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Objective  The paper aims to present a generalized modulation scheme that can improve the anti-interference performance of global navigation satellite systems (GNSS) and mitigate the ambiguity problem in BOC modulation.    Summary background data  With the exponential growth of location-based services, there is a need to improve the positioning accuracy and the capability to resist against external interference in challenging environments, such as urban canyons, forested terrains, and indoor areas, in which signal attenuation, interference, and multipath fading can seriously degrade the positioning accuracy of global navigation satellite systems (GNSS) and GNSS-like systems. The binary offset carrier (BOC) modulation has been adopted in GNSSs because of its good spectral isolation from heritage signals, high accuracy, multipath interference resistance, and flexibility in signal implementation compared with BPSK-R modulation. However, for high-order BOC modulation, the main drawback is the ambiguity in tracking due to the multiple side peaks of the autocorrelation function (ACF). The receiver may incorrectly lock onto one of these side peaks, causing intolerable measurement bias, and this undesirable behavior limits the application of this modulation scheme in navigation systems.    Methods  We present a generalized low-ambiguity anti-interference spread spectrum modulation based on frequency-hopping BOC (FH-BOC). First, we formulate the mathematical model of FH-BOC modulation and derive the analytical expressions for the normalized ACF and PSD, and we analyze the time and frequency properties of several representative FH-BOC signals. Next, we present recommended parameter selections, a generation and detection scheme for FH-BOC modulation. Finally, we analyze the characteristics of the ACF and PSD, the tracking performance, the spectral separation, and the anti-narrowband interference and multipath interference performance for several specific BOC and FH-BOC signals.    Results  The results show that FH-BOC with the largest frequency-hopping band has lower ACF ambiguity, better anti-interception performance, and better anti-intrasystem interference, narrowband interference, and multipath interference performance than BOC modulation with the same main lobe bandwidth (MLB). The tracking and anti-interference performance of FH-BOC is similar to that of BOC modulation with the same ACF main peak width.    Conclusions  FH-BOC is a generalized type of modulation that includes BOC modulation. The proposed FH-BOC signal improves the anti-interference performance and mitigates the ACF ambiguity problem of BOC modulation. The acquisition time and complexity of the receiving process for the proposed FH-BOC signal are the same for the BOC signal with the same MLB. The new modulation scheme which we proposed can serve as a new paradigm for the next-generation GNSS signal design, especially military signal design. It can also be used in the signal design for GNSS-like systems, such as systems for indoor positioning, GNSS enhancement, and pseudolite-based positioning.

FH-BOC: generalized low-ambiguity anti-interference spread spectrum modulation based on frequency-hopping binary offset carrier