Praise for Fundamentals of WiMAX

74 Chapter 3 • The Challenge of Broadband Wireless Channelsincreasingly attractive, since the required signal power can be decreaseddown to the noise floor, and the overall performance will be better than ina system with lower pathloss at the same transmit-power level.3.2.2 ShadowingAs we have seen, pathloss models attempt to account for the distance-dependent relationshipbetween transmitted and received power. However, many factors other than distance can have alarge effect on the total received power. For example, trees and buildings may be located betweenthe transmitter and the receiver and cause temporary degradation in received signal strength; on theother hand, a temporary line-of-sight transmission path would result in abnormally high receivedpower as shown in Figure 3.3. Since modeling the locations of all objects in every possible communicationenvironment is generally impossible, the standard method of accounting for these variationsin signal strength is to introduce a random effect called shadowing. With shadowing, theempirical pathloss formula becomesP⎛ do⎞= PP χ ,⎝⎜d ⎠⎟r t o(3.10)where χ is a sample of the shadowing random process. Hence, the received power is now alsomodeled as a random process. In effect, the distance trend in the pathloss can be thought of asthe mean, or expected, received power, whereas the χ shadowing value causes a perturbationfrom that expected value. It should be emphasized that since shadowing is caused by macroscopicobjects, it typically has a correlation distance on the order of meters or tens of meters.Hence, shadowing is often alternatively called large-scale fading.The shadowing value χ is typically modeled as a lognormal random variable, that is,χ=10 x/10 , where x∼N(0, σ2 ),(3.11)22where N(0, σ is a Gaussian (normal) distribution with mean 0 and variance . With thiss)σ sformulation, the standard deviation σ sis expressed in dB. Typical values for σ sare in the6–12 dB range. Figure 3.4 shows the very important effect of shadowing, where σ s= 11.8 dBand σ s= 8.9 dB, respectively.Shadowing is an important effect in wireless networks because it causes the received SINRto vary dramatically over long time scales. In some locations in a given cell, reliable high-ratecommunication may be nearly impossible. The system design and base station deployment mustaccount for lognormal shadowing through macrodiversity, variable transmit power, and/or simplyaccepting that some users will experience poor performance at a certain percentage of locations(see Sidebar 3.3). Although shadowing can sometimes be beneficial—for example, if anobject is blocking interference—it is generally detrimental to system performance because itrequires a several-dB margin to be built into the system. Let’s do a realistic numerical exampleto see how shadowing affects wireless system design.αs