Hardware-Efficient Root Value Estimation for Zadoff-Chu Sequences of Known Length

Abstract

In wireless communication, Zadoff-Chu (ZC) sequences are often used for synchronisation between transmitters and receivers due to their advantageous mathematical properties. They are extensively used in LTE and 5G systems, as well as for UAV communications and various other applications. Blind detection of ZC sequences, meaning that their structural parameters are unknown, has applications for security and privacy. However, blind ZC sequence detection is computationally expensive, especially for longer sequences, restricting deployment to centralised processing platforms.

This thesis investigates hardware efficient algorithms for the detection of ZC sequences for deployment on resource-constrained edge devices. We simulated and evaluated three algorithms: time-based cross-correlation, fast cross-correlation, and phase difference estimation. The results demonstrated that both cross-correlation algorithms achieved acceptable performance down to a Signal-to-Noise Ratio (SNR) of -14 decibels. However, the time-based cross-correlation consumed 10 times the energy, rendering it impractical. In contrast, the phase difference estimation algorithm consumed 10 times less energy than the fast cross-correlation algorithm, but the acceptable performance was limited to SNRs above -6 dB.

To further reduce energy consumption, these algorithms were also modified. This yielded significant power savings proportional to the modification degree;
however, performance decreased accordingly. Consequently, these trade-offs demonstrate that the optimal algorithm and modification configuration depend on the intended SNR environment, providing a dynamic low-power solution.

Popular Abstract

When communicating wirelessly, a fundamental challenge is determining exactly when a message starts and stops. If the receiver is off by even a fraction of a second, the entire message can be corrupted. To prevent this, systems use a digital handshake called a synchronisation sequence. This sequence tells the receiver exactly when to start listening, synchronising it to the transmitter.

While many types of synchronisation sequences exist, Zadoff-Chu sequences are widely used. For example, in drone communications, they are used to synchronise and stabilise live video footage. These sequences can both vary in length and shape, providing a large set of unique sequences. Because an operator and device share a known sequence, they can easily find each other. However, this synchronisation sequence also acts as a digital flag. Surveillance and security systems can use this flag to detect unauthorised devices and potentially intercept the data transmitted.

The catch is that these security systems don’t know what specific sequence the devices use. So, to detect a rogue device, they need to test a large number of possibilities. This process is so computationally expensive that the detection systems are bound to heavy stationary computer systems such as desktop PCs or servers. Bringing these security systems onto lightweight portable devices like microcontrollers is difficult. Therefore, this thesis investigates alternative algorithms and modifications to reduce computational requirements. Through simulations, this study maps out a range of flexible options in which detection performance is traded for reduced computational requirements. Ultimately, this framework allows the user to select the exact performance required for their device, minimising excess compute.

• author: Eriksson Rygaard, Hampus and Forsberg, Marcus
• supervisor: Johan Thunberg
• organization: Department of Electrical and Information Technology
• course: EITM01 20261
• year: 2026
• type: H2 - Master's Degree (Two Years)
• subject: Technology and Engineering
• keywords: Zadoff-Chu sequence, Signal detection, Energy efficiency
• report number: LU/LTH-EIT 2026-1149
• language: English
• id: 9236339
• date added to LUP: 2026-06-16 15:41:23
• date last changed: 2026-06-16 15:41:23