This paper proposes a short-term forecasting method for high-frequency broadcast Maximum Usable Frequency (MUF) based on Long Short-Term Memory (LSTM) to meet the demand for refined and precise high-frequency broadcast coverage. Based on the existing infrastructure of broadcast and television stations, we established an experimental verification system to collect data for approximately three years. Two links were selected based on data quality: Urumqi to Lhasa and Lanzhou to Lhasa. A short-term forecast of MUF was conducted using the data from these two links. Comparison and analysis were conducted between the forecasting results of our model and those of the REC533 model. Our proposed method outperforms the REC533 forecasting results overall, with a reduction in root mean square error (RMSE) of 0.66 MHz and an improvement in forecast accuracy of 14.77%. The comparison result demonstrates the feasibility and accuracy of our model.

The peak height of the ionospheric F2 layer (hmF2) is a critical parameter in ionospheric physics and high-frequency radio wave propagation research. This study presents a backpropagation neural network (BPNN) enhanced by wavelet transform (WT) decomposition for one-hour-ahead hmF2 forecasting. The WT method decomposes and reconstructs the hmF2 time series, preserving its primary structural characteristics. Subsequently, the BPNN provides high-accuracy predictions. The model is trained and evaluated using 2014 hmF2 measurements from four observation stations in China. Utilizing only hmF2 data, the model produces accurate one-hour-ahead forecasts. The predicted values closely align with observed diurnal variations and exhibit lower fluctuations than those of the IRI and standalone BPNN models. On the test set, the proposed model achieves an average RMSE of 17.16 km, which is 10.10 km and 8.39 km lower than the IRI and BPNN models, respectively. The average RRMSE is 5.72%, representing reductions of 2.88% and 2.64% compared to the IRI and BPNN models, respectively. These findings indicate that the hybrid model is well-suited for the Chinese region and substantially enhances short-term hmF2 forecast accuracy.

Short-wave communication, operating within the frequency range of 3–30 MHz, is extensively employed for long-distance communication because of its extended propagation range and robustness. The ionosphere undergoes complex transformations when influenced by the geomagnetic field, evolving into an uneven and anisotropic electromagnetic medium. This complex property makes the transmission of electromagnetic fields within the ionosphere extremely complex, posing significant challenges for accurately evaluating electromagnetic scattering phenomena. To address the aforementioned challenges, this paper proposes a new method for calculating short-wave ionospheric scattering based on a complex anisotropic multilayer medium transmission matrix. Firstly, by utilizing the characteristic changes of ionospheric electron density with height, the ionization layer is divided into multiple horizontal thin layers, each with an approximately uniform electron density, forming a multilayer horizontal anisotropic structure. Subsequently, the scattering characteristics of electromagnetic waves in the ionosphere were calculated using the transmission matrix approach. The results calculated using this method are consistent with actual measurement values and superior to traditional short-wave ionospheric transmission calculation methods.