## A comparison of time-sharing, DPC, and beamforming for MIMO broadcast channels with many users (2007)

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Venue: | IEEE Trans. Commun |

Citations: | 33 - 0 self |

### BibTeX

@ARTICLE{Sharif07acomparison,

author = {Masoud Sharif and Babak Hassibi},

title = {A comparison of time-sharing, DPC, and beamforming for MIMO broadcast channels with many users},

journal = {IEEE Trans. Commun},

year = {2007},

volume = {55},

pages = {11--15}

}

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### Abstract

In this paper, we derive the scaling laws of the sum rate for fading MIMO Gaussian broadcast channels using time-sharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Throughout the paper, we assume a fix av-erage transmit power and consider a block fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like M log log nN for DPC and beamforming when M is fixed and for any N (either growing to in-finity or not). On the other hand, when both M and N are fixed, the sum rate of time-sharing to the strongest user scales like min(M, N) log log n. Therefore, the asymptotic gain of DPC over time-sharing for the sum rate is M min(M,N) when M and N are fixed. It is also shown that if M grows as log n, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum rate capacity of time-sharing scales like N log log n.

### Citations

1904 | Capacity of multi-antenna Gaussian channels
- Telatar
- 1999
(Show Context)
Citation Context ... to increase the capacity of a point-to-point communication link linearly with min(M, N) for large signal to noise ratios, where M and N are the number of transmit and receiver antennas, respectively =-=[1]-=-. Recently, there has been a large amount of interest in the area of MIMO multiuser systems, more specifically, the capacity of MIMO Gaussian broadcast channels [2]. An example of a multiuser system i... |

373 | Broadcast channels
- Cover
- 1972
(Show Context)
Citation Context ...which resembles the down-link communication in cellular systems. It is known that the single antenna broadcast channel is degraded so its capacity region is known and achieved by superposition coding =-=[3, 4]-=-. Furthermore, if the users are homogeneous and the transmitter has full channel state information (CSI), using time division multiplexing and transmitting to the best user maximizes the sum rate capa... |

337 |
On the achievable throughput of a multiantenna Gaussian broadcast channel
- Caire, Shamai
- 2003
(Show Context)
Citation Context ...ng to the best user maximizes the sum rate capacity (we call this scheduling time-sharing). However, if the transmitter and the receivers have full CSI, the MIMO broadcast channel is not degraded. In =-=[6, 7, 8, 9]-=-, it is proved that the sum rate capacity with full CSI in both the transmitter and all the receivers is achieved by using dirty paper coding (DPC). In [5], it is further shown that the capacity regio... |

292 |
Eigenvalues and condition numbers of random matrices
- Edelman
- 1988
(Show Context)
Citation Context ... � E N log 1 + P ′ max λmin(H N 2 iH 1≤i≤n ′ �� � � ∗ i ) ≤ E{Rts} ≤ E max N log 1 + i=1,...,n P N max 1≤j≤M hi∗ j h i �� j . (7) It is worth noting that h i∗ j h i j’s have χ 2 (2N) distribution. In =-=[19]-=-, it is shown that Nλmin(H ′ iH ′ ∗ i ) is exponentially distributed ([19], Theorem 5.5, p.62). Therefore, using the results in extreme value theory (see Appendix A of [17] and [20]), it can be shown ... |

232 | Capacity limits of MIMO channel
- Goldsmith, Jafar, et al.
- 2003
(Show Context)
Citation Context ...and receiver antennas, respectively [1]. Recently, there has been a large amount of interest in the area of MIMO multiuser systems, more specifically, the capacity of MIMO Gaussian broadcast channels =-=[2]-=-. An example of a multiuser system is the broadcast channel which resembles the down-link communication in cellular systems. It is known that the single antenna broadcast channel is degraded so its ca... |

199 | Sum capacity of Gaussian vector broadcast channels
- Yu, Cioffi
- 2004
(Show Context)
Citation Context ...ng to the best user maximizes the sum rate capacity (we call this scheduling time-sharing). However, if the transmitter and the receivers have full CSI, the MIMO broadcast channel is not degraded. In =-=[6, 7, 8, 9]-=-, it is proved that the sum rate capacity with full CSI in both the transmitter and all the receivers is achieved by using dirty paper coding (DPC). In [5], it is further shown that the capacity regio... |

