for the receive site difficult and uncertain. Chapter 8 Radio Wave Propagation F2 Layer Double-Hop F2 Single-Hop F2 E Layer Double-Hop E Fig. 8.10 Possible multihop sky wave paths. Transmitter Receiver Fig. 8.11 Frequencies for an HF link from London to Lisbon. Time (hours) Three possible modes are shown in Figure 8.10. A first approximation can be obtained by calculating the free-space loss using equation 8.7, taking into account increased distance due to ionospheric refraction and applying this to the field strength at the transmitter site. Addi- tional losses of up to 20 dB will result from ionospheric and ground reflections, but these are very approximate values. Actual sky wave refraction losses can be calculated (Braun, 1986), as can received field strength (Damboldt, 1975). Computer propagation prediction programs are now generally employed for analyzing HF paths and predicting received signal strength because of the large number of cancelations required rather than their inherent complexity. Such programs run on desktop PC computers (Hitney, 1990), although many research establishments have larger and more sophisticated programs (Dick, 1990). Figure 8.11 shows a typical printout of a link from London to Lisbon, a great circle dis- tance of 1656 kilometers and a single-hop, F2, distance of 1757 kilometers. The program Terrestrial Line-of-Site Propagation shows the Maximum Usable Frequency (MUF) and the Lowest Usable Frequency (LUF), and at times when the LUF exceeds the MUF, HF sky wave communication is not possible. The MUF is determined by the degree of layer ionization, while the LUF is generally deter- mined by the multihop path attenuation and the noise level at the receive site. The Fre- quency of Optimum Transmission (FOT) is the frequency with maximum availability and minimum path loss, and it is generally taken as 90 percent of the MUF. HF ground wave and sky wave communications are still widely used for long-distance low-capacity services such as aeronautical ground-to-air transmissions, despite 