## Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks (2007)

Citations: | 154 - 15 self |

### BibTeX

@MISC{Özgür07hierarchicalcooperation,

author = {Ayfer Özgür and Olivier Lévêque and David Tse},

title = { Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks},

year = {2007}

}

### OpenURL

### Abstract

n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power loss of r −α as well as a random phase. We identify the scaling laws of the information theoretic capacity of the network. In the case of dense networks, where the area is fixed and the density of nodes increasing, we show that the total capacity of the network scales linearly with n. This improves on the best known achievability result of n 2/3 of [1]. In the case of extended networks, where the density of nodes is fixed and the area increasing linearly with n, we show that this capacity scales as n 2−α/2 for 2 ≤ α < 3 and n for α ≥ 3. The best known earlier result [2] identified the scaling law for α> 4. Thus, much better scaling than multihop can be achieved in dense networks, as well as in extended networks with low attenuation. The performance gain is achieved by intelligent node cooperation and distributed MIMO communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation.

### Citations

8563 | Elements of Information Theory - Cover, Thomas - 1991 |

4675 | Matrix Analysis - HORN, JOHNSON - 1990 |

2219 | Capacity of wireless networks
- Gupta, Kumar
(Show Context)
Citation Context ...s—Ad hoc wireless networks, capacity scaling, digital communications, distributed multiple-input multiple-output (MIMO), hierarchical cooperation. I. INTRODUCTION THE seminal paper by Gupta and Kumar =-=[3]-=- initiated the study of scaling laws in large ad hoc wireless networks. Their by-now-familiar model considers nodes randomly located in the unit disk, each of which wants to communicate to a random de... |

1832 | Capacity of multi-antenna Gaussian channels
- Telatar
- 1995
(Show Context)
Citation Context ...that can be jointly decoded at the receive cluster and spatial multiplexing gain can be realized. In fact, if all the nodes in the network could cooperate for free, then a classical MIMO result [11], =-=[12]-=- says that a sum-rate scaling proportional to could be achieved. However, this may be overoptimistic: communication between nodes is required to set up the cooperation and this may drastically reduce ... |

1476 | Information Theory and Reliable Communication - Gallager - 1968 |

944 |
Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ... ones that can be jointly decoded at the receive cluster and spatial multiplexing gain can be realized. In fact, if all the nodes in the network could cooperate for free, then a classical MIMO result =-=[11]-=-, [12] says that a sum-rate scaling proportional to could be achieved. However, this may be overoptimistic: communication between nodes is required to set up the cooperation and this may drastically r... |

840 |
Enumerative Combinatorics
- Stanley
- 1999
(Show Context)
Citation Context ...ts the five possible trees with branches where we relabel the resultant vertices as . In general, the number of different planar, rooted, planted trees with branches is given by the th Catalan number =-=[22]-=-. In each of these trees, the vertices take values in either or . Hence, each tree corresponds to a group of nonzero terms (24) Note that if a nonvanishing term in (18) corresponds to a graph with les... |

667 | Fundamentals of Wireless Communication - Tse, Viswanath - 2005 |

655 |
El Gamal, “Capacity theorems for the relay channel
- Cover, A
- 1979
(Show Context)
Citation Context ...e bits to the final destination, but the quantized bits are correlated across the receive nodes and hence a reduction in the overhead can be achieved by doing some Slepian–Wolf coding (as proposed in =-=[15]-=-). Such work is beyond the scope of the present paper. We studied two different scaling laws in this paper, one for dense and one for extended networks. Given a network with a specific number of nodes... |

391 | Cooperative strategies and capacity theorems for relay networks - Kramer, Gastpar, et al. - 2005 |

267 | A network information theory for wireless communications: scaling laws and optimal operation
- Xie, Kumar
- 2004
(Show Context)
Citation Context ... can do better using more sophisticated physical-layer processing. More generally, what is the information-theoretic scaling law of ad hoc networks? This question was first addressed by Xie and Kumar =-=[5]-=-. They showed that whenever the power path loss exponent of the environment is greater than (i.e., the received power decays faster than with the distance from the transmitter), then the nearest neigh... |

