2 Signal Strength Measure signal strength in dBW = 10*log(Power in Watts)dBm = 10*log(Power in mW)can legally transmit at 10dBm (1W).Most PCMCIA cards transmit at 20dBm.Mica2 (cross bow wireless node) can transmit from –20dBm to 5dBm. (10microW to 3mW)Mobile phone base station: 20W, but 60 users, so 0.3W / user, but antenna has gain=18dBi, giving effective power of 42.Mobile phone handset – 21dBm
3 Noise Interference Thermal noise From other users From other equipment E.g., microwave ovens 20dBm 50% duty-cycle with 16ms period.Noise in the electronics – e.g., digital circuit noise on analogue parts.Non-linearities in circuits.Often modeled as white Gaussian noise, but this is not always a valid assumption.Thermal noiseDue to thermal agitation of electrons. Present in all electronics and transmission media.kT(W/hz)k Boltzmann’s constant = 1.3810-23T – temperture in Kelvin (C+273)kTB(W)B bandwidthE.g.,Temp = 293,=> -203dB, -173dBm /HzTemp 293 and 22MHz => -130dB, -100dBm
4 Signal to Noise Ratio (SNR) SNR = signal power / noise powerSNR (dB) = 10*log10(signal power / noise power)Signal strength is the transmitted power multiplied by a gain – impairmentsImpairmentsThe transmitter is far away.The signal passes through rain or fog and the frequency is high.The signal must pass through an object.The signal reflects of an object, but not all of the energy is reflected.The signal interferes with itself – multi-path fadingAn object not directly in the way impairs the transmission.
5 Receiver SensitivityThe received signal must have a strength that is larger than the receiver sensitivity20dB larger would be good. (More on this later)E.g.,802.11b – Cisco Aironet 250 (the most sensitive)1Mbps: -94dBm; 2Mbps: -91dBm; 5.5Mbps: -89dBm; 11Mbps: -85dBmMobile phone base station: -119dBmMobile phone hand set: -118dBmMica2 at 868/916MHz: -98dBm
6 Simple link budgetDetermine if received signal is larger than the receiver sensitivityMust account for effective transmission powerTransmission powerAntenna gainLosses in cable and connectors.Path lossesAttenuationGround reflectionFading (self-interference)ReceiverReceiver sensitivityLosses in cable and connectors
7 Antenna gain Vertical direction Horizontal direction isotropic antenna – transmits energy uniformly in all directions.Antenna gain is the peak transmission power over any direction divided by the power that would be achieved if an isotropic antenna is used. The units is dBi.Sometime, the transmission power is compared to a ½ wavelength dipole. In this case, the unit is dBD.The ½ wavelength dipole has a gain of 2.14dB.Vertical directionHorizontal direction
8 Antenna gainAntenna gain is increased by focusing the antennaThe antenna does not create energy, so a higher gain in one direction must mean a lower gain in another.Note: antenna gain is based on the maximum gain, not the average over a region. This maximum may only be achieved only if the antenna is carefully aimed.This antenna is narrower and results in 3dB higher gain than the dipole, hence, 3dBD or 5.14dBiThis antenna is narrower and results in 9dB higher gain than the dipole, hence, 9dBD or 11.14dBi
9 Antenna gainInstead of the energy going in all horizontal directions, a reflector can be placed so it only goes in one direction => another 3dB of gain, 3dBD or 5.14dBiFurther focusing on a sector results in more gain.A uniform 3 sector antenna system would give 4.77 dB more.A 10 degree “range” 15dB more.The actual gain is a bit higher since the peak is higher than the average over the “range.”Mobile phone base stations claim a gain of 18dBi with three sector antenna system.4.77dB from 3 sectors – dBiAn 11dBi antenna has a very narrow range.
