_{Created on 11 Jan 2025 - 06:43 by Henry Chen}

Zadoff-Chu OFDM Preamble

The Zadoff-Chu (ZC) sequence is a widely used preamble in RF communication systems, valued for its sharp correlation peak, constant amplitude, and periodic nature. This article explores its mathematical properties, performance under different parameters, and real-world applications, including robust frame detection in noisy environments. Experimental results with a Pluto SDR demonstrate the ZC sequence's effectiveness in identifying OFDM frame boundaries and recovering transmitted symbols reliably.

The Zadoff-Chu Preamble

The Zadoff-Chu (ZC) Sequence is a widely used, complex-valued sequence in time-domain signal processing, particularly in RF communication systems. It has gained prominence as a preamble sequence in LTE and 5G mobile communication standards, where it plays a crucial role in frame detection at the receiver. The sequence is renowned for its sharp and isolated correlation peak, making it highly robust against noise and interference.

The Zadoff-Chu sequence offers several key properties that make it ideal for preamble sequences:

Isolated Correlation Peaks: The ZC sequence exhibits significant correlation only when fully aligned with itself, resulting in a distinct, easily detectable peak. This makes frame start detection both reliable and straightforward.
Constant Amplitude: The sequence has a constant amplitude, ensuring a predictable Peak-to-Average Power Ratio (PAPR). This is critical for maintaining signal integrity during transmission.
Periodic Nature: Its periodic structure simplifies its use in communication systems and enhances its efficiency.

The Zadoff-Chu sequence is mathematically defined as:

ZC(n) = e^{-j \pi \frac{u n^2}{N}}

n is the index of the sequence
N is the length of the sequence
u is a constant that changes the shape of the Zadoff-Chu Preamble

Performance of the Zadoff-Chu Preamble

Different ZC parameters influence the correlation behavior. Notably, as u approaches N, the erroneous correlation spikes become less pronounced, which improves frame detection by removing erroneous start of frame detections. In real-world scenarios, the alignment of the ZC sequence’s central spike is crucial for effective detection.

Higher peak thresholds may be required to prevent erroneous packet detection.
Sliding window approaches to estimate the peak can further improve performance by dynamically adjusting thresholds from a continuous baseband stream of data.

Different Zadoff Chu Parameters and their corresponding correlation over time.

Start of Packet Detection with Correlation

In experiments, a random complex sequence of 200 samples was appended to the ZC sequence. Packet detection was achieved using a threshold defined as: Threshold=Mean+3×Standard Deviation.
This method ensures that only significant correlation peaks are detected. However, to avoid multiple detections of the same packet, debouncing techniques can be applied. For example:

Ignore detected frame starts within fewer than N samples of another detected peak.

In each example, a random complex sequence of 200 samples was appended to the ZC sequence. Proposed threshold levels are indicated by the grey dotted line.

Real-World Performance

The Zadoff-Chu sequence has been tested using a Pluto SDR transmitting a 4-QAM OFDM signal at a center frequency of 915 MHz. The setup used a log-periodic antenna transmitting away from a receiving dipole antenna, creating a challenging test environment.

Key Experimental Details:

Randomized time delays were introduced to mimic "packet-like" transmissions.
Cyclic prefixes of 32 samples were added to mitigate Inter-Symbol Interference (ISI). Without this, the decoded OFDM FFT would be yield a higher error rate.
Signals were recovered and downconverted to baseband before analysis.

Test hardware setup with the Pluto SDR++

The autocorrelation peaks of ZC preambles (u=63, N=64) were successfully detected. The system demonstrated reliable frame detection and clear identification of frame boundaries in a real-world OFDM signal. Additionally, symbols within the OFDM frames are seend to be clear and easily recoverable - indicating adequate frame synchronisation.

Detected autocorrelation peaks with Zadoff-Chu Preambles u=63 and N=64.

Frame detection with a real-world OFDM signal. Note the ability to detect the preamble and identify the start and end of the frame. Also note how the symbol from the OFDM symbol can be easily recovered.

Reproduce the Code

All the code for this project can be reproduced by cloning and running the code in this repository.

_{Updated on 11 Jan 2025 - 11:35}