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## Network mimo with linear zero-forcing beamforming: Large system analysis, impact of channel estimation, and reduced-complexity scheduling,” Information Theory (2012)

Venue: | IEEE Transactions on |

Citations: | 51 - 4 self |

### Citations

1526 | Fundamentals of Wireless Communication
- Tse, Viswanath
- 2005
(Show Context)
Citation Context ...on where the distance between BSs and users changes significantly over a time-scale of the order of the tens of seconds, while the small-scale fading decorrelates completely within a few milliseconds =-=[41]-=-. Here, a “slot” indicates a block of channel uses over which the small-scale coefficients can be considered constant. The slot length (in channel uses) is approximately equal to the product of the ch... |

807 | Opportunistic beamforming using dumb antennas
- Viswanath, Tse, et al.
- 2002
(Show Context)
Citation Context ...n users near the cell (or cluster) center. In contrast, fairness scheduling has been proposed and widely studied in order to achieve a desirable balance between sum-rate and fairness (see for example =-=[19]-=-–[21] and references therein). Fairness scheduling can be systematically implemented in the framework of stochastic network optimization [20]. Such fairness scheduling algorithms dynamically allocate ... |

676 | Fair end-to-end window-based congestion control
- Mo, Walrand
- 2000
(Show Context)
Citation Context ...cate the system resources on a slot-by-slot basis, such that the long-term average (or “ergodic”) user rate point maximizes some suitable concave and componentwise increasing network utility function =-=[22]-=-. While the analytical characterization of the optimal ergodic rate point for a given network utility function may be hopelessly complicated in a realistic scenario, the system performance has been ev... |

590 |
On the achievable throughput of a multiantenna Gaussian broadcast channel
- Caire, Shamai
- 2003
(Show Context)
Citation Context ... In a single-cell setting with perfect Channel State Information at the Transmitter (CSIT), the system reduces to a vector Gaussian broadcast channel whose capacity region is completely characterized =-=[6]-=-– [10]. However, in a multi-cell scenario, we are in the presence of a vector Gaussian broadcast and interference channel, which is not yet fully understood in an information theoretic sense. A simple... |

508 | How much training is needed in multipleantenna wireless links
- Hassibi, Hochwald
- 2003
(Show Context)
Citation Context ...s said at the end of Section IV with choice of γp = γ. In fact, the “pre-log” optimality of explicit training for single-user MIMO channels with block fading in the high-SNR regime is wellknown [50], =-=[51]-=-. Also, the same result shows that if 12τ < min{A, γB}, then there is no point in using more than WT/2 jointly coordinated antennas. Finally, notice that the recently proposed schemes for “blind” inte... |

494 | Capacity of a mobile multipleantenna communication link in Rayleigh flat fading
- Marzetta, Hochwald
- 1999
(Show Context)
Citation Context ...he capacity of the resulting block-fading single-user MIMO channel with γBN transmit antennas and AN receiving antennas and fading coherence block WT = N/τ was characterized in the high-SNR regime in =-=[49]-=-, [50]. Using this result, in the case 12τ ≥ A ≥ γB, the dimensionality “pre-log” loss factor with respect to the case of ideal CSIT is given by ( 1− γBNWT ) that coincides with what is said at the en... |

372 |
Random Matrix Theory and Wireless Communications, ser
- Tulino, Verdu
- 2004
(Show Context)
Citation Context ...ly less system complexity. APPENDIX A PROOF OF THEOREM 1 For the sake of clarity, we recall some definitions and facts about random matrices with independent non-identically distributed elements (see =-=[53]-=-, [54]) of the type defined in (4), (7), that will be essential in the proof of Theorem 1. Definition 1: Consider an Nr ×Nc random matrix H = [Hi,j ], whose entries have variance Var[Hi,j ] = Pi,j Nr ... |

339 | achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels - Vishwanath, Jindal, et al. - 2003 |

322 | Sum capacity of the vector Gaussian broadcast channel and uplink downlink duality - Viswanath, Tse - 2003 |

308 | On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming,”
- Yoo, Goldsmith
- 2006
(Show Context)
Citation Context ...rdinality not larger than the number of jointly coordinated transmit antennas, such that the channel vectors of the selected users have both large norm and are mutually approximately orthogonal [31], =-=[32]-=-. This multiuser diversity selection, combined with LZFB precoding, is shown to attain the same performance as Gaussian DPC in the limit of a large 1In the unrelated context of multiuser detection, as... |

