# Wireless Propagation.

## Presentation on theme: "Wireless Propagation."— Presentation transcript:

Wireless Propagation

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

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 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

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.

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

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

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 direction Horizontal direction

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

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. 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 – dBi An 11dBi antenna has a very narrow range.

Thermal noise: -174 dBm/Hz Channel noise (22MHz): 73 dB Noise factor: 5 dB Noise power (sum of the above): -96 dBm Receiver requirements: 3 dB interference margin 0 dB is the minimum SINR Min receiver signal strength: -93 dBm

Simple link budget – 802.11 example

Required SNR For a given bit-error probability, different modulation schemes need a higher SNR Eb is the energy per bit No is the noise/Hz Bit-error is given as a function of Eb / No Required SNR = Eb / No * Bit-rate / bandwidth A modulation scheme prescribes a Bit-rate / bandwidth relationship E.g., for 10^-6 BE probability over DBPSK requires 11 dB + 3 dB = 14 dB SNR

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, Signal strength = -90dBm N = -100dBm => SNR = 10dB => 10 22106 log2(1 + 10) = 76Mbps Of course, b can only do 1Mbps when the signal strength is at –90dBm.

Propagation Required receiver signal strength – Transmitted signal strength is often around 99 dB base station -> laptop 79.2 dB b 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

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 is 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d)2) 2.4 GHz => 10 log10 ((/4d)2) = -40 dB 933 MHz => 10 log10 ((/4d)2) = -32 dB

Free Space Propagation - examples
Mobile phone downlink  = 12.5 cm PR (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 MA Mobile phone uplink d = 10^ ((153-40)/20) = 446Km 802.11 PR-PT = -90dBm d = 10^((90-40)/20) = 316 m 11Mbps needs –85dBm d = 10^((85-40)/20) = 177 m Mica2 Mote -98 dBm sensitivity 0 dBm transmission power d = 10^((98-30)/20) = 2511 m

Ground reflection Free-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.

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)  /  )

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

Ground reflection (approximate)
For d > 5ht hr, Pr = (hthr)^2 / d^4 Gr GT PT Pr – PT – 10log((hthr)^2) - log(Gr GT ) = 40 log(1/d) Examples: Mobile phone Suppose the base station is at 10m and user at 1.5 m d = 10^((155 – 12)/40) = 3.7Km 802.11 Suppose the base station is at 1.5m and user at 1.5 m d = 10^((90 – 3.5)/40) = 145m But this is only accurate when d is large 145m might not be large enough

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

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

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

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

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

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

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

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

Reflection from a Dielectric Half-Space
TE Polarization TM Polarization 90º -1 GE q GH qB no phase shift

Magnitude of Reflection Coefficients at a Dielectric Half-Space
TE Polarization TM Polarization 15 30 45 60 75 90 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reflection coefficient |GE | Incident Angle qI er=81 er=25 er=16 er=9 er=4 er=2.56 Reflection coefficient |GH |

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.

Reflection and Transmission at Walls
Transmission line formulation Homogeneous walls Attenuation in walls Inhomogeneous walls

Transmission Line Formulation for a Wall
ZdTE ZaTE w ZdTE ZaTE

Transmission Line Method
air wall air Z(w) ZL= Za Za Zw Standing Wave - w Transmitted Incident Reflected

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

Reflection Accounting for Wall Loss
The relative dielectric constant has an imaginary component Za Zw, kw Z(w) - w z

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) 15 30 45 60 75 90 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Measured data Angle of Incidence q TE Polarization G  w =  w = 30cm 15 30 45 60 75 90 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Measured data Angle of Incidence q TM Polarization G  w =  w = 30cm

Transmission Loss Through Wall, cont.
Now the  might be imaginary => phase See mathcad file

Dielectric constants When conductivity exists, use complex dielectric constant given by e = eo(er - je") where e" = s/weo and eo  10-9/36p Material* er s (mho/m) e" at 1 GHz Lime stone wall Dry marble Brick wall Cement Concrete wall Clear glass Metalized glass Lake water Sea Water Dry soil Earth * Common materials are not well defined mixtures and often contain water.

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

Knife edge diffraction
Path loss from transmitter to receiver is -10 -5 5 10 -30 -25 -20 -15 Received Signal(dB) v

Multiple diffractions
If there are two diffractions, there are some models. For more than 2 edges, the models are not very good.

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

Large-scale Path Loss Models
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 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.

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 Hata

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 where 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

Indoor propagation models
Types of propagation Line of sight Through obstructions Approaches Log-normal Site specific – attenuation factor model 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.

Path Loss Exponent and Standard Deviation Measured for Different Buildings
Frequency (MHz) n s (dB) Retail Stores 914 2.2 8.7 Grocery Store 1.8 5.2 Office, hard partition 1500 3.0 7.0 Office, soft partition 900 2.4 9.6 1900 2.6 14.1 Factory LOS Textile/Chemical 1300 2.0 4000 2.1 Paper/Cereals 6.0 Metalworking 1.6 5.8 Suburban Home Indoor Street Factory OBS 9.7 3.3 6.8

Site specific – attenuation factor 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. Building FAF (dB) s (dB) Office Building 1 Through 1 Floor 12.9 7.0 Through 2 Floors 18.7 2.8 Through 3 Floors 24.4 1.7 Through 4 Floors 27.0 1.5 Office Building 2 16.2 2.9 27.5 5.4 31.6 7.2

FAF

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