EE 499: Wireless & Mobile Communications (08) Mobile Raio Propagation: Large Scale Propagation Moeling Raio Wave Propagation Raio waves suffer from several cannel problems as tey travel troug te air. Some of tese cause very rapi variations in te envelope of te signal (resulting from small scale movements of te mobile unit or te surrounings) wile some of tem result in relatively slow envelope variations (resulting from large scale movement of te mobile unit or te surrounings). Te following figure illustrates combination of bot rapi (small scale) an slow (large scale) signal envelope variations as illustrate by te blue signal. Te local average of tis signal is inicate by te ase line wic illustrates te slow variations in te envelope only. In tis capter we talk about te slow large scale variations only. Small-Scale Propagation Large-Scale Propagation It is wort mentioning tat small scale propagation variations occur as a result of fractional wavelengt movements of te mobile pone or its surrounings on te orer of a wavelengt (0.1 1 ). For mobile pones wit frequencies in te range of 800 MHz to 000 MHz, tis correspons to movements on te orer of 1cm 10 cm. Large scale propagation variations occur as a result of multiple wavelengt movements in te range of (5 to 50 ) wic correspons to movements on te orer of 1m to 10m. 1
EE 499: Wireless & Mobile Communications (08) Free Space Propagation Moel Power Receive at a Distance from a Transmitter As a transmitte signal travels troug vacuum or air, its power gets istribute over a larger an larger spere an terefore attenuates as te square of te istance from te transmitter to te receiver. In fact, te power receive at istance from a transmitter is were PG t tgr Pr ( ) = W ( 4π ) P t G t G r is transmitte power (W) is gain of transmitting antenna (Linear not B) is gain of receiving antenna (Linear not B) is wavelengt of transmitte signal (m) is orizontal istance between transmitter an receiver (m) In B, te same relation can be written as P( ) [BW] = P [BW] + G [B] + G [B] + 0 log 0 log 4π 0 log r t t r 10 10 10 Gain of an Antenna Given te effective area of an antenna an te frequency or wavelengt of te signal it is transmitting/receiving, we can fin te gain of tat antenna. Te gain of an antenna is basically te ability of an antenna to concentrate its transmitte power at a specific irection. Tat is, compare to an isotropic antenna wic raiates equally in all irections, a transmitting antenna wit a gain of G tat is fe wit te same amount of power as an isotropic antenna raiates G times as muc as an isotropic antenna in te irection of its igest raiation irection. An antenna wit a transmitting gain of G will ave a receiving gain of G. Te gain of an antenna is given by were G = 4π Ae A e is effective area of antenna in m (relate to its surface expose to raiation)
EE 499: Wireless & Mobile Communications (08) an c π c = = f ω Pat Loss As te EM wave travels, its power rops as it is sprea over a larger spere. Tis rop in power is known as pat loss wic is given by PL( ) = ( 4π ) Relating Electric Fiel Intensity to Receive Power (Power Flux Density) Often, we nee to relate te strengt of an electric fiel at a specific istance away from a transmitting antenna to te power receive by anoter antenna at tat same point. In tis case, we nee to unerstan te concept of te Power Flux Density (PFD). Te Power Flux Density (PFD) is efine as te amount of power tat passes troug an area of 1 m tat is locate on a spere of raius (te 1 m is part of te surface of te spere). Te PFD is efine as P = EIRP PG E E t t W/m 4π = 4π = R = η fs EIRP E is Effective Isotropic Raiate Power (W) wic is equal to power fe to a transmitting antenna times its gain PG t t. Tis means tat an isotropic antenna woul ave to be fe wit PG t t Watts of power to raiate te same amount of power as tat specific antenna is magnitue of electric file intensity (V/m) R fs = η is intrinsic impeance of free space (in Ω) wic is equal to 10π Ω= 377 Ω So, = = E = PG t tgr = E Gr r e e P( ) P A A W 10π 480 π ( 4π ) 3
EE 499: Wireless & Mobile Communications (08) Large Scale Propagation Mecanisms Tere are 3 basic large scale propagation mecanisms tat affect te envelope of a transmitte electromagnetic signal: 1. Reflection. Diffraction 3. Scattering Reflection (Reflection from Dielectrics) Groun Reflection (Two Ray) Moel E LOS t Ei θ i E θ o reflect = E Grn r If te conition, > 0 t r is satisfie, ten te total electric fiel at te receiver antenna in terms of some fiel strengt E 0 at some istance 0 is E E π 0 0 t r TOT ( ) = V/m Tis allows us to use te above equation (wic is illustrate next) ETOT ( ) ETOT ( ) Gr Pr( ) = P Ae = Ae = W 10π 480 π 4
EE 499: Wireless & Mobile Communications (08) to obtain a relation of te receive power in te two ray moel tat is relate only to antenna eigts given by t r Pr( ) = PGG t t r W 4 Diffraction (Fresnel Zones) Tis configuration is calle te (Single) Knife ege Diffraction Moel α β obs t obs r γ t obs r 1 Clearly, α = β + γ an it is clear tat β γ tan 1 obs t = 1 tan 1 obs r = Using te above, we obtain a relation to fin te parameter ν given by 5
EE 499: Wireless & Mobile Communications (08) ( 1+ ) v = α ( α must be in raians not egrees) 1 Note tat α can be positive or negative. It is positive if te obstacle is iger tan te line of sigt between te transmitter an receiver, zero if it just touces te line of sigt, an negative if it is lower tan te line of sigt between transmitter an te receiver. Once ν is etermine from te above equation, a sketc (given in te book) gives te corresponing aitional gain of te signal. Tis means, you may compute te power receive by te receiving antenna assuming no obstacle exists, te actual power receive wit te presence of te obstacle is iger by a B value tat is equal to te value given in te sketc. (Unerstan tis process) Scattering A surface is consiere to be smoot (not roug) if te peak to peak variations in its surface tan c is less c = 8sinθ i θ i = incient angle Te following equations are not require Scattering loss factor ρ S is ρ = e S πσ sinθi 8 σ = stanar eviation of surface eigt about average Reflection coefficient is Γ = Γ roug ρs 6