Wireless Communication Technology Chapter 4 Radio Propagation and Propagation Path Loss Model Asst. Prof. Bijaya Shrestha Department of Electronics & Communication Engineering nec

Introduction to Radio Wave Propagation The mobile radio channel limits the performance of wireless communication systems. The transmission path between the transmitter and the receiver can vary from simple line-of-sight to the one obstructed by buildings, mountains, and foliage. Radio channels are extremely random and do not offer easy analysis. The signal level can fade rapdily with the mobile speed over small distance. The mobile radio channel is modeled normally on the basis of measurement results. By Asst. Prof. Bijaya Shrestha, nec, 2015

Introduction to Radio Wave Propagation The radio waves may undergo reflection, diffraction, and scattering. The presence of high-rise buildings causes severe diffraction loss. Due to multiple reflections from various objects, the electromagnetic waves travel along different paths of varying lengths causing multipath fading at a specific location. The strengths of the waves decrease as the distance between the transmitter and receiver increases. By Asst. Prof. Bijaya Shrestha, nec, 2015

Introduction to Radio Wave Propagation Large-Scale Propagation Models: Are the propagation models that predict the mean signal strength for an arbitrary transmitter-receiver (T-R) separation distance (several hundreds or thousands of meters). Are useful in estimating the radio coverage area of a transmitter. Small-Scale (or fading) Propagation Models: Are the propagation models that characterize the rapid fluctuations of the received signal strength over very short travel distances (a few wavelengths) or short time durations (on the order of seconds). By Asst. Prof. Bijaya Shrestha, nec, 2015

Introduction to Radio Wave Propagation By Asst. Prof. Bijaya Shrestha, nec, 2015

Large-Scale Path Loss By Asst. Prof. Bijaya Shrestha, nec, 2015

Free Space Propagation Model The free space propagation model is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line-of-sight path between them. Satellite communication systems and microwave line-of-sight radio links typically undergo free space propagation. The free space model predicts that received power decays as a function of the T-R separation distance raised to some power. By Asst. Prof. Bijaya Shrestha, nec, 2015

Free Space Propagation Model The free space power received by a receiver antenna which is separated from a radiating transmitter antenna by a distance d, is given by the Friis free space equation, where Pt is the transmitted power, Pr(d) is the received power, Gt is the transmitter antenn gain, Gr is the receiver antenna gain, d is the T-R separation distance in meters, L is the system loss factor not related to propagation (L≥1), and λ is the wavelength in meters. By Asst. Prof. Bijaya Shrestha, nec, 2015

Free Space Propagation Model The gain of an antenna is related to its effective aperture, Ae, by The effective aperture is related to the physical size of the antenna. The miscellaneous losses L are usually due to transmission line attenuation, filter losses, and antenna losses in the communication system. The Friis free space equation shows that the received power falls off as the square of the T-R separation distance. By Asst. Prof. Bijaya Shrestha, nec, 2015

Free Space Propagation Model An isotropic radiator is an ideal antenna which radiates power with unit gain uniformly in all directions, and is often used to reference antenna gains in wireless systems. The effective isotropic radiated power (EIRP) is defined as EIRP=PtGt and represents the maximum radiated power available from a transmitter in the direction of maximum antenna gain, as compared to an istropic radiator. By Asst. Prof. Bijaya Shrestha, nec, 2015

Free Space Propagation Model In practice, effective radiated power (ERP) is used instead of EIRP to denote the maximum radiated power as compared to a half-wave dipole antenna (instead of an istropic antenna). Antenna gains are given in units of dBi (dB gain with respect to an isotropic antenna) or dBd (dB gain with respect to a half-wave dipole). The path loss, which represents signal attenuation, is defined as the difference (in dB) between the effective transmitted power and the received power. By Asst. Prof. Bijaya Shrestha, nec, 2015

Free Space Propagation Model The path loss for the free space model is given by Without antenna gains, The Friis free space model is only a valid predictor of Pr for values of d which are in the far-field of the transmitting antenna. The far-field, or Fraunhofer region, of a transmitting antenna is defined as the region beyond the far-field distance df. The Fraunhofer distance is given by By Asst. Prof. Bijaya Shrestha, nec, 2015