186 | Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality
- Viswanath, Tse
- 1912
(Show Context)
Citation Context ...ng to the best user maximizes the sum rate capacity (we call this scheduling time-sharing). However, if the transmitter and the receivers have full CSI, the MIMO broadcast channel is not degraded. In =-=[6, 7, 8, 9]-=-, it is proved that the sum rate capacity with full CSI in both the transmitter and all the receivers is achieved by using dirty paper coding (DPC). In [5], it is further shown that the capacity regio... |

161 |
The capacity region of the Gaussian MIMO broadcast channel
- Weingarten, Steinberg, et al.
- 2004
(Show Context)
Citation Context ...oadcast channel is not degraded. In [6, 7, 8, 9], it is proved that the sum rate capacity with full CSI in both the transmitter and all the receivers is achieved by using dirty paper coding (DPC). In =-=[5]-=-, it is further shown that the capacity region is in fact achieved by DPC. On the other hand, traditionally beamforming has been used for the down-link scheduling in MIMO broadcast systems as a heuris... |

138 | Capacity and optimal resource allocation for fading broadcast channels: Part I: Ergodic capacity
- Li, Goldsmith
- 2001
(Show Context)
Citation Context ...d to be fixed throughout the paper. We further assume that the base station is subject to short term power constraint, i.e., the base station should satisfy the power constraint for each fading state =-=[10]-=-. 3sThroughout the paper, we use f(n) = O(g(n)) to denote that limn→∞ | f(n) | ≤ α where α is a g(n) positive constant independent of n. Similarly, f(n) = o(g(n)) denotes that the limit of the ratio o... |

106 | Multi-antenna channel-hardening and its implications for rate feedback and scheduling - Hochwald, Marzetta, et al. |

36 | Optimality of zero-forcing beamforming with multiuser diversity
- Yoo, Goldsmith
- 2005
(Show Context)
Citation Context ...g (that maximizes the sum-rate), we can use a random beamforming scheme as in [17], in which φm’s are random orthonormal vectors, to find a lower bound for the throughput of the beamforming (see also =-=[18]-=-). It is shown in [17], that under average transmit power of M (P = M), the sum rate of random beamforming scales like M log log n and M log(1+c) as M is fixed or logarithmically increases with n, res... |

30 |
Dirty paper coding vs. TDMA for MIMO broadcast channel
- Jindal, Goldsmith
- 2004
(Show Context)
Citation Context ...ach receiver is equipped with N antennas. Previously, in [14, 12], asymptotic results for the sum rate of DPC and beamforming have been derived when n and M have the same growth rate. Furthermore, in =-=[16]-=-, the asymptotic behavior of the throughput for DPC and time-sharing are obtained for large signal to noise ratios and large M when the other parameters of the system are fixed. However, motivated by ... |

17 |
achievable rates and sum rate capacity of Gaussian MIMO broadcast channels
- Vishwanath, Jindal, et al.
- 2003
(Show Context)
Citation Context |

16 | The incomplete gamma functions since Tricomi. In Tricomi’s ideas and contemporary applied mathematics (Rome/Turin
- Gautschi
- 1997
(Show Context)
Citation Context ...(A.2) It is worth noting that both arguments of the incomplete Gamma function in Eq. (A.2) are going to infinity. The asymptotic expansion of the incomplete Gamma function has been studied by Tricomi =-=[22, 23]-=- and it is shown that Γ(M, x) = e−xxM � � 2 M − 1 2(M − 1) (M − 1) 1 − + + O x − M + 1 (x − M + 1) 2 (x − M + 1) 3 (x − M + 1) 4 �� (A.3) as the modulus of √ M/(x − M) tends to zero. We can also write... |

9 |
Asymptotics of sum rate for dirty paper coding and beamforming in multiple-antenna broadcast channels
- Viswanathan, Venkatesan
- 1998
(Show Context)
Citation Context ...PC. On the other hand, traditionally beamforming has been used for the down-link scheduling in MIMO broadcast systems as a heuristic method to reduce the interference in the system. As pointed out in =-=[11, 12, 13]-=-, even though the sum rate capacity of MIMO BC using DPC can be stated as a convex problem using duality, the sum rate (or throughput) achieved by optimal beamforming cannot be written as a convex opt... |

