## 2 Concept of Operations
### CN0 of Clock and Communication Data Signals  
The power spectral density of the signal generated by the method discussed is depicted in Figure 2. This figure importantly highlights the distinctive characteristics of power and bandwidth associated with communication and clock signals. Understanding these differences is crucial: the communication signal is hindered by interference, whereas the clock or navigation signal suffers due to noise. Thus, rather than fixate on precise signal strength values on the vertical axis of Figure 2, it is aimed to emphasize these significant distinctions. Furthermore, the characterization of ICaC performance for an on-demand and non-dedicated pLEOT formation is illustrated through a comprehensive analysis of the carrier-to-noise power spectral density ratio (CN0) margins and communication capacity, among other critical factors.  
Figure 1: pLEO time scale interoperability using existing communication infrastructures.  
An integrated clock and communication (ICaC) signal from the orbital platform \(i\) can be detected with sufficient strength to generate usable measurements as long as the value of \(CN0\) meets the threshold required to acquire and track the signal and there is an unobstructed line of sight. For any duration for which the signal is available, the clock-to-interference-plus-noise ratio (CIR) denoted as \(\gamma^{i}_{clk}\) associated with the connection to the platform \(i\) is one of the key factors influencing the performance of clock data transfer.  
\[\gamma^{i}_{clk}(k)=\frac{p^{i}_{clk}(k)}{\frac{p^{i}_{clk}(k)}{B^{i}}+N^{i}_ {0}}\,, \tag{2}\]  
where \(p^{i}_{clk}(k)\) and \(p^{i}_{c}(k)\) are, respectively, the powers of the clock and communication signals at the time instant \(k\in\mathbb{T}\). Also relevant are the total bandwidth \(B^{i}\) and double-sided noise power-spectral density \(N^{i}_{0}\).  
It is important to note that the primary communication signal interferes with the non-dedicated clock signal at a relatively high power level. However, as demonstrated in (2), we can take advantage of two key factors: the very low power of the signal and the significant processing gain derived from the characteristics of the direct sequence spread spectrum. In simpler terms, the communication signal is effectively treated as white noise, meaning its power is equivalent to the total power across the entire frequency band. As a result, the interference from the communication signal is much weaker than the background noise \(N^{i}_{0}\). Therefore, the design of communication signal transmission can be optimized to minimize its impact on the clock data.  
Given the differing design requirements, any ICaC signaling system aboard the participating orbital platform \(i\) must strike a balance between two aspects: clock data transfer and communication data transport, or may choose to focus on one more than the other. For instance, the communications-to-noise ratio (CNR) denoted as \(\gamma^{i}_{c}\) serves as a performance metric that indicates the expected quality of communication services while facilitating non-dedicated clock data transfers in the realization of precise pLEOT  
\[\gamma^{i}_{c}(k)=\frac{p^{i}_{c}(k)}{N^{i}_{0}}\,. \tag{3}\]  
Based on the analysis shown in (2) and (3), the trade-offs and interactions between CN0 values associated with communication and clock data services, namely \(CN0^{i}_{clk}\) and \(CN0^{i}_{c}\) are utilized to determine the performance of the non-dedicated clock data transfer service running onboard orbital platform \(i\)  
\[\gamma^{i}_{clk}(k)=\frac{CN0^{i}_{clk}(k)}{\frac{CN0^{i}_{clk}(k)}{B^{i}}+1} \tag{4}\]  
Figure 2: Superimposing of communication and clock data signals in the proposed ICaC.  
\[\gamma^{i}_{c}(k)=CN0^{i}_{c}(k)\,, \tag{5}\]  
where, in total, the parametric variable CN0 for clock and communication data should be optimally selected to enhance the performance of non-dedicated clock data transfers and primary communication services while maintaining specific quality of service standards.