A ranging code based on the improved Logistic map for future GNSS signals: code design and performance evaluation

Abstract

Ranging code is the core component of the signal transmission scheme in any global navigation satellite system (GNSS); its performance directly influences on the technical indexes of positioning accuracy, compatibility, interoperability, anti-interference, security, synchronization realization, and so on. Therefore, research on ranging codes could provide theoretical support for the improvement of the performance of ranging codes and extension of their design methods to future satellite navigation signal structures. In order to improve the balance in classical chaotic sequences, a novel ranging code is proposed in this paper and constructed by a series of the improved Logistic-map chaotic sequences with different initial values through weighted optimization, summation, and quantization. Then a comprehensive performance evaluation method based on the Welch bound including three main indexes has been introduced, namely the performance of acquisition, tracking, and robustness against interfering narrowband signals. Finally, the three indexes are combined in a cost function by weighting to evaluate the proposed code, coarse/acquisition (C/A), Gold, Weil, and Random as well as the conventional chaotic codes, and the corresponding weighted coefficients can be adjusted flexibly according to the user groups or application types. Theoretical analysis and simulation results over an additive white Gaussian noise (AWGN) channel show that the proposed ranging code cannot only demonstrate excellent performance in acquisition and anti-narrowband interference while maintaining high quality in tracking performance as the C/A code but also significantly improve balance performance and strengthen reliability and security.