Communication Engineering Faculty of Electrical...

Wireless Communication Systems

Communication EngineeringFaculty of Electrical engineeringSahand University of Technology

Lecture2: Path loss and shadowing

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ing�The wireless radio channel poses a severe challenge as a medium for reliable high-

speed communication.

� Not only it is susceptible to noise, interference, and other channel impediments, but these impediments change over time in unpredictable ways as a result of user movement and environment dynamics.

� Path loss is caused by dissipation of the power radiated by the transmitter as well as by effects of the propagation channel.

� Shadowing is caused by obstacles between the transmitter and receiver that attenuate signal power through absorption, reflection, scattering, and diffraction.

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2016Afshin Ebrahimi, Sahand University of Technology

Path loss and shadowing

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�Received power variation due to path loss occurs over long distances (100–1000 m).

�variation due to shadowing occurs over distances that are proportional to the lengthof the obstructing object (10–100 m in outdoor environments and less in indoor environments).

�Since variations in received power due to path loss and shadowing occur over relatively large distances, these variations are sometimes referred to as large-scale propagation effects.

�There is received power variations due to the constructive and destructive addition of multipath signal components. These variations occur over very short distances, on the order of the signal wavelength, and so are sometimes referred to as small-scale propagation effects.

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�The initial understanding of radio wave propagation goes back to the pioneering work of James Clerk Maxwell, who in 1864 formulated a theory of electromagnetic propagation that predicted the existence of radio waves.

�In 1887, the physical existence of these waves was demonstrated by Heinrich Hertz. However, Hertz saw no practical use for radio waves.

�By 1897 Guglielmo Marconi had managed to send a radio signal from the Isle of Wight to a tugboat eighteen miles away, and in 1901 Marconi’s wireless system could traverse the Atlantic ocean.

�The first transmission of voice and music was made by Reginald Fessenden in 1906 using a form of amplitude modulation, as is done in all wireless systems today.

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�Electromagnetic waves propagate through environments where they are reflected, sc

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d, and diffracted by walls, terrain, buildings, and other objects.

�The ultimate details of this propagation can be obtained by solving Maxwell’s equations with boundary conditions.

�The simplest ray-tracing model is the two-ray model, which accurately describes signal propagation when there is one direct path between the transmitter and receiver and one reflected path.

�Often the complexity and variability of the radio channel make it difficult to obtain an accurate deterministic channel model. For these cases, statistical models are often used.

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�models are developed mainly for signals in the UHF and SHF bands, from .3–3 GHz and 3–30 GHz (respectively).

�This range of frequencies is quite favorable for wireless system operation because of its propagation characteristics and relatively small required antenna size.

�All the transmitted and received signals that we consider are real. That is because modulators are built using oscillators that generate real sinusoids (not complex exponentials).

�Many signals in communication systems are real bandpass signals with a frequency response that occupies a narrow bandwidth 2B centered around a carrier frequency fc with 2B << fc.

7Transmit and Receive Signal Models


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� Since bandpass signals are real, their frequency response has conjugate Symmetry.

� However, bandpass signals are not necessarily conjugate symmetric within the signal bandwidth about the carrier frequency fc.

� We represent a bandpass signal s(t) at carrier frequency fc in the following form:



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� Define the complex signal

Then u(t) is a complex lowpass signal of bandwidth B. With this definition we see that

The representation on the right-hand side of this equation is called the complex lowpass representation of the bandpass signal s(t), and the baseband signal u(t) is called the equivalent lowpass signal for s(t) or its complex envelope.



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� consider a real channel impulse response h(t) with Fourier transform H(f).

� A bandpass channel is similar to a bandpass signal: it has a real impulse response h(t) with frequency response H(f) centered at a carrier frequency fc with a bandwidth of 2B << fc.

� Because the impulse response h(t) corresponding to H(f) is a bandpass signal, it can be written using an equivalent lowpass representation as

� in many wireless channels (e.g., frequency-selective fading channels) H(f) is not conjugate symmetric about fc, in which case hl(t) is complex.



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� Assume The transmitted signal s(t) and channel impulse response h(t) are both real, so the channel output r(t) = s(t) ∗ h(t) is also real, with frequency response R(f) = H(f)S(f).

