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35 Average network c apacity (bits per second per Hz)
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Q=4 30 Q=3 25 Q=2 20
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Figure 6.15. Total network capacity (bps/Hz) versus cell radius at various Q = 1, . . . , 5 and nT = 5. The transmit power at the base station is 30 dBm, path loss exponent is 4, and the total number of users is 10.
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TABLE 6.1. Comparison of Computational Complexity (Number of Function Evaluations) of Greedy, Genetic, and Optimal Algorithms (K, Q) (10,2) (10,4) (10,5) (20,2) (20,4) (20,5) Greedy Algorithm 10 10 10 20 20 20 Genetic Algorithm 10 10 10 10 20 20 2 5 5 5 5 5 = = = = = = 20 50 50 50 100 100 Optimal Algorithm 55 385 385 210 3 645 60 459
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selected user is guaranteed to be lower than the instantaneous channel capacity, and the transmitted packet will be virtually error-free (with powerful error correction coding) in slow fading channels. However, when we have imperfect CSIT at the transmitter, the ef ciency of multiuser scheduling is reduced because the wrong set of users may be selected for transmission (misscheduling). Moreover, the scheduled data rate of any active user may be larger than the instantaneous channel capacity (which is unknown to the transmitter), and
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this results in packet transmission outage even if powerful error correction code is applied. Conventional approach to tackle the imperfect CSIT is to design the scheduler assuming perfect CSIT and analyze the performance degradation due to the imperfect CSI. It is found that there is a signi cant degradation in the system performance due to imperfect CSIs [2]. However, this approach does not offer any design insight on what should be the optimal design and performance with imperfect CSIT as the optimal design can be quite different from that with perfect CSIT. In this section, we shall focus on the design of the cross-layer scheduler for the downlink of the multiuser multiantenna systems with imperfect knowledge of CSIT. In much the same way as in the previous sections, we consider a system with K users (each with single antenna) and a base station (with nT antennas) operating in time-division duplexing (TDD) mode. Hence, the downlink CSIT can be estimated at the base station using uplink pilots due to channel reciprocity.6 The cross-layer scheduling design with imperfect CSIT is formulated as an optimization problem, and the optimal scheduling solution is found to be computationally intensive. Therefore, two computationally effective suboptimal algorithms, namely, the genetic algorithm and short-term SINR scaling, are proposed and compared with the optimal performance. 6.7.1 Multiuser Physical Layer Model with Imperfect CSIT
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In TDD mode, the base station can deduce downlink CSIT from the uplink pilots. In practice, the downlink pilot channel (from the base station) is usually allocated a higher power because it can be shared by the K users. Hence, the CSI estimation at the mobile terminals (CSIR) can be quite accurate, and we assume that the CSIR at the mobile station is perfect. On the other hand, on the uplink side, the base station estimate of the CSIT is based on the uplink pilots from the K users. Since the uplink pilots are dedicated pilots per user and cannot be shared, the power allocated in the uplink pilots are usually smaller and the CSIT obtained at the base station is likely to be imperfect. The estimated CSIT of all the K users at the base station, Hb, is given by [70,87] Hb = H + DHb (6.35)
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where H is the actual CSIT, and DHb is the CSIT estimation error matrix with components given by i.i.d. Gaussian distribution variables (zero mean, variance s 2 ). Assuming MMSE channel estimation, we have S[DHbHb] = 0 by DH orthogonal principle.
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Strictly speaking, there are different biases in the uplink and downlink of TDD systems due to different RF gains in the transmit receive path. However, the biases are slowly time-varying relative to the channel fading and can be corrected on the basis of a slow calibration loop so that the instantaneous CSIT can be deduced from the uplink pilots.
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