Path-loss and Shadowing (Large-scale Fading)

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 !# $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 !

2 = !'!!' = ! 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= '. 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.

3 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 . 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 !]

4 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: 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.

5 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 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!

6 !;= 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. (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 ?))

7 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. Empirical Studies show that ranges from 4 dB to 13dB in an outdoor channel20 = + = s+10u log s+ Why is it log-normal distributed?

8 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: expected percentage of locations within a cell where the received power at these locations is above a given area within the cell has received power lower than Some area outside of the cell has received power higher than Cell Coverage Area We can boost the transmission power at the BS Extra interference to the neighbor cells In fact, any mobile in the cell has a nonzero probability of having its received power below A m.

9 Since Normal distribution has infinite tails Make sense in the real-world: in a tunnel, blocked by large buildings, doesn t matter if it is very close to the BS24 Cell Coverage Area Cell coverage area is given by * > A m25 = y1 ( 1 > A m m ! ! / 88 ` `=1 ( y1 > A m m ! ! / 88 ` `1 if the statement is true, 0 otherwise. (indicator function) =1 ( ! / 88 ` `=1 ( (' ! '! Cell Coverage Area Q-function:26 = N = N > = 12 exp 2 Log-normal distribution s standard deviationzCell Coverage Area Solving the equations yield: ` = A mC ( , a =1' 8 -1' If A m= (27 = + exp2 2 2 average received power at cell boundary (distance=R) =12+ exp2 2 Example Find the coverage area for a cell with a cell radius of 600m a base station transmission power of 20 dBm a minimum received power requirement of -110 dBm.)))))))

10 path loss model: ( ) = tM Mv, u = , t = , s= 1, Shadowing standard deviation = dB Ans: ( = ' 01. 9 1' 0. :1 8 -1'4'' = 11 . 4 !;A ` =C11'd11 . 1. 4, a =1' 0.:1 '. 0 . 1 = 1. 4 + )* '. 4 '. 2': = '. 4(not good) If we calculate C for a minimum received power requirement of -120 dBm C= !28 = +exp2 2 2 ` = A mC ( , a =1' 8 -1' Example: road corners path loss295 m40 m10 mRadio: Chipcon CC2420 IEEE , GHzTX pwr: 0 dBm8 dBi peak gainomni-directionalantennaIntel-NTU Connected Context Computing Center Compare the Path-loss exponent of three different locations:1. Corner of NTU_CSIE building2. XinHai-Keelong intersection3. FuXing-HePing intersectionLink Measurements path loss around the corner building30123 Passing-by vehiclesOccasionally Frequently FrequentlyBuildings AroundNoFew buildingsSome high buildingsIntersection NarrowWideWide31 Doppler Effect Difference in path lengths bh = !)