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

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jinxin Zhu ◽  
Jun Shao
Keyword(s):  
Large Deviation ◽  
Type Inequality ◽  
Optimization Method ◽  
Relay Network ◽  
Secrecy Rate ◽  
Channel State ◽  
Deviation Inequality ◽  
Rate Maximization ◽  
Large Deviation Inequality ◽  
Cooperative Beamforming

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.

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

1998 ◽  
Vol 7 (1) ◽  
pp. 57-63 ◽  
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.

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

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.

scholarly journals Large Deviations for the Graph Distance in Supercritical Continuum Percolation

2011 ◽  
Vol 48 (1) ◽  
pp. 154-172 ◽  
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.

scholarly journals Near-Optimal, Distributed Edge Colouring via the Nibble Method

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

scholarly journals Large Deviations for the Graph Distance in Supercritical Continuum Percolation

2011 ◽  
Vol 48 (01) ◽  
pp. 154-172 ◽  
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.

scholarly journals A new large deviation inequality for U-statistics of order 2

1999 ◽  
Vol 3 ◽  
pp. 151-162 ◽  
Author(s):  
Jean Bretagnolle
Keyword(s):  
Large Deviation ◽  
U Statistics ◽  
Deviation Inequality ◽  
Large Deviation Inequality

scholarly journals An Artificial-Noise-Based Approach for the Secrecy Rate Maximization of MISO VLC Wiretap Channel With Multi-Eves

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 651-659
Author(s):  
Ge Shi ◽  
Yong Li ◽  
Wei Cheng ◽  
Xiang Gao ◽  
Wenjie Zhang
Keyword(s):  
Artificial Noise ◽  
Secrecy Rate ◽  
Wiretap Channel ◽  
Rate Maximization
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