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**EEE 441 Wireless And Mobile Communications**

Lecture 07 EEE 441 Wireless And Mobile Communications

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Quiz2 soln

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**Propagation of Radio Waves: Large-Scale Path Loss**

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**Radio Wave Propagation**

Large-scale path loss Observed at receiver distances that are large compared to the wavelength of the carrier signal Free-space propagation loss The 3 basic propagation mechanisms of reflection, diffraction and scattering Small-scale path loss Rapid fluctuations that occur over small movements in receiver position (a few wavelengths) Also known as fading

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**Small-Scale and Large-Scale Fading**

Received Power (dBm) -30 -40 -50 -60 This figure is just an illustration to show the concept. It is not based on read data. -70 T-R Separation (meters)

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Unit for Power Loss The decibel, dB A logarithmic unit that is used to describe a ratio Given two power values P1 and P2, the difference (as a ratio) is expressed in dB as: 10 log (P1/P2) (dB) Example Tx Power P1 = 100W, Rx Power P2 = 1W The loss = 10 log(100/1) = 20 dB

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Decibel (dB) versus Power Ratio Comparison of two Sound Systems

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Decibel milli Used to denote a power level with respect to 1mW as the reference power level Example: Tx power is P1 = 100W Loss = 10 log(100W/1mW) = 10 log (100,000) = 50 dBm

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Decibel Watt Used to denote a power level with respect to 1W as the reference power level Example: Tx power is P2 = 100W Loss = 10 log(100W/1W) = 10 log (100) = 20 dBW

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**Radio Wave Propagation**

At VLF, LF, and MF bands, radio waves follow the ground. AM radio broadcasting uses MF band reflection At HF bands, the ground waves tend to be absorbed by the earth. The waves that reach ionosphere ( km above earth surface), are reflected and sent back to earth. Ionosphere absorption

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**Radio Wave Propagation (cont’d)**

VHF Transmission LOS path Reflected Wave When directional antennas are used, waves follow more direct paths - LOS: Line-of-Sight Communication - Reflected wave interfere with the original signal

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**Coverage Environment Line-of-Sight (LOS) between Tx/Rx**

Waves obstructed and absorbed by buildings, foliage, rain … Velocity of Rx leads to Doppler effects

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**Free-Space Propagation Model**

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**Free-Space Propagation Model**

Used to predict the received signal strength when Transmitter and Receiver have clear, unobstructed LOS path between them The Rx power decays as a function of the T-R separation distance raised to some power

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**Friis Free-Space Equation**

Free space power received after a distance d is given by Friis free-space equation: Pr(d) = (PtGtGrl2) / ((4p)2d2L) Pt is transmitted power Pr is received power Gt is transmitter antenna gain (dimensionless quantity) Gr is receiver antenna gain (dimensionless quantity) d is T-R separation distance (in meters) L is system loss factor not related to propagation (L >= 1) l is wavelength (in meters)

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Antenna Gain The gain of an antenna G is related to its affective aperture Ae by: G = 4pAe / l2 The effective aperture of Ae is related to the physical dimensions of the antenna

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**Isotropic Antennas and Effective Gain**

An isotropic radiator is an ideal antenna that radiates power with unit gain uniformly in all directions Antenna gains are given in units of dBi (dB gain with respect to an isotropic antenna)

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**Path Loss Path Loss signal attenuation, measured in dB:**

PL(dB) = 10 log (Pt/Pr) = -10log[(GtGrl2)/(4p)2d2] If antennas have unity gains (exclude them): PL(dB) = 10 log (Pt/Pr) = -10log[l2/(4p)2d2]

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**Long Distance Path-Loss Model**

The average large-scale path loss is expressed as a function of distance The value of n depends on the propagation environment: n=2 for free space, higher when obstructions are present

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**Path-Loss Exponent for Different Environments**

Path Loss Exponent, n Free space 2 Urban area cellular radio 2.7 to 3.5 Shadowed urban cellular radio 3 to 5 In building line-of-sight 1.6 to 1.8 Obstructed in building 4 to 6 Obstructed in factories 2 to 3

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**What Scale is “Large-Scale”?**

For Friis free-space equation to hold, d should be in the far-field of the Tx antenna The far-field, or Fraunhofer region, is given by: df = 2D2/l D is largest physical dimension of the antenna Additionally, df >> D and df >> l

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**Reference Distance, d0 Free-space equation does not hold for d = 0**

We use a small distance d0 as the reference point d0 should be > df d0 should be < any practical distance d where we wish to measure the power of a mobile receiver Received power Pr(d), at a distance d > d0 from a transmitter, is related to Pr at d0, Pr(d0), by: Pr(d) = Pr(d0)(d0/d)2 given that d >= d0 >= df

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**Reference Distance d0 (cont’d)**

Expressing the received power in dBm and dBW: Pr(d) (dBm) = 10 log [Pr(d0)/0.001W] + 20log(d0/d) where Pr(d0) is in Watts Pr(d) (dBW) = 10 log [Pr(d0)/1W] + 20log(d0/d) where Pr(d0) is in Watts

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**Selection of Reference Distance d0**

In large coverage cellular systems About 1km In microcellular systems About 1m ~ 100m Must be in the far-field of the antenna, so that near-field effects do not result

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Fraunhofer Region For Friis equation to hold, distance d should be in the far-field of the Tx antenna The far-field, or Fraunhofer region, of a transmitting antenna is defined as: df = 2D2/l D is the largest physical dimension of the antenna. Additionally, df >> D and df >> l

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Notices Reading Rappaport, Ch 4.1 – 4.2 (selections)

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