127 | Closing the gap in the capacity of wireless networks via percolation theory - Franceschetti, Dousse, et al. - 2007 |

83 |
Upper bounds to transport capacity of wireless networks
- Jovicic, Viswanath, et al.
- 2004
(Show Context)
Citation Context ...howed that the same conclusion holds if the power path loss is exponential in the distance , a channel model proposed recently by Franceschetti et al. [6]. The work [5] was followed by several others =-=[7]-=-–[10], [2]. Successively, they improved the threshold on the path-loss exponent for which multihop is order-optimal ( in [7], in [10], and in [2]). However, the question is open for the important rang... |

59 | The transport capacity of wireless networks over fading channels - Xue, Xie, et al. - 2005 |

54 | Bounds on capacity and minimum energy-per-bit for AWGN relay channels
- Gamal, Mohseni, et al.
- 2006
(Show Context)
Citation Context ...ets the given average power constraint of , and achieves an aggregate throughput of bits/second. (The idea of using burstiness in improving the low-SNR performance of relay networks was introduced in =-=[14]-=- in the context of single-relay networks.) Note that the quantity can be interpreted as the total power transferred between a size transmit cluster and a size receive cluster, node pairs in all, with ... |

46 | On the path-loss attenuation regime for positive cost and linear scaling of transport capacity in wireless networks
- Xie, Kumar
- 2006
(Show Context)
Citation Context ... the same conclusion holds if the power path loss is exponential in the distance , a channel model proposed recently by Franceschetti et al. [6]. The work [5] was followed by several others [7]–[10], =-=[2]-=-. Successively, they improved the threshold on the path-loss exponent for which multihop is order-optimal ( in [7], in [10], and in [2]). However, the question is open for the important range of betwe... |

44 | Information-theoretic upper bounds on the capacity of large extended ad hoc wireless networks - Lévêque, Telatar - 2005 |

43 | theoretic upper bounds on the capacity of large, extended ad-hoc wireless networks - Leveque, Telatar, et al. - 2005 |

43 | On the throughput capacity of random wireless networks,” 2004, subm. for publ - Franceschetti, Dousse, et al. |

37 | Wireless ad hoc networks: Strategies and scaling laws for the fixed SNR regime
- Aeron, Saligrama
- 2007
(Show Context)
Citation Context ...icle to focus exclusively on the issue of interference. Can the interference limitation implied by the Gupta–Kumar result be overcome by more sophisticated physical-layer processing? In a recent work =-=[1]-=-, Aeron and Saligrama have showed that the answer is indeed yes: they exhibited a scheme which yields a throughput scaling of bits per second. However, it is not clear if one can do even better. The f... |

29 | Outer bounds to the capacity region of wireless networks
- Ahmad, Jovicic, et al.
- 2006
(Show Context)
Citation Context ...d that the same conclusion holds if the power path loss is exponential in the distance , a channel model proposed recently by Franceschetti et al. [6]. The work [5] was followed by several others [7]–=-=[10]-=-, [2]. Successively, they improved the threshold on the path-loss exponent for which multihop is order-optimal ( in [7], in [10], and in [2]). However, the question is open for the important range of ... |

27 | A random walk model of wave propagation - Franceschetti, Bruck, et al. - 2004 |

18 | Scaling laws for one and twodimensional random wireless networks in the low attenuation regime - Özgür, Lévêque, et al. |

14 | Degrees of freedom in some underspread MIMO fading channels - Etkin, Tse - 2006 |

7 |
Scaling Laws for One-and Two-Dimensional Random Wireless Networks in the Low-Attenuation Regime
- ÖzgÜr, LÉvÊque, et al.
- 2007
(Show Context)
Citation Context ...ed in the current paper. But the interest in an upper bound on transport capacity lies in the fact that it applies to more general communication scenarios. Reciprocally, it has been shown recently in =-=[16]-=- that for a network with a random placement of nodes, there is a natural way to deduce an upper bound on transport capacity from an upper bound on throughput, by studying cut-set bounds over multiple ... |