10 Simple link budget – 802.11b receiver sensitivity Thermal noise: -174 dBm/HzChannel noise (22MHz): 73 dBNoise factor: 5 dBNoise power (sum of the above): -96 dBmReceiver requirements:3 dB interference margin0 dB is the minimum SINRMin receiver signal strength: -93 dBm
11 Simple link budget – 802.11 example From base station+20dBm transmission power+6dBi transmit antenna gain+2.2dBi receiver antenna gain-91dBm minimum receiver power=> dB path losses=> 99 dB path losses if 20dB of link margin is added (to ensure the link works well.)From PCMCIA to base station+0dBm transmission power=> 99.4 dB path losses=> 79.2 dB path losses if 20dB of link margin is added (to ensure the link works well.)From PCMCIA to PCMCIA+2.2dBi transmit antenna gain=> 95.4 dB path losses=> 75.4 dB path losses if 20dB of link margin is added (to ensure the link works well.)
12 Simple link budget – mobile phone – downlink example Transmission power (base station): 20W (can be as high as 100W)Transmission power for voice (not control): 18WNumber of users: 60Transmission power/user: 0.3W, 300mW, 24.8dBmBase station antenna gain (3-sectors): 18dBiCable loss at base station: 2dBEffective isotropic radiated power: 40dBm (sum of the above)Receiver:Thermal noise: -174 dBm/HzMobile station receiver noise figure (noise generated by the receiver, Johnson Noise, ADC quantization, clock jitter): 7dBReceiver noise density: -167 dB/Hz (-174+7)Receiver noise: dBm (assuming 3.84MHz bandwidth for CDMA)Processing gain: 25dB (CDMA is spread, when unspread(demodulated) and filtered, some of the wide band noise is removed)Required signal strength: 7.9dBReceiver sensitivity: – =Body loss (loss due to your big head): 3dBMaximum path loss: 40 – (-118.3) –3 = 155.3
13 Simple link budget – mobile phone – uplink example Transmission power (mobile): 0.1W (21 dBm)Antenna gain: 0 dBiBody loss: 3 dBEffective isotropic radiated power: 18 dBm (sum of the above) (maximum allowabel by FCC is 33 dBm at 1900MHz and 20dBm at 1700/2100 MHzReceiver/base stationThermal noise: -174 dBm/HzMobile station receiver noise figure (noise generated by the receiver, Johnson Noise, ADC quantization, clock jitter): 5dBReceiver noise density: -169 dB/Hz (-174+5)Receiver noise: dBm (assuming 3.84MHz bandwidth for CDMA)Processing gain: 25dB (CDMA is spread, when unspread(demodulated) and filtered, some of the wide band noise is removed)Margin for interference: 3dB (more interference on the uplink than on the downlink)Required signal strength: 6.1dBReceiver sensitivity:Maximum path loss: 153.3
14 Required SNRFor a given bit-error probability, different modulation schemes need a higher SNREb is the energy per bitNo is the noise/HzBit-error is given as afunction of Eb / NoRequired SNR = Eb / No * Bit-rate / bandwidthA modulation scheme prescribes a Bit-rate / bandwidth relationshipE.g., for 10^-6 BE probability over DBPSK requires 11 dB + 3 dB = 14 dB SNR
16 Shannon CapacityGiven SNR it is possible to find the theoretical maximum bit-rate:Effective bits/sec = B log2(1 + SNR), where B is bandwidthE.g.,B = 22MHz,Signal strength = -90dBmN = -100dBm=> SNR = 10dB => 1022106 log2(1 + 10) = 76MbpsOf course, b can only do 1Mbps when the signal strength is at –90dBm.
