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The world is far from ideal, however, and as noted above, CDMA must work in the presence of interfering senders that are encoding and transmitting their data using a different assigned code But how can a CDMA receiver recover a sender's original data bits when those data bits are being tangled with bits being transmitted by other senders CDMA works under the assumption that the interfering transmitted bit signals are additive, eg, that if three senders send a 1 value, and a fourth sender sends a -1 value during the same mini-slot, then the received signal at all receivers during hat mini-slot is a 2 (since 1+ 1 + 1 - 1 = 2) In the presence of multiple senders, sender s computes its encoded transmissions, Zi,m s , in exactly the same manner as in Equation 53-1 The value received at a receiver during the mth minislot of the ith bit slot, however, is now the sum of the transmitted bits from all N senders during that minislot: Zi,m * = s=1,N Zi,m s Amazingly, if the senders' codes are chosen carefully, each receiver can recover the data sent by a given sender out of the aggregate signal simply by using the sender's code in exactly the same manner as in Equation 53-2: di = (1/M) m=1,M Zim * cm (Equation 53-3)
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Figure 53-5 illustrates a two-sender CDMA example The M-bit CDMA code being used by the upper sender is (1, 1, 1, -1, 1, -1, -1, -1), while the CDMA code being used by the lower sender is (1, -1, 1, 1, 1, -1, 1, 1) Figure 53-5 illustrates a receiver recovering the original data bits from the upper sender Note that the receiver is able to extract the data from sender 1 in spite of the interfering transmission from sender 2 Returning to our cocktail party analogy, a CDMA protocol is similar to having partygoers speaking in multiple languages; in such circumstances humans are actually quite good at locking into the conversation in the language they understand, while filtering out the remaining conversations
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Figure 53-5: A two-sender CDMA example Our discussion here of CDMA is necessarily brief and a number of difficult issues must be addressed in practice First, in order for the CDMA receivers to be able to extract out a particular sender's signal, the CDMA codes must be carefully chosen Secondly, our discussion has assumed that the received signal strengths from various senders at a receiver are the same; this can be difficult to achieve in practice There is a considerable body of literature addressing these and other issues related to CDMA; see [Pickholtz 1982, Viterbi95] for details
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522 Random Access Protocols
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The second broad class of multiple access protocols are so-called random access protocols In a random access protocol, a transmitting node always transmits at the full rate of the channel, namely, R bps When there is a collision, each node involved in the collision repeatedly retransmit its frame until the frame gets through without a collision But when a node experiences a collision, it doesn't necessarily retransmit the frame right away Instead it waits a random delay before retransmitting the frame Each node involved in a collision chooses independent random delays Because after a collision the random delays are independently chosen, it is possible that one of the nodes will pick a delay that is sufficiently less than the delays of the other colliding nodes, and will therefore be able to "sneak" its frame into the channel without a collision There are dozens if not hundreds of random access protocols described in the literature [Rom 1990, Bertsekas 1992] In this section we'll describe a few of the most commonly used random access protocols - the ALOHA protocols [Abramson 1970, Abramson 1985] and the Carrier Sense Multiple Access (CSMA) protocols [Kleinrock 1975] Later, in section 55, we'll cover the details of Ethernet [Metcalfe 1976], a popular and widely deployed CSMA protocol Slotted ALOHA Let's begin our study of random access protocols with one of the most simple random access protocols, the so-called slotted ALOHA protocol In our description of slotted ALOHA, we assume the following:
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