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## Joint spatial division and multiplexing: Opportunistic beamforming and user grouping,” arXiv preprint arXiv:1305.7252 (2013)

Citations: | 17 - 4 self |

### Citations

806 | Opportunistic beamforming using dumb antennas
- Viswanath, Tse, et al.
- 2002
(Show Context)
Citation Context ...h SINR is easily and accurately measured by including downlink pilot symbols in the downlink streams passing through the pre-beamforming matrix, as currently done in opportunistic beamforming schemes =-=[13]-=-, [14]. Each user feeds back the SINRs on all beams, i.e., for all m = 1, . . . , r∗g , and the BS decides to serve the user with the maximum SINR on a beam m.2 With this type of user selection, the a... |

671 |
Order Statistics
- David
- 1981
(Show Context)
Citation Context ...uchy’s integral theorem. B. Extreme Value Theory For the sake of completeness, we recall here some known results on the asymptotic behavior of the maximum of K ′ random variables as K ′ → ∞ (see [1], =-=[22]-=- and references therein). For an arbitrary distribution, the density of the maximum does not necessarily have a limit as K ′ goes to infinity. (Gnedenko, 1947) lists all possible limiting distribution... |

349 | On the capacity of MIMO broadcast channels with partial side information
- Sharif, Hassibi
- 2005
(Show Context)
Citation Context ...and show that opportunistic beamforming with user selection yields significant gain, and thus, channel correlation may yield a capacity improvement over the uncorrelated “isotropic” channel result of =-=[1]-=-. We prove that in the presence of different correlations among groups, a block diagonalization approach for the design of pre-beamformers achieves the optimal sum-rate scaling, albeit with a constant... |

339 | Duality,Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels.
- Vishwanath, Jindal, et al.
- 2002
(Show Context)
Citation Context ...g an upper and a lower bound. The upper bound analyzes directly the sum capacity of the underlying vector broadcast channel, exploiting the sum capacity expression provided by the dual uplink channel =-=[10]-=- (see Section III-A). Interestingly, in order to prove the lower bound we consider an explicit achievability strategy based on simple beamforming and user selection in each group. This strategy genera... |

329 | Grassmannian beamforming for multiple-input multiple-output wireless systems
- Love, Heath, et al.
- 2003
(Show Context)
Citation Context ...annel covariances of users in group g, i.e., it depends on the sets {U gk ,Λgk}. Alternately, B can be fixed apriori, for example, like the schemes of random beamforming [1], Grassmannian beamforming =-=[8]-=-, etc. The multiuser MIMO precoding matrix P is dependent on the instantaneous “effective” channel H = BHH . Denoting the pre-beamforming matrix of group g as Bg of dimensions M × bg such that ∑G g=1 ... |

308 | On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming,”
- Yoo, Goldsmith
- 2006
(Show Context)
Citation Context ... and fixed number of antennas, the problem of sum capacity scaling with user selection has been widely investigated for uncorrelated channels under random beamforming [1] and zero forcing beamforming =-=[4]-=-, and also for correlated channels under random beamforming [5]. Our work differs from these earlier works in the sense that we consider different correlations for different groups, which is an extens... |

109 | On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm.
- Dimic, Sidiropoulos
- 2005
(Show Context)
Citation Context ...erent user selection algorithms for M = 8 and M = 16 respectively, when DFT-based user grouping is applied. For the sake of comparison, we show also the performance of ZFBF with greedy user selection =-=[19]-=- (denoted by ZFBF-GUS) and ZFBF with semi-orthogonal user selection [4] (denoted by ZFBF-SUS), where instead of restricting to JSDM with per-group processing, the selection is performed across all use... |

91 |
HSDPA/HSUPA for UMTS: High Speed Radio Access for Mobile Communications.
- Holma, Toskala
- 2006
(Show Context)
Citation Context ... is easily and accurately measured by including downlink pilot symbols in the downlink streams passing through the pre-beamforming matrix, as currently done in opportunistic beamforming schemes [13], =-=[14]-=-. Each user feeds back the SINRs on all beams, i.e., for all m = 1, . . . , r∗g , and the BS decides to serve the user with the maximum SINR on a beam m.2 With this type of user selection, the achieva... |

