Algorithm 1. Search the optimal transmission radius set algorithm.

INPUT: $r$, R,$\varrho$,$\zeta$,${𝓍}_{\nabla }^{ini}$, ${\Delta }_x$.

OUTPUT: ${{\rm Y}}_o=\left\{r+{𝓍}_{\nabla }^{\mathrm{o}},r-{𝓍}_{\nabla }^o, r+2{𝓍}_{\nabla }^o,r-2{𝓍}_{\nabla }^o, \dots ,r+{\mathcal{S}}_{𝓀}{𝓍}_{\nabla }^o,r-{\mathcal{S}}_{𝓀}{𝓍}_{\nabla }^o \right\}$, ${\mathbb{E}}_{max}^o$

1: set $i=0, j=1, {{\rm Y}}_0=\left\{r\right\},$ $\aleph =1, \mu =1$

2: ${𝓍}_{\nabla }^i={𝓍}_{\nabla }^{ini}$

3: ${\mathbb{E}}_{max}^o=\infty$;   // Initialize optimized maximum energy consumption value

4: For ${𝓍}_{\nabla }^i<\frac{r-\varrho }{2}$ Do

5: Calculate energy consumption ${\mathfrak{E}}_d^r=E_d^r$ of this node using Equation (34);      // Calculate energy consumption ${\mathfrak{E}}_d^r$ at different distance from the sink with the current$r$

6: ${\mathbb{E}}_{max}^{\mathrm{cur}}=\max \left({\mathfrak{E}}_d^r\right)$ //The maximum energy consumption of the current optimal transmission radius set

7: ${𝓍}_{\nabla }^i={𝓍}_{\nabla }^i-i\times {\Delta }_x$;

8: $j=1$;

9: For $r>\varrho \&\&r<R$ Do

10: $r_{new}=r+j\times {𝓍}_{\nabla }^i$

11: For $d=d_{min}$ to $R$ Do //Calculate energy consumption under the current transmission radius $r_{new}$

12: Calculate energy consumption $E_d^{r_{new}}$ of this node using Equation (34)

13: ${\mathfrak{E}}_d^r={\mathfrak{E}}_d^r+E_d^{r_{new}}$;

14: $\overline{{\mathfrak{E}}_d^r}$ = ${\mathfrak{E}}_d^r/j$;    //The average energy consumption after j rotations

15: End for

16: ${\mathbb{E}}_{max}^i$ = $max\left(\overline{{\mathfrak{E}}_d^r}\right)$       //${\mathbb{E}}_{max}^i$ indicates the maximum energy consumption of $i^{th}$ transmission radius set

17: IF ${\mathbb{E}}_{max}^i$ < ${\mathbb{E}}_{max}^{\mathrm{cur}}$ Then  //Maximum energy consumption can be reduced after adding $r_{new}$

18: ${\mathbb{E}}_{max}^{\mathrm{cur}}={\mathbb{E}}_{max}^{\mathrm{i}}$

19: Else

20: Exit //Stop the search of the current transmission radius set

21: End if

22: $j=j+1$;

23: End For

24: If ${\mathbb{E}}_{max}^o>{\mathbb{E}}_{max}^{\mathrm{cur}}$ Then     //If the maximum energy consumption of the current transmission set is lower, then record it

25:  ${{\rm Y}}_o=\left\{r+{𝓍}_{\nabla }^o,r-{𝓍}_{\nabla }^o, r+2{𝓍}_{\nabla }^o,r-2{𝓍}_{\nabla }^o, \dots ,r+j{𝓍}_{\nabla }^o,r-j{𝓍}_{\nabla }^o \right\}$

26: End if

27: $i=i+1;$

28: End for

29: OUTPUT ${{\rm Y}}_o$, ${\mathbb{E}}_{max}^o$