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Wireless Propagation

Wireless Propagation. Signal Strength. Measure signal strength in dBW = 10*log(Power in Watts) dBm = 10*log(Power in mW) 802.11 can legally transmit at 30dBm (1W) (for 802.11a it is more complicated) Most 802.11 PCMCIA cards transmit at 10-20dBm (why?)

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Wireless Propagation

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  1. Wireless Propagation

  2. Signal Strength • Measure signal strength in • dBW = 10*log(Power in Watts) • dBm = 10*log(Power in mW) • 802.11 can legally transmit at 30dBm (1W) (for 802.11a it is more complicated) • Most 802.11 PCMCIA cards transmit at 10-20dBm (why?) • 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. • Mobile phone handset: 21dBm

  3. Noise • Interference • From other transmitters • 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 noise • Due to thermal agitation of electrons. Present in all electronics and transmission media. • kT(W/hz) • k Boltzmann’s constant = 1.3810-23 • T – temperture in Kelvin (C+273) • kTB(W) • B bandwidth • E.g., • Temp = 293,=> -203dB, -173dBm /Hz • Temp 293 and 22MHz => -130dB, -100dBm

  4. Signal to Noise Ratio (SNR) • SNR = signal power / noise power • SNR (dB) = 10*log10(signal power / noise power) • Signal strength is the transmitted power multiplied by a gain – impairments • Impairments • The 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 fading • An object not directly in the way impairs the transmission.

  5. Receiver Sensitivity • The received signal must have a strength that is larger than the receiver sensitivity • 20dB 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: -85dBm • Mobile phone base station: -119dBm • Mobile phone hand set: -118dBm • Mica2 at 868/916MHz: -98dBm

  6. Simple link budget • Determine if received signal is larger than the receiver sensitivity • Must account for effective transmission power • Transmission power • Antenna gain • Losses in cable and connectors. • Path losses • Attenuation • Ground reflection • Fading (self-interference) • Receiver • Receiver sensitivity • Losses in cable and connectors

  7. Antenna gain • 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 direction Horizontal direction

  8. Antenna gain • Antenna gain is increased by focusing the antenna • The 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 5.14dBi This antenna is narrower and results in 9dB higher gain than the dipole, hence, 9dBD or 11.14dBi

  9. Antenna gain Instead 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 5.14dBi Further 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. • Mobile phone base stations claim a gain of 18dBi with three sector antenna system. • Cover 15 degree vertical (360/15 = 24 or 10log10(24)dBi = 13.8dBi from vertical) • 3 sector, 10log10(3) =4.77 dBi • 13.8+4.77 – loss = 18dBi

  10. Simple link budget – 802.11g receiver sensitivity • 6Mbps • Thermal noise: -174 dBm/Hz • Channel noise (22MHz): 73 dB • Noise factor: 10 dB • Noise power (sum of the above): -91 dBm • Receiver requirements: • 3 dB is the minimum SNR (see next slide) • Min receiver signal strength: -88 dBm • 54Mbps • Thermal noise: -174 dBm/Hz • Channel noise (22MHz): 73 dB • Noise factor: 10 dB • Noise power (sum of the above): -91 dBm • Receiver requirements: • 20 dB is the minimum SNR (see next slide) • Min receiver signal strength: -71 dBm

  11. Required SNR 802.11 a (or g) Packet success probability vs. bit success probability

  12. Simple link budget – 802.11g example • From base station (6Mbps) • +20dBm transmission power • +6dBi transmit antenna gain • +2.2dBi receiver antenna gain • -88dBm minimum receiver power • => 116.2 dB path losses • => 113.2 dB path losses if 3dB of link margin is added (to ensure the link works well.) • From PCMCIA to base station • +10dBm transmission power • +6dBi transmit antenna gain • +2.2dBi receiver antenna gain • -88dBm minimum receiver power • => 106.2 dB path losses • => 103.2 dB path losses if 3dB of link margin is added (to ensure the link works well.) • From base station (54Mbps) • +20dBm transmission power • +6dBi transmit antenna gain • +2.2dBi receiver antenna gain • -71dBm minimum receiver power • => 99.2 dB path losses • => 96.2 dB path losses if 3dB of link margin is added (to ensure the link works well.)

