Synchronous Satellite Link: Consider a 2 GHz link between asynchronous satellite and a ground station on the equator. The bandwidth of the up-link and down-link are the same. The orbital radius of the satellite is 36,000 Km and the radius of the Earth is6,400 Km. The satellite antenna beam must just cover the wholeEarth; its transmitted power is 100 w; and its receiver noisetemperature is 300K (because the antenna is looking at the warmEarth). The ground station antenna diameter is 64 cm; its aperture efficiency is 100%; and its receiver noise temperature is 50 K(because it is looking at the cold sky). Note that RF power isusually specified in dB with respect to a reference. The most common reference is 1 mw, which gives rise to the power unit ofdBm. For example -30 dBm is 1 microwatt.
Find: (a) the beam solid angle of the satellite antenna;
(b) the gain of the satellite antenna in dB;
(c) the power received on theground in dBm;
(d) the bandwidth at which the SNR on the ground is10 dB; and
(e) the power that must be transmitted from the ground(in dBm) so the uplink channel capacity will be the same as that ofthe down link. The channel capacity C =BW*log2(1+SNR).