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and system stability are important considerations. In this case, the cross-layer optimization has to be adaptive with respect to both the channel state H(t) and the queue status Q(t). The system objective functions can be chosen according to the following concerns: 1. System Stability. When the buffer size of the system is limited, system stability is an important concern where the scheduling objectives have to be properly chosen in order to ensure that all the queues in the system do not blow up. This point will be elaborated in Section 11.4. 2. Delay Minimization. In some applications where delay of data users is important, the scheduling objective may focus on the overall average delay rather than the average throughput. For example, one possible objective function that minimizes the overall network delay is given by U(Q1, . . . , QK) = SkQk. In any case, the cross-layer scheduling optimization can be decoupled from the detail implementations of the multiuser physical layers. Speci cally, the multiuser physical layer and the scheduling algorithm in the MAC layer interface through the feasible capacity region C. The scheduling problem formulation will be the same irrespective of the speci c multiuser physical layer because different physical layers will present a different feasible region C to the scheduler. This chapter is organized as follows. In Section 11.2, we review a number of commonly used physical layer models in the cross-layer design. In Section 11.3, we elaborate on the motivation behind the cross-layer scheduling taking into account of both the physical channel state and the queue status. In Section 11.4, we focus on the concept of stability region and the corresponding scheduling design to achieve stability. In Section 11.5, we discuss another cross-layer optimization design with respect to delay minimization for homogeneous users. Finally, we conclude with a brief summary in Section 11.6.
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Different models were proposed to model the performance of the multiuser physical layer. In this section, we elaborate on three important models: the graph model, the on/off channel model, and the information-theoretic model. The choice of modeling depends on the tradeoff between simplicity and accuracy in the particular problem. Before we discuss these different physical layer models, we need to introduce a generic model of the multiuser physical layer the feasible region of the physical layer. This is illustrated in Figure 11.2. Suppose that a system has K users and user i transmits at data rate ri; then the transmission data rates of the K users can be represented by the rate tuple r = (r1, . . . , rK). A rate tuple r is called feasible if the physical layer can deliver
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Figure 11.2. Generic feasible region of multiuser physical layer.
the data rates reliably2 to the K users, respectively. The set of all feasible rate tuples r is called the feasible region of the physical layer. In this way, we decouple the cross-layer optimization problem (to be described in later sections) from the details of the multiuser physical layer designs. This is because different implementations and designs of the multiuser physical layer are all characterized by a generic feasible region and the MAC layer simply optimizes the scheduling objective with respect to the feasible region given by the underlying physical layer. 11.2.1 Graph Model
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In the graph model, the wireless link is assumed to be static and offers a constant capacity. However, there is a mutual relationship between the links as a result of mutual interference. The interference is usually modeled as a path gain matrix [64,148]. While the graph model is an over simpli ed physical layer model because it fails to capture the time-varying dynamics of wireless channels, it serves as a good rst-order approximation to de ne a multiuser physical layer s feasible capacity region based on the mutual interference relationship between wireless links. For example, the graph model is applicable to model the interference from users in the cochannel cells. It can also be used to model the multiuser interference within a single-cell scenario with power control in the base station such as CDMA systems with nonorthogonal user code.
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The term reliable transmission is a generic concept that can imply different physical meanings depending on the speci c physical layer model.
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