## 1 Introduction  
The rapid development of global navigation satellite systems (GNSS) and the exponential growth of location-based services raise a new challenge in terms of navigation signal design. In some challenging environments such as urban canyons, forested terrains and indoor areas, due to signal attenuation, interference, and multipath fading, the positioning performance of GNSS is seriously degraded [1, 2, 3, 4]. To alleviate this problem, [PERSON] et al. presented a spread spectrum modulation based on frequency-hopping binary offset carrier (FH-BOC) modulation [5]. The proposed FH-BOC modulation improves the anti-interference performance and mitigates the autocorrelation function (ACF) ambiguity problem of binary offset carrier (BOC) modulation. FH-BOC can be a potential solution for future GNSS signal design. Furthermore, the new generation of GNSS will provide multiple positioning, navigation, and timing services for users, which means that more than one signal will be broadcast in each transmission band [6, 7]. To save payload resources on satellites and make high-power amplifiers (HPAs) operate in the nonlinear saturation region, these signals must be combined into a constant-envelope composite signal. Therefore, there is further demand for finding an efficient constant-envelope frequency-hopping binary offset carrier multiplexing technique to combine several signal components. With the evolution of satellite navigation, a large number of constant-envelope modulation (CEM) techniques have emerged for GNSS signal design. The most typical techniques can be divided into two categories [8]. The first category of techniques is proposed for the combination of signal components located at the same center frequency, such as Interplex [9], majority vote (MV) [10], coherent adaptive subcarrier modulation (CASM) [11], phase-optimized constant-envelope transmission (POGET) [12], and quasi-constant envelope multiplexing [13]. The Interplex and CASM keep the signal envelope constant by introducing useless intermodulation (IM) terms. The MV, POGET, and quasi-constant envelope multiplexing construct a constant-envelope signal under the premise of ensuring the power ratio and relative phase relationship of each signal component comply with predefined values. The second category of techniques is proposed for the multiplexing of signal components at multiple frequencies. The most typical technique is alternated binary offset carrier (AltBOC) modulation, which is a dual-frequency constant-envelope multiplexing (DCEM) technique and is adopted for the Galileo E5 signal [14]. The development of the Beidou system, which has been completely established in 2020, promotes the advancement of the DCEM technique. To satisfy the demands of the Beidou signal design, some DCEM techniques have been proposed, such as time division AltBOC (TD-AltBOC) [15], non-symmetrical AltBOC [16], generalized AltBOC [17], unbalanced AltBOC [18], asymmetric constant envelope binary offset carrier (ACE-BOC) [19], generalized constant envelope BOC (GCE-BOC) [20], interlacing general AltBOC (IGAltBOC) [21], ACE-BOC with equal length subcarrier segments (ES-ACEBOC) [22] and ACE-BOC multiplexing modulation with bipolar subcarrier (BS-ACEBOC) [23]. These studies on DCEM have substantially improved the flexibility of signal design. Furthermore, with further development of GNSSs, several multicarrier CEM techniques are proposed, which combine different signals at several adjacent carrier frequencies into a constant-envelope signal. The representative multicarrier CEM techniques are rotating phase-optimized constant-envelope transmission (R-POGET) [24] and constant-envelope multiplexing via intermodulation construction (CEMIC) [25]. These techniques provide high flexibility for signal design, but the multiplexing efficiency is not satisfactory. To improve multiplexing efficiency, [PERSON] et al. [26] proposed a new multicarrier constant-envelope multiplexing technique by subcarrier vectorization.