Secrecy Outage Performance of MIMO Wiretap Channels with Multiple Jamming Signals

Costa, Daniel Benevides da; Ferdinand, Nuwan S.; Dias, Ugo Silva; Júnior, Rafael Timóteo de Sousa

doi:10.14209/jcis.2016.2

Cited by 8 publications

(21 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, we assume that all channels undergo Rayleigh fading. Thus, according to the work of da Costa et al and complying to the independent and identically distributed fading conditions, the probability density function (pdf) and the cumulative distribution function (cdf) of γ B,ϕ can be respectively written as

\begin{matrix} alignleft \\ align-1 f_{{normalγ}_{B, ϕ}}^{MRC} (z) = \frac{z^{N_{B} - 1} e^{- \frac{z}{{\bar{normalγ}}_{normalB}}}}{{\bar{normalγ}}_{normalB}^{N_{B}} Γ (N_{B})} & align-2 \end{matrix}

and

\begin{matrix} alignleft \\ align-1 F_{{normalγ}_{B, ϕ}}^{MRC} (z) = 1 - e^{- \frac{z}{{\bar{normalγ}}_{normalB}}} \sum_{u = 0}^{N_{B} - 1} \frac{1}{u!} {(\frac{z}{{\bar{normalγ}}_{normalB}})}^{u} . & align-2 \end{matrix}

…”

Section: Secrecy Performancementioning

confidence: 99%

“…On the other hand, the analysis of the jamming signals affecting Eve is presented in the work of da Costa et al, and the pdf of γ I can be written as

\begin{matrix} alignleft \\ align-1 f_{{normalγ}_{normalI}} (z) = \sum_{i = 1}^{t} \sum_{j = 1}^{{normalη}_{i}} \frac{{normalΩ}_{i, j}}{(j - 1)! {\bar{normalγ}}_{i}^{j}} z^{j - 1} e^{- \frac{z}{{\bar{normalγ}}_{i}}}, & align-2 \end{matrix}

with

{\overset{γ}{true}}_{1}, {\overset{γ}{true}}_{2}, ⋯, {\overset{γ}{true}}_{t}

denoting different values with multiplicities η 1 , η 2 ,…, η t , such that

\sum_{i = 1}^{t} η_{i} = M

, and Ω i , j is given by

\begin{matrix} alignleft \\ align-1 {normalΩ}_{i, j} = \frac{1}{({normalη}_{i} - j)! {\bar{normalγ}}_{i}^{{normalη}_{i} - j}} \frac{\partial^{{normalη}_{i} - j}}{\partial s^{{normalη}_{i} - j}} {[\prod_{k = 1, k \neq i}^{t} {(\frac{1}{1 + s {\bar{normalγ}}_{k}})}^{{normalη}_{k}}]}_{s = - \frac{1}{{\bar{normalγ}}_{i}}} . & align-2 \end{matrix}

…”

Section: Secrecy Performancementioning

confidence: 99%

“…The diversity order and the array gain give valuable insights for the secrecy performance of the system. In the high‐SNR regime (ie,

{\overset{γ}{true}}_{B,s}^{MRC} > Υ_{E,s}

{\overset{γ}{true}}_{B,s}^{MRC} \to \infty

), the asymptotic secrecy outage probability can be expressed as

\begin{matrix} alignleft \\ align-1 P_{s}^{\infty} (R_{0}) = A_{G} {({\bar{normalγ}}_{B})}^{- D_{G}} + o ({\bar{normalγ}}_{B}^{- D_{G}}), & align-2 \end{matrix}

where o ( y ) denotes higher order terms relative to y , thus satisfying

\lim_{y \to 0} o false(y false) false/ y = 0

, D G indicates the diversity gain, and A G symbolizes the array gain of the system.…”

Section: Secrecy Performancementioning

confidence: 99%

“…According to them, perfect secrecy capacity can be achieved when Tx and Rx can communicate at some positive rate, while ensuring that the eavesdropper does not get any bit of information. In the work of da Costa et al, the Tx used a transmit antenna selection (TAS) technique, while a selection combining scheme and a maximal‐ratio combining (MRC) scheme were considered at the Rx. The results showed that the diversity order is equal to

\min false(M, N_{t} N_{r} false)

, with M , N t , and N r denoting the number of jamming signals and the numbers of antennas at Tx and at Rx, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Joint effect of jamming and noise on the secrecy outage performance of wiretap channels with feedback delay and multiple antennas

