Physical-Layer Security Analysis over M-Distributed Fading Channels
"> Figure 1
<p>A wireless communication system with a transmitter (Alice), a legitimate receiver (Bob), and an eavesdropper (Eve).</p> "> Figure 2
<p>The instantaneous secrecy capacity <span class="html-italic">C</span> and the asymptotic secrecy capacity <math display="inline"><semantics> <msub> <mi>C</mi> <mi>Asy</mi> </msub> </semantics></math> for different <math display="inline"><semantics> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> </semantics></math>.</p> "> Figure 3
<p>Secrecy outage probability (SOP) versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> with different <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <msub> <mi>γ</mi> <mi>th</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> dB and <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">B</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">E</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 4
<p>SOP versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> with different <math display="inline"><semantics> <msub> <mi>γ</mi> <mi>th</mi> </msub> </semantics></math> when <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> <mo>=</mo> <mn>18</mn> </mrow> </semantics></math> dB and <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">B</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">E</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 5
<p>SOP versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> for different fading channels with <math display="inline"><semantics> <mrow> <msub> <mi>γ</mi> <mi>th</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> dB.</p> "> Figure 6
<p>Probability of strictly positive secrecy capacity (SPSC) versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> with different <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">B</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">E</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 7
<p>Probability of SPSC versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> with different <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">E</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">B</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 8
<p>Probability of SPSC versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> for different fading channels.</p> "> Figure 9
<p>Ergodic secrecy capacity (ESC) versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> with different <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">B</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">E</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 10
<p>ESC versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> with different <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">E</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">E</mi> </msub> <mo>)</mo> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi mathvariant="normal">B</mi> </msub> <mo>,</mo> <msub> <mi>β</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 11
<p>ESC versus <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <msub> <mi>γ</mi> <mi mathvariant="normal">B</mi> </msub> <mo>)</mo> </mrow> </semantics></math> for different fading channels.</p> ">
Abstract
:1. Introduction
- Under the M-distributed fading channel, the exact expression of the SOP is first derived. To reduce computational complexity, a closed-form expression for the lower bound of the SOP is obtained. It is shown that the performance gap between the exact SOP expression and its lower bound is small in the high signal-to-noise ratio (SNR) regime.
- The closed-form expression for the probability of the SPSC over the M-distributed fading channel is derived. It is found that when the target secrecy rate is set to be zero, the lower bound of SOP has the same expression as the probability of the SPSC.
- Over the M-distributed fading channel, the exact expression of the ESC with a double integral is obtained. To obtain a closed-form expression, the lower bound of ESC is then derived. It is shown that the performance gap between the exact expression and the lower bound of the ESC is small.
- As special cases of the M fading channel, the secure performance over the K, exponential, and Gamma-Gamma fading channels is derived, respectively. The accuracy of these performance analysis is verified by simulations.
2. System Model
3. Secrecy Performance Analysis
3.1. SOP Analysis
3.2. Probability of SPSC Analysis
3.3. ESC Analysis
4. Some Special Cases
4.1. K Distribution Channel
4.2. Exponential Distribution Channel
4.3. Gamma-Gamma Distribution Channels
4.4. Other Channels
5. Numerical Results
5.1. SOP Results
5.2. Probability of SPSC Results
5.3. ESC Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Distribution Models | Generation |
---|---|
K distribution | , |
Exponential distribution | , , |
Gamma-Gamma distribution | , |
Lognormal distribution | , , |
Gamma-Rician distribution | |
Gamma distribution | , |
Rice-Nakagami distribution | , |
10 dB | 20 dB | 30 dB | 40 dB | 50 dB | |
---|---|---|---|---|---|
3.699% | 3.205% | 1.880% | 1.936% | 0.293% | |
0.436% | 0.041% | 0.795% | 0.651% | 0.156% |
10 dB | 20 dB | 30 dB | 40 dB | 50 dB | |
---|---|---|---|---|---|
0.780% | 0.125% | 7.777% | 6.753% | 2.283% |
25 dB | 30 dB | 35 dB | 40 dB | 45 dB | 50 dB | |
---|---|---|---|---|---|---|
31.911% | 11.668% | 3.879% | 1.845% | 0.713% | 0.195% | |
3.112% | 0.401% | 0.419% | 0.258% | 0.221% | 0.450% |
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Lin, S.-H.; Lu, R.-R.; Fu, X.-T.; Tong, A.-L.; Wang, J.-Y. Physical-Layer Security Analysis over M-Distributed Fading Channels. Entropy 2019, 21, 998. https://doi.org/10.3390/e21100998
Lin S-H, Lu R-R, Fu X-T, Tong A-L, Wang J-Y. Physical-Layer Security Analysis over M-Distributed Fading Channels. Entropy. 2019; 21(10):998. https://doi.org/10.3390/e21100998
Chicago/Turabian StyleLin, Sheng-Hong, Rong-Rong Lu, Xian-Tao Fu, An-Ling Tong, and Jin-Yuan Wang. 2019. "Physical-Layer Security Analysis over M-Distributed Fading Channels" Entropy 21, no. 10: 998. https://doi.org/10.3390/e21100998