� Since S(f) is a bandpass signal, R(f) will also be a bandpass signal. Therefore, it has a complex lowpass representation of

� Thus, we can obtain the equivalent lowpass signal v(t) for the received signal r(t) by taking the convolution of hl(t) and u(t).

� The main purpose for the equivalent lowpass representation is to analyze bandpass communication systems using the equivalent lowpass models for the transmitted signal, channel impulse response, and received signal. This removes the carrier terms from the analysis .



Path

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ing� Suppose s(t) of power Pt is transmitted through a given channel with corresponding

received signal r(t) of power Pr. We define the linear path loss of the channel as the ratio of transmit power to receive power:

� In general, the dB path loss is a nonnegative number; the channel does not contain active elements, and thus it can only attenuate the signal.

� The dB path gain is defined as the negative of the dB path loss:

12 Path loss


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ing� Consider a signal transmitted through free space to a receiver located at

distance d from the transmitter.

� Assume there are no obstructions between the transmitter and receiver and that the signal propagates along a straight line between the two. The channel model associated with this transmission is called a line-of-sight (LOS) channel, and the corresponding received signal is called the LOS signal or ray.

� Free-space path loss introduces a complex scale factor, resulting in the received signal

13Free-Space Path Loss


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� Where √Gl is the product of the transmit and receive antenna field radiation patterns in the LOS direction. The phase shi� e^(−j2πd/λ) is due to the distance d that the wave travels.

� The power in the transmitted signal s(t) is Pt , so the ratio of received to transmitted power is

� The received signal power is also proportional to the square of the signal wavelength, so as the carrier frequency increases the received power decreases.

14Free-Space Path Loss


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� In a typical urban or indoor environment, a radio signal transmitted from a fixed source will encounter multiple objects in the environment that produce reflected, diffracted, or scattered copies of the transmitted signal.

� These additional copies of the transmitted signal, known as multipath signal components, can be attenuated in power, delayed in time, and shifted in phase and/or frequency with respect to the LOS signal path at the receiver.

� In ray tracing we assume a finite number of reflectors with known location and dielectric properties.

� The details of the multipath propagation can then be solved using Maxwell’s equations with appropriate boundary conditions.

15 Ray tracing


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Reflected, diffracted, and scattered wave components16


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ing� Comparison of the ray-tracing method with empirical data shows it to accurately

model received signal power in rural areas, along city streets when both the transmitter and receiver are close to the ground, and in indoor environments with appropriately adjusted diffraction coefficients.

� if the source or receiver are moving then the characteristics of the multiple paths vary with time. These time variations are deterministic when the number, location, and characteristics of the reflectors are known over time. Otherwise, statistical models must be used.

� if the number of reflectors is large or if the reflector surfaces are not smooth, then we must use statistical approximations to characterize the received signal.

17Reflected, diffracted, and scattered wave components


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� The two-ray model is used when a single ground reflection dominates the multipath effect.

� The received signal consists of two components: the LOS component or ray, which is just the transmitted signal propagating through free space, and a reflected component or ray, which is the transmitted signal reflected off the ground.

� the received signal for the two-ray model is

� √Gl = √GaGb is the product of the transmit and receive antenna field radiation patterns in the LOS direction, R is the ground reflection coefficient.

18Two-ray model


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ing� √Gr = √GcGd is the product of the transmit and receive antenna field radiation

patterns corresponding to the rays of length x and x’, respectively.

19Two-ray model


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� The delay spread of the two-ray model equals the delay between the LOS ray and the reflected ray: τ =(x + x’ − l )/c.

� If the transmitted signal is narrowband relative to the delay spread then u(t) ≈ u(t −τ). With this approximation, the received power of the two-ray model for narrowband transmission is

� for asymptotically large d, x + x’ ≈ l ≈ d, θ ≈ 0, Gl ≈ Gr , and R ≈ −1. Substituting these approximations, the received signal power is approximately

20Two-ray model


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� A plot as a function of distance is shown for f=900 MHz, R = −1, ht=50m, hr = 2, Gl = 1, Gr = 1, and transmit power normalized so that the plot starts at 0 dBm.