Ortega

Upadhyay

Costa

et al. 2017

Trans Emerging Tel Tech

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate the secrecy performance of multiple-inputmultiple-output wiretap channels with outdated channel state information (CSI) at the transmitter. The joint effect of multiple jamming signals and noise at the eavesdropper is studied assuming that the transmitter adopts a transmit antenna selection technique, while both the legitimate receiver and the eavesdropper use a maximal-ratio combining scheme to achieve spatial diversity in reception. Exact closed-form expressions for the nonzero secrecy rate probability and the secrecy outage probability for an arbitrary number of power distributed jamming signals are derived, by assuming both perfect and imperfect CSI. The general secrecy outage probability expressions are simplified for 2 special cases, ie, different and equal power distributed interferers. Furthermore, we conduct an asymptotic secrecy outage analysis at high signal-to-noise ratio, which reveals that the expected diversity gain cannot be realized for imperfect CSI and full diversity order can only be achieved under the perfect CSI condition. In addition, our results reveal that the number of antennas at the eavesdropper as well as the number of jamming signals do not affect the system diversity order. Simulation results are performed to illustrate the effects of imperfect feedback and other key system parameters on the secrecy performance. Finally, our analytical results are validated through Monte Carlo simulations.

show abstract

\begin{matrix} alignleft \\ align-1 f_{{normalγ}_{B, ϕ}}^{MRC} (z) = \frac{z^{N_{B} - 1} e^{- \frac{z}{{\bar{normalγ}}_{normalB}}}}{{\bar{normalγ}}_{normalB}^{N_{B}} Γ (N_{B})} & align-2 \end{matrix}

and

\begin{matrix} alignleft \\ align-1 F_{{normalγ}_{B, ϕ}}^{MRC} (z) = 1 - e^{- \frac{z}{{\bar{normalγ}}_{normalB}}} \sum_{u = 0}^{N_{B} - 1} \frac{1}{u!} {(\frac{z}{{\bar{normalγ}}_{normalB}})}^{u} . & align-2 \end{matrix}

…”

Section: Secrecy Performancementioning

confidence: 99%

“…On the other hand, the analysis of the jamming signals affecting Eve is presented in the work of da Costa et al, and the pdf of γ I can be written as

\begin{matrix} alignleft \\ align-1 f_{{normalγ}_{normalI}} (z) = \sum_{i = 1}^{t} \sum_{j = 1}^{{normalη}_{i}} \frac{{normalΩ}_{i, j}}{(j - 1)! {\bar{normalγ}}_{i}^{j}} z^{j - 1} e^{- \frac{z}{{\bar{normalγ}}_{i}}}, & align-2 \end{matrix}

with

{\overset{γ}{true}}_{1}, {\overset{γ}{true}}_{2}, ⋯, {\overset{γ}{true}}_{t}

denoting different values with multiplicities η 1 , η 2 ,…, η t , such that

\sum_{i = 1}^{t} η_{i} = M

, and Ω i , j is given by

\begin{matrix} alignleft \\ align-1 {normalΩ}_{i, j} = \frac{1}{({normalη}_{i} - j)! {\bar{normalγ}}_{i}^{{normalη}_{i} - j}} \frac{\partial^{{normalη}_{i} - j}}{\partial s^{{normalη}_{i} - j}} {[\prod_{k = 1, k \neq i}^{t} {(\frac{1}{1 + s {\bar{normalγ}}_{k}})}^{{normalη}_{k}}]}_{s = - \frac{1}{{\bar{normalγ}}_{i}}} . & align-2 \end{matrix}

…”

Section: Secrecy Performancementioning

confidence: 99%

“…The diversity order and the array gain give valuable insights for the secrecy performance of the system. In the high‐SNR regime (ie,

{\overset{γ}{true}}_{B,s}^{MRC} > Υ_{E,s}

{\overset{γ}{true}}_{B,s}^{MRC} \to \infty

), the asymptotic secrecy outage probability can be expressed as

\begin{matrix} alignleft \\ align-1 P_{s}^{\infty} (R_{0}) = A_{G} {({\bar{normalγ}}_{B})}^{- D_{G}} + o ({\bar{normalγ}}_{B}^{- D_{G}}), & align-2 \end{matrix}

where o ( y ) denotes higher order terms relative to y , thus satisfying

\lim_{y \to 0} o false(y false) false/ y = 0

, D G indicates the diversity gain, and A G symbolizes the array gain of the system.…”