Free Space Propagation Model where D is the largest physical linear dimension of the antenna. To be in the far-field region, df must satisfy df >> D and df >> λ Large-scale propagation models use a close-in distance, d0, as a known received power reference point. The received power in free space at a distance greater than d0 is given by By Asst. Prof. Bijaya Shrestha, nec, 2015

Example Find the far-field distance for an antenna with maximum dimension of 1 m and operating frequency of 900 MHz. Solution: Largest dimension of antenna, D = 1 m Operating frequency, f = 900 MHz Wavelength, λ = c/f = 0.333 m Far-field distance, By Asst. Prof. Bijaya Shrestha, nec, 2015

Example If a transmitter produces 50 W of power, express the transmit power in units of (a) dBm, and (b) dBW. If 50 W is applied to a unity gain antenna with a 900 MHz carrier frequency, find the received power in dBm at a free space distance of 100 m from the antenna. What is Pr(10 km)? Assume unity gain for the receiver antenna. Solution: Pt(dBm)=10log[Pt(mW)]=10log(50×103)=47 dBm Pt(dBW)=10log[Pt(W)]=10log(50)=17 dBW By Asst. Prof. Bijaya Shrestha, nec, 2015

Relating Power to Electric Field Where is the magnitude of electric field at distance d. By Asst. Prof. Bijaya Shrestha, nec, 2015

Example: Question By Asst. Prof. Bijaya Shrestha, nec, 2015

Example: Solution By Asst. Prof. Bijaya Shrestha, nec, 2015

The Three Basic Propagation Mechanisms 1. Reflection 2. Diffraction 3. Scattering By Asst. Prof. Bijaya Shrestha, nec, 2015

Reflection Reflection occurs when a propagating electromagnetic wave impinges upon an object which has very large dimensions when compared to the wavelength of the propagating wave. Reflections occur from the surface of the earth and from buildings and walls. When a radio wave propagating in one medium impinges upon another medium having different electrical properties, the wave is partially reflected and partially transmitted. By Asst. Prof. Bijaya Shrestha, nec, 2015

Reflection If the plane wave is incident on a perfect dielectric, part of the energy is transmitted into the second medium and part of the energy is reflected back into the first medium, and there is no loss of energy in absorption. If the second medium is a perfect conductor, then all incident energy is reflected back into the first medium without loss of energy. The electric field intensity of the reflected and transmitted waves may be related to the incident wave in the medium of origin through the Fresnel reflection coefficient Г. By Asst. Prof. Bijaya Shrestha, nec, 2015

Reflection from Dielectrics When an electromagnetic wave is incident at an angle θi with the plane of boundary between two dielectric media, part of the energy is reflected back to the first medium at an angle θr, and part of the energy is transmitted (refracted) into the second medium at an angle θr. By Asst. Prof. Bijaya Shrestha, nec, 2015

Reflection from Dielectrics The plane of incidence is defined as the plane containing the incident, reflected, and transmitted rays. In Figure (a), the E-field polarization is parallel with the plane of incidence and in Figure (b) the E-field polarization perpendicular to the plane of incidence. For a lossless diectric material, ε=ε0εr and for a lossy dielectric, some power is absorbed and its diectric constant is given by ε=ε0εr -jε’= ε=ε0εr –jσ/(2πf) By Asst. Prof. Bijaya Shrestha, nec, 2015

Reflection from Dielectrics The reflection coefficients for the two cases of parallel and perpendicular E-field polarization at the boundary of two electrics are given by where η is the intrinsic impedance given by By Asst. Prof. Bijaya Shrestha, nec, 2015

Reflection from Dielectrics According to Snell’s law, Also, note the following: By Asst. Prof. Bijaya Shrestha, nec, 2015

Reflection from Perfect Conductors Since electromagnetic energy cannot pass through a perfect conductor a plane wave incident on a conductor has all of its energy reflected. The reflected wave must be equal in magnitude to the incident wave. By Asst. Prof. Bijaya Shrestha, nec, 2015

Ground Reflection (Two-Ray) Model The received signal is the sum of two signals one from LOS path and one from reflected path. The total received E-field is approximated as The received power can be derived to be And, the path loss will be By Asst. Prof. Bijaya Shrestha, nec, 2015

