ion problems. The advantage of the axiomatic approach is its generality. It provides a simple framework for optimizing interference-coupled multiuser systems. Such simpli- fied modeling helps one to study the system in an analytical way. Analyzing the core properties of a system facilitates a rigorous framework, which is of theoretical value, but it also provides useful guidelines for the development of algorithms. Some examples will be discussed in the next section. 7.2.2.2 Resource Allocation Algorithms for Interference-Coupled Multiuser Systems In the previous section we discussed interference models. Now it will be shown how these models can be used for the optimization of interference-coupled networks. Unlike single-user systems, the optimization of coupled multiuser systems typi- cally involves a trade-off between the users' performances. Increasing one user's performance comes at the cost of other users. Increasing performance often means increasing interference to other users or occupying shared resources. Therefore, there is no such thing as "the" optimal strategy. The systems performance is char- acterized by a region, the so-called feasible set, which is the set of all possible user performances. This is illustrated in Figure 7.7. Total power minimum QoS link 2 max mink QoSk (max-min fairness) max k akQoSk (weighted sum optimization) max QoSk (best overall efficiency) QoS feasible region QoS link 1 Figure 7.7 Schematic illustration of some resource allocation problems. © 2009 by Taylor & Francis Group, LLC Cooperative Transmission Schemes Assume that the actual performance measure (the quality of service [QoS]) is a continuous, strictly monotonic function of the signal-to-interference ratio (SIR)-that is, 1<k<K. (7.8) Some examples are BER: 0(x) = Q(Vx); MMSE: (x) = 1/(1 x); BER-slope for a-fold diversity: (x) = x-;; or capacity: 0(x) = log(1+x). Let s be the inverse function of o; then Y,=Y(Q), ISkSK, (7.9) is the minimum SIR level needed by the kth user to satisfy the QoS target Qk. Thus, the problem