17 PropagationRequired receiver signal strength – Transmitted signal strength is often around99 dB base station -> laptop79.2 dB b laptop -> base station75.4 dB laptop -> laptop155.3 Mobile phone downlink153.3 Mobile phone uplink.Where does all this energy go…Free space propagation – not valid but a good startGround reflection2-ray – only valid in open areas. Not valid if buildings are nearby.Wall reflections/transmissionDiffractionLarge-scale path loss modelsLog-distanceLog-normal shadowingOkumuraHataLongley-RiceIndoor propagationSmall-scale path lossRayleigh fadingRician Fading
18 Free Space Propagation The surface area of a sphere of radius d is 4 d2, so that the power flow per unit area w(power flux in watts/meter2) at distance d from a transmitter antenna with input accepted power pT and antenna gain GT isThe received signal strength depends on the “size” or aperture of the receiving antenna. If the antenna has an effective area A, then the received signal strength isPR = PT GT (A/ (4 d2))Define the receiver antenna gain GR = 4 A/2. = c/f2.4GHz=> = 3e8m/s/2.4e9/s = 12.5 cm933 MHz => =32 cm.Receiver signal strength: PR = PT GT GR (/4d)2PR (dBm) = PT (dBm) + GT (dBi) + GR (dBi) + 10 log10 ((/4d)2)2.4 GHz => 10 log10 ((/4d)2) = -40 dB933 MHz => 10 log10 ((/4d)2) = -32 dB
19 Free Space Propagation - examples Mobile phone downlink = 12.5 cmPR (dBm) = (PTGGL) (dBm) dB + 10 log10 (1/d2)Or PR-PT - 40 dB = 10 log10(1/d2)Or 155 – 40 = 10 log10 (1/d2) =Or (155-40)/20 = log10 (1/d)Or d = 10^ ((155-40)/20) = 562Km or Wilmington DE to Boston MAMobile phone uplinkd = 10^ ((153-40)/20) = 446Km802.11PR-PT = -90dBmd = 10^((90-40)/20) = 316 m11Mbps needs –85dBmd = 10^((85-40)/20) = 177 mMica2 Mote-98 dBm sensitivity0 dBm transmission powerd = 10^((98-30)/20) = 2511 m
20 Ground reflectionFree-space propagation can not be valid since I’m pretty sure that my cell phone does reach Boston.You will soon see that the Motes cannot transmit 800 m.There are many impairments that reduce the propagation.Ground reflection (the two-ray model) – the line of sight and ground reflection cancel out.
21 Ground reflection (approximate) Approximation! When the wireless signal hits the ground, it is completely reflected but with a phase shift of pi (neither of these is exactly true).The total signal is the sum of line of sight and the reflected signal.The LOS signal is = Eo/dLOS cos(2 / t)The reflected signal is -1 Eo /dGR cos(2 / (t – (dGR-dLOS)))Phasors:LOS = Eo/dLOS 0Reflected = Eo/dGR (dGR-dLOS) 2 / For large d dLOS = dGRTotal energyE = (Eo/dLOS) ( (cos ((dGR-dLOS) 2 / ) – 1)2 + sin2((dGR-dLOS) 2 / ) ) ½E = (Eo/dLOS) 2 sin((dGR-dLOS) / )
22 Ground reflection (approximate) dGR-dLOSdGR = ((ht+hr)^2 + d^2)^1/2dLOS = ((ht-hr)^2 + d^2)^1/2dGR-dLOS 2hthr/d -> 0 as d-> inf2 sin((dGR-dLOS) / ) -> 0,For large d, 2 sin((dGR-dLOS) / ) C/dSo total energy is 1/d^2And total power is energy squared, or K/d^4
23 Ground reflection (approximate) For d > 5ht hr, Pr = (hthr)^2 / d^4 Gr GT PTPr – PT – 10log((hthr)^2) - log(Gr GT ) = 40 log(1/d)Examples:Mobile phoneSuppose the base station is at 10m and user at 1.5 md = 10^((155 – 12)/40) = 3.7Km802.11Suppose the base station is at 1.5m and user at 1.5 md = 10^((90 – 3.5)/40) = 145mBut this is only accurate when d is large 145m might not be large enough
24 Ground reflection (more accurate) When the signal reflects off of the ground, it is partially absorbed and the phase shift is not exactly pi.PolarizationTransmission line model of reflections
25 PolarizationThe polarization could be such that the above picture is rotated by pi/2 along the axis.It could also be shifted.If a rotated and shifted