Example: Question By Asst. Prof. Bijaya Shrestha, nec, 2015

Example: Solution By Asst. Prof. Bijaya Shrestha, nec, 2015

Diffraction Diffraction occurs when the radio path between the transmitter and receiver is obstructed by a surface that has sharp irregularities (edges). The secondary waves resulting from the obstructing surface are present throughout the space and even behind the obstacle. At high frequencies, diffraction, like reflection, depends on the geometry of the object, as well as the amplitude, phase, and polarization of the incident wave at the point of scattering. By Asst. Prof. Bijaya Shrestha, nec, 2015

Diffraction Diffraction allows radio signals to propagate around the curved surface of the earth, beyond the horizon, and to propagate behind obstructions. Although the received field strength decreases rapidly as a receiver moves deeper into the obstructed (shadowed) region, the diffraction field still exists and often has sufficient strength to produce a useful signal. The phenomenon of diffraction can be explained by Huygen’s principle, which states that all points on a wavefront can be considered as point sources for the production of secondary wavelets, and that these wavelets combine to produce a new wavefront in the direction of propagation. By Asst. Prof. Bijaya Shrestha, nec, 2015

Diffraction Diffraction is caused by the propagation of secondary wavelets into a shadowed region. The field strength of a diffracted wave in the shadowed region is the vector sum of the electric field components of all the secondary wavelets in the space around the obstacle. By Asst. Prof. Bijaya Shrestha, nec, 2015

Knife-Edge Diffraction Model When shadowing is caused by a single object such as a hill or mountain, the attenuation caused by diffraction can be estimated by treating the obstruction as a diffracting knife edge. By Asst. Prof. Bijaya Shrestha, nec, 2015

Knife-Edge Diffraction Model From the figure, it is apparent that the wave propagating from the transmitter to the receiver via the knife edge travels a longer distance than if a direct LOS path existed. Assumptions: h << d1, h << d2, h >> λ, α and β are small, h and h’ are virtually identical, α = β + γ. The difference between the direct path and the diffracted path, called the excess path length (∆), can be obtained from the geometry as By Asst. Prof. Bijaya Shrestha, nec, 2015

Knife-Edge Diffraction Model The corresponding phase difference is given by Also, Fresnel-Kirchoff diffraction parameter v is given by By Asst. Prof. Bijaya Shrestha, nec, 2015

Knife-Edge Diffraction Model Therfore, the phase difference between a direct LOS path and diffracted path is a function of height and position of the obstruction , as well as the transmitter and receiver location. The field strength at point R is a vector sum of the fields due to all of the secondary Huygens’s sources in the plane above the knife edge. The diffraction gain Gd(dB) due to the presence of a knife edge, as compared to the free space E-field, is the function of v and calculated as By Asst. Prof. Bijaya Shrestha, nec, 2015

Knife-Edge Diffraction Model By Asst. Prof. Bijaya Shrestha, nec, 2015

Knife-Edge Diffraction Model By Asst. Prof. Bijaya Shrestha, nec, 2015

Scattering Scattering occurs when the medium through which the wave travels consists of objects with dimensions that are small compared to the wavelength, and where the number of obstacles per unit volume is large. Scattered waves are produced by rough surfaces, small objects, or by other irregularities in the channel. In practice, foliage, street signs, and lamp posts induce scattering in a mobile communications system. When a radio wave impinges on a rough surface, the reflected energy is spread out (diffused) in all directions due to scattering, thereby providing additional radio energy at a receiver. By Asst. Prof. Bijaya Shrestha, nec, 2015

Link Budget Design Most of the radio propagation models are based on the combination of analytical and empirical (actual field measurements) methods. To use the empirical model designed for a particular frequency and/or environment at another frequency and/or environment, we need additional measured data. By using path loss models to estimate the received signal level as a function of distance, it becomes possible to predict the SNR for a mobile communication system. By Asst. Prof. Bijaya Shrestha, nec, 2015

Link Budget Design Log-Distance Path Loss Model Both theoretical and measurement-based propagation models indicate that average received signal power decreases logarithmically with distance. The average large-scale path loss for an arbitrary T-R separation is expressed as a function of distance by using a path loss exponent n ,given as where n is the path loss exponent which indicates the rate at which the path loss increases with distance. By Asst. Prof. Bijaya Shrestha, nec, 2015

Link Budget Design Log-Distance Path Loss Model (cont…) The value of n depends on the specific propagation environment. By Asst. Prof. Bijaya Shrestha, nec, 2015

