Erratum to “A Rendezvous Scheme for Self-Organizing Cognitive Radio Sensor Networks”

In the paper entitled “A rendezvous scheme for self-organizing cognitive radio sensor networks,” the corresponding author's information was not correct and it is corrected here.

We proposed an asynchronous channel hopping mechanism, called a hopping sequence guaranteeing rendezvous within a single period (HS-GRSP); cognitive radio (CR) nodes can rendezvous in a single period and reliably exchange control messages with each other. Equation (1) gives the length of guard sequence and its subsequences. However, it does not guarantee the appearance of a center channel in every subsequence in all cases. To make our scheme more robust, we changed (1) as follows:

$$\begin{array}{l}{T}_{\text{guard}}\\ \hspace{1em}=\left\{\begin{array}{ll}2,\hfill & \text{for}\hspace{0.17em}\hspace{0.17em}N\le 2,\hfill \\ \frac{N^2+6N-8}{8},\hfill & \text{for}\mathrm{\hspace{0.17em}\hspace{0.17em}}N\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{is}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{an}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{odd}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{number}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{greater}\mathrm{\hspace{0.17em}\hspace{0.17em}}\hfill \\ \hfill & \text{than}\mathrm{\hspace{0.17em}\hspace{0.17em}}2,\text{then}\mathrm{\hspace{0.17em}\hspace{0.17em}}N\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{is}\mathrm{\hspace{0.17em}\hspace{0.17em}}N+1.\hfill \end{array}\right.\end{array}$$

(1)

We also changed (2) and (3) in accordance with change of (1):

$$\begin{array}{cc}& T=\frac{N^2+3N}{2}+T_{\text{guard}},\end{array}$$

(2)

$$\begin{array}{cc}& \text{MTTR}=\frac{N^2+3N}{2}+T_{\text{guard}}.\end{array}$$

(3)

We also made a few corrections in Tables 1 and 3 according to the original HS-GRSP algorithm. When $N=1$ , we modify the group sequence and the rendezvous sequence and we modify the subsequence by modification of the rendezvous sequence in Tables 1 and 3, respectively.

Table 1

Generation of the group sequences, the guard sequence, and the rendezvous sequence.

Number of available channels	Group sequence	Guard sequence	Rendezvous sequence
1	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$
2	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$
3	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{1}}\}$	$\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$
4	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{1}}\}$	$\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$
⋮	⋮	⋮	⋮
N	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_N$ , ${\text{CH}}_{N-\mathit{1}}$ , …, ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{N-\mathit{1}}$ , ${\text{CH}}_{N-\mathit{2}}$ , …, ${\text{CH}}_{\mathit{1}}\}$ , ⋮  $\{{\text{CH}}_{N-\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_N$ , ${\text{CH}}_{\mathit{1}}\}$	$\{{\text{CH}}_{N/\mathit{2}}$ , ${\text{CH}}_{N/\mathit{2}}$ , ${\text{CH}}_{N/\mathit{2}}$ , …, ${\text{CH}}_{N/\mathit{2}}\}$	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_N$ , ${\text{CH}}_{N-\mathit{1}}$ , …, ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{N-\mathit{1}}$ , ${\text{CH}}_{N-\mathit{2}}$ , …, ${\text{CH}}_{\mathit{1}}$ , …, ${\text{CH}}_{N-\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_N$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{N/\mathit{2}}$ , ${\text{CH}}_{N/\mathit{2}}$ , ${\text{CH}}_{N/\mathit{2}}$ , …, ${\text{CH}}_{N/\mathit{2}}\}$

Table 3

Subsequences S′.

Number of available channels	Subsequence S′
1	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$
2	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ ,
	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{1}}\}$
3	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}\}$ ,
	$\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ ,
	$\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{1}}\}$ ,
	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}\}$ , $\{{\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$ ,
	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$
4	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}\}$ , $\{{\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ ,
	$\{{\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{3}}\}$ ,
	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ ,
	$\{{\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}\}$ , $\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}\}$ ,
	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{3}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{4}}\}$ ,
	$\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{1}}\}$ , $\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}\}$ ,
	$\{{\text{CH}}_{\mathit{4}}$ , ${\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$ , {CH1, ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$ ,
	$\{{\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}$ , ${\text{CH}}_{\mathit{2}}\}$
⋮	⋮
N	$\{{\text{CH}}_{\mathit{1}}$ , ${\text{CH}}_N$ , ${\text{CH}}_{N-\mathit{1}}$ , …, ${\text{CH}}_{N/\mathit{2}}$ , …, ${\text{CH}}_{\mathit{2}}\}$ ,
	$\{{\text{CH}}_N$ , ${\text{CH}}_{N-\mathit{1}}$ , ${\text{CH}}_{N-\mathit{2}}$ , …, ${\text{CH}}_{N/\mathit{2}}$ , …, ${\text{CH}}_{\mathit{1}}\}$ ,
	$\{{\text{CH}}_{N-\mathit{1}}$ , ${\text{CH}}_{N-\mathit{2}}$ , ${\text{CH}}_{N-\mathit{3}}$ , …, ${\text{CH}}_{N/\mathit{2}}$ , …, ${\text{CH}}_{N-\mathit{1}}\}$ ,
	⋮
	$\{{\text{CH}}_{N/\mathit{2}}$ , ${\text{CH}}_{N/\mathit{2}}$ , ${\text{CH}}_{N/\mathit{2}}$ , …, ${\text{CH}}_{N/\mathit{2}}\}$