View File - University of Engineering and Technology, Taxila

5.2 CAPACITY COMPARISON OFMULTIPLE-ACCESS METHODSThe capacity of multiple-access (FDMA, TDMA and CDMA) methods can beexamined in terms of the information rate that each method achieves in anideal additive white Gaussian noise (AWGN) channel of finite bandwidth B[9]. For simplicity, we assume a uniform number of users, say l. Each user hasa similar average carrier power C i ¼ C, for all values of i users wherei ¼ 1; 2; ...; l.In FDMA, each user is allocated a bandwidth (B=l). Hence, in view of(3.10) and (3.19), the capacity for each user can be expressed asC FD ¼ B logl 2 1 þ C ð5:7ÞðB=lÞN 0Superficially, this expression indicates that for a fixed bandwidth B, the totalcapacity goes to infinity as the number of users increases linearly with l. Thisis not true, as will be demonstrated later. By writing the carrier power C interms of the energy of a single bit E b as in (3.11), the normalized total capacityC n for an FDMA system can be expressed as EC n ¼ log 2 1 þ C bn ð5:8ÞN 0where C n ¼ lr b =B, which is the total bit rate for all l users per unit bandwidthand r b is the input digital bit rate of the user (bit=sec). Alternatively,E b¼ 2C n 1N 0 C nð5:9ÞFig. 5.8 shows the graph of C n versus E b =N 0 . We observe that C n increases asE b =N O increases above the minimum value of log e 2, which is the absoluteminimum value, demonstrated by Eq. (3.22), imposed on finite channelcapacity for an error free transmission.In the TDMA system, each user is allowed to transmit for T s =l of thetime through the channel of bandwidth B. The total capacity per user can beexpressed as!C TD ¼ B T sClogl 2 1 þBT s =l ð5:10ÞN 0This expression is identical to that of the FDMA system in (5.7). In the TDMAsystem, however, it may not be possible for the transmitter to sustain anCopyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.