8 |
Asymptotische Eigenschaften der unvollstaändigen Gammafunktion, Mathematische Zeitschrift 53
- Tricomi
- 1950
(Show Context)
Citation Context ...(A.2) It is worth noting that both arguments of the incomplete Gamma function in Eq. (A.2) are going to infinity. The asymptotic expansion of the incomplete Gamma function has been studied by Tricomi =-=[22, 23]-=- and it is shown that Γ(M, x) = e−xxM � � 2 M − 1 2(M − 1) (M − 1) 1 − + + O x − M + 1 (x − M + 1) 2 (x − M + 1) 3 (x − M + 1) 4 �� (A.3) as the modulus of √ M/(x − M) tends to zero. We can also write... |

5 |
coding theorem for broadcast channel with degraded components
- Bergman
- 1973
(Show Context)
Citation Context ...which resembles the down-link communication in cellular systems. It is known that the single antenna broadcast channel is degraded so its capacity region is known and achieved by superposition coding =-=[3, 4]-=-. Furthermore, if the users are homogeneous and the transmitter has full channel state information (CSI), using time division multiplexing and transmitting to the best user maximizes the sum rate capa... |

5 |
Extreme value theory under weak mixing conditions,” Studies in Probability Theory, MAA studies in Mathematics
- Leadbetter
- 1978
(Show Context)
Citation Context ...) distribution. In [19], it is shown that Nλmin(H ′ iH ′ ∗ i ) is exponentially distributed ([19], Theorem 5.5, p.62). Therefore, using the results in extreme value theory (see Appendix A of [17] and =-=[20]-=-), it can be shown that, � Pr log nM + (N − 2) log log nM + O(log log log n) ≤ max 1≤i≤nM,1≤j≤M hi∗ j h i j � ≤ log nM + N log log nM + O(log log log n) = 1 − O where h i∗ j h i j for i = 1, . . . , n... |

3 |
Sum power waterfilling for Gaussian broadcast channels
- Jindal, Jafar, et al.
- 2002
(Show Context)
Citation Context ...PC. On the other hand, traditionally beamforming has been used for the down-link scheduling in MIMO broadcast systems as a heuristic method to reduce the interference in the system. As pointed out in =-=[11, 12, 13]-=-, even though the sum rate capacity of MIMO BC using DPC can be stated as a convex problem using duality, the sum rate (or throughput) achieved by optimal beamforming cannot be written as a convex opt... |

3 |
Space time multiple access: Linear growth in the sum rate,” presented at the 40th Annu. Allerton Conf
- Hochwald, Viswanath
- 2002
(Show Context)
Citation Context ...ty of Gaussian MIMO broadcast channels with many users n using time-sharing, DPC, and beamforming and when the transmitter has M antennas and each receiver is equipped with N antennas. Previously, in =-=[14, 12]-=-, asymptotic results for the sum rate of DPC and beamforming have been derived when n and M have the same growth rate. Furthermore, in [16], the asymptotic behavior of the throughput for DPC and time-... |

2 |
Downlink capcity evaluation of cellular networks with known interference cancellation
- Vishwanathan, Venkatesan, et al.
- 2003
(Show Context)
Citation Context ...PC. On the other hand, traditionally beamforming has been used for the down-link scheduling in MIMO broadcast systems as a heuristic method to reduce the interference in the system. As pointed out in =-=[11, 12, 13]-=-, even though the sum rate capacity of MIMO BC using DPC can be stated as a convex problem using duality, the sum rate (or throughput) achieved by optimal beamforming cannot be written as a convex opt... |

1 |
Some results on the sum rate capacity of MIMO fading broadcast channel
- Xie, Georghiades
- 2002
(Show Context)
Citation Context ...0) and having M ≤ 5 which is about log n, we consider a different region in which n is large and M is either fixed 2sor growing to infinity with much less pace, i.e., logarithmically with n (see also =-=[15]-=-). This work also generalizes a result in [17] where the scaling laws of the sum rate of DPC is derived for the case where M is fixed and N = 1. Furthermore, we use the sum rate of the random beamform... |

1 |
On the capacity of MIMO BC channel with partial side information
- Sharif, Hassibi
- 2005
(Show Context)
Citation Context ...onsider a different region in which n is large and M is either fixed 2sor growing to infinity with much less pace, i.e., logarithmically with n (see also [15]). This work also generalizes a result in =-=[17]-=- where the scaling laws of the sum rate of DPC is derived for the case where M is fixed and N = 1. Furthermore, we use the sum rate of the random beamforming proposed in [17] as a lower bound for the ... |