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## Multiple-input multiple-output two-way relaying: A space-division approach (2013)

Venue: | IEEE TRANS. INF. THEORY |

Citations: | 12 - 8 self |

### Citations

12423 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...el (MAC). Let , be the rate of user for the CD strategy. Then, the uplink rate-region of the CD strategy, denoted by , is given by (6a) (6b) which follows from the well-known MAC capacity region [27]–=-=[29]-=-. C. Achievable Rates of the PNC Strategy For the PNC strategy, it is required that the two user-signals lie in the same spatial direction [5], [6]. This is not guaranteed here due to the availability... |

7459 | Convex Optimization
- Boyd, Vandenberghe
- 2004
(Show Context)
Citation Context ...the bottom of the page. This is a standard weighted sum-rate maximization problem for a MIMO multiple-access channel with two users [34]. The optimal solution can be computed using convex programming =-=[30]-=- or the iterative water-filling technique in [34]. 3) Determining Power Allocation for PNC Streams: Now we consider the optimization of and . Given and , the optimal and can be determined by solving t... |

1965 | Network information flow
- Ahlswede, Cai, et al.
(Show Context)
Citation Context ...(MIMO), physical-layer network coding, space-division precoding, two-way relay channel (TWRC). I. INTRODUCTION D URING the past decade, tremendous progress has beenmade in the field of network coding =-=[1]-=-. In [2]–[4], the concept of physical-layer network coding (PNC) was introduced and applied to wireless networks. The simplest model for PNC is a two-way relay channel (TWRC), in which two users and e... |

1526 | Fundamentals of wireless communications
- Tse, Viswanath
- 2005
(Show Context)
Citation Context ...ces to maximize subject to (49b). This formulation is similar to the power allocation problem for point-to-pointMIMO, and it is known that equal power allocation is asymptotically optimal at high SNR =-=[33]-=-. 2) Determining and : Given in (52), the optimization problem in (49) can be decoupled into two separate problems by predetermining the power allocated to the two signal subspaces. Let be the power o... |

737 | Cooperative strategies and capacity theorems for relay networks
- Kramer, Gastpar, et al.
- 2005
(Show Context)
Citation Context ...ing approaches on MIMO TWRCs focus on classical relaying strategies borrowed from one-way relay channels, such as amplify-and-forward [7]–[10], compress-and-forward [11], [12], and decode-and-forward =-=[13]-=-–[15]. These strategies generally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss [15]. Recently, several relaying schemes have been proposed to sup... |

469 |
for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems,
- Standard
- 2001
(Show Context)
Citation Context ...tation of user terminals, it is usually more convenient to implement more antennas at the relay station than at the user ends, as suggested in the standards of next generation wireless networks [23], =-=[24]-=-. In this paper, we propose a new space-division-based PNC scheme for MIMO TWRCs. We first establish a novel joint channel decomposition to characterize the mutual orthogonality of the channel directi... |

372 |
Random Matrix Theory and Wireless Communications, ser
- Tulino, Verdu
- 2004
(Show Context)
Citation Context ... circularly symmetric complex Gaussian random variables. Then, the matrices and in (14) are truncated uniformly distributed unitary matrices or, alternatively, are asymptotically free random matrices =-=[31]-=-. Thus, we can use the theory of free probability to derive the asymptotic eigenvalue distribution (a.e.d.) of as tends to infinity, with the result given in the lemma below. Define . Lemma 5: As with... |

354 | Embracing wireless interference: Analog network coding - Katti, Gollakota, et al. - 2007 |

313 | Iterative water-filling for Gaussian vector multiple-access channels,''
- Yu, Rhee, et al.
- 2004
(Show Context)
Citation Context ...l and to (49) can be found by solving the problem in (55), given at the bottom of the page. This is a standard weighted sum-rate maximization problem for a MIMO multiple-access channel with two users =-=[34]-=-. The optimal solution can be computed using convex programming [30] or the iterative water-filling technique in [34]. 3) Determining Power Allocation for PNC Streams: Now we consider the optimization... |

254 | The analogues of entropy and of Fisher’s information measure in free probability theory. VI. Liberation and mutual free information.
- VOICULESCU
- 1999
(Show Context)
Citation Context ...ate case of . Then, using the definition in (41b), we obtain (85) Combining (81)–(85), we complete the proof of Theorem 3. APPENDIX E PROOF OF LEMMA 5 We prove by using the theory of free probability =-=[32]-=-. The a.e.d. of is given by Let be a random variable with PDF . Its Stieltjes transform is given by (cf., [31, (2.40)]) Then, the inverse function of is given by Using the relation between Stieltjes t... |

