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## 1 Instantaneous Relaying: Optimal Strategies and Interference Neutralization

### Citations

7498 | Matrix Analysis - Horn, Johnson - 1988 |

284 |
Handbook of Matrices
- Lütkepohl
- 1996
(Show Context)
Citation Context ... C, the relay processing matrix R that satisfies the interference neutralization requirement (8) is determined by vec(R) = ( GTrt⊗GHdr )† vec(S). (12) Proof: From (8), using vec(ABC) = (CT ⊗A) vec(A) =-=[28]-=-, we obtain (GTrt⊗GHdr) vec(R) = vec(S). For a consistent system [29, P.12, Section 0.4.2], a sufficient condition is to have the number of equations (length of vec(S)) less than or equal to the numbe... |

206 |
Spectral efficient protocols for halfduplex fading relay channels
- Rankov, Wittneben
- 2007
(Show Context)
Citation Context ...uplex, instantaneous relay is a kind of full-duplex relays. 2 reaching the destination. This general idea has been applied in deterministic channels [9], [10] and in two-hop relay channels [3], [11], =-=[12]-=-, also known as multi-user zero-forcing and orthogonalize-andforward. To distinguish from IN, aligned interference neutralization (AIN), which is a combination of interference alignment and interferen... |

101 |
A distributed numerical approach to interference alignment and applications to wireless interference networks
- Gomadam, Cadambe, et al.
(Show Context)
Citation Context ...n in [6], [7] that instantaneous IRC can achieve degrees-of-freedom (DOF), or the multiplexing-gain, higher than the classical cut-set bound but can greatly simplify the interference alignment scheme =-=[8]-=-. Interference neutralization (IN) is a technique of canceling, zero-forcing or neutralizing interference signals by a careful selection of forwarding strategies when the signal travel through relay n... |

92 | Shitz) “Degrees of freedom region of the MIMO
- Jafar, Shamai
- 2008
(Show Context)
Citation Context ...alignment and IN by using instantaneous relay with memory and symbol extensions) is employed in [5], [13]. Note that symbol extensions are shown to achieve desirable DOF. For details, please refer to =-=[17]-=-. We assume linear relay processing which is considered in all aforementioned work. For non-linear instantaneous relaying, please refer to [18]. However, the performance analysis of the IRC is not lim... |

90 | Complete characterization of the Pareto boundary for the MISO interference channel
- Jorswieck, Larsson, et al.
- 2008
(Show Context)
Citation Context ...of R (RIN) – the Pareto boundary (PB) of R (RIN) – is a set of operating points at which one user cannot increase its own rate without simultaneously decreasing other users rate. Definition 1 ( [16], =-=[30]-=-): A rate-tuple (r1, . . . , rK) is Pareto optimal if there is no other rate tuple (q1, . . . , qK) such that (q1, . . . , qK) ≥ (r1, . . . , rK) and (q1, . . . , qK) 6= (r1, . . . , rK)5. By definiti... |

87 | Optimal beamforming for two-way multi-antenna relay channel with analogue network coding - Zhang, Liang, et al. - 2009 |

65 | Interference alignment with asymmetric complex signaling
- Jafar, Cadambe, et al.
(Show Context)
Citation Context ...or the transmit symbols simply the derivation as the achievable rate is the Shannon rate. For the degrees-of-freedom and achievable rates improvement with improper Gaussian signaling, please refer to =-=[26]-=-, [27] respectively. The received signal at Dj , j = 1, . . . ,K, is yj = K∑ l=1 ( hjl + g H jrRgrl ) xl + g H jrRnr + nj (2) For brevity, denote p = [P1, . . . , PK ]T ∈ RK×1+ . The Signal-to-Interfe... |

54 | Rank-constrained separable semidefinite programming with applications to optimal beamforming - Huang, Palomar - 2010 |

53 | Aligned interference neutralization and the degrees of freedom of the 2x2x2 interference channel
- Gou, Jafar, et al.
- 2012
(Show Context)
Citation Context ...ols as in conventional relays3. The authors further point out that a relay-without-delays is only a conventional relay with one extra delay on the link from S to D. A visual example is given later in =-=[5]-=- where in a network with multiple S-D pairs and conventional relay nodes, some naive relays only AF signals and some smart relays can gather channel state information (CSI) and forward linear processi... |

