ScienTECH ST2115, Руководство пользователя

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ST2115
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Types of Code Division Multiplexing
Synchronous CDMA:
Synchronous CDMA, also known as Code Division Multiplexing (CDM), exploits at
its core mathematical properties of orthogonally. Suppose we represent data signals as
vectors. For example, the binary string "1011" would be represented by the vector (1,
0, 1, 1). We may wish to give a vector a name, we may do so by using boldface
letters, e.g. a. We also use an operation on vectors, known as the dot product, to
"multiply" vectors, by summing the product of the components. The operation is
denoted with a dot between the vectors. For example, the dot product of a = (1, 0, 1,
1) and b = (1,- 1, -1, 0), written as a.b, would be (1)
×
(1) + (0)
×
(-1) + (1)
×
(-1) +
(1)
×
(0) = 1+ (-1) = 0. For the special case when the dot product of two vectors is
identically 0, the two vectors are said to be orthogonal to each other. The dot product
has a number of properties, which will aid in understanding how CDM works. For
vectors
a , b , c :
a.(b+c) = a.b + a.c, and
a.kb=k (a.b), where k is an arbitrary constant, and not a vector
The square root of a.a is a real number, and is called the magnitude of the vector a. It
is denoted as
. a a a
=
Suppose vectors a and b are orthogonal. Then:
2 2
2 2
2 2
2 2
.( ) since a.a + a.b = 0
.( ) since -a.a + a.b = - 0,
.( ) since b.a + b.b = 0 +
.( ) since b.a - b.b = 0 -
a a b a a
a a b a a
b a b b b
a a b b b
+ = +
− + = − +
+ =
− = −
Example:
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