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## Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection – Secure

### Citations

1189 |
Communication theory of secrecy systems
- Shannon
- 1948
(Show Context)
Citation Context ...ecurity communication system consists of three nodes – a transmitter (Alice), a legitimate receiver (Bob), and a passive eavesdropper (Eve). Information theoretic security study was opened by Shannon =-=[1]-=- with the notion of perfect secrecy. The wiretap channel model was first introduced by Wyner [2] and secrecy capacity is defined in [3] as the maximum achievable rate of Bob preventing Eve from obtain... |

797 | R.Laroia, “Opportunistic Beamforming using Dumb Antennas
- Viswanath
- 2002
(Show Context)
Citation Context ... secrecy constraint. The multiuser diversity, exploiting multiuser dimensions by serving the selected users with good channel conditions, can enhance the performance of wireless communication systems =-=[14]-=-–[19]. In many cases, the multiuser diversity asymptotically achieves the optimal performance with considerably reduced channel 3feedback overhead. Recently, the opportunistic interference alignment (... |

740 |
Broadcast Channels with Confidential Messages
- Csiszar, Korner
- 1978
(Show Context)
Citation Context ...Eve). Information theoretic security study was opened by Shannon [1] with the notion of perfect secrecy. The wiretap channel model was first introduced by Wyner [2] and secrecy capacity is defined in =-=[3]-=- as the maximum achievable rate of Bob preventing Eve from obtaining any information. Positive secrecy capacity was shown to be achieved when Bob’s channel is less noisy than Eve’s. For guaranteeing p... |

343 | On the capacity of MIMO broadcast channels with partial side information - Sharif, Hassibi - 2005 |

301 |
The wire-tap channel,” Bell Syst
- Wyner
- 1975
(Show Context)
Citation Context ...ver (Bob), and a passive eavesdropper (Eve). Information theoretic security study was opened by Shannon [1] with the notion of perfect secrecy. The wiretap channel model was first introduced by Wyner =-=[2]-=- and secrecy capacity is defined in [3] as the maximum achievable rate of Bob preventing Eve from obtaining any information. Positive secrecy capacity was shown to be achieved when Bob’s channel is le... |

205 |
Interference alignment and degrees of freedom of the K user interference channel
- Cadambe, Jafar
- 2008
(Show Context)
Citation Context ...ly. The secure DoFs for those cases were shown to be N−2 2N−2 and N−2 2N , respectively, while a half DoF per orthogonal dimension is to be achievable via the interference alignment (IA) scheme [12], =-=[13]-=- in the absence of the secrecy constraint. The multiuser diversity, exploiting multiuser dimensions by serving the selected users with good channel conditions, can enhance the performance of wireless ... |

200 | On the Secrecy Capacity of Fading Channels
- Gopala, Lai, et al.
- 2008
(Show Context)
Citation Context ...enarios that CSI for Eve’s channel is not known to Alice. Since Eve’s CSI is hard to know even when Eve’s presence is known, many schemes that work in the absence of Eve’s CSI have been proposed [8], =-=[31]-=-, [32]. The authors in [8] proposed relay chatting for half-duplexing two-hop amplify-and-forward (AF) relay communication systems. In the relay chatting scheme, the best relay forwards the received s... |

156 |
Guaranteeing secrecy using artificial noise
- Goel, Negi
- 2008
(Show Context)
Citation Context ...itive secrecy capacity was shown to be achieved when Bob’s channel is less noisy than Eve’s. For guaranteeing positive secrecy rate, artificial noise was additionally transmitted from the transmitter =-=[4]-=-. The authors in [5] showed that the artificial noise can enlarge the secrecy rate region in a symmetric interference channel. The secrecy issues were also studied in cooperative relay systems [6]–[8]... |

95 | Ergodic interference alignment
- Nazer, Gastpar, et al.
(Show Context)
Citation Context ...mit their symbols with proper scaling over several consecutive time slots. Then, the signals are aligned at eavesdropper’s receiver and hence Eve’s DoF becomes zero. In ESA, the concept of ergodic IA =-=[25]-=- was extended to secrecy communications. In [26], cooperative jammers were exploited to increase secure DoF in a Gaussian wiretap channel, where transmitter and cooperative jammers send jointly design... |