26 PolarizationThe peak of the electric field rotates around the axis.
27 PolarizationIf a antenna and the electric field have orthogonal polarization, then the antenna will not receive the signal
28 Polarization Vertically/ horizontally polarized When a linearly polarized electric field reflects off of a vertical or horizontal wall, then the electric field maintains its polarization.In practice, there are non-horizontal and non-vertical reflectors, and antenna are not exactly polarized. In practice, a vertically polarized signal can be received with a horizontally polarized antenna, but with a 20 dB loss.Theoretically, and sometimes in practice, it is possible to transmit two signals, one vertically polarized and one horizontally.Vertically/ horizontally polarized
29 Snell's Law for Oblique Incidence yqqTqqTxGraphical interpretation of Snell’s law
30 Transmission Line Representation for Transverse Electric (TE) Polarization yqzxqTEz+ -Hx
31 Transmission Line Representation for Transverse Magnetic (TM) Polarization yqzxqTEx+ -Hz
32 Reflection from a Dielectric Half-Space TE PolarizationTM Polarization90º-1GEqGHqBno phase shift
33 Magnitude of Reflection Coefficients at a Dielectric Half-Space TE PolarizationTM Polarization1530456075900.10.20.30.126.96.36.199.80.91Reflection coefficient |GE |Incident Angle qIer=81er=25er=16er=9er=4er=2.56Reflection coefficient |GH |
35 Path losses Propagation Ground reflection Other reflections We could assume that walls are perfect reflectors (||=1). But that would be poor approximation for some angles and materials. Also, this would assume that the signal is not able to propagate into buildings, which mobile phone users know is not the case.
36 Reflection and Transmission at Walls Transmission line formulationHomogeneous wallsAttenuation in wallsInhomogeneous walls
37 Transmission Line Formulation for a Wall ZdTEZaTEwZdTEZaTE
38 Transmission Line Method airwallairZ(w)ZL= ZaZaZwStanding Wave- wTransmittedIncidentReflected
39 Reflection at Masonry Walls (Dry Brick: er 5, e”=0) 20cm1020304050607080900.20.40.60.81900MHzTE1.8GHzTMAngle of Incidence qI (degree) G 2BZaTEZdTEZaTEBrewster angle
40 Reflection Accounting for Wall Loss The relative dielectric constant has an imaginary componentZaZw, kwZ(w)- wz
41 Comparison with Measured |G| 4 GHz for Reew = 4, Imew = 0 Comparison with Measured |G| 4 GHz for Reew = 4, Imew = 0.1 and l = 30 cm Landron, et al., IEEE Trans. AP, March 1996)1530456075900.10.20.30.188.8.131.52.80.91Measured dataAngle of Incidence qTE PolarizationG w = w = 30cm1530456075900.10.20.30.184.108.40.206.80.91Measured dataAngle of Incidence qTM PolarizationG w = w = 30cm
42 Transmission Loss Through Wall, cont. Now the might be imaginary => phaseSee mathcad file
43 Dielectric constantsWhen conductivity exists, use complex dielectric constant given bye = eo(er - je") where e" = s/weo and eo 10-9/36pMaterial* er s (mho/m) e" at 1 GHzLime stone wallDry marbleBrick wallCementConcrete wallClear glassMetalized glassLake waterSea WaterDry soilEarth* Common materials are not well defined mixtures and often contain water.
44 Diffraction sources Idea: The wave front is made of little sources that propagate in all directions.If the line of sight signal is blocked, then the wave front sources results propagation around the corner.The received power is from the sum of these sourcessourcesDefine excess path = h2 (d1+d2)/(2 d1d2)Phase difference= 2/Normalize Fresnel-Kirchoff diffraction parameter
45 Knife edge diffraction Path loss from transmitter to receiver is-10-5510-30-25-20-15Received Signal(dB)v
46 Multiple diffractions If there are two diffractions, there are some models. For more than 2 edges, the models are not very good.