279 | Sum capacity of Gaussian vector broadcast channels - Yu, Cioffi - 2004 |

273 | Communication on the grassmann manifold: a geometric approach to the noncoherent multiple-antenna channel,” Information Theory
- Zheng, Tse
- 2002
(Show Context)
Citation Context ...acity of the resulting block-fading single-user MIMO channel with γBN transmit antennas and AN receiving antennas and fading coherence block WT = N/τ was characterized in the high-SNR regime in [49], =-=[50]-=-. Using this result, in the case 12τ ≥ A ≥ γB, the dimensionality “pre-log” loss factor with respect to the case of ideal CSIT is given by ( 1− γBNWT ) that coincides with what is said at the end of S... |

159 | Multiple-antenna channel hardening and its implications for rate feedback and scheduling,”
- Hochwald, Marzetta, et al.
- 2004
(Show Context)
Citation Context ...iuser diversity yields larger throughput per user for lowdimensional systems, but this gain reduces as the system dimension grows. This is a manifestation of the “channel hardening effect” noticed in =-=[33]-=-, and agrees with the theoretical findings in [34], showing that the probability of finding a subset of approximately orthogonal users vanishes as the system dimension increases. Hence, as the system ... |

120 | Coordinated beamforming for the multicell multi-antenna wireless system.
- Dahrouj, Yu
- 2010
(Show Context)
Citation Context ...limit the system capacity. A variety of inter-cell cooperation schemes have been proposed to mitigate ICI, ranging from a fully cooperative network MIMO [11]–[14] to partially coordinated beamforming =-=[15]-=-–[17]. In this work, we focus on the network MIMO approach with limited cooperation, where clusters of cooperating base stations (BSs) act as a single distributed MIMO transmitter and interference fro... |

114 | Multiuser MIMO achievable rates with downlink training and channel state feedback.
- Caire, Jindal, et al.
- 2010
(Show Context)
Citation Context ...n comparison with concurrent existing literature, we notice that the LZFB MU-MIMO performance analysis with non-ideal CSIT was extensively studied in the finite-dimensional case (see for example [35]–=-=[37]-=-) and in the large-system limit (see for example [38]–[40]). Unlike concurrent works, our paper focuses explicitly on the system optimization under the fairness criteria in the multi-cell downlink wit... |

109 | On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm.
- Dimic, Sidiropoulos
- 2005
(Show Context)
Citation Context ...ith cardinality not larger than the number of jointly coordinated transmit antennas, such that the channel vectors of the selected users have both large norm and are mutually approximately orthogonal =-=[31]-=-, [32]. This multiuser diversity selection, combined with LZFB precoding, is shown to attain the same performance as Gaussian DPC in the limit of a large 1In the unrelated context of multiuser detecti... |

103 |
Mobile WiMAX - Part I: A technical overview and performance evaluation,”
- Forum
- 2006
(Show Context)
Citation Context ...as noise. In a cellular environment, the received signal power is a polynomially decreasing function of the distance between transmitter and receiver, with a dynamic range typically larger than 30 dB =-=[18]-=-. Thus, users close to the cell (or cluster of coordinated cells) boundary experience strong inter-cell interference, whereas the desired signal is relatively weak. These “edge” users cannot be just i... |

102 | Impact of antenna correlation on the capacity of multiantenna channels
- Tulino, Lozano, et al.
- 2005
(Show Context)
Citation Context ...s system complexity. APPENDIX A PROOF OF THEOREM 1 For the sake of clarity, we recall some definitions and facts about random matrices with independent non-identically distributed elements (see [53], =-=[54]-=-) of the type defined in (4), (7), that will be essential in the proof of Theorem 1. Definition 1: Consider an Nr ×Nc random matrix H = [Hi,j ], whose entries have variance Var[Hi,j ] = Pi,j Nr (56) s... |

92 | Networked MIMO with clustered linear precoding
- Zhang, Chen, et al.
- 2009
(Show Context)
Citation Context ...an investigate the tradeoff between ICI reduction owing to BS cooperation and the cost of estimating larger and larger dimensional channels. Unlike previous results that assumed ideal CSIT at no cost =-=[24]-=-, [25], [27], we observe that there exist an optimal cooperation cluster size that depends on the channel coherence time and bandwidth, beyond which cooperative network MIMO is not convenient, consist... |

86 |
Resource Allocation and CrossLayer
- Georgiadis, Neely, et al.
(Show Context)
Citation Context ...ble balance between sum-rate and fairness (see for example [19]–[21] and references therein). Fairness scheduling can be systematically implemented in the framework of stochastic network optimization =-=[20]-=-. Such fairness scheduling algorithms dynamically allocate the system resources on a slot-by-slot basis, such that the long-term average (or “ergodic”) user rate point maximizes some suitable concave ... |

