Praise for Fundamentals of WiMAX

214 Chapter 6 • Orthogonal Frequency Division Multiple Access∑Kk=1log. (6.9)Although originally designed for a single-channel time-slotted system, the PF scheduler canbe adapted to an OFDMA system. In an OFDMA system, due to the multiple parallel subcarriersin the frequency domain, multiple users can transmit on different subcarriers simultaneously.The original PF algorithm can be extended to OFDMA by treating each subcarrier independently.Let R (, t n ) be the supportable data rate for user k in subcarrier n at time slot t. Then forkeach subcarrier, the user with the largest R is selected for transmission. Letk(, t n)/ Tk() tΩ k() tdenote the set of subcarriers in which user k is scheduled for transmission at time slot t, then theaverage user throughput is updated asT k⎛ 1 ⎞ 1Tk( t+ 1)= 1−Tk() t⎝⎜ t ⎠⎟ +tc∑c n∈ΩkRk(, t n)() t(6.10)for k =1,2, ⋯,K. Other weighted adaptations and evolutions of PF scheduling of OFDMA arecertainly possible.6.3.5 Performance ComparisonIn this section, we briefly compare the performance of the various scheduling algorithms forOFDMA that we have discussed, in order to gain intuition on their relative performance andmerits. In these results, an exponentially decaying multipath profile with six multipath componentswas used to generate the frequency diversity. All users have the same average SNR. Theabsolute-capacity numbers are not especially important, what is important are the trendsbetween the curves.6.3.5.1 ThroughputFirst, we consider the multiuser diversity gains of the various types of algorithms. Figure 6.9shows the capacity, normalized by the total bandwidths for static TDMA (round-robin), proportionalfairness, and the MSR algorithm. As expected, the MSR algorithm achieves the best totalthroughput, and the gain increases as the number of users increases, on the order of log log K.Static TDMA achieves no multiuser gain, since the users transmit independent of their channelrealizations. It can be seen that the PF algorithm approaches the throughput of the MSR algorithm,with an expected penalty owing to its support for underserved users.6.3.5.2 FairnessNow, let’s consider how the worst user in the system does (Figure 6.10). As expected, the MFalgorithm achieves the best performance for the most underserved user, with a slight gain foroptimal power allocation over its allocated subcarriers (waterfilling) relative to an equal-powerallocation. Also as expected, the MSR algorithm results in a starved worst-case user; in fact, it istypical for several users to receive no resources at all for substantial periods of time. StaticTDMA performs in between the two, with the percentage loss relative to the MF algorithm