able transmission powers. This dependency can be compli- cated and nonlinear because the interference can adapt to the current power alloca- tion. Therefore, instead of developing a model for each particular system layout, we can focus on some core properties, summarized by the following framework of axioms. © 2009 by Taylor & Francis Group, LLC Cooperative Transmission Schemes Definition 7.1 We say that I : P R is an interference function if the following axioms are fulfilled: A1 (non-negativity) I(p) 0 A2 (scale invariance) I(ap)=al(p) = Aa R++ A3 (monotonicity) if pp' This definition differs slightly from Yates's original definition [55]. The difference is that the model [18] was developed for a particular power control problem, whereas the preceding model can be used in a more flexible and versatile way. We use the term "interference" in a very broad sense that is not limited to physical interference power [51]. This will become clear with following examples. Example 7.1 In power control theory (e.g., references [49] and [59]), it is customary to model the interference coupling between users by a Kx K link gain matrix (7.2) The vector Vk ERK contains the interference coupling coefficients of the kth user. Introducing an extended power vector p = [p, (7.3) where o2 is the noise variance and the interference plus noise experi- enced by this user is (7.4) Example 7.2 Consider K users with signal-to-interference ratios STRAP) (7.5) where I, IK are arbitrary interference functions. A vector (7.6) is said to be feasible if and only if [52] (7.7) © 2009 by Taylor & Francis Group, LLC Long Term Evolution: 3GPP LTE Radio and Cellular Technology Here, C(y) is a single measure for the joint performance of the K-user channel. The function C(y) is an interference function. The properties A1-A3 of the underlying interference functions I., I are preserved by the min-max optimization. These two examples show that the theory of interference functions can be exploited in quite different ways and is not limited to power allocat