^{1}

^{2}

^{3}

^{2, 4}

^{1}

^{2}

^{3}

^{4}

Control channel is used to transmit protocol or signal information between wireless network nodes and is a key component of wireless network. Compared with data information, protocol or signal information is usually much less, so the spectrum bandwidth requirement of control channel is also much less than that of data channel. In order to optimize the usage of the limited spectrum resources, this paper focuses on the issue of control channel selection. We propose a greedy algorithm which minimizes the total spectrum bandwidth of the set of control channels. Theoretical analysis proves that the proposed algorithm can achieve the optimal set of control whose sum of the spectrum bandwidth is the minimum. Simulation results also show that the proposed algorithm consumes less spectrum resources than other algorithms in the same wireless network environment.

Recently, with the rapid development of the wireless communication technology, wireless network has been the most important infrastructure in the daily life. In order to organize each node in wireless networks to work together, control channel is used to transmit protocol or signal information between wireless network nodes and is a key component of wireless network. Control channel is usually divided into two categories: in-band control channel and out-of-band control channel. The in-band control channel means that protocol or signal information is transmitted in the same channel with data information. On the contrary, out-of-band control channel is different from the channel used to transmit data information. Channel assignment [

In wireless networks, each node needs to select one channel from its available channels as the control channel to transmit protocol or signal information with its neighbor nodes. To transmit protocol or signal information, each control channel needs to occupy spectrum bandwidth. The problem is how to select the set of control channels for the whole wireless network which minimizes the total spectrum bandwidth of the control channels. If all nodes in wireless networks have the same available channels, the channel with the minimum spectrum bandwidth will be selected as the control channel. However, in real wireless networks, the available channel set of each node may be different. For example, in cognitive wireless networks, due to the geographical location difference and activity of primary user, the available channel set of each node is quite different, and the spectrum bandwidth of each available channel is also different. In this paper, we set the spectrum bandwidth as channel weight and propose a greedy algorithm to solve the problem of optimal selection of control channel under the constraint of different nodes with different available channel sets. The proposed algorithm is composed of two parts. In the first part of the algorithm, we delete the wireless network node whose accessible channel set completely includes that of some other nodes. Then, in the second part of the algorithm, we iteratively choose the channel which has the minimum spectrum bandwidth in an accessible channel set containing the maximum spectrum bandwidth in the current iteration.

The problem of the optimal control channel selection and related research methods which are also akin to self-organization and evolutionary game theory have been paid attention widely [

To solve the selection of the control channel, we make the following assumptions.

Each of the wireless network nodes has a set of the available channels. In this paper, the spectrum bandwidth occupied by the channel is monotonous. We assume that, as long as the index of the channel is bigger, the spectrum bandwidth it occupies is bigger.

Wireless network nodes can transmit protocol or signal information with one another through their common control channels. Note that our objective is to find the optimal set of control channels with the sum of spectrum bandwidth as small as possible.

Let

The objective is to find a subset

We describe the algorithm in this section. For an arbitrary instance, the wireless network nodes

Input:

Output: The optimal control channels set

(1) For

(2) If

(3)

(4) End If;

(5) End For;

(6)

(7) While

(8)

(9)

(10) For

(11) If

(12)

(13) End If;

(14) End For;

(15) End While;

For showing that the output of the algorithm is optimal, we first give the following lemma.

When the algorithm terminates,

Let the value of

If

If

To conclude the above two possible cases, we get that, for any

Then the main result of the paper is presented as follows.

The subset

We first claim that

From the proof of Lemma

By induction, we show that

From the algorithm we define

At each iteration of Steps

Obviously, the number of iterations in Step

To conclude, the time complexity of the algorithm is

In this section, we use the numerical simulation method to evaluate the proposed algorithm compared with the proposed algorithm by Zhong [

The simulation topology is as shown in Figure

Topology of simulation networks.

In the simulation, for each run, we use the random number generator to generate the random set of available channels for each node. The simulation executes 60 times of runs in total, sums all simulation results (number of control channels, total spectrum bandwidth of control channels) of each run, and calculates the average values.

Figure

Comparison of number of control channels.

Comparison of total spectrum bandwidth of control channels.

In this paper, we design an optimal algorithm to find the set of control channels with the minimum spectrum bandwidth for wireless networks. We also present simulation results to show that the proposed algorithm consumes less spectrum resources than Zhong’s algorithm in the same wireless network environment. Furthermore, in some other applications, such as spectrum allocation which usually sorts all channels by descending order, the function for spectrum bandwidth of each channel is monotonously decreasing. It is easy to modify the proposed algorithm and obtain similar results for the case.

The authors thank the referees for their helpful comments and suggestions. This work is supported by the National Science Foundation of China under Grant no. 61301159, Open Fund of Lab of Military Network Technology, and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (13KJB1100188).