# Performance Evaluation of the New Compound-Carrier-Modulated Signal for Future Navigation Signals
## 2 NSCC and Its Properties
### ACF and PSD  
The important basic characteristics NSCC processes are presented in terms of ACF and PSD. The signal ACF should have a narrow peak to realize precise range measurement. For efficient spectral utilization, the signal PSD should possess a narrow profile to allow the co-existence of a number of other signals with minimal mutual interference. In essence, the NSCC is the sum of the \(M\) individual subcarriers with BPSK modulation. The normalized PSD for NSCC can be expressed as:  
\[G_{NSCC}\left(f\right)=\frac{1}{M}\sum_{m=0}^{M-1}f_{\epsilon}\left|\frac{ \sin\left[\pi\left(f-f_{m}\right)T_{\epsilon}\right]}{\pi\left(f-f_{m}\right)} \right|^{2} \tag{2}\]where, \(f_{m}\) is the m-th subcarrier frequency, \(f_{c}\) is the chip rate of spread spectrum PRN code modulating the subcarriers, \(T_{c}\) is the symbol period. According to the Wiener-Khintchine theorem, a signal ACF function and its PSD function constitute a Fourier transform pair. Therefore, the NSCC ACF can be derived from the inverse Fourier transformation of its PSD:  
\[R_{NSCC}\left(t\right)=\int\limits_{-B_{r}/2}^{B_{r}/2}\frac{1}{M}\sum_{m=0}^{ M-1}f_{c}\left|\frac{\sin\left[\pi\left(f-f_{m}\right)T_{c}\right]}{\pi\left(f-f_{m} \right)}\right|^{2}e^{i2\pi ft}df \tag{3}\]  
where, \(B_{r}\) stands for the pre-filtering bandwidth of GNSS receiver. The PSDs of the monomedal and the bimodal NSCC signal are illustrated in Figure 1. The baseline structures adopt a constant power distribution within the active subcarriers. Their subcarrier configuration selects BPSK modulation, 1.023 Mcps code rate and 1.023 MHz frequency spacing. The number of sub-carriers is 19 for monomodal and 18 for bimodal mode with a similar spectrum content over the 20 MHz bandwidth. The two baselines occupy the same bandwidth and can coordinate the spectrum with preexisting signals over the shared bandwidth. Note that their OOB emissions are nearly equal due to the similar sub-carrier configurations. Figure 1: Comparison of PDSs for NSCC baseline structures. Figure 2: Comparison of PSDs for NSCC and legacy navigation signal modulations. The PSDs of NSCC and legacy navigation signals are shown in Figure 2. The profiles of signal PSDs reflect the spectral efficiency and adjacent channel interference (ACI) suppression properties. To illustrate the details of the PSD profiles, the relative power attenuations between the first side lobe and the main lobe are given in Table 1. The modulations include BPSK(1), BPSK(10), BOC(10,5), QPSK(10) used in GPS, BPSK(5), MBOC(6,1,1/11), BOC(10,5), BOC(15,2.5), AltBOC(15,10) used in Galileo, BOC(15,2.5), BOC(14,2), MBOC(6,1,1/11), QPSK(10) used in Beidou system. Only monomodal NSCC is adopted because of the similarity of spectral characteristics with the bimodal one except for the split feature. Obviously, the energy of the NSCC signal is mostly concentrated within the main lobe and the magnitude of the side lobes decreases sharply. The NSCC modulation makes the PSD more compact than BOC modulation and its derivatives. This property implies better spectrum efficiency and less vulnerability to adjacent channels. We note that the MSK signal presents the best spectrum efficiency and the side lobes fall off sharpest because of its constant envelope modulation, but the relatively smaller bandwidth is a restriction for the ultimate performance. The ACFs of NSCC and the legacy signals are shown in Figure 3. A signal ACF profile is closely related to its bandwidth since the high-frequency component determines the details. The simulation bandwidths are set as 2, 4, 10 and 20 MHz, respectively. The monomodal NSCC is selected for comparison in the simulation. For the 2 MHz bandwidth, the MSK modulation possesses a narrower ACF peak than BPSK(1) modulation because its main lobe concentrates more power within 2 MHz. Then, the BOC(1,1) modulation outperforms the MSK modulation at 4 MHz bandwidth due to the more high-frequency components it possesses.