  13. Simple link budget – mobile phone – downlink example • Transmission power (base station): 20W (can be as high as 100W) • Transmission power for voice (not control): 18W • Number of users: 60 • Transmission power/user: 0.3W, 300mW, 24.8dBm • Base station antenna gain (3-sectors): 18dBi • Cable loss at base station: 2dB • Effective isotropic radiated power: 40dBm (sum of the above) • Receiver: • Thermal noise: -174 dBm/Hz • Mobile station receiver noise figure (noise generated by the receiver, Johnson Noise, ADC quantization, clock jitter): 7dB • Receiver noise density: -167 dB/Hz (-174+7) • Receiver noise: -101.2 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: 7.9dB • Receiver sensitivity: -101.2 – 25 + 7.9 = -118.3 • Body loss (loss due to your big head): 3dB • Maximum path loss: 40 – (-118.3) –3 = 155.3

  14. Simple link budget – mobile phone – uplink example • Transmission power (mobile): 0.1W (21 dBm) • Antenna gain: 0 dBi • Body loss: 3 dB • Effective isotropic radiated power: 18 dBm (sum of the above) (maximum allowable by FCC is 33 dBm at 1900MHz and 20dBm at 1700/2100 MHz • Receiver/base station • Thermal noise: -174 dBm/Hz • Mobile station receiver noise figure (noise generated by the receiver, Johnson Noise, ADC quantization, clock jitter): 5dB • Receiver noise density: -169 dB/Hz (-174+5) • Receiver noise: -103.2 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: 6.1dB • Receiver sensitivity: -119.0 • Maximum path loss: 153.3

  15. Shannon Capacity • Given SNR it is possible to find the theoretical maximum bit-rate: • Effective bits/sec = B log2(1 + SNR), where B is bandwidth • E.g., • B = 22MHz, • SNR = 2.5 dB (where 802.11 at 6Mbps gives a low bit error) • 22106 log2(1 + 10^(2.5/10)) = 32Mbps • Of course, 802.11a/g can only do 6Mbps when the SNR = 2.5 dB • Today, Shannon capacity is not possible, but we can get within a few dB. • SNR ~ 2.5 dB – 3 dB • 22106 log2(1 + 10^((2.5-3)/10)) = 20Mbps

  16. Propagation • Required receiver signal strength minus Transmitted signal strength is often approximately • 99 dB 802.11 base station -> laptop • 79.2 dB 802.11b laptop -> base station • 75.4 dB laptop -> laptop • 155.3 Mobile phone downlink • 153.3 Mobile phone uplink. • Where does all this energy go… • Free space propagation – not valid but a good start • Ground reflection • 2-ray – only valid in open areas. Not valid if buildings are nearby. • Wall reflections/transmission • Diffraction • Large-scale path loss models • Log-distance • Log-normal shadowing • Okumura • Hata • Longley-Rice • Indoor propagation • Small-scale path loss • Rayleigh fading • Rician Fading

  17. 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  pTand antenna gain  GTis • The 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 is • PR = PT GT (A/ (4  d2)) • Define the receiver antenna gain GR = 4  A/2. •  = c/f • 2.4GHz=> = 3e8m/s/2.4e9/s = 12.5 cm • 933 MHz => =32 cm. • Receiver signal strength: PR = PT GT GR (/4d)2 • PR (dBm) = PT (dBm) + GT (dBi) + GR (dBi) + 10 log10 ((/4)2)-10log10(d2) • 2.4 GHz => 10 log10 ((/4)2) = -40 dB • 933 MHz => 10 log10 ((/4)2) = -32 dB

  18. Free Space Propagation - examples • Mobile phone downlink •  = 12.5 cm • PR (dBm) = (PT GT GRL) (dBm) - 40 dB + 10 log10 (1/d2) • Or PR – (PT +GT +GR + L) - 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 MA • Mobile phone uplink • d = 10^ ((153-40)/20) = 446Km • 802.11 • PR - PT = -113.2dBm • 6 Mbps • d = 10(113.2-40)/20 = 4500 m • d = 10(113.2-40 - 3)/20 = 3235 m with 3 dB gain margin • d = 10(113.2-40 – 3 - 9)/20 = 1148 m with 3 dB gain margin and neglecting antenna gains • 54Mbps needs –85dBm • d = 10(99.2-40)/20 = 912 m • d = 10(99.2-40 - 3)/20 = 646 m with 3 dB gain margin • d = 10(99.2-40 – 3 - 9)/20 = 230 m with 3 dB gain margin and neglecting antenna gains • Mica2 Mote • -98 dBm sensitivity • 0 dBm transmission power • d = 10^((98-30)/20) = 2511 m

  19. Ground reflection • Free-space propagation can not be valid since I’m pretty sure that my cell phone does reach Boston. • There are many impairments that reduce the propagation. • Ground reflection (the two-ray model) – the line of sight and ground reflection cancel out.