92 | Shitz) “Degrees of freedom region of the MIMO
- Jafar, Shamai
- 2008
(Show Context)
Citation Context ...ectively. The secure DoFs for those cases were shown to be N−2 2N−2 and N−2 2N , respectively, while a half DoF per orthogonal dimension is to be achievable via the interference alignment (IA) scheme =-=[12]-=-, [13] in the absence of the secrecy constraint. The multiuser diversity, exploiting multiuser dimensions by serving the selected users with good channel conditions, can enhance the performance of wir... |

65 | Quantization bounds on Grassmann manifolds and applications in MIMO systems
- Dai, Liu, et al.
- 2008
(Show Context)
Citation Context ...mers to obtain the target secure DoF. 10 IV. GEOMETRIC INTERPRETATIONS A. Geometric Interpretations of Jamming Channels The Grassmann manifold GNr,Nj (C) is set of all Nj-dimensional subspaces in CNr =-=[33]-=-–[35]. Since each jammer and Bob have Nj and Nr antennas, respectively, the channel matrix from each jammer to Bob constructs an Nj-dimensional subspace in CNr . Let Hk be the subspace formed by the c... |

59 |
Physical-Layer Security: from Information Theory to Security Engineering
- Bloch, Barros
- 2011
(Show Context)
Citation Context ...at the required jammer scaling for the target secure DoF is the same even in practical scenarios that Alice has no information about Eve. In this paper, we adopt the quasi-static fading channel model =-=[27]-=-, where the coherent interval is longer than the jammer selection procedure and the length of a codeword. That is, the channel coefficients remain constant over the transmission of an entire codeword ... |

41 | Interference alignment for secrecy
- Koyluoglu, Gamal, et al.
- 2008
(Show Context)
Citation Context ...was found in an X network. For N-user Gaussian interference channels, an interference channel with confidential message and an interference channel with an external eavesdropper were studied in [10], =-=[11]-=-, respectively. The secure DoFs for those cases were shown to be N−2 2N−2 and N−2 2N , respectively, while a half DoF per orthogonal dimension is to be achievable via the interference alignment (IA) s... |

40 | Bounds on packings of spheres in the Grassmann manifold - Barg, Nogin - 2002 |

37 |
The capacity gain from intercell scheduling in multi-antenna systems
- Choi, Andrews
- 2008
(Show Context)
Citation Context ...ecy constraint. The multiuser diversity, exploiting multiuser dimensions by serving the selected users with good channel conditions, can enhance the performance of wireless communication systems [14]–=-=[19]-=-. In many cases, the multiuser diversity asymptotically achieves the optimal performance with considerably reduced channel 3feedback overhead. Recently, the opportunistic interference alignment (OIA) ... |

35 | Limited feedback-based block diagonalization for the MIMO broadcast channel
- Ravindran, Jindal
- 2008
(Show Context)
Citation Context ...rages is larger than the average of the minimums. The inequality (b) holds from Jensen’s inequality and the independence between H̃ and Λ. Finally, we obtain (15) from the fact that E[Λs′ k ] = NjINj =-=[30]-=-. In the subspace-based jammer selection scheme, we minimize the upper bound given in (15) denoted by R−(2)Bob instead of (14). We can rewrite R−(2)Bob as R−(2)Bob , EH̃ [ min s′1,...,s ′ K ,V log2 ∣∣... |

30 | Degrees of freedom of wireless X networks
- Cadambe, Jafar
- 2008
(Show Context)
Citation Context ... and jammers was studied and opportunistic jamming and relay chatting was proposed. As an alternative measure to secrecy capacity, secure degrees of freedom (DoF) have popularly been investigated. In =-=[9]-=-, the secure DoF was found in an X network. For N-user Gaussian interference channels, an interference channel with confidential message and an interference channel with an external eavesdropper were ... |

22 | Secure degrees of freedom of the Gaussian wiretap channel with helpers and no eavesdropper CSI: Blind cooperative jamming,” CISS
- Xie, Ulukus
- 2013
(Show Context)
Citation Context ...to how much we can align the K jamming signals by directly picking each jamming signal among S jamming signals. There have been many studies on utilizing jammers for increasing secure DoF [23], [24], =-=[26]-=-. In [23], cooperative jamming with structured jamming signals based on lattice coding was proposed for a Gaussian wiretap channel. In multiple access fading channels, [24] proposed two ergodic alignm... |