47 Large-scale Path Loss Models Log-distancePL(d) = K (d/do)nPL(d) (dB) = PL(do) + 10 n log10(d)Redo examples
48 Large-scale Path Loss Models Log-normal shadowingPL(d) (dB) = PL(do) + 10 n log10(d) + XX is a Gaussian distributed random number32% chance of being outside of standard deviation.16% chance of signal strength being 10^(11/10) = 12 times larger/smaller than 10 n log10(d)2.5% chance of the signal being 158 times larger/smaller.The fit shown is not very good.This model is very popular.
49 Outdoor propagation models OkumuraEmpirical modelSeveral adjustments to free-space propagationPath Loss L(d) = Lfree space + Amu(f,d) – G(ht) – G(hr) – GAreaA is the median attenuation relative to free-spaceG(ht) = 20log(ht /200) is the base station height gain factorG(hr) is the receiver height gain factorG(hr) = 10log(hr /3) for hr <3G(hr) = 20log(hr /3) for hr >3Garea is the environmental correction factorHata
50 Hata Model Valid from 150MHz to 1500MHz A standard formula For urban areas the formula is:L50(urban,d)(dB) = logfc loghte – a(hre) (44.9 – 6.55loghte)logd wherefc is the ferquency in MHzhte is effective transmitter antenna height in meters (30-200m)hre is effective receiver antenna height in meters (1-10m)d is T-R separation in kma(hre) is the correction factor for effective mobile antenna height which is a function of coverage areaa(hre) = (1.1logfc – 0.7)hre – (1.56logfc – 0.8) dB for a small to medium sized city
51 Indoor propagation models Types of propagationLine of sightThrough obstructionsApproachesLog-normalSite specific – attenuation factor modelPL(d)[dBm] = PL(d0) + 10nlog(d/d0) + Xsn and s depend on the type of the buildingSmaller value for s indicates the accuracy of the path loss model.
52 Path Loss Exponent and Standard Deviation Measured for Different Buildings Frequency (MHz)ns (dB)Retail Stores9142.28.7Grocery Store1.85.2Office, hard partition15003.07.0Office, soft partition9002.49.619002.614.1Factory LOSTextile/Chemical13002.040002.1Paper/Cereals6.0Metalworking1.65.8Suburban HomeIndoor StreetFactory OBS220.127.116.11
53 Site specific – attenuation factor model PL(d) (dB) = PL(do) + 10 n log(d/do) + FAF + PAFFAF floor attenuation factor - Losses between floorsNote that the increase in attenuation decreases as the number of floors increases.PAF partition attenuation factor - Losses due to passing through different types of materials.BuildingFAF (dB)s (dB)Office Building 1Through 1 Floor12.97.0Through 2 Floors18.72.8Through 3 Floors24.41.7Through 4 Floors27.01.5Office Building 216.22.927.55.431.67.2
55 Small-scale path loss See matlab file They are summed as phasors. The received signal is the sum of the contributions of each reflection.They are summed as phasors.The received signal is the phasor sum of the contributions of each reflection.A small change in the position of the receiver or transmitter can cause a large change in the received signal strength.See matlab file
56 Rayleigh and Rician Fading The inphase and quadrature parts can be modeled as independent Gaussian random variables.The energy is the (X^2 + Y^2)^ ½ where X and Y are Gaussian => the energy is Rayleigh distributed.The power is (X^2 + Y^2) which is exponentially distributed.Rician – if there is a strong line-of-sight component as well as reflections. Then the signal strength has a Ricain distribution.
57 SummaryThe signal strength depends on the environment in a complicate way.If objects are possible obstructing, then the signal strength may be log-normal distributed => large deviation from free-spaceIf the signal is narrow band, then the the signal could be completely canceled out due to reflections and multiple paths.Reflection, transmission, and diffraction can all be important
58 Path Losslocation 1, free space loss is likely to give an accurate estimate of path loss.location 2, a strong line-of-sight is present, but ground reflections can significantly influence path loss. The plane earth loss model appears appropriate.location 3, plane earth loss needs to be corrected for significant diffraction losses, caused by trees cutting into the direct line of sight.location 4, a simple diffraction model is likely to give an accurate estimate of path loss.location 5, loss prediction fairly difficult and unreliable since multiple diffraction is involved.