Section: Secrecy Performancementioning

confidence: 99%

\min false(M, N_{t} N_{r} false)

, with M , N t , and N r denoting the number of jamming signals and the numbers of antennas at Tx and at Rx, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Joint effect of jamming and noise on the secrecy outage performance of wiretap channels with feedback delay and multiple antennas

Ortega

Upadhyay

Costa

et al. 2017

Trans Emerging Tel Tech

Self Cite

View full text Add to dashboard Cite

show abstract

“…while at Eve the capacity is limited by the jamming (denoted by [8] as interference) generated by the relay node. Thus, we represent the signal-to-interference ratio (SIR) at Eve following the same notation of [8], so that Υ I = γAE γI , where γ I = nR k=0γ RE,k |h RE,k | 2 is the jamming interference, written as the sum of all jamming signals sent by each k-th antenna of the relay. As a result, the capacity of Eve's channel can be written as…”

Section: B Artificial-noise (An)mentioning

confidence: 99%

On the Secure Energy Efficiency of TAS/MRC With Relaying and Jamming Strategies

Farhat¹,

Brante²,

Souza³

2017

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

In this paper we investigate the secure energy efficiency (SEE) in a cooperative scenario where all nodes are equipped with multiple antennas. Moreover, we employ secrecy rate and power allocation at Alice and at the relay in order to maximize the SEE, subjected to a constraint in terms of a minimal required secrecy outage probability. Only the channel state information (CSI) with respect to the legitimate nodes is available. Then, we compare the Artificial-Noise (AN) scheme with CSI-Aided Decode-and-Forward (CSI-DF), which exploits the CSI to choose the best communication path (direct or cooperative). Our results show that CSI-DF outperforms AN in terms of SEE in most scenarios, except when Eve is closer to the relay or with the increase of antennas at Eve. Additionally, we also show that the maximization of SEE implies in an optimal number of antennas to be used at each node, which is due to the trade-off between secure throughput and power consumption.

show abstract

Exploiting Opportunistic Scheduling Schemes to Improve Physical-Layer Security in MU-MISO NOMA Systems

Shim

Nguyen

2019

IEEE Access

View full text Add to dashboard Cite

This paper studies opportunistic scheduling schemes to enhance the secrecy performance in multi-user multiple-input single-output (MU-MISO) non-orthogonal multiple access (NOMA) systems, in which a multiple antenna base station (BS) serves multiple single-antenna cell-center and cell-edge users in the presence of multiple single-antenna eavesdroppers. In order to improve the secrecy performance, we propose an opportunistic scheduling scheme, called the proposed antenna/users selection (PAUS) scheme. Additionally, we consider two practical eavesdropping scenarios, namely colluding and non-colluding eavesdroppers. We derive the exact closed-form expression for secrecy outage probability (SOP) and asymptotic SOP of the PAUS scheme under different eavesdropping scenarios. We provide the 2D golden section search-based algorithm to find the optimal values of the transmit power and power allocation coefficient that minimize the system secrecy outage performance. The developed analyses are verified by Monte Carlo simulations. The numerical results show that the PAUS scheme improves secrecy performances compared to the benchmark random antenna/users selection (RAUS) scheme. To provide further insights into the system secure performance, the effects of transmit signal-to-noise ratio (SNR), power allocation coefficient, the number of transmit antennas at the BS, number of cell-center and cell-edge users, and the eavesdropper placements are extensively evaluated and discussed.INDEX TERMS Multi-user multiple-input single-output, non-orthogonal multiple access, opportunistic scheduling, physical layer security, secrecy outage probability.

show abstract

Secrecy Outage Performance of MIMO Wiretap Channels with Multiple Jamming Signals

Cited by 8 publications

References 30 publications

Joint effect of jamming and noise on the secrecy outage performance of wiretap channels with feedback delay and multiple antennas

Joint effect of jamming and noise on the secrecy outage performance of wiretap channels with feedback delay and multiple antennas

On the Secure Energy Efficiency of TAS/MRC With Relaying and Jamming Strategies

Exploiting Opportunistic Scheduling Schemes to Improve Physical-Layer Security in MU-MISO NOMA Systems

Contact Info

Product

Resources

About