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## The degrees of freedom region of two-user and certain three-user MIMO broadcast channel with delayed CSI

Venue: | IEEE Trans. Inf. Theory |

Citations: | 20 - 1 self |

### Citations

12231 |
Elements of Information Theory,
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...y region of the given delayed-CSIT MIMO BC by assuming that the ith user knows the channel outputs Yj(t), ∀ j > i, instantaneously, and also the messages Mj , ∀ j > i. Now, applying Fano’s inequality =-=[18]-=- at the ith user, we obtain Ri ≤ 1 n I ( Mi;Y [i:K](n),M[i+1:K], H(n) ) + n = 1 n I ( Mi;Y [i:K](n) ∣∣∣M[i+1:K], H(n))+ n (2) = 1 n h ( Y [i:K](n) ∣∣∣M[i+1:K], H(n))− h(Y [i:K](n)∣∣∣M[i:K], H(n))+ ... |

149 | broadcast channels with finite rate feedback,”
- Jindal
- 2006
(Show Context)
Citation Context ...sight about the DoF behavior under imperfect CSIT has thus been to seek higher DoF under quantized CSIT by improving CSIT quality through a sufficiently fast scaling of the quantization rate with SNR =-=[5]-=-–[8]. Another recent approach that is well-suited for channels, with high user mobility for example, in which the coherence time is relatively short compared to the delay incurred in channel estimatio... |

125 |
Completely stale transmitter channel state information is still very useful,”
- Maddah-Ali, Tse
- 2012
(Show Context)
Citation Context ...in which the coherence time is relatively short compared to the delay incurred in channel estimation and feedback, is that of DoF characterization under delayed CSIT proposed by Maddah-Ali and Tse in =-=[9]-=-. The authors of [9] prove a surprising and interesting result that even in an i.i.d. fading channel – in which predicting the current channel state based on past channel states would be meaningless –... |

66 | Isotropic fading vector broadcast channels: The scalar upper bound and loss in degrees of freedom
- Jafar, Goldsmith
- 2005
(Show Context)
Citation Context ...=1Ni}. On the other hand, without any CSIT whatsoever, and for a broad class of fading channel distributions, the DoF region collapses to what can be achieved just through time-division [2] (see also =-=[3]-=-, [4]), so that the sum DoF collapse to min{M,maxiNi}. Moreover, even for the practically realizable assumption of imperfect CSIT, assumed fixed relative to SNR, the maximum sum-DoF known to be achiev... |

55 |
On degrees of freedom region of MIMO networks without channel state information at transmitters
- Huang, Jafar, et al.
- 2012
(Show Context)
Citation Context .... On the other hand, without any CSIT whatsoever, and for a broad class of fading channel distributions, the DoF region collapses to what can be achieved just through time-division [2] (see also [3], =-=[4]-=-), so that the sum DoF collapse to min{M,maxiNi}. Moreover, even for the practically realizable assumption of imperfect CSIT, assumed fixed relative to SNR, the maximum sum-DoF known to be achievable ... |

49 | Aiming perfectly in the dark-blind interference alignment through staggered antenna switching
- Gou, Wang, et al.
- 2011
(Show Context)
Citation Context ...d and hence, by themselves, those results are inconclusive. Finally, we mention that the connection between the achievable schemes of [9] and blind interference alignment previously obtained in [16], =-=[17]-=- are explored in [13] which was also the first paper to provide examples of (retrospective) interference alignment schemes for some networks with distributed transmitters. The next section describes t... |

39 | The degrees of freedom region and interference alignment for the MIMO interference channel with delayed CSIT
- Vaze, Varanasi
(Show Context)
Citation Context ... arbitrary number of antennas at each of the four terminals under the delayed CSIT assumption results in a tight outer bound on the DoF region of that network and was recently found by the authors in =-=[11]-=-. Furthermore, the outer-bound for the K-user MIMO BC is shown to be tight for the two-user MIMO BC by specifying a DoF-regionoptimal achievability scheme based on interference alignment. Since there ... |

35 | The degrees of freedom regions of MIMO broadcast, interference, and cognitive radio channels with no CSIT
- Vaze, Varanasi
- 2012
(Show Context)
Citation Context ...gument follows from Theorem 1. Hence, we focus below on the achievability part. Consider first the case where M ≤ N . Here, the region Dd−CSIK=3 ( M,N,N,N ) with M ≤ N is achievable even without CSIT =-=[2]-=-, and hance, also with delayed CSIT. Thus, it is sufficient to deal with the case of N < M < 2N , which is the topic of the remainder of this section. We prove that the region Dd−CSIK=3 ( M,N,N,N ) is... |

