Radio Science Bulletin 325 - June 2008 - URSI

∂ϕ∂ϕ1 kϕ∂r=− +, (12)∂β ∂θ rsinθ k ∂θk r kwhere θ k and ϕ k are the spherical polar coordinates of kwith respect to ˆr , ˆ θ , ˆϕ as local Cartesian axes. Theautomated homing algorithm proceeds by shooting a ray,computing the miss distances to the desired homing point( ∆ θ , ∆ ϕ ), and adjusting the ray-launch azimuth andelevation by∂θ∂ϕ∆ϕ− ∆θ∂β∂β∆ α = , (13)∂ θ ∂ ϕ ∂ θ ∂ ϕ−∂β ∂α ∂α ∂β∂θ∆θ− ∆α∆ β =∂α, (14)∂θ∂βand then iterating the procedure until the ray lands withinsome specified tolerance from the desired landing point.An example of the performance of the automated rayhomingalgorithm is shown in Figure 3. In this case, weused the ionosphere represented in Figure 1, and sought aray connecting latitude 36°N and longitude 90°W to ahoming point at latitude 30°N and longitude 85.6°W. Theinitial ray (10 MHz) was launched at an azimuth of 155°from north and at an elevation of 20°. The convergencetolerance was set to get the final ray within 0.01 km of thedesired homing point. Eight iterations were required, takingonly about a tenth of a second on my 2.0 GHz laptop. Thefinal azimuth and elevation angles were 149.352316° and25.637033°, respectively. In this case, as is typical, thealgorithm found the low ray mode nearest the initial launchdirection that reached the desired homing point.The automated ray-homing algorithm has also beenincorporated in the ray-tracing package TRACKER,developed at Los Alamos National Laboratory [14].3. HF Channel ModelingDuring the Cold War, it was assumed that in the caseof a massive nuclear attack, the military might have to relyon HF communications. However, the HF ionosphericcommunication channel would then be highly disturbed,and it was necessary to estimate this level of disturbance sothat modems could be hardened by appropriate codingschemes that would be resilient to the channel disruptions.Small-scale ionization structure will cause a propagated HFsignal to suffer angular scattering, so that received signalsare spread over a range of angles and delays, owing to theextra delay of the scattered “micro-multipath” signalelements, or “micro-rays.” Moving ionization (or movinglink geometry through ionization) will introducecorresponding spread in signal Doppler frequency due tothe spread in impinging angles of “micro-rays” on thesmall-scale ionization structures causing the scatter. Thespreads in signal delay and Doppler are characterized by thescattering function, the delay-Doppler power spectrum ofthe received signal.Figure 3. The miss distance as a function of the iterationnumber, using the automated ray-homing algorithm.Figure 4. A plan view of a primary ray path (solid arrow)and associated micro-rays (dotted lines), scattered by anintervening phase-changing screen representing smallscaleionization structure. The phase screen was movingtransversely to the primary ray with speed v .40TheRadio Science Bulletin No 325 (June 2008)