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This expression neglects losses other than the free-space loss. As noted earlierin this chapter, a major digital satellite link design condition is to ensure thatthe E b =N 0 ratio is sufficiently large to guarantee that the bit error rate (BER)performance criteria are met. The relationship between C=N and E b =N 0 wasestablished in Chap. 3, Eq. (3.11) asE bN 0¼ C BN r bð4:15Þwhere r b is the data bit rate. Thus, substituting the bit rate expression of (3.7)in (4.15):E b¼C 1 þ að4:16ÞN 0 N log 2 Mwhere a is the channel filter roll-off factor and M is the possible values orsymbols the phase of carrier takes during a modulation scheme. For an idealfilter, a ¼ 0.The fundamental relationship expressed by (4.14) can be used tocalculate the receiver C=N for each link in turn. If we use subscripts u, s,and d, respectively, for the uplink, satellite transponder, and downlink, eachlink’s expressions are developed as follows.Uplink equations: CNu¼ 10 logðG T P T Þ 20 log 4pR uþ 10 log G sl uT s10 logðB s kÞþ10 logðL u Þ ð4:17Þwhere G T P T is the EIRP of the transmitting earth station, L u (other lossesassociated with the upward transmission), B s is the transponder bandwidth,and ðG s =T s Þ is the figure-of-merit (FOM) of the satellite transponder.Downlink equations: C¼ 10 logðGNs P s Þ 20 log 4pR dþ 10 log G ddl dT d10 logðkB r Þþ10 logðL d Þ ð4:18Þwhere G s P s is the EIRP of the satellite, L d (other losses associated with thedownward transmission), B r is the receiving earth station’s bandwidth, andðG d =T d Þ is the figure-of-merit (FOM) of the receiving earth station.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.