Numerical Results and Discussions

The numerical results in Fig. 7.1 show the coverage probability versus the base station density in three different fading environments. The three combi-nations of the fading models for the desired and interference channels are: (1) Nakagami-2 fading in the desired channel and Rayleigh fading in the inter-ference channels; (2) Rayleigh fading in all channels (3) Rayleigh fading and log-normal shadowing in the desired channel and Rayleigh fading in the inter-ference channels. As can be seen, the analytical results perfectly match with the simulated results, which indicates our analysis is correct and accurate.

The coverage probability initially increases along the base station intensity and then gradually becomes constant in the large intensity regime. This phe-nomenon has been point out in the previous analysis, that is, deploying many base stations in a given area is not an effective method to improve the cov-erage probability. Also, we can observe the fact that shadowing indeed plays a pivotal role that weakens the coverage probability. However, shadowing effects are neglected in most of prior work on the stochastic-geometry-based

0.050 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Number of Base Stations per User (Then Intesntiy of User is 370/km²)

Coverage Probability

(Analytic) Rayleigh fading channel (Simulated) Rayleigh fading channel (Analytic) 2−Nakagami fading channel (Simulated) 2−Nakagami fading channel

(Analytic) Rayleigh fading and log−normal shadowed channel (Simulated) Rayleigh fading and log−normal shadowed channel (Analytic) 2−Nakagami fading and log−normal shadowed channel (Simulated) 2−Nakagami fading and log−normal shadowed channel (Analytic) Lower−bound in Rayleigh fading and log−normal shadowed channel

Figure 7.1: Coverage probability versus the number of the base stations per user. All the solid lines represent the analytical results and all the lines with circles stand for the simulation results: The red lines are for the case of all channels with Rayleigh fading. The back lines are for the case of the desired channel with Nakgami-2 fading and the dual-slope path loss law and the interference channels with Rayleigh fading. Whereas the blue lines are for the case of all channels with Rayleigh fading and log-normal shadowing.

analysis in cellular network.

Fig. 7.2 presents the numerical results for the coverage probability versus the SINR threshold in the three different fading environments, as the same combinations used in Fig. 7.1. In this figure, we also verify the accuracy of

0 0.2 0.4 0.6 0.8 1 0.4

0.5 0.6 0.7 0.8 0.9 1

SINR threshold

Coverage Probability

Figure 7.2: Coverage probability versus SINR threshold. All colorful lines have the same representative meaning as those in Fig. 7.1.

our previous analysis again, and we also can see that shadowing significantly impacts on the coverage performance especially when the SINR thresholds are small. Hence, showing effects should not be neglected in the cellular networks under the stochastic geometry framework.

Chapter 8 Conclusion

In this paper, first we investigate how the desired channel and interference channels impact the coverage performance when they experience inconsistent fading and shadowing in a Poisson small cell network. A very neat formula of the coverage probability with Rayleigh fading and log-normal shadowing is found and it intuitively shows the severe impact of shadowing on the coverage performance of a user. We also show that coverage performance cannot be improved in a dense (interference-limited) network. A low-complexity expression of the coverage probability is found for the case that all channels follow the dual-slop path loss law, the desired signal channel has Nakagami-m fading and Rayleigh fading exists in all interference channels. This expression reflects a more practical coverage performance in a cellular network. Finally, some simulation results are provided to support the correctness and accuracy of our analysis.

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Vita

Vita

Jiajia Chen

She was born in Zhejiang, China in 1991. She received a B.S. in Depart-ment of Information Science Electronic Engineering from Zhejiang University in 2012. From September 2012 to August 2014, she worked her Master degree in the Mobile Communications and Cloud Computing Lab in the Department of Communication Engineering at National Chiao-Tung University. Her re-search interests are in the field of wireless communications.

Publication List

Publication

Jiajia Chen and L. C. Wang, “Performance Analysis of Small Cells Using Stochastic Geometry Approach in Nakagami Fading Channels,” IEEE Inter-national Conference on Communications in China , pp. 22–26, 2013.

Jiajia Chen , L. C. Wang and C. H. Liu “Coverage Probability of Small Cell Networks with Composite Shadowing and Fading,” IEEE Annnual Interna-tional Symposlum on Personal, Indoor, and Mobile Radio Communications , 2014.