209 |
Interference alignment and the degree of freedom for the K user interference channel
- Cadambe, Jafar
- 2008
(Show Context)
Citation Context ...ists. In that case, the DoF of our proposed scheme reduces to that of the CD scheme. We note that such a loss of DoF is a common problem for all existing signal-alignment based techniques [16], [17], =-=[36]-=-. Corollary 4: The optimal that minimizes in (59b) satisfies (61) With this choice of , the asymptotic rate gap is at most bits, which occurs when . Proof: The proof follows straightforwardly from (59... |

190 | Hot topic: Physical-layer network coding
- Zhang, Liew, et al.
- 2006
(Show Context)
Citation Context ...physical-layer network coding, space-division precoding, two-way relay channel (TWRC). I. INTRODUCTION D URING the past decade, tremendous progress has beenmade in the field of network coding [1]. In =-=[2]-=-–[4], the concept of physical-layer network coding (PNC) was introduced and applied to wireless networks. The simplest model for PNC is a two-way relay channel (TWRC), in which two users and exchange ... |

170 | Joint physical layer coding and network coding for bidirectional relaying - Wilson, Narayanan, et al. - 2010 |

159 | Optimal design of non-regenerative MIMO wireless relays,”
- Tang, Hua
- 2007
(Show Context)
Citation Context ... and the relay are all equipped with multiple antennas. Most existing approaches on MIMO TWRCs focus on classical relaying strategies borrowed from one-way relay channels, such as amplify-and-forward =-=[7]-=-–[10], compress-and-forward [11], [12], and decode-and-forward [13]–[15]. These strategies generally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss... |

158 | Compute-and-forward: Harnessing interference through structured codes,” Information Theory
- Nazer, Gastpar
- 2011
(Show Context)
Citation Context ...rally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss [15]. Recently, several relaying schemes have been proposed to support PNC in MIMO TWRCs [16]–=-=[22]-=-. The basic idea is to jointly decompose the channel matrices of the two users to create multiple scalar channels, over which multiple PNC streams are transmitted. Let , , and denote the number of ant... |

132 | Multiple access channels - Liao - 1972 |

128 | Noisy network coding
- Lim, Kim, et al.
- 2011
(Show Context)
Citation Context ...multiple antennas. Most existing approaches on MIMO TWRCs focus on classical relaying strategies borrowed from one-way relay channels, such as amplify-and-forward [7]–[10], compress-and-forward [11], =-=[12]-=-, and decode-and-forward [13]–[15]. These strategies generally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss [15]. Recently, several relaying sche... |

117 |
The capacity region of a channel with two senders and two receivers
- Ahlswede
- 1974
(Show Context)
Citation Context ...channel (MAC). Let , be the rate of user for the CD strategy. Then, the uplink rate-region of the CD strategy, denoted by , is given by (6a) (6b) which follows from the well-known MAC capacity region =-=[27]-=-–[29]. C. Achievable Rates of the PNC Strategy For the PNC strategy, it is required that the two user-signals lie in the same spatial direction [5], [6]. This is not guaranteed here due to the availab... |

115 | Physical network coding in two-way wireless relay channels
- Popovski, Yomo
- 2007
(Show Context)
Citation Context ...ical-layer network coding, space-division precoding, two-way relay channel (TWRC). I. INTRODUCTION D URING the past decade, tremendous progress has beenmade in the field of network coding [1]. In [2]–=-=[4]-=-, the concept of physical-layer network coding (PNC) was introduced and applied to wireless networks. The simplest model for PNC is a two-way relay channel (TWRC), in which two users and exchange info... |

96 | Capacity of the Gaussian two-way relay channel to within 1/2 bit
- Nam, Chung, et al.
(Show Context)
Citation Context ...itor for Communications. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2013.2271632 bit per user =-=[5]-=-, [6], and its gap to the capacity vanishes at high-signal-to-noise-ratio (SNR) regime. Recently, research effort has been directed toward efficient communications over MIMO TWRCs, in which the two us... |

90 | Optimal beamforming for two-way multi-antenna relay channel with analogue network coding
- Zhang, Liang, et al.
- 2009
(Show Context)
Citation Context ...e relay is denoted by , and the channel matrix from the relay to user is denoted by . We assume that the channel matrices are always of full column or row rank, whichever is smaller.1 As in [5], [6], =-=[9]-=-, [10], [16], and [17], we also assume that these channel matrices are globally known by both users as well as by the relay. In practice, the channel state information (CSI) is usually not known perfe... |

