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The dielectric constant ε, the magnetic permeability μ and the conductivity σ are expressed as ε = ε 0 [1 + δε(r, z)] (1) μ = μ0 (2) σ = 0, (3) where r = ix x + iy y (ix and iy denote the unit vectors of x and y coordinates, respectively) and ε 0 and μ0 are the dielectric constant and the magnetic permeability for free space, respectively. The function δε(r, z) is a Gaussian random function with the properties: δε(r, z) = 0 (4) δε(r1 , z1 ) · δε(r2 , z2 ) = B(r− , z+ , z− ), (5) where r− = r1 − r2 , z+ = (z1 + z2 )/2, z− = z1 − z2 , B(r− , z+ , z− ) is the correlation function of random dielectric constant and the bracket notation · denotes an ensemble average of the 32 4 Advances in Satellite Communications Will-be-set-by-IN-TECH quantity inside the brackets.
The received intensity in free space Iin (z) and the average received intensity affected by atmospheric turbulence I (z) are respectively given by Iin (z) = I (z) = ∞ −∞ ∞ −∞ in dr M11 (r, 0, z) exp − 2r2 a2e dr M11 (r, 0, z) exp − 2r2 a2e (41) . (42) Under the condition where the DOC is almost unity, we can reduce the number of the surface integral in calculation of (40) and then obtain BER derived from the average received intensity as follows: ⎞ ⎛ 1 E E b ⎠ = 1 erfc PEI = erfc ⎝ (43) SI · b , 2 N0 2 N0 where the normalized average received intensity S I is given by ∞ SI = Eb I (z) = = Eb Iin (z) 2r2 a2e −∞ ∞ 2r2 in dr M11 (r, 0, z) exp − 2 ae −∞ dr M11 (r, 0, z) exp − .