35 | Limited feedback-based block diagonalization for the MIMO broadcast channel - Ravindran, Jindal - 2008 |

34 |
The feedback capacity of degraded broadcast channels
- Gamal
- 1978
(Show Context)
Citation Context ... an outer-bound to that of BCo. In BC1 the side-information available to the transmitter can be considered as being obtained via Shannon-sense feedback from each receiver. However, from the result of =-=[10]-=-, feedback can not enhance the capacity region of the physically degraded BC. Hence, the capacity region of BC1 remains unchanged even if the transmitter is unaware of {Yi(n), Hi(n)}Ki=1 ∀ n < t and ∀... |

29 | Interference alignment for the MIMO interference channel with delayed local CSIT,” Feb. 2011, available on arXiv :1102.5673v1 - Ghasemi, Motahari, et al. |

25 |
On the degrees of freedom of three-user MIMO broadcast channel with delayed CSIT
- Abdoli, Ghasemi, et al.
- 2011
(Show Context)
Citation Context ...ss of three-user MIMO BCs in which all three receivers have the same number of antennas and the transmitter has no more than twice the number of antennas at each receiver. For this class of MIMO BCs, =-=[12]-=- recently determined the sum-DoF with delayed CSIT. Leveraging the scheme of [12] and DoF region optimal scheme for the general two-user MIMO BC, we expand the sum-DoF result of [12] to establish the ... |

22 | Multiuser MIMO Downlink Made Practical: Achievable Rates with Simple Channel State Estimation and Feedback Schemes”. Submitted to - Caire, Jindal, et al. - 2007 |

22 | Exploiting channel correlations - simple interference alignment schemes with no CSIT
- Jafar
(Show Context)
Citation Context ...rovided and hence, by themselves, those results are inconclusive. Finally, we mention that the connection between the achievable schemes of [9] and blind interference alignment previously obtained in =-=[16]-=-, [17] are explored in [13] which was also the first paper to provide examples of (retrospective) interference alignment schemes for some networks with distributed transmitters. The next section descr... |

21 | The Generalized Degrees of Freedom Region of the MIMO Interference Channel and Its Achievability
- Karmakar, Varanasi
- 2012
(Show Context)
Citation Context ...t the region Dd−CSIouter is an outer-bound on the DoF region of the MIMO BC with Shannon feedback, where the transmitter knows the channel states and the channel outputs with a finite delay. See also =-=[19]-=-, where an outer-bound on the DoF region of the MIMO IC with Shannon feedback is obtained using the techniques that were developed for the MIMO IC with delayed CSIT in [11]. Remark 4 (Comparison of th... |

7 |
The capacity region of multiple-input multiple-output broadcast channels
- Weingarten, Steinberg, et al.
- 2006
(Show Context)
Citation Context ... of antennas at the receivers. Index Terms Broadcast channel, degrees of freedom, delayed CSIT, interference alignment, outer bound. I. INTRODUCTION THE capacity region of the MIMO BC was obtained in =-=[1]-=- under the assumption of perfect(and instantaneous) CSIT. Under this idealized assumption, the degrees of freedom (DoF) region – defined as the set of high SNR slopes of the rate-tuples in the capacit... |

5 |
CSI feedback scaling rate vs multiplexing gain tradeoff for DPC-based transmission
- Vaze, Varanasi
- 2010
(Show Context)
Citation Context ...t about the DoF behavior under imperfect CSIT has thus been to seek higher DoF under quantized CSIT by improving CSIT quality through a sufficiently fast scaling of the quantization rate with SNR [5]–=-=[8]-=-. Another recent approach that is well-suited for channels, with high user mobility for example, in which the coherence time is relatively short compared to the delay incurred in channel estimation an... |

4 |
the degrees of freedom of X channel with delayed CSIT
- “On
- 2011
(Show Context)
Citation Context ... DoF region of the 2-user MIMO IC in [11], there are several recent works that provide interference alignment schemes for networks with distributed transmitters under the delayed CSIT assumption [13]–=-=[15]-=-. However, no tight outer bounds are provided and hence, by themselves, those results are inconclusive. Finally, we mention that the connection between the achievable schemes of [9] and blind interfer... |

3 |
Retrospective interference alignment,” Sep. 2010, Available: http://arxiv.org/PS cache/arxiv/pdf/1009/1009.3593v1.pdf
- Maleki, Jafar, et al.
(Show Context)
Citation Context ...plete DoF region of the 2-user MIMO IC in [11], there are several recent works that provide interference alignment schemes for networks with distributed transmitters under the delayed CSIT assumption =-=[13]-=-–[15]. However, no tight outer bounds are provided and hence, by themselves, those results are inconclusive. Finally, we mention that the connection between the achievable schemes of [9] and blind int... |