  20. 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0 • Reflected = Eo/dGR (dGR-dLOS) 2  /  • For large d dLOS = dGR • Total energy • E = (Eo/dLOS) ( (cos ((dGR-dLOS) 2  /  ) – 1)2 + sin2((dGR-dLOS) 2  /  ) ) ½ • E = (Eo/dLOS) 2 sin((dGR-dLOS)  /  )

  21. Ground reflection (approximate) • dGR-dLOS dGR = ((ht+hr)^2 + d^2)^1/2 dLOS = ((ht-hr)^2 + d^2)^1/2 dGR-dLOS 2hthr/d -> 0 as d-> inf 2 sin((dGR-dLOS)  /  ) -> 0, For large d, 2 sin((dGR-dLOS)  /  )  C/d So total energy is 1/d^2 And total power is energy squared, or K/d^4

  22. Ground reflection (approximate) • or • Examples: • Mobile phone • Suppose the base station is at 10m and user at 1.5 m • do = 1.5 Km • d = 10^((155 – 40 + 20log10(do) )/40) = 29Km • 802.11 • Suppose the base station is at 1.5m and user at 1.5 m • do = 226m • 6 Mbps (20 dB transmit power) • d = 10(113.2-40 + 20log10(do))/40 = 1016 m • d = 10(113.2-40 -3 – 8.2 + 20log10(do))/40 = 533 m 3 dB gain margin and neglecting antenna gains • 54 Mbps (20 dB transmit power) • d = 10(99.2-40 + 20log10(do))/40 = 453 m • d = 10(99.2-40 -3 – 8.2 + 20log10(do))/40 = 238 m 3 dB gain margin and neglecting antenna gains • What is the impact of 3dB of power • Mobile phone: 34 Km • 802.11: ~100 m (at 6Mbps) and ~50m (at 54Mbps)

  23. Ground reflection (more accurate) • When the signal reflects off of the ground, it is partially absorbed and the phase shift is not always . • Polarization • Transmission line model of reflections

  24. Polarization The 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

  25. Polarization The peak of the electric field rotates around the axis.

  26. Polarization If a antenna and the electric field have orthogonal polarization, then the antenna will not receive the signal

  27. 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

  28. Snell's Law for Oblique Incidence q q q x q qT qT y Graphical interpretation of Snell’s law

  29. Transmission Line Representation for Transverse Electric (TE) Polarization y Ez + - q q Hx x z qT

  30. Transmission Line Representation for Transverse Magnetic (TM) Polarization y Ex + - q q Hz x z qT

  31. Reflection from a Dielectric Half-Space GE 90º q -1 GH 90º qB q -1 • TE Polarization (e.g., vertical polarization hitting a vertical wall) • TM Polarization (e.g., horizontal polarization hitting a vertical wall) no phase shift

  32. Magnitude of Reflection Coefficients at a Dielectric Half-Space 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 15 30 45 60 75 90 0 15 30 45 60 75 90 TE Polarization TM Polarization Reflection coefficient |GE| er=81 er=81 Reflection coefficient |GH| er=25 er=25 er=16 er=16 er=9 er=9 er=4 er=4 er=2.56 er=2.56 Incident Angle qI Incident Angle qI • Different materials give different behavior • TE polarization has 180o phase shift • TM has 180o phase shift only for high incident angle • At incident angle reaches 90o, the reflection coefficient reached 1. What is happening? • What is happening when reflection coefficient equals 0? Nothing is reflected!

  33. Transmission Line Method Incident Za Zw Za Transmitted Reflected ZL=Za Z(w) Standing Wave - w 0 air wall air If the standing wave is “just so,” then the reflected signal cancels with the standing wave and nothing is reflected This occurs at the Brewster angle

  34. Reflection at Masonry Walls(Dry Brick: er  5, e”=0) 1 0.8 900MHz 20cm TE 0.6  G 2 1.8GHz TE 0.4 900MHz TM 0.2 1.8GHz TM 0 0 10 20 30 40 50 60 70 80 90 Angle of Incidence qI (degree) B ZaTE ZdTE ZaTE Brewster angle

  35. Reflections width receiver width = 7 m width = 35 m Brick Brick Concrete Concrete - 10 - 10 d Glass Glass 2 2 1/d 1/d - 20 1.47 - 20 1.38 1/d 1/d channel gain (dB) - 30 - 30 transmitter - 40 - 40 walls - 50 - 50 0 100 200 300 0 100 200 300 d The RF signals reflect off of walls and the ground, but the strength and the phase are impacted • The strength of the reflected signal depends on • The angle the signal hits the wall/ground • The material that the wall/ground is made of • The thickness of the wall.