21 | Ergodic secret alignment
- Bassily, Ulukus
- 2012
(Show Context)
Citation Context ...anged to how much we can align the K jamming signals by directly picking each jamming signal among S jamming signals. There have been many studies on utilizing jammers for increasing secure DoF [23], =-=[24]-=-, [26]. In [23], cooperative jamming with structured jamming signals based on lattice coding was proposed for a Gaussian wiretap channel. In multiple access fading channels, [24] proposed two ergodic ... |

19 |
Opportunistic relaying for secrecy communications: Cooperative jamming vs. relay chatting
- Ding, Leung, et al.
- 2011
(Show Context)
Citation Context ...[4]. The authors in [5] showed that the artificial noise can enlarge the secrecy rate region in a symmetric interference channel. The secrecy issues were also studied in cooperative relay systems [6]–=-=[8]-=-. In [7], [8], joint selection of relays and jammers was studied and opportunistic jamming and relay chatting was proposed. As an alternative measure to secrecy capacity, secure degrees of freedom (Do... |

18 |
Sphere-packing bounds in the Grassmann and Stiefel manifolds
- Henkel
- 2005
(Show Context)
Citation Context ...to obtain the target secure DoF. 10 IV. GEOMETRIC INTERPRETATIONS A. Geometric Interpretations of Jamming Channels The Grassmann manifold GNr,Nj (C) is set of all Nj-dimensional subspaces in CNr [33]–=-=[35]-=-. Since each jammer and Bob have Nj and Nr antennas, respectively, the channel matrix from each jammer to Bob constructs an Nj-dimensional subspace in CNr . Let Hk be the subspace formed by the channe... |

15 |
On the throughput cost of physical layer security in decentralized wireless networks
- Zhou, Ganti, et al.
- 2011
(Show Context)
Citation Context ...s that CSI for Eve’s channel is not known to Alice. Since Eve’s CSI is hard to know even when Eve’s presence is known, many schemes that work in the absence of Eve’s CSI have been proposed [8], [31], =-=[32]-=-. The authors in [8] proposed relay chatting for half-duplexing two-hop amplify-and-forward (AF) relay communication systems. In the relay chatting scheme, the best relay forwards the received signal ... |

14 | Providing Secrecy with Lattice Codes
- He, Yener
- 2008
(Show Context)
Citation Context ... is changed to how much we can align the K jamming signals by directly picking each jamming signal among S jamming signals. There have been many studies on utilizing jammers for increasing secure DoF =-=[23]-=-, [24], [26]. In [23], cooperative jamming with structured jamming signals based on lattice coding was proposed for a Gaussian wiretap channel. In multiple access fading channels, [24] proposed two er... |

13 |
Joint relay and jammer selection for secure two-way relay networks
- Chen, Zhang, et al.
- 2012
(Show Context)
Citation Context ... authors in [5] showed that the artificial noise can enlarge the secrecy rate region in a symmetric interference channel. The secrecy issues were also studied in cooperative relay systems [6]–[8]. In =-=[7]-=-, [8], joint selection of relays and jammers was studied and opportunistic jamming and relay chatting was proposed. As an alternative measure to secrecy capacity, secure degrees of freedom (DoF) have ... |

13 |
Shitz), “Information theoretic security,” Found
- Liang, Poor, et al.
- 2009
(Show Context)
Citation Context ...∣INe + P Nt G0G † 0 ( INe + P Nj K∑ k=1 GskG † sk )−1∣∣∣∣∣∣ . (2) Therefore, the secrecy rate [RBob − CEve]+ is achievable at Bob for each channel realization through the Wyner’s encoding scheme [2], =-=[28]-=- with nested code structure, where [·]+ denotes max(·, 0). In an average sense, we obtain the secrecy rate and the secure DoF given, respectively, by Secrecy rate = E { [RBob − CEve] + } , Secure DoF ... |

11 |
Bounds on distance distributions in codes of known size
- Ashikhmin, Cohen, et al.
(Show Context)
Citation Context ... non-overlapped such that [33]–[35] δp(Q) , max{δ : B(Qi, δ) ∩B(Qj , δ) = ∅ ∀i 6= j}. The covering radius of Q denoted by δc(Q) is the minimum radius of the metric ball covering whole space such that =-=[36]-=-, [37] δc(Q) , min{δ : B(Q1, δ) ∪ · · · ∪B(QM , δ) = C Nr}. (10) A graphical representation of the packing and the covering radii of a codebook are given in Fig. 4(a) and Fig. 4(b), respectively. Obvi... |

