Effect of horizontal gradients on ionospherically reflected or transionospheric paths using a precise homing-in method

Abstract

A homing-in method is presented for determining ionospheric reflected or transionospheric paths between fixed transmitter and receiver locations in the presence of ionospheric gradients or ripples. Both initial elevation and azimuth are automatically adjusted to find the path that arrives exactly at the receiver. The method can be used for any 3D ionospheric model to find precise ray paths and phase and group delays for both magneto-ionic modes. The method takes full account of path location, geomagnetic field orientation and the bending of the ray path resulting from horizontal as well as vertical gradients of electron density. It can also find multiple paths e.g. low and high angle, 1- and 2-hops for both ordinary and extraordinary modes. Examples of its use are given for both terrestrial HF links and Earth to Satellite paths. For paths reflected from the ionosphere, the effect of gradients of both critical frequency and height of maximum electron density are determined and the comparative effect of gradients on high and low angle and 1- and 2-hops paths for both magneto-ionic modes investigated. Path variation with frequency for a fixed link is also studied and the bandwidth of the ionospheric background channel (dispersive bandwidth) and its reciprocal (the pulse rise time), important for wideband digital HF broadcasting or spread spectrum HF communications, is estimated for a range of frequencies, for high- and low-angle rays and 1- and 2-hop paths. For Earth–satellite paths, the effect of the ionosphere and horizontal ionospheric gradients is determined for a range of frequencies and elevation angles. It is shown that the method can also enable the determination of second-order errors in satellite navigation methods, such as GPS, due to ionospheric gradients and the effect of the geomagnetic field.