WP 1, D2 – Functional System Parameters description

BROADWAY, IST-2001-32686 WP1-D2 version 1, date 10-10-02 Programme: IST⎛ n ⋅ ⎞M = ⎜ ⎟ + n ⋅ λ ⋅ d ,⎝ 2 ⎠thwhere n denotes the n -Fresnel ellipse, λ the wavelength, and d (major axis) the distance between thetransmitting and receiving antenna located at the focal points of the Fresnel ellipses.2.2.2.2. Fresnel Clearance for Reflectionλ 2thThe principle of Fresnel clearance applies also to reflection. The n Fresnel zone on a reflecting surfaceencloses all points on the interface for which the additional path length to the receiver is less than n timeshalf a wavelength. The Fresnel zones on the surface of the obstacles are ellipses (see Fig. 2.2-7). As a rule ofthumb, at least the first of these Fresnel zones must be fully contained in the surface of the obstacle.Otherwise Fresnel’s reflection and transmission coefficient starts to predict the reflected and transmitted fieldwrongly. Hence, the effect of wave reflection may be overestimated if the size of the reflecting surface is notlarge enough.The needed size of a surface to fully reflect the incident wave can be estimated from Fig. 2.2-5 by drawing aline across the ellipses that corresponds to the location of the obstacle’s surface with respect to thetransmitting and receiving antenna. Dependent on the orientation of the obstacle’s surface with respect to thedirect ray between the transmitter and receiver the size of the first Fresnel zone might vary vastly.With reference to Fig. 2.2-7 the major axis dMAof the Fresnel ellipse within the plane and smooth surface ofthe wall is determined bydMA( d − d )= 2 , whereMLdM⎛⎜⎝h⎞⎟⎠Tx= ⎜ ⋅ dhhTx+ h ⎟ , andRxd L2 2nλd = ( hTx+ hRx) + dh, C1= − d ,2C2 27h − TxC3= .2− C6± C6− 4C5C7= with2CC52C3= ,2C1C4dh= ,C1C5 1 C 4C6= 2CC , and2= − ,3 416