## 4 Performance Analysis
### C. Average Ergodic Channel Capacity
Figure 3: Outage probability (OP) for \(N\)-hop FSOC system with different fog conditions. Figure 5a demonstrates the effects of different normalized jitter standard deviations on the OP of \(N\)-hop FSOC system, which considers CSI-assisted relays and light fog weather. With a fixed transmitted power, the OP of a single-hop FSOC system changes little by increasing the normalized jitter standard deviation. The OP of a multi-hop FSOC system increases significantly with increasing the normalized jitter standard deviation. For example, when \(N=1\) and \(P_{t}=30\) dBm, the OPs with \(\sigma_{H}/r=\sigma_{V}/r=3\) and \(\sigma_{H}/r=\sigma_{V}/r=7\) are \(4.28\times 10^{-1}\) and \(5.26\times 10^{-1}\), respectively, and the system OP is basically unchanged. When \(N=3\) and \(P_{t}=30\) dBm, the OPs with \(\sigma_{H}/r=\sigma_{V}/r=3\) and \(\sigma_{H}/r=\sigma_{V}/r=7\) are \(2.95\times 10^{-4}\) and \(1.25\times 10^{-2}\), respectively, and the system OP increases by about two orders. The reason is that when the total link length is fixed, on a single-hop link, the optical power attenuation caused by fog is more serious than that caused by normalized jitter standard deviation. Therefore, increasing the normalized jitter standard deviation has little effect on the system SNR, and the system OP is basically unchanged. As the number of hops increases, the optical power attenuation caused by fog at each hop link decreases significantly. Increasing the normalized jitter standard deviation significantly reduces the SNR of each hop link, thereby significantly reduces the SNR of the \(N\)-hop FSOC system, and significantly increases the OP of the \(N\)-hop FSOC system. Figure 5b demonstrates the effects of different normalized boresight errors on the OP of \(N\)-hop FSOC system, which considers CSI-assisted relays and light fog weather. With a fixed transmitted power, the OP of a single-hop FSOC system changes little by increasing the normalized boresight error. With the increase in normalized boresight error, the OP of the multi-hop FSOC system increases significantly. For example, when \(N=1\) and \(P_{t}=30\) dBm, the OPs with \(\mu_{H}/r=\mu_{V}/r=3\) and \(\mu_{H}/r=\mu_{V}/r=7\) are \(4.28\times 10^{-1}\) and \(\mu_{H}/r=\mu_{V}/r=7\) are \(4.28\times 10^{-1}\) and \(\mu_{H}/r=\mu_{V}/r=7\) respectively. The OPs with \(\sigma_{H}/r=\sigma_{V}/r=3\) and \(\sigma_{H}/r=\sigma_{V}/r=7\) are \(2.95\times 10^{-4}\) and \(1.25\times 10^{-2}\), respectively, and the system OP increases by about two orders. The reason is that when the total link length is fixed, on a single-hop link, the optical power attenuation caused by fog is more serious than that caused by normalized jitter standard deviation. Therefore, increasing the normalized jitter standard deviation has little effect on the system SNR, and the system OP is basically unchanged. As the number of hops increases, the optical power attenuation caused by fog at each hop link decreases significantly. Increasing the normalized jitter standard deviation significantly reduces the SNR of each hop link, thereby significantly reduces the SNR of the \(N\)-hop FSOC system, and significantly increases the OP of the \(N\)-hop FSOC system. Figure 5b demonstrates the effects of different normalized boresight errors on the OP of \(N\)-hop FSOC system, which considers CSI-assisted relays and light fog weather. With a fixed transmitted power, the OP of a single-hop FSOC system changes little by increasing the normalized boresight error. With the increase in normalized boresight error, the OP of the multi-hop FSOC system increases significantly. For example, when \(N=1\) and \(P_{t}=30\) dBm, the OPs with \(\mu_{H}/r=\mu_{V}/r=3\) and \(\mu_{H}/r=\mu_{V}/r=7\) are \(4.28\times 10^{-1}\) and \(\mu_{H}/r=\mu_{V}/r=7\) respectively. The OPs with \(\sigma_{H}/r=\sigma_{V}/r=3\) and \(\sigma_{H}/r=\sigma_{V}/r=7\) are \(2.95\times 10^{-4}\) and \(1.25\times 10^{-2}\), respectively, and the system OP increases by about two orders.