Praise for Fundamentals of WiMAX

6.3 Resource-Allocation Techniques for OFDMA 213power allocation and to settle for a near-optimal subcarrier and power allocation that can beachieved with manageable complexity. The near-optimal approach is derived and outlined in[32, 33] and a low-complexity implementation developed in [40].6.3.4 Proportional Fairness SchedulingThe three algorithms discussed thus far attempt to instantaneously achieve an objective such asthe total sum throughput (MSR algorithm), maximum fairness (equal data rates among all users),or preset proportional rates for each user. Alternatively, one could attempt to achieve such objectivesover time, which provides significant additional flexibility to the scheduling algorithms. Inthis case, in addition to throughput and fairness, a third element enters the trade-off: latency. In anextreme case of latency tolerance, the scheduler could simply wait for the user to get close to thebase station before transmitting. In fact, the MSR algorithm achieves both fairness and maximumthroughput if the users are assumed to have the same average channels in the long term—on theorder of minutes, hours, or more—and there is no constraint with regard to latency. Since latencies,even on the order of seconds, are generally unacceptable, scheduling algorithms that balancelatency and throughput and achieve some degree of fairness are needed. The most popular frameworkfor this type of scheduling is proportional fairness (PF) scheduling [36, 38].The PF scheduler is designed to take advantage of multiuser diversity while maintainingcomparable long-term throughput for all users. Let R () denote the instantaneous data rate thatktuser k can achieve at time t, and let T () be the average throughput for user k up to time slot t.ktThe PF scheduler selects the user, denoted as k * , with the highest R for transmission.k()/ t Tk()tIn the long term, this is equivalent to selecting the user with the highest instantaneous rate relativeto its mean rate. The average throughput T () t for all users is then updated according tokT k ( t + 1)=⎧⎛11–⎝--⎞ 1⎪ Tk () t + -- Rt c⎠ t k () t⎪c⎨⎪ ⎛ 11 –⎝--⎞ Tk () t⎪ t c⎠⎩k=k∗k≠k∗. (6.9)Since the PF scheduler selects the user with the largest instantaneous data rate relative to itsaverage throughput, “bad” channels for each user are unlikely to be selected. On the other hand,consistently underserved users receive scheduling priority, which promotes fairness. The parametert ccontrols the latency of the system. If t cis large, the latency increases, with the benefit ofhigher sum throughput. If t cis small, the latency decreases, since the average throughput valueschange more quickly, at the expense of some throughput.The PF scheduler has been widely adopted in packet date systems, such as HSDPA and1xEV-DO, where t cis commonly set between 10 and 20. One interesting property of PF schedulingis that as t c→∞,the sum of the logs of the user data rates is maximized. That is, PFscheduling maximizes