Multi-path time delay spread is a very important factor in the bit error rate of high-frequency ionospheric communication channels and in the target detection performance of over-the-horizon radars. In this study, the probability density distribution of multi-path time delay and Doppler shift of ionospheric radio signal are derived using Rayleigh fading. Moreover, the probability density distribution of time delay, average power of the received signal, and received signal variance are discussed in detail. Using a designed experimental circuit, the measured value of the multi-path time delay spread is obtained from three given radio paths by the sweep-frequency pulse sounding technique. The average value of the multi-path time delay spread that changes with the ratio K, which is the operating frequency of the basic maximum usable frequency, is also analyzed and fitted using the least-squares fitting method. Theoretical and statistical research shows that for a given radio path and specific frequency, the multi-path time delay spread approximately follows a normal distribution. The average time delay spread decreases with the increase in the ratio K; however, it eventually approaches a steady value. The results of this research provide an empirical reference for further prediction and estimation of the time delay spread of a radar wave propagating through the ionosphere.
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