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Let us first give an analogy CDMA simply means communication with different codes For example, in a large room with many people, two people can talk in English if nobody else understands English Another two people can talk in Chinese if they are the only ones who understand Chinese, and so on In other words, the common channel, the space of the room in this case, can easily allow communication between several couples, but in different languages (codes)
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Let us assume we have four stations 1, 2, 3, and 4 connected to the same channel The data from station 1 are d l , from station 2 are d 2 , and so on The code assigned to the first station is cI, to the second is c2, and so on We assume that the assigned codes have two properties
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1 If we multiply each code by another, we get O 2 If we multiply each code by itself, we get 4 (the number of stations)
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With these two properties in mind, let us see how the above four stations can send data using the same common channel, as shown in Figure 1223 Station 1 mUltiplies (a special kind of multiplication, as we will see) its data by its code to get d l Cl' Station 2 multiplies its data by its code to get d 2 c2' And so on The
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Figure 1223 Simple idea of communication with code
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+ d2 c2 + d3 ('3 + d4 ('4
Data
Common channel
data that go on the channel are the sum of all these terms, as shown in the box Any station that wants to receive data from one of the other three multiplies the data on the channel by the code of the sender For example, suppose stations 1 and 2 are talking to each other Station 2 wants to hear what station I is saying It multiplies the data on the channel by cl' the code of station 1 Because (cl cl) is 4, but (c2 cI), (c3 cI), and (c4 cl) are all Os, station 2 divides the result by 4 to get the data from station 1
data
= (d} Cj + dz Cz + d 3 C3 + d4 c4) Cl
Chips
Cl Cj
+ dz Cz Cl + d 3 C3
Cl
+ d 4 C4' CI
=4 X d 1
CDMA is based on coding theory Each station is assigned a code, which is a sequence of numbers called chips, as shown in Figure 1224 The codes are for the previous example
Figure 1224 Chip sequences
[+1 +1 +1 +11
1[+1 -1 +1 -I)
C3 [+1 +\ -I - 11
[+\ -1 -1 +IJ
Later in this chapter we show how we chose these sequences For now, we need to know that we did not choose the sequences randomly; they were carefully selected They are called orthogonal sequences and have the following properties: 1 Each sequence is made of N elements, where N is the number of stations
SECTION 123
CHANNELIZATION
2 If we multiply a sequence by a number, every element in the sequence is multiplied by that element This is called multiplication of a sequence by a scalar For example,
2 [+1 +1-1-1]=[+2+2-2-2]
3 If we multiply two equal sequences, element by element, and add the results, we get N, where N is the number of elements in the each sequence This is called the inner product of two equal sequences For example,
[+1 +1-1
-n [+1 +1 -1 -1] = 1 + 1 + 1 + 1 = 4
4 If we multiply two different sequences, element by element, and add the results, we get O This is called inner product of two different sequences For example,
[+1 +1 -1 -1] [+1 +1 +1 +1] = 1 + 1 - 1 - 1 = 0
5 Adding two sequences means adding the corresponding elements The result is another sequence For example,
[+1+1-1-1]+[+1+1+1+1]=[+2+2 00]
Data Representation
We follow these rules for encoding: If a station needs to send a 0 bit, it encodes it as -1; if it needs to send a 1 bit, it encodes it as + 1 When a station is idle, it sends no signal, which is interpreted as a O These are shown in Figure 1225 Figure 1225
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