interference calculus a general framework for interference management and network utility optimization

[...]... later (Theorem 3.23) that all concave interference functions have a structure that enables ecient algorithmic solutions Examples are the interference balancing algorithms from Chapters 5 and 6 1.4.3 Receive Strategies The next example shows that the interference functions (1.14) and (1.16) can be understood within a more general and abstract framework of receive strategies adaptive 1.4 Examples  Interference. .. The theory was further analyzed and extended in [11, 34, 74, 75] It will be shown in Section 2.4 that the axiomatic framework A1 , A2 , A3 with additional strict monotonicity provides an equivalent way of modeling standard interference functions Hence, standard interference functions can be regarded as a special case, and most results derived in this book immediately transfer to standard interference. .. 1.2 Basic Axiomatic Framework of Interference Functions Axiomatic characterizations have a long-standing tradition in science Wellknown examples include the axiomatic bargaining theory introduced by Nash [16, 17] (see also [18, 19]) and the axiomatic characterization of the Shannon entropy by Khinchin [20] and Faddeev [21] (see also [22]) Analyzing the basic building blocks of a theoretical model often... optimization of multi-user communication systems [24] Many examples can be found, for example, in the context of multi-user MIMO and robust optimization [2530] 1.3.1 Convex and Concave Interference Functions Standard convex optimization strategies are applicable to any kind of convex problem However, standard approaches typically ignore the particular analytical structure of the problem at hand Thus,... if r ≥ r The framework A1 , A2 , A3 is related to the concept of standard interference functions introduced by Yates [1], where scalability was required instead of scale invariance Scalability was motivated by a specic power control probA1 A2 lem It will be shown in Section 2.4 that standard interference functions can be comprehended within the framework A1 , A2 , A3 Concrete examples of interference. .. framework A1 , A2 , A3 In this section we discuss how noise can be included in the axiomatic framework This is closely connected with the concept of functions The results apppeared in [11] standard interference 2.4.1 Standard Interference Functions Yates [1] introduced an axiomatic framework of tions standard interference func- Denition 2.11 A function J : RKu → R++ is said to be a + standard inter-... users in an orthogonal manner, and residual interference is treated as noise Then the system becomes a collection of quasi-independent communication links This practical approach greatly simplies the analysis of multi-user systems However, assigning each user a separate resource is not always an ecient way of organizing the system If the number of users is high, then each user only gets a small fraction... most general case where the interference functions are only characterized by the axioms A1 , A2 , A3 (see p 4 in Section 1.2) The overall performance of the system is typically a function of all interference values, which depend on the same underlying resource vector r Specic examples were already discussed in Section 1.4 The analysis and optimization of such a system is complicated by the fact that the... resource allocation strategies depends on the interference coupling This book proposes an abstract theory for the analysis and optimization of interference- coupled multi-user systems At the core of this theory lies the concept of an interference function, which is dened by a framework of axioms (positivity, scale-invariance, monotonicity), as introduced in Section 1.2 This axiomatic approach has the advantage... the advantage of being quite general It is applicable to various kinds of interference- coupled systems The proposed axiomatic framework was strongly inuenced and motivated by power control theory It generalizes some known concepts and results For example, linear interference functions are included as special cases It will be shown later that certain key properties of a system with linear interference . Boche Interference Calculus A General Framework for Interference Management and Network Utility Optimization ABC Series Editors: Wolfgang Utschick TU Munich Associate Institute for Signal Processing Arcisstrasse. concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Dupli- cation of. does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Scientific Publishing