# Impact of Beamforming on the Path Connectivity in Cognitive Radio Ad Hoc Networks

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## Abstract

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## 1. Introduction

- We examine the combined influence of different antenna types and beamforming schemes on the path connectivity of CRAHNs. Particularly, we consider how SUs equipped with two popular directional antennas, i.e., uniform linear array (UCA) and uniform circular array (UCA) antennas, communicate with each other by using two simple and efficient beamforming schemes, i.e., randomized beamforming and center directed beamforming. Especially, we show that, in contrast to AHNs, using beamforming in CRAHNs does not always improve network connectivity. To be more specific, in all evaluating scenarios, only the UCA antenna gives higher path connectivity than omnidirectional antennas.
- We show that the influence of beamforming on path connectivity greatly depends on the degree of channel path loss. Specifically, when path loss exponent $\alpha $ = 3, path connectivity remains stable, but the maximum values are lower than that when $\alpha $ = 2.
- We find that the number of antenna elements of directional antennas significantly affects path connectivity. For each type of directional antenna, the number of antenna elements, at which the highest path connectivity is obtained, is different.

## 2. System Model

#### 2.1. Antenna Model

#### 2.2. Network Model

#### 2.3. Wireless Link Model

## 3. The Impact of Beamforming on the Connectivity of Cognitive Radio Ad Hoc Networks

**Randomized beamforming**: This beamforming scheme is considered as the simplest one, i.e., each node chooses the direction of its main beam from $[0,2\pi ]$ based on uniform random distribution, and completely independent of other nodes.**Center-directed beamforming**: According to this beamforming scheme, it is required that all nodes know the center of network area. Then, they point their main beams toward the network center.

## 4. Experimental Results and Discussions

#### 4.1. Effect of SU Density

#### 4.2. Effect of PU Density

#### 4.3. Effect of the Average Active Rate of PU

#### 4.4. Effect of the Configuration of Directional Antenna

#### 4.5. Effect of Path Loss

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Difference in the network connectivity of CRAHNs with (

**a**) omidirectional antenna and (

**b**) directional antenna.

**Figure 2.**Gain patterns of ULA as the numbers of antenna elements and main beam directions are varied.

**Figure 3.**Gain patterns of UCA as the numbers of antenna elements and main beam directions are varied.

**Figure 4.**The network model of CRAHNs where SUs employ directional antennas and PUs use omnidirectional antennas.

**Figure 5.**Illustration of two beamforming schemes used to evaluate the connectivity of CRAHNs: (

**a**) randomized beamforming; (

**b**) center-directed beamforming.

**Figure 6.**Path connectivity corresponding to different kinds of antennas and beamforming schemes as a function of the number of SUs; a = 500 m, M = 6, ${N}_{P}$ = 3, ${\lambda}_{P}$ = 0.1, $\alpha $ = 3, ${\gamma}_{th}$ = 50 dB.

**Figure 7.**Path connectivity corresponding to different kinds of antennas and beamforming schemes as a function of the number of PUs; a = 500 m, M = 6, ${N}_{S}$ = 200, ${\lambda}_{P}$ = 0.5, $\alpha $ = 3, ${\gamma}_{th}$ = 50 dB.

**Figure 8.**Path connectivity corresponding to different kinds of antennas and beamforming schemes as a function of the average active rate of PU; a = 500 m, M = 6, ${N}_{S}$ = 200, ${N}_{P}$ = 3, $\alpha $ = 3, ${\gamma}_{th}$ = 50 dB.

**Figure 9.**Path connectivity corresponding to different kinds of antennas and beamforming schemes as a function of the number of antenna elements; a = 500 m, ${N}_{S}$ = 200, ${N}_{P}$ = 3, ${\lambda}_{P}$ = 0.1, $\alpha $ = 3, ${\gamma}_{th}$ = 50 dB.

**Figure 10.**Path connectivity corresponding to different kinds of antennas and beamforming schemes as a function of the number of SUs with path loss exponent $\alpha $ = 2 and 3, a = 500, M = 6, ${N}_{S}$ = 200, ${N}_{P}$ = 3, ${\lambda}_{P}$ = 0.1, ${\gamma}_{th}$ = 50 dB.

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**MDPI and ACS Style**

Dung, L.T.; Hieu, T.D.; Choi, S.-G.; Kim, B.-S.; An, B. Impact of Beamforming on the Path Connectivity in Cognitive Radio Ad Hoc Networks. *Sensors* **2017**, *17*, 690.
https://doi.org/10.3390/s17040690

**AMA Style**

Dung LT, Hieu TD, Choi S-G, Kim B-S, An B. Impact of Beamforming on the Path Connectivity in Cognitive Radio Ad Hoc Networks. *Sensors*. 2017; 17(4):690.
https://doi.org/10.3390/s17040690

**Chicago/Turabian Style**

Dung, Le The, Tran Dinh Hieu, Seong-Gon Choi, Byung-Seo Kim, and Beongku An. 2017. "Impact of Beamforming on the Path Connectivity in Cognitive Radio Ad Hoc Networks" *Sensors* 17, no. 4: 690.
https://doi.org/10.3390/s17040690