Link Budget Design Log-Normal Shadowing The log-distance path loss model does not consider the fact that the surrounding environmental clutter may be vastly different at two different locations having the same T-R separation. Measurements have shown that at any value of d, the path loss at a particular location is random and distributed log-normally about the mean distance-dependent value. That is, By Asst. Prof. Bijaya Shrestha, nec, 2015

Link Budget Design Log-Normal Shadowing (contd…) And, where Xσ is a zero-mean Gaussian distributed random variable (in dB) with standard deviation σ (in dB). The log-normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R separation, but have different levels of clutter on the propagation path. This phenomenon is referred to as log-normal shadowing. By Asst. Prof. Bijaya Shrestha, nec, 2015

Link Budget Design Log-Normal Shadowing (contd…) Since PL(d) is a random variable with a normal distribution in dB about the distance-dependent mean, so is Pr(d), and the Q-function or error function (erf) may be used to determine the probability that the received signal level will exceed (or fall below) a particular level. The Q-function is defined as Also, By Asst. Prof. Bijaya Shrestha, nec, 2015

Link Budget Design Log-Normal Shadowing (contd…) The probability that the received signal level will exceed a certain value γ can be calculated from the cumulative density function as And, the probability that the received signal level will be below γ is given by By Asst. Prof. Bijaya Shrestha, nec, 2015

Outdoor Propagation Models The terrain profile, the presence of trees, buildings, and other obstacles must be taken into account while estimating the path loss. There are different propagation models to predict the signal strength at a particular receiving point. The models vary in their approach, complexity, and accuracy The commonly used outdoor propagation models are: Longley-Rice Model Okumura Model Hata Model By Asst. Prof. Bijaya Shrestha, nec, 2015

Longley-Rice Model The Longley-Rice model is applicable to point-to-point communication systems in the frequency range from 40 MHz to 100 GHz, over different kinds of terrain. The median transmission loss is predicted using the path geometry of the terrain profile and the refractivity of the troposphere. Two-ray ground reflection model is used to predict signal strengths within the radio horizon. Diffraction losses over isolated obstacles are estimated using the Fresnel-Kirchoff knife-edge models. By Asst. Prof. Bijaya Shrestha, nec, 2015

Longley-Rice Model The shortcomings of Longley-Rice model are It does not provide a way of determining corrections due to environmental factors in the immediate vicinity of the mobile receiver, or consider correction factors to account for the effects of buildings and foliage. Multipath is not considered. By Asst. Prof. Bijaya Shrestha, nec, 2015

Okumura Model Okumura model is one of the most widely used models for signal prediction in urban areas. This model is applicable for frequencies in the range 150 MHz to 1920 MHz (extended upto 3000 MHz) and distances of 1 km to 100 km. It can be used for base station antenna heights ranging from 30 m to 1000 m. The model can be expressed as where L50 is the 50th percentile (i.e., median) value of propagation path loss, LF is the free space propagation loss, Amu is the median attenuation relative to free space, G(hte) is the base station antenna height gain factor, G(hre) is the mobile antenna height gain factor, and GAREA is the gain due to the type of environment. By Asst. Prof. Bijaya Shrestha, nec, 2015

Okumura Model By Asst. Prof. Bijaya Shrestha, nec, 2015

Okumura Model This model is wholly based on measured data and does not provide any analytical explanation. Okumura’s model is considered to be among the simplest and best in terms of accuracy in path loss prediction for mobile radio systems in cluttered environments. The major disadvantage with the model is its slow response to rapid changes in terrain, therefore the model is fairly good in urban and suburban area, but not as good in rural areas. By Asst. Prof. Bijaya Shrestha, nec, 2015

Example Calculate the mean path loss using Okumura’s model for d = 50 km, hte = 100 m, hre = 10 m in a suburban environment. If the base station transmitter radiates an EIRP of 1 kW at a carrier frequency of 900 MHz, find EIRP (dBm) and the power at the receiver where gain at receiving antenna is 10 dB. Solution By Asst. Prof. Bijaya Shrestha, nec, 2015

Hata Model This model incorporates the graphical information from Okumura model and develops it further to realize the effects of diffraction, reflection, and scattering caused by city structures. It is valid from 150 MHz to 1500 MHz. The standard formula for median path loss in urban areas is given by By Asst. Prof. Bijaya Shrestha, nec, 2015

