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tion; that is, log e ð1 þ xÞ x to estimate the total capacity, where 1 x 1.In view of (5.13) and upon application of the well-known power-seriesapproximation, we can writeEC x C b =N oxlog1 þ C x ðl 1ÞE b =N eð5:15ÞoAlternatively,C x log 2 e 1log e 2< 1log e 21E b =N 01E b =N 0ð5:16ÞThe preceding expressions and Fig. 5.9 show that the total capacity does notincrease with number of users as in FDMA and TDMA systems.Case II: Cooperative CDMAIn the cooperative CDMA case, the receiver for each user code or signal doesknow the spreading waveforms of the other users. As a consequence, thesystem receiver comprising a bank of l single-user receivers knows all l users’spreading waveforms and jointly detects and demodulates all users’ codes. Ifwe assign each userA transmission rate R ri (where i ¼ 1; 2; ...; l)A codebook containing a set of 2 kðL c 1Þ) codewords* of carrier powerC I (where k ¼ number of input bits and L c ¼ constraint length y )then the achievable l-dimensional rate region for the l users may berepresented byR r ¼ PlR ri < B log 2 1 þ lC ið5:17ÞNi¼1Note that this expression assumes equal carrier power C i ¼ C for each user.*A codeword is the number of bits transmitted in a block. For example, if we transmit n bits in ablock, which is made up of k message bits plus r parity check bits, then the n-bit block is called acodeword.y Constraint length is defined as the number of shifts over which a single message bit can influencethe encoder output. This definition becomes clearer in Chap. 6.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.