The Degrees of Freedom of Wireless Networks Via Cut-Set Integrals

被引:20
作者
Franceschetti, Massimo [1 ]
Migliore, Marco Donald [2 ]
Minero, Paolo [3 ]
Schettino, Fulvio [2 ]
机构
[1] Univ Calif San Diego, Dept Elect & Comp Engn, Calif Inst Telecommun & Informat Technol CALIT2, Adv Network Sci Grp ANS, San Diego, CA 92093 USA
[2] Univ Cassino, DAEIMI, Microwave Lab, I-03043 Cassino, FR, Italy
[3] Univ Notre Dame, Dept Elect Engn, Notre Dame, IN 46556 USA
基金
美国国家科学基金会;
关键词
Capacity; degrees of freedom (d.o.f.); interference; scaling laws; wireless networks; AD-HOC NETWORKS; HIERARCHICAL COOPERATION; INTERFERENCE ALIGNMENT; CAPACITY; NUMBER;
D O I
10.1109/TIT.2011.2120150
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The problem of determining the number of spatial degrees of freedom (d.o.f.) of the signals carrying information in a wireless network is reduced to the computation of the geometric variation of the environment with respect to the cut through which the information must flow. Physically, this has an appealing interpretation in terms of the diversity induced on the cut by the possible richness of the scattering environment. Mathematically, this variation is expressed as an integral along the cut, which we call cut-set integral, and whose scaling order is evaluated exactly in the case of planar networks embedded in arbitrary three-dimensional (3-D) environments. Presented results shed some new light on the problem of computing the capacity of wireless networks, showing a fundamental limitation imposed by the size of the cut through which the information must flow. In an attempt to remove what may appear as apparent inconsistencies with previous literature, we also discuss how our upper bounds relate to corresponding lower bounds obtained using the techniques of multihop, hierarchical cooperation, and interference alignment.
引用
收藏
页码:3067 / 3079
页数:13
相关论文
共 34 条
[1]  
Abramowitz M., 1972, Handbook on Mathematical Functions with Formulas, Graphs, and Mathematical Tables
[2]   Wireless ad hoc networks:: Strategies and scaling laws for the fixed SNR regime [J].
Aeron, Shuchin ;
Saligrama, Venkatesh .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (06) :2044-2059
[3]  
[Anonymous], 2010, Lecture notes on network information theory
[4]  
AVESTIMEHR S, IEEE T INF THEORY
[5]   ON THE DEGREES OF FREEDOM OF SCATTERED FIELDS [J].
BUCCI, OM ;
FRANCESCHETTI, G .
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 1989, 37 (07) :918-929
[6]   ON THE SPATIAL BANDWIDTH OF SCATTERED FIELDS [J].
BUCCI, OM ;
FRANCESCHETTI, G .
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 1987, 35 (12) :1445-1455
[7]   Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples [J].
Bucci, OM ;
Gennarelli, C ;
Savarese, C .
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 1998, 46 (03) :351-359
[8]  
CACCIOPPOLI R, 1927, REND ACC NAZ LINCEI, V6, P142
[9]   Interference alignment and degrees of freedom of the K-user interference channel [J].
Cadambe, Viveck R. ;
Jafar, Syed Ali .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (08) :3425-3441
[10]  
FRANCESCHETTI M, 2009, P 2009 INT C EL ADV