76 |
Matrix Theory
- Franklin
- 1968
(Show Context)
Citation Context ...a 2. The eigenvalues µm,2(x), . . . , µm,rg(x) are non-positive ∀ x ≥ 0. Proof: Denoting by λi(Am1) and λi(Am2) the ith largest eigenvalues of Am1 and Am2 , we have for i > 1, using Weyl’s inequality =-=[15]-=-, we have µm,i(x) ≤ λi(Am1)− xλrg(Am2) ≤ 0− xλrg(Am2) ≤ 0 (22) implying µm,i(x) ≤ 0, ∀ i > 1 Since the eigenvalues µm,2, . . . , µm,rg are negative and do not contribute to the integral (20), we can u... |

72 |
Achieving ‘massive MIMO’ spectral efficiency with a not-so-large number of antennas
- Huh, Caire, et al.
- 2012
(Show Context)
Citation Context ... matrix gives good results and, based on this observation, we propose a simplified user grouping algorithm when the number of antennas becomes very large (massive MIMO). Motivated by the work of [6], =-=[7]-=-, we focus on the regime where the number of users is proportional to the number of antennas, and propose a probabilistic scheduling algorithm, where users within each group are pre selected at random... |

66 |
Least squares quantization in PCM,” Information Theory
- Lloyd
- 1982
(Show Context)
Citation Context ...Clustering K-means Clustering is a standard iterative algorithm which aims at partitioning K observations into G clusters such that each observation belongs to the cluster with the nearest mean [16], =-=[17]-=-. This results in a partition of the observation space into Voronoi cells. In our problem, the K user covariance dominant eigenspaces, i.e., {U ∗k : k = 1, . . . ,K} form the observation space. Hence,... |

52 | Large system analysis of linear precoding in correlated MISO broadcast channels under limited feedback,”
- Wagner, Couillet, et al.
- 2012
(Show Context)
Citation Context ... ζ2g = NSg tr ( HHgBgB H gH g )−1 . In the limit of N → ∞, the terms SINRngk for all users in the same subgroup converge to the same deterministic quantity, that depends only on the subgroup index gk =-=[20]-=-, [6] SINRngk N→∞−→ SINRogk (56) As a result, the achievable normalized throughput fora subgroup k of group g is given by R̄gk = γgk log(1+SINR o gk), reducing the optimization problem (50) to maximiz... |

51 | Network MIMO with linear zeroforcing beamforming: Large system analysis, impact of channel estimation, and reduced-complexity scheduling
- Huh, Tulino, et al.
- 2012
(Show Context)
Citation Context ...sform matrix gives good results and, based on this observation, we propose a simplified user grouping algorithm when the number of antennas becomes very large (massive MIMO). Motivated by the work of =-=[6]-=-, [7], we focus on the regime where the number of users is proportional to the number of antennas, and propose a probabilistic scheduling algorithm, where users within each group are pre selected at r... |

41 | Bounds on packings of spheres in the Grassmann manifolds,”
- Barg, Nogin
- 2002
(Show Context)
Citation Context ...pically a subset of Cn. 15 In a similar fashion, we need to define a notion of the mean of (tall) unitary matrices. Given N unitary matrices {U ∗1,U ∗2, . . . ,U ∗N}, the mean Ū ∗ ∈ CM×p is given as =-=[18]-=- Ū ∗ = eig [ 1 N N∑ n=1 U ∗nU ∗H n ] , (29) where eig(X ) denotes the unitary matrix formed by the p dominant eigenvectors of X . At this point, we can formulate the K-means algorithm for the user ch... |

37 |
MIMO techniques in WiMAX and LTE: a feature overview
- Li, Li, et al.
- 2010
(Show Context)
Citation Context ...his max SINR). Hence, the achievability scheme has some practical interest since it is similar to the present “opportunistic beamforming” schemes with Channel Quality Indicator (CQI) (see for example =-=[11]-=-, [12]). A. Converse a) Case M > ∑G g=1 rg: Denoting the power allocated to a user k in group g as Pgk , lettingQg = diag(Pg1 , . . . , Pg(K′)) with trace Pg = ∑K′ k=1 Pgk , H g = [hg1 . . .hg(K′) ] a... |

