## 1 Introduction  
With the recent modernization of GPS and GLONASS signals and the emerging Compass and Galileo systems, the number of navigation satellite signals in space is increasing drastically and anticipated to surpass 400 by 2030. Such a large number of signals will further exacerbate an already crowded radio spectrum in the 1164-1610 MHz L band and negatively impact the performance of all navigation systems sharing these limited resources [1].  
In order to solve the above problem, the International Telecommunication Union (ITU) has successively allocated the S band (2483.5-2500 MHz) and C band (5010-5030 MHz) to satellite navigation services. Although signal performance in a single S or C band cannot surpass the L band's due to the smaller available bandwidth and the higher path losses [2; 3; 4], the signal combination of L band and S or C band could improve positioning accuracy and timing performance and comprehensively promote the performance of radio navigation services [3; 5; 6]. Therefore, the multi-band combined navigation and compatibility among different navigation systems has become a research hotspot in recent years [7; 8].  
Compared to multi-frequency signals in the L band, multi-band multi-frequency signals can not only mostly reduce ionosphere delays and strengthen ionospheric correction capability, but also ease carrier phase integer ambiguity resolution to improve robustness and position accuracy, and enhance the anti-interference ability of GNSS signals [2; 3; 5; 6]. As is well-known, signal structure is one of the decisive factors for GNSS and modulation is one of the key technologies which must be resolved during the system design and upgrading process. CPM has been widely used in the field of satellite communication [9; 10], which has high spectrum efficiency and constant-envelope features. Besides, it has many other excellent characteristics, such as a large number of alternative waveforms, flexible parameter adjustment, better compatibility with existing signals and so on.  
In the L band, a special subclass of CPM with semi-integer modulation index \(h\) ( \(h=H+1/\) 2, \(H\in\mathbf{N}\) ) greater than one and satisfying a constraint \(h/\,2T_{{}_{\mathit{cpm}}}=n\times 1.023\) MHz can exhibit a similar spectral main lobe and yield comparable navigation performance compared to conventional binary offset carrier (BOC) denoted as BOC(\(n\), \(m\)), where \(m\times 1.023\) MHz is the spread spectrum code rate, \(n\times 1.023\) MHz is the frequency of sub-carrier and \(T_{{}_{\mathit{cpm}}}\) denotes the CPM signal symbol time [11]. The IRNSS will transmit navigation signals in the lower S band. BPSK(\(m\)) and BOC(\(n\), \(m\)) centered on a frequency close to 2491 MHz are the specific waveforms [12]. Meanwhile, minimum shift keying (MSK) as a potentially promising C band signal waveform that has been investigated for the Galileo system [13], which is a special case of CPM. Unfortunately, the above modulation schemes can't meet the requirement of compatibility in the S and C bands very well due to relatively high side lobes. Furthermore, different modulation waveforms employed by each band undoubtedly increase the user terminal complexity in the multi-band combined navigation mode. In view of this, we propose a universal modulation scheme based on the CPM family and design two specific CPM signals as S and C band solutions by virtue of their properties, which will make a single modulation waveform design possible and accelerate the practicality of multi-band combined navigation technology.  
The rest of this paper is organized as follows: Section 2 describes the mathematical model and power spectrum density (PSD) of CPM signals. The Section 3 provides a comprehensive evaluationcriterion for GNSS signal design and introduces analytical methods in terms of anti-jamming performance. The proposed CPM signals together with other candidates are comprehensively evaluated in Sections 4 and 5, respectively. Finally, we conclude the paper in Section 6.