On high frequencies (HF, defined to be 3-30 MHz), radio waves can travel long distances by multiple reflections off the ionosphere and off the earth. The focus of this research is to develop an appropriate mathematical model for HF radio waves which a ship travelling across the ocean will use for communications and to receive weather and traffic reports. In order to serve a shipboard receiver moving on a turbulent ocean better, MHA model is improved with the introduction of Doppler shift, multipath delay as well as symbol error rate (SER) to indicate the communication quality in the ship's navigation.

High frequency (HF) propagation can achieve long distance, low cost communications and it is one of the most important communication methods. The focus of this research is to develop an appropriate mathematical model for HF radio waves to communicate efficiently over various surface of the earth. First of all, the multi-hop attenuation (MHA) model is established which takes free space loss, ionosphere loss and surface reflection loss into account. [1] The effect of the free space loss and the ionosphere loss is simplified, and subsequently the relationship between signal attenuation and frequency variation under different wind speed is revealed. At the same time, the contrast of signal attenuation off a calm ocean and a turbulent one is conducted. [2].