Hata Model where fc is the frequency (in MHz) from 150 MHz to 1500 MHz, hte is the effective transmitter (base station) antenna height (in meters) ranging from 30 m to 200 m, hre is the effective receiver (mobile) antenna height (in meters) ranging from 1 m to 10 m, d is the T-R separation distance (in km), and a(hre) is the correction factor for effective mobile antenna height which is a function of the size of the coverage area. For a small to medium sized city, the mobile antenna correction factor is given by By Asst. Prof. Bijaya Shrestha, nec, 2015

Hata Model And for a large city, it is given by For suburban areas, For open rural areas, The predictions of the Hata model compare very closely with the original Okumura model, as long as d exceeds 1 km. By Asst. Prof. Bijaya Shrestha, nec, 2015

Indoor Propagation Models The radio wave propagation inside buildings is strongly influenced by the layout of the building, the construction materials, and the building type. Indoor radio propagation is dominated by the same mechanisms as outdoor: reflection, diffraction, and scattering. However, conditions are much more variable. In general, indoor channels may be classified either as line-of-sight or obstructed, with varying degrees of clutter. By Asst. Prof. Bijaya Shrestha, nec, 2015

Indoor Propagation models Indoor propagation models include Log-distance path loss model Ericsson multiple breakpoint model Attenuation factor model By Asst. Prof. Bijaya Shrestha, nec, 2015

Partition Losses Buildings have a wide variety of partitions and obstacles. Partitions may be of wood frame, plaster board, or nonreinforced concrete between floors. Partitions vary widely in their physical and electrical characteristics, making it difficult to apply general models to specific indoor installations. By Asst. Prof. Bijaya Shrestha, nec, 2015

Log-Distance Path Loss Model According to this model, the path loss is given by where the value of n depends on the surroundings and building type, and Xσ represents a normal random variable in dB having a standard deviation of σ dB. By Asst. Prof. Bijaya Shrestha, nec, 2015

Ericsson Multiple Breakpoint Model This model is obtained by measurements in a multiple floor office building. The model has four break points and it is based on measurements conducted at 900 MHz. The model considers both an upper and lower bound on the path loss. As we move away from the transmitter, the path loss exponent increases. By Asst. Prof. Bijaya Shrestha, nec, 2015

Ericsson Multiple Breakpoint Model By Asst. Prof. Bijaya Shrestha, nec, 2015

Attenuation Factor Model The attenuation factor model is given by where nSF represents the exponent value for the “same floor” measurement, FAF represents a floor attenuation factor for a specified number of building floors, and PAF represents the partition attenuation factor . Alternately, the model can be expressed as where nMF denotes a path loss exponent based on measurements through multiple floors. By Asst. Prof. Bijaya Shrestha, nec, 2015

Attenuation Factor Model Devasirvatham found that in-building path loss obeys free space plus an additional loss factor which increases exponentially with distance such that where α is the attenuation constant for the channel with units of dB per meter. By Asst. Prof. Bijaya Shrestha, nec, 2015

Small-Scale Fading and Multipath By Asst. Prof. Bijaya Shrestha, nec, 2015

Small-Scale Fading and Multipath By Asst. Prof. Bijaya Shrestha, nec, 2015

Small-Scale Fading Small-scale fading, or simply fading, is used to describe the rapid fluctuations of the amplitudes, phases, or multipath delays of a radio signal over a short period of time or travel distance. Fading is caused by interference between two or more versions of the transmitted signal which arrive at the receiver at slightly different times. These waves, called multipath waves, combine at the receiver antenna to give a resultant signal which can vary widely in amplitude and phase, depending on the distribution of the intensity and relative propagation time of the waves and the bandwidth of the transmitted signal. By Asst. Prof. Bijaya Shrestha, nec, 2015

Small-Scale Multipath Propagation Multipath in the radio channel creates small-scale fading effects. The three most important effects are: Rapid changes in signal strength over a small travel distance or time interval. Random frequency modulation due to varying Doppler shifts on different multipath signals. Time dispersion (echoes) caused by multipath propagation delays. In urban areas, fading occurs because the height of the mobile antennas is well below the height of the surrounding structures, so there is no single LOS path to the base station. By Asst. Prof. Bijaya Shrestha, nec, 2015

