Code-Division Multiple Access (CDMA)

Code-Division Multiple Access

Code-Division Multiple Access (CDMA) lets multiple users transmit over the same time interval and frequency band. A receiver separates a selected user by correlating the received signal with that user's spreading code.

Frequency Division (FDM): Users are assigned separate frequency bands, so their transmissions occupy different parts of the spectrum.
Time Division (TDM): Users share a frequency band through recurring time slots assigned to individual transmissions.
Code Division (CDMA): Users share the band and time, while distinct spreading codes let a synchronized receiver select one signal by correlation.

The code changes the signal waveform in a user-specific way. The receiver uses the corresponding code replica to recover the desired data while contributions from other users remain as multiple-access interference determined by their cross-correlation and received powers.

Spread-Spectrum Principle

CDMA is a form of technology. The occupied bandwidth is set mainly by the chip rate, pulse shaping, and the selected spreading code.

The process starts with a user's data signal, which is narrow-band. This signal is then combined with a much faster, wideband code called a . Multiplication by the chip sequence spreads the data energy over a wider frequency range. A receiver without code and timing synchronization sees a noise-like waveform. Confidentiality requires a separate cryptographic mechanism.

How It Works: Spreading and Despreading

CDMA processing has two stages: spreading at the transmitter and correlation-based despreading at the receiver.

At the Transmitter: Spreading

A user's slow data stream (made of bits) is taken.
The bit and each chip are represented by bipolar values, usually $+1$ and $-1$ , and are multiplied. In a binary implementation, the same operation can be represented by XOR. The elements of the code are called chips.
The ratio of the chip rate to the bit rate is the ( $G_p = T_b / T_c = R_c / R_b$ ). Its value follows from the selected chip and bit rates. For example, a linear gain from 100 to 10,000 corresponds to 20 to 40 dB; other systems use different values according to their rates.
The resulting signal is now a wideband signal with low power density, ready for transmission.

At the Receiver: Despreading

The receiver gets a mixture of signals from all users. To detect a specific user, it correlates the mixture with that user's code replica:

The incoming mixture is multiplied and integrated with the same PN code replica. Chip timing, carrier phase, and code alignment must be estimated with the required accuracy.
For an aligned desired code, the chip products add coherently, so the correlator output contains the desired data symbol and correlation concentrates its energy at that output.
Other users contribute according to their cross-correlation with the selected code. Spreading and filtering can reduce these terms. Non-orthogonal codes and timing offsets leave residual cross-correlation.
A correlator or integrate-and-dump detector then decides the data bit from the output. Residual noise and multiple-access interference determine the resulting error probability.

Correlation can be checked directly for bipolar code vectors. For example, let $c_1=(+1,+1,+1,+1)$ and $c_2=(+1,-1,+1,-1)$ . Their normalized correlation is $\rho_{12}=\frac{c_1\cdot c_2}{4}=0$ , so an aligned correlator for $c_1$ rejects the ideal $c_2$ contribution. Non-orthogonal codes or a chip-timing offset produce a nonzero cross-correlation.

Types of Spread Spectrum Techniques

CDMA implementations most often use direct-sequence spreading. Spread-spectrum systems are also described by three common methods:

Direct Sequence Spread Spectrum (DSSS): The data is multiplied by a faster chip sequence, as described above. DSSS is used in CDMA systems such as 3G mobile networks (WCDMA) and GPS.
Frequency Hopping Spread Spectrum (FHSS): The carrier frequency changes among a set of channels according to a hopping sequence. A synchronized receiver follows that sequence to demodulate the signal. Bluetooth Classic is an example of FHSS use.
Time Hopping Spread Spectrum (THSS): The signal is transmitted in short bursts, and the burst position varies according to a time-hopping code. Time hopping is used in some Ultra-Wideband (UWB) communication schemes.

Advantages and Applications of CDMA

Frequency Reuse: In cellular CDMA planning, a reuse factor of 1 can be used, so adjacent cells share the carrier band with interference controlled by power and code planning.
Soft Capacity: CDMA has no fixed user count independent of quality targets. As more users transmit, the interference level rises and the allowed data rates or coverage margin decrease.
Narrow-Band Interference Rejection: After despreading, a narrow-band interferer is distributed across the detector bandwidth. The suppression depends on processing gain, interferer power, and receiver filtering.
Soft Handoff: In cellular systems that support it, a mobile can communicate with two or more base stations during a transition. This reduces the interruption risk when the serving cell changes.
Cryptographic Confidentiality: A noise-like spectrum and an unknown PN code can hinder casual reception. Confidentiality requires a separate cryptographic mechanism.

Key applications include 3G cellular standards such as UMTS/WCDMA and CDMA2000, as well as the Global Positioning System (GPS), whose DSSS signals rely on defined code sequences, timing, and correlation.