78 |
Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency,”
- Foschini, Karakayali, et al.
- 2006
(Show Context)
Citation Context ... as noise. In this case, ICI may significantly limit the system capacity. A variety of inter-cell cooperation schemes have been proposed to mitigate ICI, ranging from a fully cooperative network MIMO =-=[11]-=-–[14] to partially coordinated beamforming [15]–[17]. In this work, we focus on the network MIMO approach with limited cooperation, where clusters of cooperating base stations (BSs) act as a single di... |

78 |
Interference Coordination and Cancellation for 4G Networks.
- Boudreau, Panicker, et al.
- 2009
(Show Context)
Citation Context ... the system capacity. A variety of inter-cell cooperation schemes have been proposed to mitigate ICI, ranging from a fully cooperative network MIMO [11]–[14] to partially coordinated beamforming [15]–=-=[17]-=-. In this work, we focus on the network MIMO approach with limited cooperation, where clusters of cooperating base stations (BSs) act as a single distributed MIMO transmitter and interference from oth... |

73 |
Inequalities: Theory Majorization.
- Marshall, Olkin
- 1979
(Show Context)
Citation Context ..., without changing the sum throughput. We assume that the network utility function gives the same priority to statistically equivalent users. This is captured by 6restricting g(·) to be Schur-concave =-=[42]-=-.2 It follows that the network utility function is always maximized at a point for which R(i)k = Rk for all users i in group k. Therefore, letting R = (R1, · · · , RA) and redefining the function g(·)... |

66 |
Shitz), “The capacity region of the Gaussian multiple-input multiple-output broadcast channel
- Weingarten, Steinberg, et al.
- 2006
(Show Context)
Citation Context ... single-cell setting with perfect Channel State Information at the Transmitter (CSIT), the system reduces to a vector Gaussian broadcast channel whose capacity region is completely characterized [6]– =-=[10]-=-. However, in a multi-cell scenario, we are in the presence of a vector Gaussian broadcast and interference channel, which is not yet fully understood in an information theoretic sense. A simple and p... |

64 | Multiple antenna broadcast channels with shape feedback and limited feedback,”
- Ding, Love, et al.
- 2007
(Show Context)
Citation Context ...t). In comparison with concurrent existing literature, we notice that the LZFB MU-MIMO performance analysis with non-ideal CSIT was extensively studied in the finite-dimensional case (see for example =-=[35]-=-–[37]) and in the large-system limit (see for example [38]–[40]). Unlike concurrent works, our paper focuses explicitly on the system optimization under the fairness criteria in the multi-cell downlin... |

48 | Aiming perfectly in the dark-blind interference alignment through staggered antenna switching
- Gou, Wang, et al.
- 2011
(Show Context)
Citation Context ...sult shows that if 12τ < min{A, γB}, then there is no point in using more than WT/2 jointly coordinated antennas. Finally, notice that the recently proposed schemes for “blind” interference alignment =-=[52]-=-, exploiting reconfigurable antennas at the user terminals, still require channel state information at the receiver (CSIR) for coherent detection at each user terminal. Since the resulting channel is ... |

41 | Design and analysis of low-complexity interference mitigation on vector channels
- Mueller, Verdú
- 2001
(Show Context)
Citation Context ...tem results were used to design low-complexity linear multiuser detectors based on the polynomial approximations, where the polynomial coefficients were obtained from large random matrix theory [29], =-=[30]-=-. 3number of users and fixed number of transmit antennas. However, in this limit, the throughput per user vanishes as O( log lognn ) where n is the number of users. Therefore, a more meaningful regime... |

33 | Increasing downlink cellular throughput with limited network
- Huang, Trivellato, et al.
- 2009
(Show Context)
Citation Context ...estigate the tradeoff between ICI reduction owing to BS cooperation and the cost of estimating larger and larger dimensional channels. Unlike previous results that assumed ideal CSIT at no cost [24], =-=[25]-=-, [27], we observe that there exist an optimal cooperation cluster size that depends on the channel coherence time and bandwidth, beyond which cooperative network MIMO is not convenient, consistently ... |

33 | Base station cooperation on the downlink: Large system analysis,”
- Zakhour, Hanly
- 2012
(Show Context)
Citation Context ...e that the LZFB MU-MIMO performance analysis with non-ideal CSIT was extensively studied in the finite-dimensional case (see for example [35]–[37]) and in the large-system limit (see for example [38]–=-=[40]-=-). Unlike concurrent works, our paper focuses explicitly on the system optimization under the fairness criteria in the multi-cell downlink with inter-cell cooperation. This particular angle allows us ... |

