Foundations of Code Division Multiple Access

Code Division Multiple Access (CDMA) is a digital cellular technology that enables multiple users to transmit simultaneously over the same frequency band by assigning each user a unique spreading code. Unlike time-division multiple access (TDMA) or frequency-division multiple access (FDMA), which partition resources in time or frequency slots, CDMA relies on spread-spectrum principles to overlay user signals. This approach provides higher spectral efficiency, inherent security, and robust resistance to interference and multipath fading. A thorough understanding of CDMA encoding and decoding processes is essential for anyone working with 2G/3G networks, satellite communications, or modern wireless systems that build upon these fundamentals.

Spread Spectrum Fundamentals

At the heart of CDMA lies direct-sequence spread spectrum (DSSS). In DSSS, the transmitted signal’s bandwidth is artificially widened by multiplying the data stream with a high-rate pseudorandom sequence. The result is a signal that occupies far more bandwidth than the original data requires. The receiver, knowing the same spreading sequence, can “despread” the signal to recover the original narrowband data. This technique makes the transmitted signal appear noise-like to unintended receivers and provides frequency diversity that combats narrowband interference and multipath.

Two critical properties of DSSS are processing gain and the near-far problem. Processing gain is the ratio of the spread bandwidth to the original data bandwidth and directly determines how many simultaneous users can be supported and how much interference the system can tolerate. The near-far problem arises when a nearby mobile transmitter overwhelms a distant one at the base station receiver. Effective power control mechanisms are therefore integral to any CDMA system.

Spreading Codes in CDMA

The uniqueness and orthogonality of spreading codes define CDMA performance. Two main types of codes are used: orthogonal codes and pseudorandom noise (PN) sequences.

Walsh Codes (Orthogonal Codes)

Walsh codes are a set of perfectly orthogonal sequences, typically used in the forward link (base station to mobile). In IS-95 and CDMA2000, 64-chip Walsh codes allow each channel to be separated without mutual interference under ideal synchronous conditions. The orthogonality means that the cross-correlation between any two different Walsh codes is zero, enabling the base station to transmit multiple user channels simultaneously without creating interference among them.

Pseudorandom Noise Sequences

PN sequences, such as m-sequences or Gold codes, are used for scrambling and for the reverse link (mobile to base station). These codes are not perfectly orthogonal but exhibit low cross-correlation values. They provide additional privacy by making user signals indistinguishable from noise to an eavesdropper and help mitigate multipath interference through the use of rake receivers. In IS-95, a long PN code (242-1 chip period) scrambles the reverse link, while short PN codes are used for base station identification.

CDMA Signal Encoding Process

The encoding process transforms raw user data into a spread-spectrum waveform ready for transmission. The steps are outlined below.

Data Multiplication with Spreading Code

Each user’s binary data (e.g., voice or packet data) is first multiplied by a dedicated spreading code. In the forward link, this code is typically a Walsh code; in the reverse link, a PN sequence is used. The spreading code runs at a much higher chip rate than the data rate. For example, in IS-95 the chip rate is 1.2288 Mcps (megachips per second), while voice data is encoded at 9.6 kbps. This yields a processing gain of approximately 128 (21 dB).

Modulation and Carrier Upconversion

After spreading, the resulting chip stream is modulated using either binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) variants. In the forward link, QPSK modulation is used to improve spectral efficiency. The modulated signal is then upconverted to the carrier frequency, amplified, and transmitted via the antenna. Additional processing such as interleaving and forward error correction coding (e.g., convolutional codes) is applied before spreading to increase robustness against channel errors.

Power Control Insertion

A critical part of encoding is the inclusion of power control commands. The base station continuously measures each mobile’s received signal strength and sends power adjustment bits. The mobile’s transmitter adjusts its output power in fine steps (typically 1 dB) every 1.25 ms in CDMA2000. This closed-loop power control ensures that all user signals arrive at the base station with nearly equal power, mitigating the near-far problem.

CDMA Signal Decoding Process

Decoding is the reverse of encoding and involves several sophisticated techniques to recover the original data from the composite received signal.

Correlation and Despreading

The receiver first downconverts the received signal to baseband. The core of decoding is correlation: the incoming complex baseband signal is multiplied by a locally generated replica of the intended user’s spreading code, synchronized in time. Because the autocorrelation of the spreading code features a sharp peak at zero offset, the correlator output yields a high signal amplitude only when the code sequence is aligned. All other user signals (using different codes) appear as low-level noise after correlation. This process is called despreading because the desired signal collapses to its original narrow bandwidth, while interference remains spread.

