In order for all GPS satellites to broadcast simultaneously and provide precise ranging measurements to users, each satellite's signal is overlayed with a binary code sequence, or a spreading code. The current GPS signals use spreading codes that were designed before the recent boom in computing, with the most commonly used GPS signal today using codes designed in the 1960s. However, starting launches in 2026, the GPS IIIF satellites will be the first to have a fully-digital, reprogrammable payload, allowing for new opportunities to re-explore the design of the GPS spreading codes.

We explore new frameworks to design the GPS codes, leveraging stochastic optimization strategies and present-day computational tools. We additionally demonstrate that our designed codes have lower self- and inter-signal interference than competitive sets of Gold and Weil codes, which are code families used by GPS today.

Related Publications:

• T. Mina, A. Yang, and G. Gao, “Designing long GPS memory codes using the cross entropy method,” NAVIGATION, Journal of the Institute of Navigation, submitted.

• A. Yang, T. Mina, and G. Gao, “Fast spreading code optimization under modeled Doppler effects,” in Institute of Navigation (ION) International Technical Meeting (ITM) Conference, Long Beach, CA, Jan. 2024, abstract accepted.

• A. Yang, T. Mina, and G. Gao, “Spreading code design via mixed-integer convex optimization,” NAVIGATION, Journal of the Institute of Navigation, submitted.

• A. Yang, T. Mina, and G. Gao, “Spreading code optimization for low-Earth orbit satellites via mixed-integer convex programming,” EURASIP Journal on Advances in Signal Processing, submitted.

• A. Yang, T. Mina, and G. Gao, “Spreading code sequence design is a convex optimization problem with binary constraints,” in Institute of Navigation (ION) GNSS+ Conference, Denver, CO, Sep. 2023, accepted.

• T. Mina, A. Yang, and G. Gao, “Designing long GPS memory codes using the cross entropy method,” in Institute of Navigation (ION) GNSS+ Conference, Denver, CO, Sep. 2023, accepted.

• A. Yang, T. Mina, and G. Gao, “Binary sequence set optimization for CDMA applications via mixed-integer quadratic programming,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Rhodes Island, Greece, Jun. 2023, pp. 1–5. [paper]

• T. Mina and G. Gao, “Designing low-correlation GPS spreading codes with a natural evolution strategy machine-learning algorithm,” NAVIGATION, Journal of the Institute of Navigation, vol. 69, no. 1, 2022. [paper] [video]

• T. Mina and G. Gao, “Designing low-correlation GPS spreading codes via a policy gradient reinforcement learning algorithm,” in Institute of Navigation (ION) GNSS+ Conference, St. Louis, MO, Sep. 2020, pp. 1968–1983. Best Presentation of the Session Award. [paper] [slides] [video]

T. Mina and G. Gao, “Devising high-performing random spreading code sequences using a multi-objective genetic algorithm,” in Institute of Navigation (ION) GNSS+ Conference, Miami, FL, Sep. 2019, pp. 1076–1089. Best Presentation of the Session Award. [paper] [slides]