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Physical Layer Security with Maximal Ratio Combining over Heterogeneous \(\kappa {-}\mu \) and \(\eta {-}\mu \) Fading Channels

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Abstract

This paper investigates physical layer security of maximal ratio combining (MRC) in a heterogeneous fading environment, where the legitimate channel and the wiretap channel are modeled as \(\kappa {-}\mu \) and \(\eta {-}\mu \) fading distributions, respectively. The legitimate receiver adopts MRC to maximize the probability of secure transmission, whereas the eavesdropper adopts MRC to maximize the probability of successful eavesdropping. If the eavesdropper’s channel state information (CSI) is available at the transmitter, the exact and asymptotic expressions of the average secrecy capacity are derived as the security performance metrics. While, if the eavesdropper’s CSI is not available at the transmitter, the exact and asymptotic expressions of the secrecy outage probability are derived as the security performance metrics. In both of the two cases, the impact of the number of antennas as well as the channel fading parameters on the the secrecy performance is further analyzed. Finally, the simulation results are given to verify the validity of the theoretical analysis.

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Notes

  1. For the \({\kappa }{-}{{\mu }_{B}}\) distribution, the parameter \(\kappa \) is the ratio of the total power of the dominant components to the total power of the scattered waves, and \(\mu _B\) is the number of multipath clusters.

  2. For the \({\eta }-{{\mu }_{E}}\) distribution, the parameter \({\eta }\) is defined under two formats: In format I, the in-phase and quadrature phase components of the fading signal within each cluster are assumed to be independent of each other and have different average powers. The parameter \(\eta \in \left( 0,\infty \right) \) is the ratio of these powers. In format II, the in-phase and quadrature phase components within each cluster are assumed to be correlated and have identical powers. The parameter \(\eta \in \left( -1,1 \right) \) is the correlation coefficient between these components. In both the formats, the parameter \(\mu _E\) denotes the number of multipath clusters.

  3. For the physical \({\eta }{-}{\mu _E}\) channel, parameter \({\mu _E}\) can also take half-integer values. In the context of this paper, however, only the case of integer \({\mu _E}\) is considered.

  4. In format I, \(h=\left( 2+{{\eta }^{-1}}+\eta \right) /4\) and \(H=\left( {{\eta }^{-1}}-\eta \right) /4\). In format II, \(h=1/\left( 1-{{\eta }^{2}} \right) \) and \(H=\eta /\left( 1-{{\eta }^{2}} \right) \). According to [14], format I can be converted into format II using a simple bilinear transformation. Therefore, without loss of generality, we only consider format I in this paper.

  5. Since \({{\bar{\gamma }}_{E}}\rightarrow \infty \), the probability of successful eavesdropping approaches one. As such, we shall not consider \({{\bar{\gamma }}_{E}}\rightarrow \infty \).

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Authors and Affiliations

  1. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, China

    Yang Gao & Jianhua Ge

  2. School of Electro-Mechanical Engineering, Xidian University, Xi’an, China

    Hongwei Gao

Authors
  1. Yang Gao
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  2. Jianhua Ge
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  3. Hongwei Gao
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Corresponding author

Correspondence to Yang Gao.

Additional information

This work was supported by the Fundamental Research Funds for the Central Universities Grant No. JB140106, the National Natural Science Foundation of China under Grant 61372067, the National Hightech R&D Program of China (2014AA01A704), and the 111 Project under Grant B08038.

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Gao, Y., Ge, J. & Gao, H. Physical Layer Security with Maximal Ratio Combining over Heterogeneous \(\kappa {-}\mu \) and \(\eta {-}\mu \) Fading Channels. Wireless Pers Commun 86, 1387–1400 (2016). https://doi.org/10.1007/s11277-015-2996-8

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