� In the first segment, power falloff is constant and proportional to 1/(ht)^2 ; for distances between ht and dc, power falls off at −20 dB/decade; and at distances greater than dc, power falls off at −40 dB/decade.

21Two-ray model


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� Power falloff with distance in both the ten-ray model and urban empirical data is typically propor�onal to d ^(−2), even at rela�vely large distances.

22Ten-Ray Model


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� For this model, the building database (height, location, and dielectric properties) and the transmitter and receiver locations relative to the buildings must be specified exactly.

� the strength of each component is derived explicitly based on the building locations and dielectric properties.

� In general, the LOS and reflected paths provide the dominant components of the received signal, since diffraction and scattering losses are high.

� Diffraction occurs when the transmitted signal “bends around” an object in its path to the receiver.

23General Ray Tracing


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ing� Diffraction results from many phenomena, including the curved surface of the

earth, hilly or irregular terrain, building edges, or obstructions blocking the LOS path between the transmitter and receiver.

� Diffraction is most commonly modeled by the Fresnel knife-edge diffraction model because of its simplicity.

24Ten-Ray Model


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� for h small relative to d and d’ , the signal must travel an additional distance relative to the LOS path of approximately

� Approximations for knife-edge diffraction path loss (in dB) relative to LOS path loss are given by as

� The knife-edge diffraction model yields the following formula for the received diffracted signal:

25Ten-Ray Model: “Fresnel knife-edge diffraction model”


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� A scattered ray, by the segments s and s’ , has a path loss proportional to the product of s and s’. This multiplicative dependence is due to the additional spreading loss that the ray experiences after scattering.

� The received signal due to a scattered ray is given by the bistatic radar equation

26Ten-Ray Model


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� σ (in square meters) is the radar cross-section of the scattering object, which depends on the roughness, size, and shape of the scatterer:

�if we have a LOS ray, Nr reflected rays, Nd diffracted rays, and Ns diffusely scattered rays, the total received signal is

27Ten-Ray Model


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� These models are mainly based on empirical measurements over a given distance in a given frequency range for a particular geographical area or building.

� empirical measurements of Pr/Pt as a function of distance include the effects of path loss, shadowing, and multipath.

� In order to remove multipath effects, empirical measurements for path loss typically average their received power measurements and the corresponding path loss at a given distance over several wavelengths.

� This average path loss is called the local mean attenuation (LMA) at distance d, and it generally decreases with d owing to free-space path loss and signal obstructions.

28Empirical Path-Loss Models


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� Thus, the empirical path loss PL(d) for a given environment (a city, suburban area,or office building) is defined as the average of the LMA measurements at distance daveraged over all available measurements in the given environment.

Okumura Model

� This model is applicable over distances of 1–100 km and frequency ranges of 150–1500 MHz.

� The empirical path-loss formula of Okumura at distance d parameterized by the carrier frequency fc is given by



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� where L(fc,d) is free-space path loss at distance d and carrier frequency fc, Aμ(fc,d) is the median attenuation in addition to free-space path loss across all environments.

� GAREA is the gain due to the type of environment.

Hata Model

� The Hata model is an empirical formulation of the graphical path-loss data provided by Okumura and is valid over roughly the same range of frequencies, 150–1500 MHz.



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� The standard formula for empirical path loss in urban areas under the Hata model is

� a(hr) is a correction factor for the mobile antenna height based on the size of the coverage area. For small to medium-sized cities, this factor is given by

� and for larger cities at frequencies fc > 300 MHz by

31Empirical Path-Loss Models: Hata model


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� where K ranges from 35.94 (countryside) to 40.94 (desert).

� Unlike the Okumura model, the Hata model does not provide for any path-specific correction factors.

� The Hata model well approximates the Okumura model for distances d > 1 km.Hence it is a good model for first-generation cellular systems, but it does not modelpropagation well in current cellular systems with smaller cell sizes and higherfrequencies. Indoor environments are also not captured by the Hata model.

32Empirical Path-Loss Models: Hata model


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� The Hata model was extended by the European cooperative for scientific and technical research (EURO-COST) to 2 GHz as

� where a(hr) is the same correction factor as before and where CM is 0 dB for medium sized cities and suburban and is 3 dB for metropolitan areas.

