How CDMA works

Code Division Multiple Access (CDMA) lets all stations use the whole bandwidth at the same time. Each station is assigned a unique chip sequence (code), and the codes are mutually orthogonal. A bit is spread by its code before sending, and the receiver recovers one station's data by taking the inner product of the received sum with that station's code.

Principles

• Data 1 is sent as +code, data 0 as −code, and silence as 0.
• Orthogonal codes: inner product of two different codes is 0, and of a code with itself is N (code length).
• The channel adds the signals of all stations.
• To recover station X's data, multiply the total signal by X's code, add up, and divide by N: result +1 means bit 1, −1 means bit 0, 0 means silent.

Example (N = 4, Walsh codes)

A = [+1 +1 +1 +1], B = [+1 −1 +1 −1], C = [+1 +1 −1 −1], D = [+1 −1 −1 +1].

Let A send bit 1 (+1), B send bit 0 (−1), C silent (0), D send bit 1 (+1).

 A*(+1) = +1 +1 +1 +1
 B*(-1) = -1 +1 -1 +1
 C*( 0) =  0  0  0  0
 D*(+1) = +1 -1 -1 +1
 Total  = +1 +1 -1 +3

Decoding the total [+1 +1 −1 +3]:

• A: (1+1−1+3)/4 = +1, so bit 1
• B: (1−1−1−3)/4 = −1, so bit 0
• C: (1+1+1−3)/4 = 0, so silent
• D: (1−1+1+3)/4 = +1, so bit 1

All four are recovered correctly. Used in IS-95 and 3G (WCDMA); close to DSSS in principle.