50 |
Cooperative interference management with MISO beamforming
- Zhang, Cui
- 2010
(Show Context)
Citation Context ... definition, the operation points on the PB can be evaluated by maximizing one user’s rate while keeping other users’ rates constant. Other optimization techniques for PB evaluation has been proposed =-=[15]-=-, [31]. Here, the PB problem is formulated as the maximization of SINR1 subject to the constraints on SINRj ≥ γj for some pre-determined target SINR values γj , j = 2, . . . ,K. Problem Statement 1: T... |

42 |
Degrees of freedom of wireless networks with relays, feedback, cooperation and full duplex operation
- Cadambe, Jafar
- 2009
(Show Context)
Citation Context ...hrough the naive relays are equivalent to direct links from S to D with one extra delay. Hence, the network is equivalent to an IRC equipped with smart relays-without-delays only. It is shown in [6], =-=[7]-=- that instantaneous IRC can achieve degrees-of-freedom (DOF), or the multiplexing-gain, higher than the classical cut-set bound but can greatly simplify the interference alignment scheme [8]. Interfer... |

40 | On the capacity of the interference channel with a relay
- Marić, Dabora, et al.
- 2008
(Show Context)
Citation Context ...ce alignment is implemented on a M -user IRC with each node equipped with a single antenna. The power scaling of the relay is computed in order to guarantee a degrees-of-freedom M2 in the channel. In =-=[20]-=-–[22], instead of neutralizing interference signals at the destination nodes, the relay is responsible for forwarding interference signals to the destination nodes so that the strength of the interfer... |

31 |
Coordinated beamforming for MISO interference channel: Complexity analysis and efficient algorithms
- Liu, Luo
- 2011
(Show Context)
Citation Context ...ay. 4 optimal in the sense of Pareto optimality (see Section III for details), is not trivial as it closely resembles an IC which is well known for the NP-hard complexity of the transmit optimization =-=[25]-=-, in terms of the number of users in the system. However, we are able to compute an upper bound using the Semi-Definite-Relaxation (SDR) techniques which relaxes the optimization problem to a convex p... |

30 | Relay networks with delays - ElGamal, Hassanpour, et al. - 2007 |

29 | QoS-based transmit beamforming in the presence of eavesdroppers: An optimized artificialnoise-aided approach
- Liao, Chang, et al.
- 2011
(Show Context)
Citation Context ...∗ir ⊗ IK) and the matrix Z which satisfies vec(RT ) = Z vec(R) is called a commutation matrix [28, Section 9.2]. Z has elements zeros and ones and Z = ZT . Utilizing the Charnes-Cooper Transform [36]–=-=[38]-=-, we let η /t = vec(R) where t ∈ C and v = [ηT , t]T ∈ C(K2+1)×1. The SINR of user i is SINRi = |hiit+ (gri⊗g∗ir)T η |2Pi∑K l 6=i |hilt+ (grl⊗g∗ir)T η |2Pl + ‖ηT ZT (g∗ir⊗ IK) ‖2 + |t|2 (a) = |hiit+ (... |

26 | Transmission techniques for relayinterference networks
- Mohajer, Diggavi, et al.
(Show Context)
Citation Context ... [2]. 3In the terminology of half-duplex and full-duplex, instantaneous relay is a kind of full-duplex relays. 2 reaching the destination. This general idea has been applied in deterministic channels =-=[9]-=-, [10] and in two-hop relay channels [3], [11], [12], also known as multi-user zero-forcing and orthogonalize-andforward. To distinguish from IN, aligned interference neutralization (AIN), which is a ... |

25 |
The Matrix Reference Manual
- Brookes
- 2005
(Show Context)
Citation Context ...S)∗ (d) = vec(S)H ( G−∗rt G −T rt ⊗G−1dr gir gHir G−Hdr ) vec(S) = vec(S)H ( G−∗rt G −T rt ⊗ ei eTi ) vec(S). (44) The transition (a) is due to the Kronecker product properties, aTBTC = vec(B)T (a⊗C) =-=[39]-=-. The commutation matrix Z of dimension K × K satisfies Z vec(S) = vec(ST ), [28, Section 9.2]. The transition (b) uses such properties and (A1⊗B1)(A2⊗B2) = A1A2⊗B1B2. Then in transition (c), we use t... |