32 | Cooperative multi-cell block diagonalization with per-base-station power constraints
- Zhang
- 2010
(Show Context)
Citation Context ... be improved further. Moreover, even for a fixed set of active users, the problem of optimal LZFB precoding subject to a per-BS power constraint is non-trivial and has been recently addressed in [43]–=-=[45]-=- through fairly involved numerical algorithms. Because of these difficulties, problem (6) has so far escaped a clean analytical solution and most studies resorted to extensive and costly Monte Carlo s... |

32 | Training and feedback optimization for multiuser MIMO downlink
- Kobayashi, Jindal, et al.
(Show Context)
Citation Context ...e, this can be done with a moderate use of the uplink feedback total capacity, provided that the number of users feeding back their CSIT is not too large (see for example the optimization tradeoff in =-=[48]-=-). For the sake of simplicity, here we assume an ideal genie-aided CSIT feedback that provides Ĥ directly to the centralized cluster controller at no 22 additional costs, either in terms of rate or i... |

30 | Large system analysis of linear Precoding in MISO broadcast channels with limited feedback,”
- Wagner, Couillet, et al.
- 2012
(Show Context)
Citation Context ...notice that the LZFB MU-MIMO performance analysis with non-ideal CSIT was extensively studied in the finite-dimensional case (see for example [35]–[37]) and in the large-system limit (see for example =-=[38]-=-–[40]). Unlike concurrent works, our paper focuses explicitly on the system optimization under the fairness criteria in the multi-cell downlink with inter-cell cooperation. This particular angle allow... |

27 | Downlink macro-diversity in cellular networks - Jing, Tse, et al. - 2007 |

23 |
Limited downlink network coordination in cellular networks,
- Boccardi, Huang
- 2007
(Show Context)
Citation Context ...network utility function may be hopelessly complicated in a realistic scenario, the system performance has been evaluated so far through computationally very intensive Monte Carlo simulation [3]–[5], =-=[13]-=-, [14], [23]–[26], where the actual scheduling algorithm evolves in time and the ergodic rates are computed as time averages. The capacity of a multi-cell network MIMO system under fairness criteria w... |

22 |
Cellular vs network MIMO: A comparison including channel state information overhead
- Ramprashad, Caire
- 2009
(Show Context)
Citation Context ...unction may be hopelessly complicated in a realistic scenario, the system performance has been evaluated so far through computationally very intensive Monte Carlo simulation [3]–[5], [13], [14], [23]–=-=[26]-=-, where the actual scheduling algorithm evolves in time and the ergodic rates are computed as time averages. The capacity of a multi-cell network MIMO system under fairness criteria was evaluated in t... |

20 | MIMO downlink scheduling with non-perfect channel state knowledge,”
- Shirani-Mehr, Caire, et al.
(Show Context)
Citation Context ...rs near the cell (or cluster) center. In contrast, fairness scheduling has been proposed and widely studied in order to achieve a desirable balance between sum-rate and fairness (see for example [19]–=-=[21]-=- and references therein). Fairness scheduling can be systematically implemented in the framework of stochastic network optimization [20]. Such fairness scheduling algorithms dynamically allocate the s... |

20 | Rethinking network MIMO: Cost of CSIT, performance analysis, and architecture comparisons,”
- Caire, Ramprashad, et al.
- 2010
(Show Context)
Citation Context ...n cluster size that depends on the channel coherence time and bandwidth, beyond which cooperative network MIMO is not convenient, consistently with the finite-dimensional simulation findings of [26], =-=[28]-=-. 3) We provide novel results in random matrix theory, in particular, related to the evaluation of the coefficients appearing in the per-BS power constraint. 4) We use our asymptotic analysis in order... |

18 | Multiuser MISO transmitter optimization for intercell interference mitigation - Huh, Papadopoulos, et al. - 2010 |

17 | Asymptotic analysis of improved linear receivers for BPSK-CDMA subject to fading
- Tulino, Verdu
- 2001
(Show Context)
Citation Context ...ge-system results were used to design low-complexity linear multiuser detectors based on the polynomial approximations, where the polynomial coefficients were obtained from large random matrix theory =-=[29]-=-, [30]. 3number of users and fixed number of transmit antennas. However, in this limit, the throughput per user vanishes as O( log lognn ) where n is the number of users. Therefore, a more meaningful ... |

