power equally in all directions. As the power is radiated uniformly, we can assume that a 'sphere' of power is formed, as shown in Figure 2.7. The surface area of this power sphere is: A=4rR2 (2.1) The power density S at any point at a distance R from the antenna can be expressed as: S = P*G/A (2.2) where P is the power transmitted by the antenna, and G is the antenna gain. Thus, the received power Pr at a distance R is: (2.3) where G1 and G, are the gain of the transmitting and receiving antennas respectively. On converting this to decibels we have: Pr(dB) = P(dB) + G,(dB) + G,(dB) + 20log (x/4) - 20log d. (2.4) Last two terms in equation 2.4 are together called the path loss in free space, or the free- space loss. The first two terms (P and G1) combined are called the effective isotropic radiated power, or EIRP. Thus: Free-space loss (dB) = EIRP +G,(dB) - P,(dB). (2.5) The free-space loss can then be given as: LdB =92.5+20logf+ 20log d (2.6) where f is the frequency in GHz and d is the distance in km. RADIO NETWORK PLANNING AND OPTIMISATION Equation 2.6 gives the signal power loss that takes place from the transmitting antenna to the receiver antenna. Radio Wave Propagation Concepts Propagation of the radio wave in free space depends heavily on the frequency of the signal and obstacles in its path. There are some major effects on signal behaviour, briefly described below. Reflections and Multipath The transmitted radio wave nearly never travels in one path to the receiving antenna, which also means that the transmission of the signal between antennas is never line-of-sight (LOS). Thus, the signal received by the receiving antenna is the sum of all the components of the signal transmitted by the transmitting antenna. Diffraction or Shadowing Diffraction is a phenomenon that takes place when the radio wave strikes a surface and changes its direction of propagation owing to the inability of the surface to absorb it. The loss due to diffraction depends upon the kind of obstruction in the path. In practice, the mobi