Praise for Fundamentals of WiMAX

206 Chapter 6 • Orthogonal Frequency Division Multiple AccessFigure 6.5 shows the PDF of h max for various values of K. As the number of users increases,the PDF of h max shifts to the right, which means that the probability of getting a large channelgain improves. Figure 6.6 shows how this increased channel gain improves the capacity and biterror rate for uncoded QPSK. Both plots show that the multiuser diversity gain improves as thenumber of users in the system increases, but the majority of the gain is achieved from only thefirst few users. Specifically, it has been proved, using extreme-value theory, that in a K -usersystem, the average capacity scales as log log K[31], assuming just Rayleigh fading. If i.i.d. lognormalshadowing is present for each of the users, which is a reasonable assumption, the scalingimproves to log K [5].In a WiMAX system, the multiuser diversity gain will generally be reduced by averagingeffects, such as spatial diversity and the need to assign users contiguous blocks of subcarriers.This conflict is discussed in more detail in Section 6.4.3. Nevertheless, the gains from multiuserdiversity are considerable in practical systems. Although we focus on the gains in terms ofthroughput (capacity) in this chapter, it should be noted that in some cases, the largest impactfrom multiuser diversity is on link reliability and overall coverage area.6.2.2 Adaptive Modulation and CodingWiMAX systems use adaptive modulation and coding in order to take advantage of fluctuationsin the channel. The basic idea is quite simple: Transmit as high a data rate as possible when thechannel is good, and transmit at a lower rate when the channel is poor, in order to avoid excessivedropped packets. Lower data rates are achieved by using a small constellation, such asQPSK, and low-rate error-correcting codes, such as rate 1/2 convolutional or turbo codes. Thehigher data rates are achieved with large constellations, such as 64 QAM, and less robust errorcorrectingcodes; for example, rate 3/4 convolutional, turbo, or LDPC codes. In all, 52 configurationsof modulation order and coding types and rates are possible, although most implementationsof WiMAX offer only a fraction of these. These configurations are referred to as burstprofiles and are enumerated in Table 8.4.A block diagram of an AMC system is given in Figure 6.7. For simplicity, we first considera single-user system attempting to transmit as quickly as possible through a channel with a variableSINR—for example, due to fading. The goal of the transmitter is to transmit data from itsqueue as rapidly as possible, subject to the data being demodulated and decoded reliably at thereceiver. Feedback is critical for adaptive modulation and coding: The transmitter needs to knowthe “channel SINR” γ , which is defined as the received SINR γ rdivided by the transmit powerP t, which itself is usually a function of γ . The received SINR is thus γ .r= PtγFigure 6.8 shows that by using six of the common WiMAX burst profiles, it is possible toachieve a large range of spectral efficiencies. This allows the throughput to increase as the SINRincreases following the trend promised by Shannon’s formula C = log . In this case,2(1 + SNR)the lowest offered data rate is QPSK and rate 1/2 turbo codes; the highest data-rate burst profileis with 64 QAM and rate 3/4 turbo codes. The achieved throughput normalized by the bandwidthis defined as