Small-Scale Multipath Propagation Even when a LOS exists, multipath still occurs due to reflections from the ground and surrounding structures. The incoming radio waves arrive from different directions with different propagation delays. The signal received by the mobile at any point in space may consist of a large number of plane waves having randomly distributed amplitudes, phases, and angles of arrival. These multipath components combine vectorially at the receiver antenna, and can cause the signal received by the mobile to distort or fade. By Asst. Prof. Bijaya Shrestha, nec, 2015

Small-Scale Multipath Propagation Even when a mobile receiver is stationary, the received signal may fade due to movement of surrounding objects in the radio channel. Due to the constructive and destructive effects of multipath waves summing at various points in space, a receiver moving at high speed can pass through several fades in a small period of time. Due to the relative motion between the mobile and the base station, each multipath wave experiences an apparent shift in frequency (called the Doppler shift) and is directly proportional to the velocity and direction of motion of the mobile with respect to the direction of the arrival of the received multipath wave. By Asst. Prof. Bijaya Shrestha, nec, 2015

Factors Influencing Small-Scale Fading Multipath Propagation: The presence of reflecting objects and scatterers in the channel creates a constantly changing environment that dissipates the signal energy in amplitude, phase, and time. These effects result in multiple versions of the transmitted signal that arrive at the receiving antenna, displaced with respect to one another in time and spatial orientation. The random phase and amplitudes of the different multipath components cause fluctuations in signal strength, thereby inducing small-scale fading, signal distortion, or both. Multipath propagation often lengthens the time required for the baseband portion of the signal to reach the receiver which can cause signal smearing due to intersymbol interference. By Asst. Prof. Bijaya Shrestha, nec, 2015

Factors Influencing Small-Scale Fading Speed of the Mobile The relative motion between the base station and the mobile results in random frequency modulation due to different Doppler shifts on each of the multipath components. Doppler shift will be positive or negative depending on whether the mobile receiver is moving toward or away from the base station. Speed of Surrounding Objects If objects in the radio channel are in motion, they induce a time varying Doppler shift on multipath components. By Asst. Prof. Bijaya Shrestha, nec, 2015

Factors Influencing Small-Scale Fading The Transmission Bandwidth of the Signal If the transmitted radio signal bandwidth is greater than the bandwidth of the multipath channel, the received signal will be distorted, but the received signal strength will not fade much over a local area. By Asst. Prof. Bijaya Shrestha, nec, 2015

Doppler Shift ∆l = dcos(θ) = v∆tcos(θ) where ∆l is the difference in path lengths, v is the velocity of mobile, d is the distance covered by the mobile, ∆t is the time required for the mobile to travel from X to Y, θ is the angle of arrival of wave from the source S. The phase change in the received signal due to the difference in path lengths is By Asst. Prof. Bijaya Shrestha, nec, 2015

Doppler Shift And hence the apparent change in frequency, or Doppler shift, is given by Multipath components arriving from different directions contribute to Doppler spreading of the received signal, thus increasing the signal bandwidth. By Asst. Prof. Bijaya Shrestha, nec, 2015

Time and Frequency Dispersion The mobile channel introduces delay spread into the received signal. That is, the received signal has a longer duration than that of transmitted signal due to the different delays of different propagation paths. This phenomenon is referred to as time dispersion. Also, the mobile channel introduces Doppler spread into the received signal. That is, the received signal has a larger bandwidth than that of the transmitted signal due to the different Doppler shifts introduced by the multipath components. This phenomenon is referred to as frequency dispersion. By Asst. Prof. Bijaya Shrestha, nec, 2015

Time and Frequency Dispersion By Asst. Prof. Bijaya Shrestha, nec, 2015

Coherence Time and Coherence Bandwidth Coherence Time, Tcoh Coherence time is the time duration over which the channel impulse response is essentially invariant, and quantifies the similarity of the channel response at different times. In practice, “50 % coherence time” is the most used definition, which means that two states of the channel, measured less than Tcoh seconds apart, have correlation equal to 0.5 or more. Coherence Bandwidth, Bcoh Coherence bandwidth is the maximum transmission bandwidth over which the channel can be assumed to be approximately constant in frequency. That is, a signal having frequencies within a bandwidth Bcoh will be affected approximately similarly by the channel. In practice, “50 % coherence bandwidth” is defined accordingly. By Asst. Prof. Bijaya Shrestha, nec, 2015