22 | Gaussian Z-interference channel with a relay link: Type II channel and sum capacity bound
- Yu, Zhou
- 2009
(Show Context)
Citation Context ...ignment is implemented on a M -user IRC with each node equipped with a single antenna. The power scaling of the relay is computed in order to guarantee a degrees-of-freedom M2 in the channel. In [20]–=-=[22]-=-, instead of neutralizing interference signals at the destination nodes, the relay is responsible for forwarding interference signals to the destination nodes so that the strength of the interference ... |

22 | Rates region frontiers for n-user interference channel with interference as noise
- Charafeddine, Sezgin, et al.
- 2007
(Show Context)
Citation Context ...ition, the operation points on the PB can be evaluated by maximizing one user’s rate while keeping other users’ rates constant. Other optimization techniques for PB evaluation has been proposed [15], =-=[31]-=-. Here, the PB problem is formulated as the maximization of SINR1 subject to the constraints on SINRj ≥ γj for some pre-determined target SINR values γj , j = 2, . . . ,K. Problem Statement 1: The Par... |

22 |
MIMO relay design for multipoint-to-multipoint communications with imperfect channel state information
- Chalise, Vandendorpe
- 2009
(Show Context)
Citation Context ...ZT (g∗ir ⊗ IK) and the matrix Z which satisfies vec(RT ) = Z vec(R) is called a commutation matrix [28, Section 9.2]. Z has elements zeros and ones and Z = ZT . Utilizing the Charnes-Cooper Transform =-=[36]-=-–[38], we let η /t = vec(R) where t ∈ C and v = [ηT , t]T ∈ C(K2+1)×1. The SINR of user i is SINRi = |hiit+ (gri⊗g∗ir)T η |2Pi∑K l 6=i |hilt+ (grl⊗g∗ir)T η |2Pl + ‖ηT ZT (g∗ir⊗ IK) ‖2 + |t|2 (a) = |hi... |

20 |
Game theory and the flat-fading Gaussian interference channel
- Larsson, Jorswieck, et al.
- 2009
(Show Context)
Citation Context ...ular importance because it is highly desirable in the system’s interest to operate on the Pareto boundary, i.e., Pareto efficient: no user can improve its own rate without decreasing other users rate =-=[14]-=-–[16]. It is the purpose of this paper to characterize the Pareto boundary of the instantaneous IRC with (a) the optimal AF relay processing matrix and (b) interference neutralization. Our work differ... |

19 | Cooperative distributed multiuser MMSE relaying in wireless ad-hoc networks
- Berger, Wittneben
- 2005
(Show Context)
Citation Context ...full-duplex, instantaneous relay is a kind of full-duplex relays. 2 reaching the destination. This general idea has been applied in deterministic channels [9], [10] and in two-hop relay channels [3], =-=[11]-=-, [12], also known as multi-user zero-forcing and orthogonalize-andforward. To distinguish from IN, aligned interference neutralization (AIN), which is a combination of interference alignment and inte... |

18 |
Sawtooth relaying
- Yao, Khormuji, et al.
- 2008
(Show Context)
Citation Context ...n to achieve desirable DOF. For details, please refer to [17]. We assume linear relay processing which is considered in all aforementioned work. For non-linear instantaneous relaying, please refer to =-=[18]-=-. However, the performance analysis of the IRC is not limited to IN. Other interference management techniques, such as interference alignment and interference forwarding, are shown to achieve promisin... |

16 |
Relay-aided interference alignment for the quasi-static X channel
- Nourani, Motahari, et al.
(Show Context)
Citation Context ... performance analysis of the IRC is not limited to IN. Other interference management techniques, such as interference alignment and interference forwarding, are shown to achieve promising results. In =-=[19]-=-, on a quasi-static channel, interference alignment is implemented on a M -user IRC with each node equipped with a single antenna. The power scaling of the relay is computed in order to guarantee a de... |

12 |
Recent advances in amplify-and-forward two-hop relaying
- Berger, Kuhn, et al.
- 2009
(Show Context)
Citation Context ...lay employs an amplify-and-forward (AF) strategy which provides flexibility in implementation as the relay is oblivious to the modulation and coding schemes in the communication between S and D nodes =-=[3]-=-. The novel notion of relay-without-delays, also known as instantaneous relays, originally proposed in [4], refers to a type of relays that can forward signals consisting of both the current symbol an... |

