Praise for Fundamentals of WiMAX

3.3 Cellular Systems 77To summarize the example: Although 75 percent of users can use BPSK modulation andhence get a PHY data rate of 10 MHz • 1 bit/symbol • 1/2 = 5 Mbps, less than 1 percent of userscan reliably use 16 QAM (4 bits/symbol) for a more desirable data rate of 20Mbps. Additionally,whereas without shadowing, all the users could at least get low-rate BPSK through, with shadowing,25 percent of the users appear unable to communicate at all. Interestingly, though, withoutshadowing, 16 QAM could never be sent; with shadowing, it can be sent a small fraction ofthe time. Subsequent chapters describe adaptive modulation and coding, alluded to here, in moredetail and also show how other advanced techniques may be used to further increase the possibledata rates in WiMAX.Sidebar 3.3 Why is the shadowing lognormal?Although the primary rationale for the lognormal distribution for the shadowingvalue χ is accumulated evidence from channel-measurement campaigns,one plausible explanation is as follows. Neglecting the pathloss for a moment,if a transmission experiences N random attenuations β i , i = 1, 2,..., N betweenthe transmitter and receiver, the received power can be modeled asN∏P r = P t β ii = 1(3.22)which can be expressed in dB asP r ( dB) = P t ( dB) + 10N∑i = 1log 10 β i(3.23)Then, using the Central Limit Theorem, it can be argued that the sum termwill become Gaussian as N becomes large—and often the CLT is accurate forfairly small N—and since the expression is in dB, the shadowing is hence lognormal.3.3 Cellular SystemsAs explained in Section 3.2, owing to pathloss and, to a lesser extent, shadowing, given a maximumallowable transmit power, it is possible to reliably communicate only over some limiteddistance. However, we saw in Sidebar 3.2 that pathloss allows for spatial isolation of differenttransmitters operating on the same frequency at the same time. As a result, pathloss and shortrangetransmissions in fact increase the overall capacity of the system by allowing more simultaneoustransmissions to occur. This straightforward observation is the theoretical basis for theubiquity of modern cellular communication systems.