25 |
Classification, Estimation and Pattern Recognition.
- Young, Calvert
- 1974
(Show Context)
Citation Context ...means Clustering K-means Clustering is a standard iterative algorithm which aims at partitioning K observations into G clusters such that each observation belongs to the cluster with the nearest mean =-=[16]-=-, [17]. This results in a partition of the observation space into Voronoi cells. In our problem, the K user covariance dominant eigenspaces, i.e., {U ∗k : k = 1, . . . ,K} form the observation space. ... |

24 | How much does transmit correlation affect the sum-rate scaling of MIMO Gaussian broadcast channels
- Al-naffouri, Sharif, et al.
- 2009
(Show Context)
Citation Context ...ing with user selection has been widely investigated for uncorrelated channels under random beamforming [1] and zero forcing beamforming [4], and also for correlated channels under random beamforming =-=[5]-=-. Our work differs from these earlier works in the sense that we consider different correlations for different groups, which is an extension of [5] for multiple correlated channels. We show that follo... |

19 | Multi-user diversity vs. accurate channel feedback for MIMO broadcast channels
- Ravindran, Jindal
- 2008
(Show Context)
Citation Context ...x SINR). Hence, the achievability scheme has some practical interest since it is similar to the present “opportunistic beamforming” schemes with Channel Quality Indicator (CQI) (see for example [11], =-=[12]-=-). A. Converse a) Case M > ∑G g=1 rg: Denoting the power allocated to a user k in group g as Pgk , lettingQg = diag(Pg1 , . . . , Pg(K′)) with trace Pg = ∑K′ k=1 Pgk , H g = [hg1 . . .hg(K′) ] and owi... |

19 |
Joint spatial division and multiplexing: Realizing massive MIMO gains with limited channel state information
- Nam, Ahn, et al.
- 2012
(Show Context)
Citation Context ...ve users by clustering them into groups such that users within a group have approximately similar channel covariances, while users across groups have near orthogonal covariances. JSDM was proposed in =-=[21]-=- and analyzed in the large system limit in [2] under the assumption that the user channel covariance matrices are grouped into sets with exact the same eigenspace. In this paper, we have significantly... |

12 |
Toeplitz forms and their application, Univ. of California Press,
- Grenander, Szego
- 1958
(Show Context)
Citation Context ...ct and approximate BD are given in [2]. Furthermore, when M is large, in the special case of uniform linear arrays, the channel covariance takes on a Toeplitz form. Owing to Szego’s asymptotic theory =-=[9]-=-, [2], the eigenvectors of the channel covariances can be well approximated by the columns of a Discrete Fourier Transform (DFT) matrix. In this special case, if users in different groups have disjoin... |

6 |
On the selection of semi-orthogonal users for zero-forcing beamforming
- Tomasoni, Caire, et al.
- 2009
(Show Context)
Citation Context ...to a quantization of the AoA/AS plane. This requires only the knowledge of the AoAs and ASs of the users, instead of the whole covariance matrix. As far as user selection is concerned, we notice from =-=[3]-=- that in the limit of N →∞ user selection schemes max SINR or SUS) become less and less effective 20 0 200 400 600 800 100020 25 30 35 40 45 Number of Users Su msra te FQ−AoA/AS FQ−DFT K−means (a) ZFB... |

2 |
Joint spatial division and multiplexing,” arXiv:1209.1402v1 [cs.IT
- Adhikary, Nam, et al.
- 2012
(Show Context)
Citation Context ...otice that with our assumptions it is possible that some user achieves the maximum on more than one beam, in which case the BS selects to send multiple streams to that user. Remark 2. It is proven in =-=[2]-=- that JSDM with PGP is optimal when the eigenvectors of the different groups satisfy the tall unitary condition. When this is true, i.e., choosing Bg = U g makes the inter-group interference term equa... |