� This model is referred to as the COST 231 extension to the Hata model and is restricted to the following range of parameters: 1.5 GHz < fc < 2 GHz, 30 m <ht< 200 m, 1 m < hr < 10 m, and 1 km < d < 20 km.

33COST 231 Extension to Hata Model


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� A signal transmitted through a wireless channel will typically experience random variation due to blockage from objects in the signal path, giving rise to random variations of the received power at a given distance.

� The location, size, and dielectric properties of the blocking objects – as well as the changes in reflecting surfaces and scattering objects that cause the random attenuation – are generally unknown, so statistical models must be used to characterize this attenuation.

� The most common model for this additional attenuation is log-normal shadowing.� In the log-normal shadowing model, the ratio of transmit-to-receive power ψ = Pt /Pr

is assumed to be random with a log-normal distribution given by

34Shadow Fading


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� where ξ = 10/ln10, μ(ψ)dB is the mean of ψdB = 10 log10 ψ in decibels, and σ(ψ)dB is the standard deviation of ψdB (also in dB).

� Performance in log-normal shadowing is typically parameterized by the log mean μ(ψ)dB , which is referred to as the average dB path loss and is given in units of dB.

� With a change of variables we see that the distribution of the dB value of ψ is Gaussian with mean μ(ψ)dB and standard deviation σ(ψ)dB :

35Shadow Fading


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� Most empirical studies for outdoor channels support a standard deviation σ(ψ)dB ranging from 4 dB to 13 dB.

� The mean power μ(ψ)dB depends on the path loss and building properties in the area under consideration.

� The mean power μ(ψ)dB varies with distance; this is due to path loss and to the fact that average attenuation from objects increases with distance owing to the potential for a larger number of attenuating objects.

36Shadow Fading


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� Models for path loss and shadowing can be superimposed to capture power falloff versus distance along with the random attenuation about this path loss from shadowing.

� In this combined model, average dB path loss (μ(ψ)dB ) is characterized by the path-loss model while shadow fading, with a mean of 0 dB, creates variations about this path loss.

� For this combined model, the ratio of received to transmitted power in dB is given by

� the variations due to shadowing change more rapidly.

37Combined Path Loss and Shadowing


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ing� In wireless systems there is typically a target minimum received power level Pmin

below which performance becomes unacceptable (e.g., the voice quality in a cellular system becomes too poor to understand).

� We define outage probability Pout(Pmin,d) under path loss and shadowing to be the probability that the received power at a given distance d, Pr(d), falls below Pmin: Pout(Pmin,d) = p(Pr(d) < Pmin).

� For the combined path-loss and shadowing model this becomes

38Outage Probability under Path Loss and Shadowing


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� The cell coverage area in a cellular system is defined as the expected percentage of locations within a cell where the received power at these locations is above a given minimum.

� The transmit power at the base station is designed for an average received power at the cell boundary, averaged over the shadowing variations.

� shadowing will cause some locations within the cell to have received power below average PR, and others will have received power exceeding average PR.

39Cell Coverage Area


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Contours of constant received power40


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� It is not possible for all users at the cell boundary to receive the same power level.

� Thus, either the base station must transmit extra power to ensure users affected by shadowing receive their minimum required power Pmin, which causes excessive interference to neighboring cells, or some users within the cell will find their minimum received power requirement unmet.

� In fact, since the Gaussian distribution has infinite tails, any mobile in the cell has a nonzero probability of experiencing received power below its required minimum, even if the mobile is close to the base station.

� This makes sense intuitively because a mobile may be in a tunnel or blocked by a large building, regardless of its proximity to the base station.

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Contours of constant received power


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� The outage probability of the cell is defined as the percentage of area within the cell that does not meet its minimum power requirement Pmin; that is, P cell out = 1− C.

� Given the log-normal distribution for the shadowing, we have

� Locations within the cell with received power below Pmin are said to be outage locations.

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� If the target minimum received power equals the average power at the cell boundary, Pmin = P(r)(R), then a = 0 and the coverage area simplifies to

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