  36. Transmission Through Walls brick concrete glass 0 same height - 10 elevated wall - 20 channel gain (dB) - 30 15 m - 40 receiver transmitter 0 10 20 30 0 10 20 30 0 10 20 30 d distance from wall The RF signals can pass through walls, but the strength and the phase are impacted • The strength of the transmitted signal depends on • The angle the signal hits the wall • The material that the wall is made of • The thickness of the wall Note that the signal strength does not necessarily increase as the transmitter moves closer to the receiver

  37. Ground reflection • See Mathcad file

  38. Diffraction • 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 sources sources • Define excess path •  = h2 (d1+d2)/(2 d1d2) • Phase difference • = 2/ Normalize Fresnel-Kirchoff diffraction parameter

  39. Knife edge diffraction 5 0 -5 -10 Received Signal(dB) -15 -20 -25 -30 -10 -5 0 5 10 v • Path loss from transmitter to receiver is • Note that at v = 0 (i.e., h=0 on previous slide), the signal power is still reduced by 6dB. • Even when h>0, the signal power is still impacted by diffraction

  40. Diffraction With diffraction With diffraction Free Free - - space only space only Diffraction allows the signal to “bend” around corners 20 transmitter transmitter 5m 5m 30 5m 5m 40 Channel gain (dB) 50 h h 5m 5m 60 receiver receiver 70 0 10 20 30 40 h (m)

  41. 2 Edge Diffraction With diffraction With diffraction Free Free - - space only space only Diffraction allows the signal to “bend” around corners 30 60 Channel gain (dB) h 90 5m 5m 50m transmitter receiver 120 0 20 40 h (m) The signal strength is greatly reduced after two diffractions. For 802.11, two diffractions results in negligible signal strength

  42. Multiple diffractions • If there are two diffractions, there are some models. For more than 2 edges, the models are not very good. • On the other hand, there is so much loss after more than 2 edges, that the models are not very useful. For example, the signal might be stronger from just passing through the object than diffracting around it.

  43. Large-scale Path Loss Models • Log-distance • PL(d) = K (d/do)n • PL(d) (dB) = PL(do) + 10 n log10(d) Redo examples

  44. Large-scale Path Loss Models with Shadowing • Log-normal shadowing • PL(d) (dB) = PL(do) + 10 n log10(d) + X • X is a Gaussian distributed random number • 32% chance of being outside of standard deviation. • 16% chance of signal strength being 11.8 dB larger (or smaller) than 10 n log10(d) • 2.5% chance of the signal being 23.6 dB times larger (or smaller) • 11.8 dB and 23.6 dB are very large! • The fit shown is not very good. • This model is very popular.

  45. Correlated Lognormal Shadowing weakest signal strongest signal • Stochastic models of propagation are specialized for single hop communication. • Networking is focused on graphs, e.g., (k-) connectivity, graph diameter, shortest-path, max-flow, largest clique, minimum dominating subgraph. • Even with correlations, stochastic models of propagation do not produce realistic graphs. • In urban scenarios, the propagation is strongly influenced by the map of the city.

  46. Outdoor propagation models • Okumura • Empirical model • Several adjustments to free-space propagation • Path Loss L(d) = Lfree space + Amu(f,d) – G(ht) – G(hr) – GArea • A is the median attenuation relative to free-space • G(ht) = 20log(ht /200) is the base station height gain factor • G(hr) is the receiver height gain factor • G(hr) = 10log(hr /3) for hr <3 • G(hr) = 20log(hr /3) for hr >3 • Garea is the environmental correction factor

  47. Hata Model • Valid from 150MHz to 1500MHz • A standard formula • For urban areas the formula is: • L50(urban,d)(dB) = 69.55 + 26.16logfc - 13.82loghte – a(hre) + (44.9 – 6.55loghte)logdwhere fc is the ferquency in MHz hte 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 km a(hre) is the correction factor for effective mobile antenna height which is a function of coverage area a(hre) = (1.1logfc – 0.7)hre – (1.56logfc – 0.8) dB for a small to medium sized city

  48. Indoor propagation models • Types of propagation • Line of sight • Through obstructions • Approaches • Log-normal • Site specific – attenuation factor model • Log-normal • PL(d)[dBm] = PL(d0) + 10nlog(d/d0) + Xs • n and s depend on the type of the building • Smaller value for s indicates the accuracy of the path loss model.

  49. Path Loss Exponent and Standard Deviation Measured for Different Buildings

  50. Site specific – attenuation factor (AF) model • PL(d) (dB) = PL(do) + 10 n log(d/do) + FAF +  PAF • FAF floor attenuation factor - Losses between floors • Note 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 • Use straight line between transmitter and receiver and count objects the line passes through

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