11 |
The interference channel with MIMO relay: Degrees of freedom
- Tannious, Nosratinia
(Show Context)
Citation Context ...DOF IR/CR Method 2 M M 1 3M/4 IR AIN [5], potent relay SUD S-D 2 1 1 2 2 CR AIN [13], potent relay K 1 K 1 K IR IN, non-potent relay (this paper) K 1 K 1 K CR IN, ME, non-potent relay (Pr ∼ O(P 2s )) =-=[23]-=- MUD S-D 2 1 (1,2) 1 2 IR MUD, non-potent relay [2] of IRC with instantaneous relays and relays-with-delays (conventional relays) in Table I4. Note that the degrees-of-freedom is only a performance me... |

10 |
Relay without delay
- Hassanpour
- 2006
(Show Context)
Citation Context ... is oblivious to the modulation and coding schemes in the communication between S and D nodes [3]. The novel notion of relay-without-delays, also known as instantaneous relays, originally proposed in =-=[4]-=-, refers to a type of relays that can forward signals consisting of both the current symbol and the symbols in the past, instead of only the past symbols as in conventional relays3. The authors furthe... |

10 |
Improper Gaussian signaling on the two-user SISO interference channel
- Ho, Jorswieck
- 2012
(Show Context)
Citation Context ... transmit symbols simply the derivation as the achievable rate is the Shannon rate. For the degrees-of-freedom and achievable rates improvement with improper Gaussian signaling, please refer to [26], =-=[27]-=- respectively. The received signal at Dj , j = 1, . . . ,K, is yj = K∑ l=1 ( hjl + g H jrRgrl ) xl + g H jrRnr + nj (2) For brevity, denote p = [P1, . . . , PK ]T ∈ RK×1+ . The Signal-to-Interference-... |

9 |
Approximate capacity of a class of Gaussian relayinterference networks
- Mohajer, Tse, et al.
(Show Context)
Citation Context ... 3In the terminology of half-duplex and full-duplex, instantaneous relay is a kind of full-duplex relays. 2 reaching the destination. This general idea has been applied in deterministic channels [9], =-=[10]-=- and in two-hop relay channels [3], [11], [12], also known as multi-user zero-forcing and orthogonalize-andforward. To distinguish from IN, aligned interference neutralization (AIN), which is a combin... |

4 |
Beamforming on the MISO interference channel with multi-user decoding capability”, (Invited paper
- Ho, Gesbert, et al.
- 2010
(Show Context)
Citation Context ...importance because it is highly desirable in the system’s interest to operate on the Pareto boundary, i.e., Pareto efficient: no user can improve its own rate without decreasing other users rate [14]–=-=[16]-=-. It is the purpose of this paper to characterize the Pareto boundary of the instantaneous IRC with (a) the optimal AF relay processing matrix and (b) interference neutralization. Our work differs fro... |

2 |
Capacity of Strong and Very Strong Gaussian Interference Relay-without-delay Channels,” preprint, available at http://arXiv:1108.2846v1
- Chang, Chung
- 2011
(Show Context)
Citation Context ...reful selection of forwarding strategies when the signal travel through relay nodes before 2For the results on instantaneous relay capacity with multi-user decoding destination nodes, please refer to =-=[2]-=-. 3In the terminology of half-duplex and full-duplex, instantaneous relay is a kind of full-duplex relays. 2 reaching the destination. This general idea has been applied in deterministic channels [9],... |

2 |
Low-complexity Multiple-relay Strategies for Improving Uplink Coverage
- Yilmaz, Knopp, et al.
- 2010
(Show Context)
Citation Context ...he resulted gain largely outweighs the cost in low mobility environments [3]. A distributed smart relays system, which is capable of gathering CSI, matching the LTE standard, is recently demonstrated =-=[24]-=-. In Section II, we describe the channel model. An achievable rate region and the Pareto boundary formulation for (a) AF strategy optimization and (b) AF and IN strategy are given in Section III. In t... |

1 |
Interference Neutralization on the Multi-User Interference Relay Channel
- Ho, Jorswieck
- 2012
(Show Context)
Citation Context ...mework of the European research project SAPHYRE, which is partly funded by the European Union under its FP7 ICT Objective 1.1 - The Network of the Future. 1Part of this work is submitted to ISIT 2012 =-=[1]-=-. 10. Mai 2014 DRAFT Interference relay channel; Interference neutralization; Non-potent relay; Full-duplex relay; Pareto Boundary; Semi-definite relaxation; Convex optimization; Amplify-and-forward r... |