15 |
Multiuser MIMO downlink with limited intercell cooperation: Approximate interference alignment in time, frequency and space
- Caire, Ramprashad, et al.
- 2008
(Show Context)
Citation Context ...oise. In this case, ICI may significantly limit the system capacity. A variety of inter-cell cooperation schemes have been proposed to mitigate ICI, ranging from a fully cooperative network MIMO [11]–=-=[14]-=- to partially coordinated beamforming [15]–[17]. In this work, we focus on the network MIMO approach with limited cooperation, where clusters of cooperating base stations (BSs) act as a single distrib... |

13 | Multi-cell MIMO downlink with cell cooperation and fair scheduling: A large-system limit analysis,” arXiv:1006.2162v1 [cs.IT],
- Huh, Caire, et al.
- 2010
(Show Context)
Citation Context ...ling algorithm evolves in time and the ergodic rates are computed as time averages. The capacity of a multi-cell network MIMO system under fairness criteria was evaluated in the large2system limit in =-=[27]-=-, assuming ideal channel state knowledge and the Gaussian Dirty Paper Coding (DPC) transmission strategy. In [27], the asymptotic analysis method based on large random matrix results demonstrated its ... |

13 | MIMO broadcast channel optimization under general linear constraints - Huh, Papadopoulos, et al. - 2009 |

11 |
Fundamental simulated performance of downlink fixed wireless cellular networks with multiple antennas
- Huang, Valenzuela
- 2005
(Show Context)
Citation Context ...ity function may be hopelessly complicated in a realistic scenario, the system performance has been evaluated so far through computationally very intensive Monte Carlo simulation [3]–[5], [13], [14], =-=[23]-=-–[26], where the actual scheduling algorithm evolves in time and the ergodic rates are computed as time averages. The capacity of a multi-cell network MIMO system under fairness criteria was evaluated... |

10 | On the optimal number of cooperative base stations in network MIMO systems - Hoydis, Kobayashi, et al. - 2010 |

10 |
Channel state feedback schemes for multiuser MIMO-OFDM downlink
- Shirani-Mehr, Caire
- 2009
(Show Context)
Citation Context ...DMA/TDMA, or exploiting the MIMO-MAC nature of the uplink in order to allow a number of users proportional to the number of receiving antennas to send their feedback signals simultaneously (see [37], =-=[46]-=-, [47] and references therein). Analyzing the system in the presence of a specific feedback scheme is possible [37]. However, from the results in the above mentioned papers we know that a well-designe... |

7 |
Shitz), “Zero-forcing precoding and generalized inverses
- Wiesel, Eldar, et al.
- 2008
(Show Context)
Citation Context ...annot be improved further. Moreover, even for a fixed set of active users, the problem of optimal LZFB precoding subject to a per-BS power constraint is non-trivial and has been recently addressed in =-=[43]-=-–[45] through fairly involved numerical algorithms. Because of these difficulties, problem (6) has so far escaped a clean analytical solution and most studies resorted to extensive and costly Monte Ca... |

6 |
On the selection of semi-orthogonal users for zero-forcing beamforming
- Tomasoni, Caire, et al.
- 2009
(Show Context)
Citation Context ...for lowdimensional systems, but this gain reduces as the system dimension grows. This is a manifestation of the “channel hardening effect” noticed in [33], and agrees with the theoretical findings in =-=[34]-=-, showing that the probability of finding a subset of approximately orthogonal users vanishes as the system dimension increases. Hence, as the system becomes large, there is diminishing return in sele... |

5 | Channel state feedback over the MIMO-MAC
- Kumar, Caire
- 2009
(Show Context)
Citation Context ...MA, or exploiting the MIMO-MAC nature of the uplink in order to allow a number of users proportional to the number of receiving antennas to send their feedback signals simultaneously (see [37], [46], =-=[47]-=- and references therein). Analyzing the system in the presence of a specific feedback scheme is possible [37]. However, from the results in the above mentioned papers we know that a well-designed digi... |

3 | Realistic performance of HSDPA MIMO in macro-cell environment - Landre, Saadani, et al. - 2009 |

3 |
3GPP LTE downlink system performance
- Farajidana, Chen, et al.
- 2009
(Show Context)
Citation Context ...der multiuser MIMO (MU-MIMO) as one of the core technologies. A considerable research effort has been dedicated to the performance evaluation of MU-MIMO systems in realistic cellular environments [3]–=-=[5]-=-. In a single-cell setting with perfect Channel State Information at the Transmitter (CSIT), the system reduces to a vector Gaussian broadcast channel whose capacity region is completely characterized... |

2 | Precoding methods for multi-user TDD MIMO systems - Jose, Ashikhmin, et al. - 2008 |