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users. For instance, it may be bene cial to give different priorities to users according to their instantaneous CSI. Hence, not only is the physical layer adaptive (with varying throughput) but the multiaccess layer can also be adaptive to exploit the multiuser diversity. This refers to cross-layer optimization. On the other hand, we have shown in previous chapters that the number of independent spatial channels in a MIMO link is given by m* = min[nT, nR]. Hence, no spatial multiplexing gain can be expected when the mobile receiver has a single antenna only. However, the situation is different in multiuser systems. For instance, when there are multiple antennas at the base stations, the capacity of the multiuser systems can be increased substantially (even if the mobile users have single antenna only) by exploiting the distributed nT K con guration formed by the base station and K single-antenna mobile stations as illustrated in Figure 6.1. One can imagine that the virtual receiver has K receive antennas, but the processing is distributed over the K users. In this chapter, we focus on the cross-layer design of multiuser systems with a multiantenna base station, exploiting both the multiuser diversity and distributed spatial multiplexing. Cross-optimization between the link layer and the MAC layer has been generally ignored in the traditional MAC layer design because of the enormous complexity involved. Some investigators have tried to take advantage of the optimization gap by cooperative scheduling, which factors the link-level metrics into scheduling decisions [16,60]. For example, the scheduling ef ciency is shown to be greatly enhanced in a single-input single-output (SISO) system with a variable-throughput adaptive physical layer [84] by a jointly adaptive approach in which a scheduling decision is
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Figure 6.1. Illustration of distributed spatial multiplexing.
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made by considering the instantaneous throughput achievable by the user. The case for multiple antennas has been demonstrated [75,76]. However, all the works cited are above based on a heuristic approach and the performance is evaluated through simulations. With the heuristic approach, we do not have design insight and do not know how far the performance of the algorithm is from the optimal. Tse and Hanly [132] proposed an analytical framework to optimize the reverse-link scheduling algorithm for SISO multiuser system with average power constraint based on an information-theoretic approach with respect to the utility function Uthp. It is shown that the optimal scheduling policy is to allocate resource to at most a single user (with the best channel condition) at a time. However, when multiple antennas are introduced to the multiuser system, the resource space is expanded to include the spatial dimension as well. Hence, the framework and the results do not generalize directly to multiuser multiple-antenna systems. Finally, it is worth mentioning that the advantage of scheduling with respect to network coverage is a relatively unexplored topic. An interesting work [25] considered the coverage performance of an uplink scheduling algorithm and showed that network coverage could also bene t from multiuser selection diversity through wireless scheduling. In general, the cross-layer optimization problem is a complex problem involving both information theory (to model the physical layer) and queuing theory (to model the application level delay). In this chapter, we shall tackle the cross-layer optimization problem from the information-theoretic angle only. Speci cally, we shall ignore the effect of source statistics and assume that all buffers have in nite size and always contain payloads to be transmitted once a resource is scheduled to the user. Hence, queueing theory is decoupled from information theory. In 11, we shall discuss the general problem of cross-layer design taking into account the queuing-theoretic angle as well. This chapter is organized as follows. In Section 6.2, we discuss what we mean by system performance in multiuser systems. In Section 6.3, we outline the multiuser forward link channel model, the multiuser physical layer model, as well as the multiaccess control (MAC) layer model. In Section 6.4, we formulate the analytical design framework for spacetime scheduling problem with convex utility functions. In Section 6.5, low-complexity heuristics, namely, greedy-based and genetic-based algorithms, are introduced. In Section 6.6, we present numerical results to evaluate the performance of optimal and lowcomplexity spacetime schedulers. In Section 6.7, we extend the design framework for cross-layer scheduling with imperfect CSIT. Finally, we conclude with a brief summary of results in Section 6.8.
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