52 | The case for structured random codes in network capacity theorems - Nazer, Gastpar - 2008 |

32 | Relay networks with delays,” - Gamal, Hassanpour, et al. - 2007 |

21 | Optimal design of spatial source-and-relay matrices for a non-regenerative two-way MIMO relay system,”
- Xu, Hua
- 2011
(Show Context)
Citation Context ... the relay are all equipped with multiple antennas. Most existing approaches on MIMO TWRCs focus on classical relaying strategies borrowed from one-way relay channels, such as amplify-and-forward [7]–=-=[10]-=-, compress-and-forward [11], [12], and decode-and-forward [13]–[15]. These strategies generally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss [15]... |

20 | MIMO two-way relay channel: diversity-multiplexing tradeoff analysis,” Asilomar Conf. Signals, Systems, Computers,
- Gunduz, Goldsmith, et al.
- 2008
(Show Context)
Citation Context ...pproaches on MIMO TWRCs focus on classical relaying strategies borrowed from one-way relay channels, such as amplify-and-forward [7]–[10], compress-and-forward [11], [12], and decode-and-forward [13]–=-=[15]-=-. These strategies generally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss [15]. Recently, several relaying schemes have been proposed to support ... |

13 |
Asymptotic capacity of the separated MIMO two-way relay channel
- Yang, Chun, et al.
- 2011
(Show Context)
Citation Context ... generally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss [15]. Recently, several relaying schemes have been proposed to support PNC in MIMO TWRCs =-=[16]-=-–[22]. The basic idea is to jointly decompose the channel matrices of the two users to create multiple scalar channels, over which multiple PNC streams are transmitted. Let , , and denote the number o... |

13 | A new physicallayer network coding scheme with eigen-direction alignment precoding for MIMO two-way relaying
- Yang, Yuan, et al.
- 2013
(Show Context)
Citation Context ...wise algebraic operations for network-coding and conventional channel coding. These two operations are generally required in all regenerative relaying schemes utilizing network coding [2], [5], [16], =-=[17]-=-, [35]. In particular, the algebraic operations involve simple additions and multiplications in finite fields. Thus, the overall complexity of the re-encoding process is dominated by channel coding, f... |

11 |
Achieving on the AWGN channel with lattice encoding and decoding
- Erez, Zamir
- 2004
(Show Context)
Citation Context ...ection operation creates an aligned scalar channel given by (7) with the effective channel coefficients given by and . Let be the rate of user , . It was shown in [5] that, with nested lattice coding =-=[25]-=-, the following rates are achievable over the scalar TWRC in (7): (8) where represents the transmission power of user . Note that the above rates are achieved by decoding the lattice-modulo of (referr... |

8 | Reduced-dimension cooperative precoding for MIMO two-way relay channels - Yang, Yuan, et al. - 2012 |

5 | Joint beamforming and power management for nonregenerative MIMO two-way relaying channels,” - Leow, Ding, et al. - 2011 |

2 |
Capacity of a class of modulo-sum relay channels
- Yu
- 2009
(Show Context)
Citation Context ... with multiple antennas. Most existing approaches on MIMO TWRCs focus on classical relaying strategies borrowed from one-way relay channels, such as amplify-and-forward [7]–[10], compress-and-forward =-=[11]-=-, [12], and decode-and-forward [13]–[15]. These strategies generally perform well away from the channel capacity, e.g., due to noise amplification and multiplexing loss [15]. Recently, several relayin... |

2 |
Design of irregular repeat-accumulate coded physical-layer network coding for Gaussian two-way relay channels
- Huang, Yang, et al.
- 2013
(Show Context)
Citation Context ...lgebraic operations for network-coding and conventional channel coding. These two operations are generally required in all regenerative relaying schemes utilizing network coding [2], [5], [16], [17], =-=[35]-=-. In particular, the algebraic operations involve simple additions and multiplications in finite fields. Thus, the overall complexity of the re-encoding process is dominated by channel coding, for whi... |

1 |
Physical-layer MIMO relaying,” presented at the
- Khina, Kochman, et al.
- 2011
(Show Context)
Citation Context ...act of imperfect CSI later in Section V; cf., Remark 8. The system operates in a half-duplex mode. Two time-slots are employed for each round of information exchange. Following the convention in [16]–=-=[18]-=-, we assume that the two time-slots have the same duration. The extension of our results to the case of unequal durations is straightforward. In the first time-slot (referred to as the uplink phase), ... |

1 | WirelessMIMO switching: Weighted sum mean square error and sum rate optimization - Guo |