Rake Receiver for Multipath Diversity

In a multipath environment, the transmitted signal arrives via multiple paths with different delays. A CDMA receiver typically employs a rake receiver with several “fingers.” Each finger correlates the incoming signal with the spreading code shifted by a specific delay corresponding to a multipath component. The outputs from all fingers are then coherently combined (often using maximal ratio combining) to maximize the signal-to-noise ratio. This technique exploits the inherent multipath diversity of spread-spectrum signals and significantly improves performance in fading channels.

Data Demodulation and Error Correction

After despreading and combining, the chip stream is demodulated (e.g., QPSK demapper) and deinterleaved. The resulting soft decisions are passed to a Viterbi decoder (for convolutional codes) or a turbo decoder (for 3G variants). The decoder recovers the original user data with a low bit error rate. Additionally, the receiver performs automatic frequency control and phase tracking to maintain synchronization.

Power Control in CDMA Systems

Power control is not merely an ancillary feature but a fundamental requirement for CDMA. Without it, the near-far problem would render the system unusable. There are two types of power control:

  • Open-loop power control: The mobile estimates the path loss based on the received power from the base station and sets its initial transmit power accordingly. This is used for initial access and during rapid changes (e.g., when a mobile suddenly emerges from a tunnel).
  • Closed-loop power control: The base station sends explicit power adjustment commands to each mobile every 1.25 ms (in 1xRTT). The mobile adjusts its output power in 1 dB steps to maintain a target received signal-to-interference ratio. This loop compensates for slow fading and changes in channel conditions.

Power control directly impacts system capacity: every decibel of unnecessary transmission power reduces the number of users that can be supported. Advanced algorithms such as outer-loop power control further optimize the target SIR based on frame error rates.

Key Variants: IS-95 vs. WCDMA

While the basic encoding and decoding principles are common, notable differences exist between the two dominant CDMA standards.

IS-95 (cdmaOne)

The first commercial CDMA standard, IS-95, uses a chip rate of 1.2288 Mcps and a fixed spreading factor of 128 for voice channels. It employs Walsh codes (64-ary) on the forward link and long PN codes for scrambling on the reverse link. The air interface supports a maximum data rate of 14.4 kbps per channel, which is sufficient for voice and low-rate data.

WCDMA (Wideband CDMA)

WCDMA, used in UMTS (3G), employs a chip rate of 3.84 Mcps, giving a wider bandwidth of 5 MHz per carrier. This allows variable spreading factors from 4 to 512, enabling flexible data rates from ~12 kbps to 2 Mbps. WCDMA uses orthogonal variable spreading factor (OVSF) codes to support multiple data rates while maintaining orthogonality. The modulation can be QPSK or 16-QAM for high-speed downlink packet access (HSDPA). Additionally, WCDMA introduces a more advanced turbo coding scheme and faster power control (1500 Hz update rate).

Advantages and Challenges of CDMA Encoding/Decoding

The encoding and decoding processes endow CDMA with unique advantages while imposing certain challenges.

Advantages

  • High spectral efficiency: CDMA can support more users per Hertz than TDMA or FDMA, especially with voice activity detection and soft handoff.
  • Inherent security: Spreading codes make unauthorized despreading extremely difficult without knowledge of the code and timing.
  • Resistance to interference: The processing gain provides immunity to narrowband jammers and multipath.
  • Soft handover: Mobile terminals can communicate with multiple base stations simultaneously, reducing call drops and improving quality.
  • Graceful degradation: When capacity is exceeded, the system degrades gradually rather than abruptly blocking new calls.

Challenges

  • Need for precise power control: Without fast and accurate power control, the near-far problem destroys capacity.
  • Complex receiver design: Rake receivers, channel estimation, and multi-user detection add cost and power consumption.
  • Self-interference: Non-orthogonal spreading codes on the reverse link cause multiple-access interference, limiting the capacity.
  • Synchronization overhead: Long PN codes require precise timing acquisition and tracking, especially during handover.

Conclusion

CDMA signal encoding and decoding processes are sophisticated yet elegant mechanisms that enable reliable, high-capacity wireless communication. By spreading user data with unique codes and employing correlation-based despreading, CDMA systems simultaneously serve many users while providing inherent security and resilience against interference. The evolution from IS-95 to WCDMA demonstrates how advances in coding, power control, and receiver design have pushed the limits of what spread-spectrum technology can achieve. For engineers working with modern 4G LTE (which uses OFDMA but incorporates CDMA-like concepts in its random access channels) or 5G, understanding these fundamental processes remains invaluable. Further exploration of topics such as Qualcomm’s CDMA innovations, advanced multi-user detection, and 3GPP CDMA2000 specifications provides deeper insight into the continued relevance of CDMA encoding and decoding.