## 4 Simulation and Results
However, the adaptive transmission scheme can better utilize the channel capacity when the Ka-band channel turns it into a _good_ state, which leads to a higher throughput in a long-term program. On the other hand, if the two-thresholds policy is optimal as in Figure 6b, _betting opportunistically_ is also performed well, but still has a gap remaining compared to our adaptive transmission scheme due to the reward from \"gamble\", and \"play safe\" will be better than sensing the channel sometimes. Figure 5: Numerical result of our POMDP-based transmission policy: (**a**) optimality of a one-threshold policy scenario; (**b**) optimality of a two-thresholds policy scenario. Figure 6: Expected reward of adaptive transmission schemes with different setups: (**a**) \(\tau=0.4\), one-threshold policy; (**b**) \(\tau=0.1\), two-thresholds policy. So far, we have demonstrated our POMDP-based transmission policy can perform well with different communication setups. In the following, we simulate and compare the adaptive transmission schemes under Ka-band channel communications. Assume the threshold of the two-state GE channel noise temperature is \(T_{th}=20\) K, and the corresponding transition probability of the GE channel is \(\mathbf{G}= \begin{bmatrix}0.9773&0.0223\\ 0.1667&0.8333\end{bmatrix} \), according to [24]. If the channel state is bad, the channel bit error rate (BER) is \(10^{-3}\), and we select four different BERs \(10^{-8}\), \(10^{-7}\), \(10^{-6}\) and \(10^{-5}\) as the channel state is good. Assume normalized the data bit \(R_{g}=1\) when BER is \(10^{-8}\), then we can calculate data bits \(R_{b}\) and \(R_{g}\) with other BER values according to the error function [24]. We simulate the adaptive transmission schemes in two cases, Earth-to-Moon (\(\tau=0.03\)), and Earth-to-Mars (\(\tau=1\)), and the transmission schemes are as follows. _Case 1_: The transmitter adopts the action of _betting conservatively_ regardless of the channel state, which can ensure \(R_{b}\) data bits are successfully transmitted. _Case 2_: The transmitter only adopts the action of _betting aggressively_, if the channel state is good, \(R_{g}\) bits are successfully transmitted; else, if the channel state is bad, all data bits are lost. _Case 3_: The transmitter only adopts the action of _betting opportunistically_, if the channel state is good, \((1-\tau)R_{g}\) bits can be received; else, if the channel state is bad, \((1-\tau)R_{b}\) bits can be received successfully:  
_Case 4_: The transmitter chooses optimal action by using delayed feedback CSI and and Theorem 2, the adaptive data transmission action space is \(a\), \(a\in\{A,C\}\). _Case 5_: The transmitter chooses optimal action by using delayed feedback CSI and Theorem 3, the adaptive data transmission action space is \(a\), \(a\in\{A,O,C\}\). _Case 6_: We directly give the outage capacity bounds of the corresponding channels. The simulation results of throughput performance of the 5 transmission schemes above and the capacity bounds are shown in Figure 7, and we can see that if the right transmission scheme with certain channel conditions can be selected by using our derived thresholds, it can increase the throughput in Ka-band SIN communications. Figure 7: Throughput comparison of different data transmission schemes: (**a**) Moon-to-Earth scenario; (**b**) Mars-to-Earth scenario. Based on the previous analysis, we can expect that the two-thresholds policy is optimal for the Moon-to-Earth scenario in Figure 7a as the sensing cost is \(\tau=0.03\). Therefore, the transmitter can access the sensing action with little cost. As it can be seen in Figure 7a, the total number of transmitted bits of _betting opportunistically_ is substantially augmented and the two-thresholds policy transmission scheme performs close to the capacity bounds.