Outage Constraint Robust Cooperative Beamforming and Jamming Design for Secure AF Relay Networks

This paper investigates a joint robust scheme in a secrecy relay network where distributed relays perform cooperative beamforming and a friendly jammer transmits jamming signal to enhance the information security. Specifically, we consider the outage constraint secrecy rate maximization design with imperfect channel state information. Through semidefinite relaxation and one-dimensional search, we propose a two-layer optimization method to solve the nonconvex problem. In addition, the Bernstein-type inequality and large deviation inequality are utilized to convert the probabilistic constraint. Simulation results demonstrate the performance of the proposed design.

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A large deviation inequality for vector functions on finite reversible Markov Chains

The Annals of Applied Probability ◽

10.1214/105051607000000078 ◽

2007 ◽

Vol 17 (4) ◽

pp. 1202-1221 ◽

Cited By ~ 4

Author(s):

Vladislav Kargin

Keyword(s):

Markov Chains ◽

Large Deviation ◽

Deviation Inequality ◽

Large Deviation Inequality ◽

Reversible Markov Chains

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A Large Deviation Inequality for Functions of Independent, Multi-Way Choices

Combinatorics Probability Computing ◽

10.1017/s0963548397003246 ◽

1998 ◽

Vol 7 (1) ◽

pp. 57-63 ◽

Cited By ~ 11

Author(s):

D. A. GRABLE

Keyword(s):

Randomized Algorithms ◽

High Probability ◽

Large Deviation ◽

Individual Choice ◽

Difference Property ◽

Classic Result ◽

Deviation Inequality ◽

Large Deviation Inequality ◽

Large Deviation Result ◽

Independent Indicator

Often when analysing randomized algorithms, especially parallel or distributed algorithms, one is called upon to show that some function of many independent choices is tightly concentrated about its expected value. For example, the algorithm might colour the vertices of a given graph with two colours and one would wish to show that, with high probability, very nearly half of all edges are monochromatic.The classic result of Chernoff [3] gives such a large deviation result when the function is a sum of independent indicator random variables. The results of Hoeffding [5] and Azuma [2] give similar results for functions which can be expressed as martingales with a bounded difference property. Roughly speaking, this means that each individual choice has a bounded effect on the value of the function. McDiarmid [9] nicely summarized these results and gave a host of applications. Expressed a little differently, his main result is as follows.

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Secrecy Outage Performance of Cognitive Radio Network with Selection Combining at Eavesdropper

Recent Advances in Computer Science and Communications ◽

10.2174/2213275912666190807122631 ◽

2020 ◽

Vol 13 (5) ◽

pp. 987-998

Author(s):

Khyati Chopra ◽

Ranjan Bose ◽

Anupam Joshi

Keyword(s):

Cognitive Radio ◽

Outage Probability ◽

Relay Network ◽

Selection Combining ◽

Secrecy Rate ◽

Channel State ◽

Relay System ◽

Interference Constraints ◽

Secrecy Outage ◽

Diversity Scheme

Background:: Based on the idea of cooperative communication, recently a lot of attention has been drawn to cooperative spectrum access for the secure information transmission in a Cognitive Radio Network (CRN). Security is one of the most important aspects of these networks, as due to their open and dynamic nature, they are extremely vulnerable to malicious behavior. Cooperative cognitive radio has emerged as a dynamic spectrum access technique, where an unlicensed (secondary) user is allowed to simultaneously access the licensed channels dedicated to a Primary User (PU), as long as the Quality of Service (QoS) of primary communication is not affected. Method:: This paper investigates the secrecy outage performance of threshold-based cognitive decode-andforward relay network, with interference constraints from primary licensed user. Threshold-based relaying is considered where; the source message is successfully decoded by the relay, only if the received SNR satisfies the particular threshold. Outage probability expressions have been derived for the worst-case scenario, where only the eavesdropper can achieve the advantage of diversity. The Selection Combining (SC) diversity scheme is employed only at the secondary eavesdropper. Results:: The system secrecy performance is better for SC diversity scheme at the eavesdropper than Maximal Ratio Combining (MRC) diversity scheme, as MRC has better diversity performance than SC. We have shown that the improvement in desired secrecy rate, predetermined threshold, eavesdropper channel quality and interference constraints affect the secrecy performance of the cognitive radio system. The outage probability decreases accordingly with an increase in the maximum tolerable interference level at primary destination. The outage probability of Optimal relay Selection (OS) scheme is derived for a multi-relay system, when either the Instantaneous Channel State Information (ICSI) or the Statistical Channel State Information (SCSI) is available. We have shown that the secrecy performance of the OS with ICSI of the system is better than with SCSI. Also, the OS improves the performance of the multi-relay system, when the number of relays is increased. Conclusion:: The secrecy outage probability of threshold-based DF underlay cognitive relay network is evaluated. Both interference and maximum transmit power constraints are considered at secondary source and secondary relay. Also, the relay can successfully decode the message, only if it meets the pre-defined threshold. We have investigated the performance of MRC and SC diversity schemes at the secondary eavesdropper and have shown that the system secrecy performance is better for SC than MRC, as MRC has better diversity performance than SC. We have shown that the system secrecy performance is significantly affected by the required secrecy rate, pre-defined threshold, interference constraints and choice of diversity scheme (MRC/SC) at the eavesdropper. The outage probability of OS scheme is derived for a multi-relay system, when either the ICSI or the SCSI is available. We have shown that the secrecy performance of the OS with ICSI of the system is better than with SCSI. Also, the OS improves the performance of the multi-relay system, when the number of relays is increased.

