“…The core of the pulse propagation and scattering problems in random media is that of ÿnding the two-position and two-frequency MCF, therefore so many works have been devoted to solutions, respectively for plane wave, spherical wave, beam wave and their applications. There are several excellent books (Ishimaru, 1997;Tatarskii, 1971;Tatarskii et al, 1993;Uscinski, 1977), some earlier investigations (e.g., Fante, 1974Fante, , 1981Brown, 1972;Hong and Ishimaru, 1976;Hong et al, 1977;Ishimaru and Hong, 1975;Lee, 1974;Fremouw et al, 1980;Knepp, 1983Knepp, , 1985Liu et al, 1974;Yeh, 1977,1981;Prokhorov et al, 1975;Sreenivasiah and Ishimaru, 1979;Sreenivasiah et al, 1976;Yeh and Liu, 1982;Booker et al, 1985;Flattà e, 1983;Rino et al, 1981), and some more recent works (e.g., Kravtsov, 1992;Oz and Heyman, 1996;Wu, 1999;Liu, 1986, 1989;Young et al, 1996;Gherm et al, 2000;Samelsohn and Freilikher, 2002;Xu et al, 2003b,c,d). Besides the above literature on transionospheric propagation, Gherm et al (1997a, b) has presented a detailed numerical investigation of the two-frequency MCF for HF wave propagation in the uctuating ionosphere.…”