CDM - code division multiplexing (easy to understand)

One 、 brief introduction

· Code division multiplexing is short for CDM
· It can realize multiple users meanwhile Use Same frequency communicate
· How to achieve ？—— Distinguish by the code sequence of each user .

Two 、CDMA principle

2.1 Express

1、 Each bit （0 or 1） Send in a sequence of codes
（m Bit encoding divides each bit into m）

Chip ： A data signal （ Like logic 1 or 0） Usually, multiple coded signals are used for coding , Then one of the coded signals is called a chip

2、 A data signal （ Like logic 1 or 0） Usually, multiple coded signals are used for coding , If this station wants to send 1, Send the original code of the chip , To send 0, Just send the inverse code to the chip

Each station will assign a chip sequence , So how to choose the chip sequence ？

2.2 How to choose chip sequence

The chip sequence of each user is unique , We are required to pass （ If two vectors are orthogonal , Then their order of magnitude is 0, Or the inner product of a vector is 0） To realize this idea . It only needs that each user chip is orthogonal to each other

Implementation of orthogonality ：

${\sum }_{i=1}^{n}Si\cdot Ti=0$（ Through this formula, we can judge whether two different chip sequences are legal ）

summary ： own × own =1 , own × others =0 , own × Inverse code =-1

3、 ... and 、 flow chart

The sender

① S Station and T Stations are assigned unique chip sequences , In the figure, it is shown as S and T
② Known data symbol bits 110, It is said to send 1 If so, send their respective chip sequences （ Each chip sequence in the figure take 1 Expressed as 1,0 Expressed as -1, Above the horizontal axis indicates 1, Below is -1） The original code of , send out 0 It is the inverse code of sending chip sequence , remember S The station is sending $S_x$,T The station is sending $T_x$
③ At the transmitting end, the two kinds of transmitted signals have the superposition effect because they have the same frequency at the same time ,$S_x+T_x$（1 and 1 Add to 2,1 and -1 Add to 0, Shown in the figure ）

The receiver

Main purpose ： Take out the signal sent by each station from the received stacked chip , To judge whether each station sends signals before , And the signal sent is 1 still 0
principle ： For example, the receiving end wants to see S Whether the station sends signals , And it sends 1 still 0：
$S\ast （S_x+T_x）=X$
if $X=1$, Express S The station sent a signal 1.
if $X=0$, It means that the superimposed signal does not $S_x$, It means it is useless to send signals
if $X=-1$, Because the inner product of self and inverse code is 0, It means that the signal is sent 0

Four 、 Example