9 | Asymptotic analysis on the interaction between spatial diversity and multiuser diversity in wireless networks - Zhou, Dai - 2007 |

9 | On the achievable dof and user scaling law of opportunistic interference alignment in 3transmitter MIMO interference channels - Lee, Choi - 2013 |

5 | Random beamforming with heterogeneous users and selective feedback: Individual sum rate and individual scaling laws - Huang, Rao - 2013 |

5 |
Multiuser diversity in interfering broadcast channels: Achievable degrees of freedom and user scaling law
- Lee, Choi, et al.
- 2013
(Show Context)
Citation Context ...nsiderably reduced channel 3feedback overhead. Recently, the opportunistic interference alignment (OIA) has been proposed by the authors in order to resolve the difficulties of IA implementation [20]–=-=[22]-=-. In the OIA scheme, user dimensions are exploited to align interfering channels; each transmitter has multiple users and selects a single user having the most aligned interfering channels. The OIA sc... |

4 | Cooperative secret communication with artificial noise in symmetric interference channel
- Zhu, Mo, et al.
- 2010
(Show Context)
Citation Context ...ty was shown to be achieved when Bob’s channel is less noisy than Eve’s. For guaranteeing positive secrecy rate, artificial noise was additionally transmitted from the transmitter [4]. The authors in =-=[5]-=- showed that the artificial noise can enlarge the secrecy rate region in a symmetric interference channel. The secrecy issues were also studied in cooperative relay systems [6]–[8]. In [7], [8], joint... |

4 |
On the secure degrees of freedom
- Koyluoglu, Gamal, et al.
- 2008
(Show Context)
Citation Context ...e DoF was found in an X network. For N-user Gaussian interference channels, an interference channel with confidential message and an interference channel with an external eavesdropper were studied in =-=[10]-=-, [11], respectively. The secure DoFs for those cases were shown to be N−2 2N−2 and N−2 2N , respectively, while a half DoF per orthogonal dimension is to be achievable via the interference alignment ... |

4 |
Mubs and Hadamards of order six
- Bengtsson, Bruzda, et al.
- 2007
(Show Context)
Citation Context ... Nj − tr(H̃ † kQQ †H̃k), (7) where the equality (a) holds because Nr ≥ Nt +Nj and tr(AB) = tr(BA). Note that H̃kH̃†k and QQ† are the projection matrices onto the subspaces Hk and Q, respectively. See =-=[29]-=- for more details on the chordal distance. Lemma 1. The squared chordal distance between Hk and Q is equivalent to d2c(Hk,Q) = tr((Q ⊥)†H̃kH̃ † k(Q ⊥)), (8) 11 where Q⊥ ∈ CNr×Nt is the generator matri... |

3 | Choi,“Throughput Characteristics by Multiuser Diversity in a Cognitive Radio System - Hong, W - 2011 |

2 |
Multi-user Diversity for Secrecy
- Vasudevan, Adams, et al.
(Show Context)
Citation Context ...ter [4]. The authors in [5] showed that the artificial noise can enlarge the secrecy rate region in a symmetric interference channel. The secrecy issues were also studied in cooperative relay systems =-=[6]-=-–[8]. In [7], [8], joint selection of relays and jammers was studied and opportunistic jamming and relay chatting was proposed. As an alternative measure to secrecy capacity, secure degrees of freedom... |

1 |
Opportunistic interference alignment by receiver selection in a K-user 1
- Lee, Choi
- 2011
(Show Context)
Citation Context ...th considerably reduced channel 3feedback overhead. Recently, the opportunistic interference alignment (OIA) has been proposed by the authors in order to resolve the difficulties of IA implementation =-=[20]-=-–[22]. In the OIA scheme, user dimensions are exploited to align interfering channels; each transmitter has multiple users and selects a single user having the most aligned interfering channels. The O... |

1 | A diversity guarantee and SNR performance for unitary limited feedback mimo systems
- Mondal, Heath
- 2008
(Show Context)
Citation Context ... can make the alignment measure of the K jamming subspaces by opportunistic jammer selection for a given number of total jammers S. To answer this question, we adopt subspace quantization theory [33]–=-=[37]-=-. Suppose that we quantize an arbitrary Nj-dimensional subspace into one of M (Nr −Nt)-dimensional subspaces. We define a subspace codebook Q , {Q1, . . . ,QM} comprised of M (Nr −Nt)-dimensional 13 s... |