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A large deviation inequality forβ-mixing time series and its applications to the functional kernel regression model

Statistics & Probability Letters ◽

10.1016/j.spl.2017.09.013 ◽

2018 ◽

Vol 133 ◽

pp. 50-58 ◽

Cited By ~ 1

Author(s):

Johannes T.N. Krebs

Keyword(s):

Time Series ◽

Regression Model ◽

Large Deviation ◽

Mixing Time ◽

Kernel Regression ◽

Deviation Inequality ◽

Large Deviation Inequality

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Large Deviations for the Graph Distance in Supercritical Continuum Percolation

Journal of Applied Probability ◽

10.1239/jap/1300198142 ◽

2011 ◽

Vol 48 (1) ◽

pp. 154-172 ◽

Cited By ~ 8

Author(s):

Chang-Long Yao ◽

Ge Chen ◽

Tian-De Guo

Keyword(s):

Large Deviation ◽

Geometric Graph ◽

Graph Distance ◽

Homogeneous Poisson Process ◽

Random Geometric Graph ◽

Asymptotic Shape ◽

Deviation Inequality ◽

Large Deviation Inequality ◽

Palm Measure ◽

Infinite Component

Denote the Palm measure of a homogeneous Poisson process Hλ with two points 0 and x by P0,x. We prove that there exists a constant μ ≥ 1 such that P0,x(D(0, x) / μ||x||2 ∉ (1 − ε, 1 + ε) | 0, x ∈ C∞) exponentially decreases when ||x||2 tends to ∞, where D(0, x) is the graph distance between 0 and x in the infinite component C∞ of the random geometric graph G(Hλ; 1). We derive a large deviation inequality for an asymptotic shape result. Our results have applications in many fields and especially in wireless sensor networks.

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Optimal joint cooperative beamforming and artificial noise design for secrecy rate maximization in AF relay networks

2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC) ◽

10.1109/spawc.2013.6612072 ◽

2013 ◽

Cited By ~ 18

Author(s):

Ye Yang ◽

Qiang Li ◽

Wing-Kin Ma ◽

Jianhua Ge ◽

Meilu Lin

Keyword(s):

Relay Networks ◽

Artificial Noise ◽

Secrecy Rate ◽

Rate Maximization ◽

Cooperative Beamforming ◽

Af Relay

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Large Deviations for the Graph Distance in Supercritical Continuum Percolation

Journal of Applied Probability ◽

10.1017/s0021900200007695 ◽

2011 ◽

Vol 48 (01) ◽

pp. 154-172 ◽

Cited By ~ 2

Author(s):

Chang-Long Yao ◽

Ge Chen ◽

Tian-De Guo

Keyword(s):

Large Deviation ◽

Geometric Graph ◽

Graph Distance ◽

Homogeneous Poisson Process ◽

Random Geometric Graph ◽

Asymptotic Shape ◽

Deviation Inequality ◽

Large Deviation Inequality ◽

Palm Measure ◽

Infinite Component

Denote the Palm measure of a homogeneous Poisson process H λ with two points 0 and x by P0,x . We prove that there exists a constant μ ≥ 1 such that P0,x (D(0, x) / μ||x||2 ∉ (1 − ε, 1 + ε) | 0, x ∈ C ∞) exponentially decreases when ||x||2 tends to ∞, where D(0, x) is the graph distance between 0 and x in the infinite component C ∞ of the random geometric graph G(H λ; 1). We derive a large deviation inequality for an asymptotic shape result. Our results have applications in many fields and especially in wireless sensor networks.

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Near-Optimal, Distributed Edge Colouring via the Nibble Method

BRICS Report Series ◽

10.7146/brics.v3i11.19974 ◽

1996 ◽

Vol 3 (11) ◽

Author(s):

Devdatt P. Dubhashi ◽

David A. Grable ◽

Alessandro Panconesi

Keyword(s):

Failure Probability ◽

Positive Constant ◽

Maximum Degree ◽

Large Deviation ◽

Random Variables ◽

Randomized Algorithm ◽

Independent Random Variables ◽

Deviation Inequality ◽

Large Deviation Inequality ◽

Edge Colouring

We give a distributed randomized algorithm to edge colour a network. Let G be a graph with n nodes and maximum degree Delta. Here we prove: If Delta = Omega(log^(1+delta) n) for some delta > 0 and lambda > 0 is fixed, the algorithm almost always colours G with (1 + lambda)Delta colours in time O(log n). If s > 0 is fixed, there exists a positive constant k such that if Delta = omega(log^k n), the algorithm almost always colours G with Delta + Delta / log^s n = (1+o(1))Delta colours in time O(logn + log^s n log log n). By "almost always" we mean that the algorithm may fail, but the failure probability can be made arbitrarily close to 0. The algorithm is based on the nibble method, a probabilistic strategy introduced by Vojtech R¨odl. The analysis makes use of a powerful large deviation inequality for functions of independent random variables.

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