Editing Code-division multiple access (section)

==Steps in CDMA modulation==
CDMA is a spread-spectrum multiple-access technique. A spread-spectrum technique spreads the bandwidth of the data uniformly for the same transmitted power.  A spreading code is a [[Pseudorandom binary sequence|pseudo-random code]] in the time domain that has a narrow [[ambiguity function]] in the frequency domain, unlike other narrow pulse codes. In CDMA a locally generated code runs at a much higher rate than the data to be transmitted.  Data for transmission is combined by bitwise [[XOR#Bitwise operation|XOR]] (exclusive OR) with the faster code.  The figure shows how a spread-spectrum signal is generated. The data signal with pulse duration of <math>T_b</math> (symbol period) is XORed with the code signal with pulse duration of <math>T_c</math> (chip period). (Note: [[Bandwidth (signal processing)|bandwidth]] is proportional to <math>1/T</math>, where <math>T</math> = bit time.) Therefore, the bandwidth of the data signal is <math>1/T_b</math> and the bandwidth of the spread spectrum signal is <math>1/T_c</math>.  Since <math>T_c</math> is much smaller than <math>T_b</math>, the bandwidth of the spread-spectrum signal is much larger than the bandwidth of the original signal. The ratio <math>T_b/T_c</math> is called the spreading factor or processing gain and determines to a certain extent the upper limit of the total number of users supported simultaneously by a base station.<ref name="ref 1"/><ref name="ref 2"/>

[[File:Generation of CDMA.svg|thumb|500px|center|Generation of a CDMA signal]]

Each user in a CDMA system uses a different code to modulate their signal. Choosing the codes used to modulate the signal is very important in the performance of CDMA systems. The best performance occurs when there is good separation between the signal of a desired user and the signals of other users. The separation of the signals is made by [[Cross-correlation|correlating]] the received signal with the locally generated code of the desired user. If the signal matches the desired user's code, then the correlation function will be high and the system can extract that signal.  If the desired user's code has nothing in common with the signal, the correlation should be as close to zero as possible (thus eliminating the signal); this is referred to as [[cross-correlation]]. If the code is correlated with the signal at any time offset other than zero, the correlation should be as close to zero as possible.  This is referred to as auto-correlation and is used to reject multi-path interference.<ref name="ref 3">{{cite book| title= Digital Communications: Fundamentals and Applications, 2nd ed.| year=2014|last1=Sklar|first1=Bernard|last2=Ray|first2=Pabitra K.}}</ref><ref name="ref 4">{{cite book| title=Wireless Communications, 2nd ed.| year=2010|last1=Molisch|first1=Andreas}}</ref>

An analogy to the problem of multiple access is a room (channel) in which people wish to talk to each other simultaneously.  To avoid confusion, people could take turns speaking (time division), speak at different pitches (frequency division), or speak in different languages (code division). CDMA is analogous to the last example where people speaking the same language can understand each other, but other languages are perceived as [[noise]] and rejected.  Similarly, in radio CDMA, each group of users is given a shared code.  Many codes occupy the same channel, but only users associated with a particular code can communicate.

In general, CDMA belongs to two basic categories: synchronous (orthogonal codes) and asynchronous (pseudorandom codes).