Path-loss and Shadowing (Large-scale ... - 國立臺灣大學

1 path - loss and Shadowing (Large-scale Fading)PROF. MICHAEL TSAI2011/10/20 FriisFormulaTX AntennaEIRP= Power spatial density 14 RX Antenna = 4 2 Antenna Aperture Antenna Aperture=Effective Area Isotropic Antenna s effective area , Isotropic Antenna s Gain=1 = Friis Formula becomes: = ! = ! 3 = 4 FriisFormula ! is often referred as Free-Space path loss (FSPL) Only valid when d is in the far-field of the transmitting antenna Far-field: when ! > !#, Fraunhofer distance !#= $ , and it must satisfies !

2 # $and !# D: Largest physical linear dimension of the antenna &: Wavelength We often choose a !'in the far-field region, and smaller than any practical distance used in the system Then we have != !'!!' = ! 4 Received Signal after Free -Space path loss = ( )* , ! !-. )*, #/ phase difference due to propagation distanceFree-Space path LossComplex envelopeCarrier (sinusoid)5 Example: Far-field Distance Find the far-field distance of an antenna with maximum dimension of 1m and operating frequency of 900 MHz (GSM 900) Ans: Largest dimension of antenna: D=1m Operating Frequency: f=900 MHz Wavelength: =/#=0 1'23'' 1'4= '.

3 00 !#= 6 = '.00= 4. '4(m)6 Example: FSPL If a transmitter produces 50 watts of power, express the transmit power in units of (a) dBmand (b) dBW. If 50 watts is applied to a unity gain antenna with a 900 MHz carrier frequency, find the received power in dBmat a free space distance of 100 m from the antenna. What is the received power at 10 km? Assume unity gain for the receiver antenna. Ans: 1' 8 -1'9' = 1: !;<= : =>? Received Power at 100m (1''A) =9' 1 1 0 1'23'' 1'4 1'' = 0. 9 1'C4 <= 9.

4 9 (!;<) Received Power at 10km 1'DA= 1''A1''1'''' = 0. 9 1'C1'<= 3 .9 (!;<)7 Two -ray ModelTX Antenna EFGG RX Antenna J K L MN C JOP =QR&4 J LSTP exp X2 F&F+Q K MSTP [ exp X2 G + G\&G + G\expX2 ]KPDelayed since x+x is longer. [ = (G + G\ F)/_R: ground reflection coefficient (phase and amplitude change)8 Two -ray Model: Received Power = ` a8+ / ! )*C,bc)d)\ The above is verified by empirical results. bc = () + )\ 8)/ ) Z )\+ 8 e Z e Z ! +e + e Z ! 9lxx x xTwo -ray Model: Received Power When !]

5 E + e , bc = )d)fC8 e e ! For asymptotically large d, ) + )\ h !, E ',ijik / !, l 1 (phase is inverted after reflection) ` a8+ / ! )*C,bc)d)\ ` a! 1 + )* ,bc 1 + )* ,bc =1 / bc + m bc = nopbc = m (bc ) bc ` a ! e e ! qr= ` ae e ! qr10 Independent of &now11 K=4 & Could be a natural choice of cell sizeIndoor Attenuation Factors which affect the indoor Path-loss : Wall/floor materials Room/hallway/window/open area layouts Obstructing objects location and materials Room size/floor numbers Partition loss :12 Partition typePartition loss (dB) for 900-1300 MHzFloor10-20 for the first one,6-10 per floor for the next 3,A few dB per floor plasterboard wall13 Aluminum metal26 Simplified Path-loss Model Back to the simplest.

6 S: reference distance for the antenna far field (usually 1-10m indoors and 10-100m outdoors) t: constant Path-loss factor (antenna, average channel attenuation), and sometimes we use u: Path-loss exponent13 = t s vt =&4 s Some empirical results14 Measurements in Germany CitiesEnvironmentPath- loss ExponentFree-space2 Urban area cellular radio urban cellular radio3-5In building to in building4 to 6 Obstructed in factories2 to 3 Empirical Path-loss Model Based on empirical measurements over a given distance in a given frequency range for a particular geographical area or building Could be applicable to other environments as well Less accurate in a more general environment

7 Analytical model: / is characterized as a function of distance. Empirical Model: / is a function of distance including the effects of path loss , Shadowing , and multipath. Need to average the received power measurements to remove multipath effects Local Mean Attenuation (LMA) at distance : Okumura Model Okumura Model: w! !;= w#/, ! + x#/, ! e e (y w#/, !: FSPL, x#/, !: median attenuation in addition to FSPL =20 log~s( ss) , 10 log~s , 3 ,20 log~s , 3 < < 10 .:antenna height gain factor.)

8 (y : gain due to the type of environment16 Example: Piecewise Linear Model N segments with N-1 breakpoints Applicable to both outdoor and indoor channels Example dual-slope model: t: constant Path-loss factor u~: Path-loss exponent for s~ K u : Path-loss exponent after K17 = t s v t K v Kv s K, " Fading Same T-R distance usually have different path loss Surrounding environment is different Reality: simplified Path-loss Model represents an average How to represent the difference between the average and the actual path loss ?)

9 Empirical measurements have shown that it is random (and so is a random variable) Log-normal distributed18 Log -normal distribution A log-normal distribution is a probability distribution of a random variable whose logarithmis normally distributed: G:the random variable (linear scale) , :mean and variance of the distribution (in dB) 19] G; , =1G 2 exp log G 2 logarithm of the random variablenormalized so that the integration of the pdf=1 Log -normal Shadowing Expressing the path loss in dB, we have :Describes the random Shadowing effects ~ (', )(normal distribution with zero mean and variance) Same T-R distance, but different levels of clutter.

10 Empirical Studies show that ranges from 4 dB to 13dB in an outdoor channel20 = + = s+10u log s+ Why is it log-normal distributed? Attenuation of a signal when passing through an object of depth d is approximately: :Attenuation factor which depends on the material If is approximately the same for all blocking objects: = : sum of all object depths By central limit theorem, ! ~ (x, )when the number of object is large (which is true).21 = exp = exp = exp path loss , Shadowing , and Multi-Path22 Cell Coverage Area Cell coverage area.