficient into high and low‐frequency sequences, which effectively shortens the calculation time of the model. Then, we determine the optimal hyperparameters of the LSTM models through ISOA, achieving high‐precision forecasting of the hmF2. In single‐step forecasting, the forecasting values of the hybrid model in diurnal and seasonal changes are highly consistent with the observation, which can better capture the severe changes in the hmF2. The model's RMSE, MAE, MAPE, and CC evaluation metrics are 15.86, 11.03 km, 4.76%, and 0.93 in the test set. Compared to IRI, GRU, and LSTM models, taking RMSE as an example, the forecasting accuracy of the models increased by 65.24%, 29.89%, and 29.60%, respectively. In multi‐step forecasting, the proposed model is better at forecasting the changing trend of hmF2, and the forecasting accuracies are significantly better than the IRI model. The data from multiple stations also verified the applicability of the proposed model for hmF2 forecasting. The above results indicate that the hybrid model has high accuracy in hmF2 short‐term forecasting and good applicability in multiple multi‐step forecasting, which can further improve the accurate forecasting of space weather.

As one of the key technologies of HF communication, the maximum usable frequency (MUF) prediction method has been widely discussed. To experimentally confirm the reliability of commonly used MUFs prediction models for high-frequency communication, we have compared maximum observed frequencies (MOFs) and predicted MUFs to assess the accuracy of two typical prediction models. The root-mean-square error (RMSE) and relative RMSE (RRMSE) between oblique sounding MOFs and the predicted MUFs were used to assess the model’s accuracy. The oblique sounding path was from Changchun to Jinyang, and the vertical-sounding ionosonde was located in Beijing, which was approximately the midpoint of the oblique sounding circuit. The statistical analysis results show that: (a) the trend of prediction results from the Lockwood and the Istituto Nazionale di Geofisica e Vulcanologia (INGV) model are in good agreement with the observations: the mean RMSE and RRMSE of the INGV model are less than those of the Lockwood model; (b) in the four different periods (sunrise, daytime, sunset, and nighttime) of the whole day, the maximum difference of RMSE between the Lockwood and INGV model is 0.14 MHz (the INGV performs better than the LWM), with the corresponding differences of RRMSE being 0.31% at sunrise and 0.68% at daytime; (c) in the four seasons of spring, summer, autumn, and winter, the minimum RMSE values of the Lockwood and INGV models are 1.51 MHz and 1.37 MHz, respectively, which are obtained in winter, and the corresponding RRMSEs are 11.47% and 11.79%, respectively; (d) in the high and low solar activity epochs, the mean RMSEs of the Lockwood and INGV models are 1.63 MHz, and 1.54 MHz, with corresponding mean RRMSE values of 11.47% and 11.55%. In conclusion, the INGV model is more suitable for MUF prediction over Beijing and its adjacent mid-latitude regions from the RMSE comparison of the two models.

For improving the accuracy and robustness of predicting radio propagation in the frequency bands of FM Broadcasting Services, we proposed a propagation prediction model suitable for multi-band and multi-scenario based on Support Vector Regression (SVR). The modeling is based on Beijing’s measurement data, covering various environments, such as rural, suburban, and urban areas, with a frequency range of 86.7MHz-106.6MHz. A comparison will be made to verify the model’s performance with the ITU-R P.1546 model, an internationally common model recommended by ITU. The results show that the model exhibits superior prediction accuracy and stability compared to ITU-R P.1546, and the average relative error of ITU-R P.1546 model prediction in each frequency band is prominent, from 3.01% to 4.77%. Moreover, the average relative error of each frequency band of the model is distributed by about 2%-2.5%. In addition, SVR’s the predicted direction and details are highly similar to ITU-R P.1546, which can better fit the trend of propagation loss with propagation distance and other conditions. As a result, the research can provide a reference for regional application and localization research of radio propagation prediction methods.

The evaporation duct height (EDH) can reflect the main characteristics of the near-surface meteorological environment, which is essential for designing a communication system under this propagation mechanism. This study proposes an EDH prediction network with multi-layer perception (MLP). Further, we construct a multi-dimensional EDH prediction model (multilayer-MLP-EDH) for the first time by adding spatial and temporal “extra data” derived from the meteorological measurements. The experimental results show that: (1) compared with the naval-postgraduate-school (NPS) model, the root-mean-square error (RMSE) of the meteorological-MLP-EDH model is reduced to 2.15 m, and the percentage improvement reached 54.00%; (2) spatial and temporal parameters can reduce the RMSE to 1.54 m with an improvement of 66.96%; (3) the multilayer-MLP- EDH model can match measurements well at both large and small scales by attaching meteorological parameters at extra height, the error is further reduced to 1.05 m, with 77.51% improvement compared with the NPS model. The proposed model can significantly improve the prediction accuracy of the EDH and has great potential to improve the communication quality, reliability, and efficiency of ducting in evaporation ducts.