## Appendix B
\begin{array}{l}\text{Im}[R_{\text{A3}}(t)]=\frac{\sin(2\theta)}{2 MT_{c}} \left\{2\sum\limits_{i=0}^{M-1}\sum\limits_{m=0}^{N_{-1}-1}N_{n-1}^{N_{-1}-1}(- 1)^{m+n}\left[\begin{array}{l}\Pi_{[\frac{mt_{c}^{2}}{2}+\frac{t_{i}^{2}}{4}, \frac{\tau_{c}^{2}}{4}+\frac{t_{i}^{2}}{4}-t_{\theta_{\theta}}^{i},T_{c}]}(t )+\Pi_{[\frac{mt_{c}^{2}}{2}+\frac{t_{i}^{2}}{4},\frac{\tau_{c}^{2}}{4}-t_{ \theta_{\theta}}^{i},T_{c}]}(t)\\ +\Pi_{[\frac{mt_{c}^{2}}{2}+\frac{t_{i}^{2}}{4},\frac{\tau_{c}^{2}}{4},T_{c}]}(t )-\Pi_{[\frac{mt_{c}^{2}}{2}+\frac{t_{i}^{2}}{4},\frac{\tau_{c}^{2}}{4}+t_{ \theta_{\theta}}^{i},T_{c}]}(t)+\Pi_{[0,\frac{mt_{c}^{2}}{2}+\frac{t_{i}^{2}}{4 },\frac{\tau_{c}^{2}}{4}+t_{\theta_{\theta}}^{i},T_{c}]}(t)\\ +\Pi_{[0,\frac{mt_{c}^{2}}{2}+\frac{t_{i}^{2}}{4},\frac{\tau_{c}^{2}}{4}]}(t)+ 2\Pi_{[0,\frac{mt_{c}^{2}}{2},T_{c}]}(t)\end{array}\right]+\text{MI}[_{[0, \frac{mt_{c}^{2}}{2}+\frac{t_{i}^{2}}{4},\frac{\tau_{c}^{2}}{4}]}(t)\end{array} \right] (15)  
The PSD of the Type-I ACE-FHBOC signal can be formulated as  
\[ \begin{array}{l}G_{\text{A2}}(f)=\frac{4}{MT_{c}\pi^{2}f^{2}}\sum\limits_{i= 0}^{M-1}\frac{\sin^{2}(\pi fT_{c})}{\cos^{2}(\pi fT_{c}^{2}/2)}\left\{4+4\cos^ {2}\left(\frac{1}{2}\pi fT_{h}^{i}\right)-2\cos\left(2\pi ft_{\theta}^{i}\right) \cos\left(\frac{1}{2}\pi fT_{h}^{i}\right)\right.\\ \left.-\sin\left[2\pi f\left(\frac{\tau_{h}^{i}}{2}-2t_{\theta}^{i}\right) \right]-2\cos\left[2\pi f\left(\frac{\tau_{h}^{i}}{4}-t_{\theta}^{i}\right) \right]\cos\left(\frac{1}{2}\pi fT_{h}^{i}\right)-4\cos\left(\frac{1}{4}\pi fT_ {h}^{i}\right)\cos\left(\frac{1}{2}\pi fT_{h}^{i}\right)\right.\\ \left.-2\sin(2\theta)\sin\left(\pi f\frac{\tau_{h}^{i}}{2}\right)+2\sin\left[2\pi f \left(\frac{\tau_{h}^{i}}{4}-t_{\theta}^{i}\right)\right]\cos\left(\frac{1}{2} \pi fT_{h}^{i}\right)+2\sin\left(2\pi ft_{\theta}^{i}\right)\cos\left(\frac{1}{2} \pi fT_{h}^{i}\right)\right.\\ \left.-\sin\left(4\pi ft_{\theta}^{i}\right)+4\sin(2\theta)\sin\left(\pi f\frac{ \tau_{h}^{i}}{4}\right)\cos\left(\frac{1}{2}\pi fT_{h}^{i}\right)\right\} \end{array}  \tag{16}\]  
The PSD of the Type-III ACE-FHBOC signal can be formulated as  
\[\begin{array}{l}G_{\text{A3}}(f)=\frac{4}{\pi^{2}f^{2}T_{c}}\sum\limits_{i=0}^{M-1 }\frac{\sin^{2}(\pi fT_{c})}{\cos^{2}\left(\pi fT_{h}^{i}/2\right)}\left\{1- \cos^{2}(\theta)\left[ \begin{array}{l}\cos\left(2\pi f\left(\frac{\tau_{h}^{i}}{4}-t_ {\theta}^{i}\right)\right)\cos\left(\pi fT_{h}^{i}\right)\\ +\cos\left(2\pi f_{\theta}^{i}\right)\cos\left(\frac{1}{2}\pi fT_{h}^{i}\right) \end{array} \right]\\ +\frac{1}{2}\sin(2\theta)\left[ \begin{array}{l}\frac{1}{2}\sin\left(\pi fT_{h}^{i} \right)+\sin\left(2\pi ft_{\theta}^{i}\right)\cos\left(\frac{1}{2}\pi fT_{h}^{i} \right)\\ -\frac{3}{2}\sin\left(2\pi ft_{\theta}^{i}\right)-\frac{1}{2}\sin\left[2\pi f\left( \frac{\tau_{h}^{i}}{2}-t_{\theta}^{i}\right)\right]\end{array} \right]+\left[ \begin{array}{l}\cos^{2}(\theta)\cos^{2}\left(\frac{1}{2}\pi fT_{h}^{i} \right)\\ -\sin^{2}(\theta)\cos\left(\frac{1}{2}\pi fT_{h}^{i}\right)\end{array} \right]\}  
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