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**Propagation Characteristics**

Lecture 2

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**Frequencies for communication**

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**Frequencies and regulations**

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Signal propagation Propagation in free space always like light (straight line) Receiving power proportional to 1/d² (d = distance between sender and receiver) Receiving power additionally influenced by Fading (frequency dependent) Shadowing Reflection at large obstacles Refraction depending on the density of a medium Scattering at small obstacles Diffraction at edges

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Signal propagation

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Real world example

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**Free space loss, ideal isotropic antenna**

Pt = signal power at transmitting antenna Pr = signal power at receiving antenna λ = carrier wavelength d = propagation distance between antennas c = speed of light (3x108 m/s) where d and λ are in the same units (e.g., meters)

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Free Space Loss Free space loss equation can be rewritten:

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**Free Space Loss Free space loss accounting for gain of other antennas**

Isotropic ant : Gt=1, Gr=1 Gt = gain of transmitting antenna Gr = gain of receiving antenna At = effective area of transmitting antenna Ar = effective area of receiving antenna

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Free Space Loss Free space loss accounting for gain of other antennas can be recast as

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**Propagation model Path loss: function of distance between TX and RX**

d0 : close-in distance, received power reference point, commonly 1Km used d :T-R separation: distance n: path loss exponent Log-normal shadowing: amplitude has a log-normal PDF Addition of random variable Xσ : zero-mean Gaussian distributed random variable (in dB) with standard deviation σ

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**Path loss model parameter**

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**Path loss model parameter**

Two values are computed from measured data, using linear regression method

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**Empirical Models Okumura model Hata model Cost 231 Model:**

Empirically based (site/freq specific) Awkward (uses graphs) Hata model Analytical approximation to Okumura model Cost 231 Model: Extends Hata model to higher frequency (2 GHz) Walfish/Bertoni: Cost 231 extension to include diffraction from rooftops Commonly used in cellular system simulations

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(Okumura) model

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Hata model

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**Propagation Characteristics**

Path Loss (includes average shadowing) Shadowing (due to obstructions): reflection, refraction, diffraction Multipath Fading Pr/Pt d=vt Pr Pt v Very slow Slow Fast

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**Channel characteristics**

Channel characteristics change over time and location signal paths change different delay variations of different signal parts different phases of signal parts quick changes in the power received (short term fading) Additional changes in distance to sender obstacles further away slow changes in the average power slow changes in the average term fading received (long term fading)

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**Combined Path Loss & Fading**

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**Path Loss Modeling Maxwell’s equations Free space path loss model**

Complex and impractical Free space path loss model Too simple Ray tracing models Requires site-specific information Simplified power falloff models Main characteristics: good for high-level analysis Empirical Models Don’t always generalize to other environments

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Small Scale fading Variations due to shadowing occur over relatively large distances– often many meters Signals in multipath environments also undergo small scale fading – variations that occur over the wavelength of the signal This is due to the different multipath components combining either constructively or destructively

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Small-scale fading (2) Offset of only a fraction of a wavelength can lead to large change in signal level:

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**Multipath propagation**

Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction Time dispersion: signal is dispersed over time interference with “neighbor” symbols Inter Symbol Interference (ISI) The signal reaches a receiver directly and phase shifted distorted signal depending on the phases of the different parts

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**The Effects of Multipath Propagation**

• Due to the different paths taken by the multipath components, they may arrive at different times • If the symbol period TS is smaller than the delay spread, i.e. TS < Tm, Inter-Symbol Interference (ISI) will occur • The receiver cannot determine which symbol each multipath component belongs to:

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**The Effects of Multipath Propagation**

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Delay Spread The Delay Spread Tm is defined as the difference between times-of arrival of the first and last multipath components Typical values are as follows:

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(Doppler shift)

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Fading

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Coherence Bandwidth The Coherence Bandwidth Bc is a statistical measure of the range of frequencies over which the attenuation of the channel is approximately constant Two frequency components f1 and f2 will experience similar attenuation if (f1 – f2) << Bc Coherence Bandwidth is approximately related to the Delay Spread by: Bc (Hz) = 1/Tm e.g. in a particular factory environment, Tm = 120ns, Bc = 1/(120 x 10-9) = 8.33 MHz

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**Coherence Bandwidth (2)**

If the transmitted signal has a bandwidth (Bu) much smaller than the Coherence Bandwidth(Bc), i.e. Bu << Bc, all frequency components will be attenuated similarly. This is called Flat Fading Else, it will undergo Frequency-selective fading, with different components attenuated differently. This causes distortion of the signal

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