A wideband HF simulator has been constructed on the basis of a detailed physical model of propagation which can generate a time realization of the HF wideband channel for any HF carrier frequency, bandwidth, transmitter receiver path and background, and stochastic (irregularity) ionosphere models. To accomplish this, a comprehensive solution has been obtained on the basis of the complex phase method (Rytov's method) to the problem of HF wave propagation for the most general case of a three-dimensional (3-D) inhomogeneous ionosphere with time-varying electron density fluctuations. A simulation is presented for a 1000 km path for which E and low- and high-angle F mode paths exist. The time-varying field owing to each of these paths is summed at the receiving location, enabling the calculation of the scattering function and also the time realization of the received signal shown as a function of both fast and slow time.