We present the results of experimental studies of propagation of short radio waves on a long transequatorial path of Laverton (Australia) -Rostov-on-Don, which were obtained with the help of an ionosonde/direction finder with chirp modulation of the signal. It is shown that conditions for propagation of anomalous signals by means of sideband reflection of radio waves from the Himalayan Hills and the Plateau of Iran and also due to scattering of radio waves from the high-latitude ionosphere of the northern hemisphere are realized on the given path. The propagation of radio waves is modeled with allowance for their scattering by anisotropic magnetic field-aligned irregularities of a high-latitude ionosphere, which are located on the northern wall of the main ionospheric trough of the F layer. It is shown that the results of the experiment agree well with the calculated data.