What is Code Division Multiplexing?

Code Division Multiplexing (CDM) is an advanced multiplexing technique used in cellular telephone systems and satellite communications. The specific version used in cell phones is called Code Division Multiple Access (CDMA).

Unlike other multiplexing methods that rely on physical properties like frequency or time, CDM uses a mathematical concept based on orthogonal vector spaces. This allows multiple signals to be combined and separated without interference.

How CDM Works

In CDM, each sender is assigned a unique binary code called a chip sequence (C_i). These chip sequences are chosen to be orthogonal vectors, meaning the dot product of any two chip sequences equals zero. When a sender has data to transmit (V_i), it multiplies its chip sequence by the data value: C_i × V_i. All senders transmit simultaneously, and their signals are added together at the receiver.

To extract a specific sender's data, the receiver multiplies the combined signal by the desired sender's chip sequence.

Example of CDM Process

Consider two senders with the following chip sequences and data:

First, binary values are converted to vectors using ?1 to represent 0:

C? = (1, ?1), V? = (1, ?1, 1, ?1)
C? = (1, 1), V? = (?1, 1, 1, ?1)

Multiplying each chip sequence by its data produces encoded signals that are then summed:

Sender A: ((1, ?1), (?1, 1), (1, ?1), (?1, 1))
Sender B: ((?1, ?1), (1, 1), (1, 1), (?1, ?1))

Combined signal: (0, ?2, 0, 2, 2, 0, ?2, 0)

To recover the original data, the receiver multiplies the combined signal by the appropriate chip sequence and converts positive values to 1 and negative values to 0.

Advantages of CDM

• High capacity ? Multiple users can transmit simultaneously on the same frequency

• Lower delay ? Unlike Time Division Multiplexing where senders must wait turns, CDM allows continuous transmission

• Interference resistance ? Orthogonal codes prevent cross-talk between users

• Security ? Unique chip sequences provide inherent encryption

Conclusion

Code Division Multiplexing uses orthogonal chip sequences to enable multiple simultaneous transmissions without interference. This mathematical approach offers superior scalability and reduced delays compared to traditional time-based multiplexing methods.