Algorithm 1: The pseudocode of the proposed algorithm for finding the expected throughput $E_K^n(n_0,\mathit{S},\mathit{\mu },e_K^{total})$, the optimal transmission energy $e_{opt}^{tr}\left(n\right)$ and the action for channel n.

Notations:

K denotes the number of slots for calculating the channel sensing order.

$\mathit{S}\subseteq \left\{1,2,\dots ,N\right\}$ denotes the set of sensed channels, which are arranged in sensed order.

$\widehat{\mathit{S}}$ denotes the set of not yet sensed channels.

$e_K^{total}$ denotes the packets of energy in the battery at the beginning of each time slot.

$e_{SS}$ and $e_{CS}$ denote the energy packets consuming for sensing per channel and channel switching per step, respectively.

Input: $K,n,n_0,\mathit{S},{\mathit{\mu }}_K,e_K^{total}$; Output: Action (Active or Silent), $E_K^n(n_0,\mathit{S},{\mathit{\mu }}_K,e_K^{total})$ and $e_{opt}^{tr}\left(n\right)$.

1: $\mathit{S}=\mathit{S}\cup \left\{n\right\}$; $\widehat{\mathit{S}}=\left\{1,2,\dots ,N\right\}\backslash \mathit{S}$; use Equation (4) to calculate $\theta (.)$ for each channel.

2: if $e_K^{total}<\left(\sum e_{SS}+\sum e_{CS}\right)$ // Remaining energy is not enough for sensing channel n

3:  Action = Silent, $E_K^n(n_0,\mathit{S},{\mathit{\mu }}_K,e_K^{total})=0$, $e_{opt}^{tr}\left(n\right)=0$

4: else

// Calculate the expected throughput when Action = Silent

5:  if $K=1$ // the current time slot is the last time slot

6:   $E{s}_K(n_0,\mathit{S},{\mathit{\mu }}_K,e_K^{total})=0$

7:  else

8:   Use Equation (9) to update ${\mathit{\mu }}_{K-1}$; use Equation (16) to update $e_{K-1}^{total}$; and use Equation (18) to calculate $E{s}_K(n_0,\mathit{S},\mathit{\mu },e_K^{total})$= $E_{K-1}(n_0,\mathit{S}=\varnothing ,{\mathit{\mu }}_{K-1},e_{K-1}^{total})$, recursively.

9:  end if

// Calculate the expected throughput when the CU stays in the state Active

10:  if $K=1$ // the current time slot is the last.

11:   $E_{K-1}(n_0=n,\mathit{S}=\varnothing ,{\mathit{\mu }}_{K-1}^{\mathbf{f}},e_{K-1}^{total})=0$, $E_{K-1}(n_0=n,\mathit{S}=\varnothing ,{\mathit{\mu }}_{K-1}^{\mathbf{b}},e_{K-1}^{total})=0$.

12:   if $\left(\widehat{\mathit{S}}=\varnothing \right)$ .

13:    set $E_K(n_0,\mathit{S}\cup \left\{n\right\},{\mathit{\mu }}_K^{\mathbf{b}},e_K^{total})=0$, use Equation (13) to calculate $e_{opt}^{tr}\left(n\right)$, and use Equation (15) to calculate $E{a}_K^n(n_0,\mathit{S},{\mathit{\mu }}_K,e_K^{total})$.

14:   else

15:    calculate $E_K(n_0,\mathit{S}\cup \left\{n\right\},{\mathit{\mu }}_K^{\mathbf{b}},e_K^{total})$ recursively, use Equation (13) to calculate $e_{opt}^{tr}\left(n\right)$ and use Equation (15) to calculate $E{a}_K^n(n_0,\mathit{S},{\mathit{\mu }}_K,e_K^{total})$.

16:   end if

17:  else

18:   calculate $E_{K-1}(n_0=n,\mathit{S}=\varnothing ,{\mathit{\mu }}_{K-1}^{\mathbf{f}},e_{K-1}^{total})$ and $E_{K-1}(n_0=n,\mathit{S}=\varnothing ,{\mathit{\mu }}_{K-1}^{\mathbf{b}},e_{K-1}^{total})$, recursively (use Equation (16) to update $e_{K-1}^{total}$); then combine with Equation (17) to calculate $e_{opt}^{tr}\left(n\right)$

19:   if $\left(\widehat{\mathit{S}}=\varnothing \right)$ set $E_K(n_0,\mathit{S}\cup \left\{n\right\},{\mathit{\mu }}_K^{\mathbf{b}},e_K^{total}=0$

20:   else calculate $E_K(n_0,\mathit{S}\cup \left\{n\right\},{\mathit{\mu }}_K^{\mathbf{b}},e_K^{total})$ recursively

21:   end if

22:   use Equation (19) to decide the Action (Active or Silent), and calculate $E_K^n(n_0,\mathit{S},{\mathit{\mu }}_K,e_K^{total})$ and $e_{opt}^{tr}\left(n\right)$

23: end if