In this paper we consider propagation through a structured ionosphere separating a monostatic or bistatic radar and its target. A new analytic calculation of the correlation function of the received, demodulated signal is presented. This result is a function of the locations of the transmit and receive apertures and of time during the duration of the received pulse. Strong scattering is assumed where the one-way scintillation index is unity; under this assumption the parabolic wave equation can be solved using the quadratic approximation for the phase structure-function; this facilitates tractable expressions for the mutual coherence function (MCF) for both one- and two-way propagation. A new expression is given for the two-position, two-time, two-frequency MCF for spherical wave propagation that allows simultaneous description of all effects of the ionospheric propagation channel (or transmission medium) on a propagating radar signal. To obtain useful and tractable results, the transmitted signal is assumed to be a chirp (linear FM) pulse, a waveform used by most long-range defense radars. The result for the correlation function of the received signal is a function of the basic parameters that describe wave propagation through the ionospheric structure, including the channel decorrelation distance, decorrelation time, and coherence bandwidth. Both the two-way enhancement in average power and aperture averaging effects are explicitly included in this derivation, and new results are presented that relate these effects to the characteristics of the propagation channel. The results are useful for propagation under conditions of saturated scintillation, for example HF through UHF radar in the natural equatorial environment and HF through gigahertz-band radars that are required to operate in a disturbed propagation environment (i.e., in chemical releases or nuclear detonations).