Time-Flat vs. Time-Selective Channels Time-Flat (Slow Fading) Channels Time-flat channels are time invariant, which means that the duration of a transmitted symbol T is far less than the coherence time Tcoh, i.e., T << Tcoh. An example is a transmitter and receiver that are both physically stationary, with the propagation environment unchanging. Time-Selective (Fast Fading) Channels Time-selective channels are time variant, which means that the duration of a transmitted symbol is more than the coherence time, i.e., T > Tcoh . An example is a wireless terminal moving through the environment and undergoing channel variations. By Asst. Prof. Bijaya Shrestha, nec, 2015

Frequency-Flat vs. Frequency-Selective Channels Frequency-Flat Channels: Frequency-flat channels have coherence bandwidth Bcoh much greater than bandwidth W of the transmitted signal, i.e., Bcoh >> W. That means the frequency response of a channel is approximately flat over a bandwidth greater than bandwidth of the transmitted signal. Frequency-Selective Channels: Frequency-selective channels have a coherence bandwidth less than bandwidth of the transmitted signal, i.e., Bcoh < W. An example is a multipath channel with significant delay spread relative to the symbol period of the transmitted symbol. By Asst. Prof. Bijaya Shrestha, nec, 2015

Determining Tcoh The “50 % coherence time” is determined as where BD is the Doppler spread or maximum Doppler shift given as By Asst. Prof. Bijaya Shrestha, nec, 2015

Determining Bcoh To determine coherence bandwidth , we need to know the power-delay profile of the channel. From the power delay profile, we get the average delay (mean excess delay) as By Asst. Prof. Bijaya Shrestha, nec, 2015

Determining Bcoh The rms delay spread is defined by where From a rule of thumb, the “50 % coherence bandwidth” is approximated by By Asst. Prof. Bijaya Shrestha, nec, 2015

Rayleigh Fading Distribution In mobile radio channels, the Rayleigh distribution is commonly used to describe the statistical time varying nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component. The Rayleigh distribution has a probability density function (pdf) given by where σ is the rms value of the received voltage signal, and σ2 is the time-average power of the received signal. By Asst. Prof. Bijaya Shrestha, nec, 2015

Rayleigh Fading Distribution The probability that the envelope of the received signal does not exceed a specified value R is given by the corresponding cumulative distribution function (CDF) The mean value of the Rayleigh distribution is given by The variance of the Rayleigh distribution which represents the ac power in the signal envelope is given by The median value of r is found by solving and is By Asst. Prof. Bijaya Shrestha, nec, 2015

Rayleigh Fading Distribution By Asst. Prof. Bijaya Shrestha, nec, 2015

Ricean Fading Distribution The Rayleigh fading model assumes that all paths are relatively equal, that is, there is no dominant path. In case there exists a strong line-of-sight path, the radio channel is said to have a Ricean distribution. The complex envelope can now be expressed as h = αejφ+vejθ , where α follows the Rayleigh distribution and v is a constant such that v2 is the power of the LOS signal component. As the dominant signal becomes weaker, the composite signal resembles a noise signal which has an envelope that is Rayleigh. By Asst. Prof. Bijaya Shrestha, nec, 2015

Ricean Fading Distribution The Ricean distribution is given by where parameter A (≥ 0)deontes the peak amplitude of the dominant signal. I0(.) is the modified Bessel function of the first kind and zero-order. The Ricean distribution is often described in terms of a parameter K which is defined as the ratio between the deterministic signal power and the variance of the multipath. That is, By Asst. Prof. Bijaya Shrestha, nec, 2015

Ricean Fading Distribution The parameter K is known as the Ricean factor. As the dominant path decreases in amplitude, the Ricean distribution degenerates to a Rayleigh distribution. By Asst. Prof. Bijaya Shrestha, nec, 2015

References Theodore S. Rappaport, Wireless Communications, second edition, Prentice Hall, 2012. Hata Model, “https://en.wikipedia.org/wiki/Hata_model_for_urban_areas [Nov. 23, 2015]. By Asst. Prof. Bijaya Shrestha, nec, 2015