A complex radio signal in ionospheric plasma

Analytic solution of the problem on propagation of a frequency-modulated radio pulse in cold isotropic collisional plasma is presented. The solution does not involve the Fourier integral and is not restricted to the distance of propagation or to the a priori choice of the shape of the initial pulse envelope. Rectangle pulses with linear and V-shaped frequency modulation and a trapezoidal pulse with linear frequency modulation are considered. The obtained solution is applied to analysis of distortions of such pulses during propagation along an ionospheric path. It is shown that the solution is efficient in the analysis of the uncertainty function of a propagating pulse