Zadoff-Chu Sequence in LTE

The Zadoff-Chu (ZC) sequence, often referred to as a CAZAC (Constant Amplitude Zero Auto-Correlation) sequence, is a popular choice in LTE (Long-Term Evolution) technology. It’s favored for its beneficial properties that enhance signal quality and reduce interference.

The Zadoff-Chu sequence possesses the following key features:

• Small Time Variation: This contributes to good power amplification properties of the complex modulated signal in the LTE modem. Essentially, it helps maintain a consistent signal strength.
• Small Frequency Variation: This simplifies channel estimation at the receiver. Accurate channel estimation is crucial for proper signal demodulation.
• Low Cross-Correlation Property: This characteristic minimizes inter-cell interference. Lower interference means a cleaner signal and better performance, especially at cell edges.

Zadoff-Chu Sequence Definition

The Zadoff-Chu sequence is defined by the following mathematical equation:

The equation mathematically represents the generation of the Zadoff-Chu sequence.

Zadoff-Chu Sequence Properties

The Zadoff-Chu sequence exhibits several important properties:

• Constant Amplitude: The signal strength remains consistent.
• Zero Circular Auto-Correlation: This means the signal is highly distinct from shifted versions of itself, crucial for timing and synchronization.
• Flat Frequency Domain Response: This even distribution of energy across frequencies simplifies signal processing.
• Low Circular Cross-Correlation: Two different Zadoff-Chu sequences have minimal interference with each other.
• Constant Amplitude (when L is prime): The constant amplitude characteristic is guaranteed if the length of the sequence, denoted by L, is a prime number.

LTE Physical Signals/Channels Using Zadoff-Chu Sequences

The Zadoff-Chu sequence is employed in several key physical signals and channels within LTE:

• P-SS (Primary Synchronization Signal): The Zadoff-Chu sequence is used for this signal, which is essential for cell search and initial synchronization.
• RS (Reference Signal): Used in both uplink and downlink, the Zadoff-Chu sequence provides a known signal for channel estimation.
• PUCCH (Physical Uplink Control Channel): The Zadoff-Chu sequence is used in the PUCCH, which carries control information from the user equipment (UE) to the base station (eNodeB).