EKT 450 Mobile Communication System

Transcription

1 EKT 450 Mobile Communication System Chapter 2: Mobile Radio Propagation Characteristics Dr. Azremi Abdullah Al-Hadi School of Computer and Communication Engineering 1

2 Introduction The mobile radio channel places fundamental limitations on the performance of wireless communication systems. Paths can vary from simple line-of-sight to ones that are severely obstructed by buildings, mountains, and foliage. Radio channels are extremely random and difficult to analyze. The speed of motion also impacts how rapidly the signal level fades as a mobile terminals moves about. 2

3 Interferences Interference from other service providers. Interference from other users (same network) : Co-channel interference due to frequency reuse. Adjacent channel interference due to Base/Mobile Station design limitations & large number of users sharing finite bandwidth. 3

4 Propagation Models Predicting the average received signal strength at a given distance from the base station + variability of the signal strength in close proximity to a particular location. 4

5 Small-scale and Large-scale Fading Figure 4.1 Small-scale and large-scale fading.

6 Small-scale Fading Characterize rapid fluctuations of the received signal strength over very short travel distance or short time duration. Sum of many contributions from different directions. Random phases sum on contributions varies obey Rayleigh Distribution. Variation as much as 30-40dB when the mobile station is moved only a fraction of wavelength. 6

7 Large-scale Fading Predict mean signal strength for an arbitrary large Base-mobile station separation distance. As mobile station moves away from base station over much larger distances, the local average received signal will gradually decrease. Typically, local average received power is calculated by averaging signal measurements over a measurement track of 5 λ to 40 λ. 7

8 Line-of-Sight (LOS) Line Of Sight (LOS) Non Line Of Sight (NLOS) 8

9 Line-of-Sight (LOS) LOS is the direct propagation of radio waves between antennas that are visible to each other. The received signal is directly received at the receiver the effects such as reflection, diffraction and scattering doesn t affect the signal reception that much. Radio signals can travel through many nonmetallic objects, radio can be picked up through walls. This is still LOS propagation. Examples would include propagation between a satellite and a ground antenna or reception of television signals from a local TV transmitter. 9

10 Free Space Propagation Model Predict received signal strength when the base and mobile stations have a clear unobstructed LOS path between them e.g. satellite and microwave line-of-sight radio links. Friis free space equation: PP rr (dd) = PP ttgg tt GG rr λλ 2 4ππ 2 dd 2 LL GG = 4ππAA ee λλ 2 λλ = cc ff = 2ππππ ωω cc 10

11 Friis Free Space Equation P t = Transmitted power P r (d) = Received power G t = Transmitter antenna gain G r = Receiver antenna gain d = transmit-receive separation distance (m) L = System loss factor related to propagation system losses (antennas, transmission lines between equipment and antennas, atmosphere, etc.) L = 1 for zero loss A e = Effective antenna aperture The equation shows that the received power falls off as the square of transmit-receive separation distance, d 2 11

12 Free Space Propagation Model Isotropic radiator = an ideal antenna which radiates power with unit gain uniformly in all directions reference antenna gains in wireless systems. Effective Isotropic Radiated Power (EIRP)= P t G t represents max. radiated power available from transmitter in the direction of maximum antenna gain compared to isotropic radiator. Practically: Effective Radiated Power (ERP)= P t G t max. radiated power as compared to half-wave dipole antenna. 12

13 Free Space Propagation Model Path Loss (PL) signal attenuation as a positive quantity measured in db difference (in db) between the effective transmitted power and the received power With antenna gain, PL = PPPP dddd = 10 log PP tt PP rr = 10 log GG ttgg rr λλ 2 4ππ 2 dd 2 Antenna gains are excluded, PL = PPPP dddd = 10 log PP tt PP rr = 10 log λλ 2 4ππ 2 dd 2 13

14 Free Space Propagation Model In practice, power can be measured at d 0 and predicted at d using the relation, d d 0 d f. d 0 d Where d f is Fraunhofer (far-field) distance, which complies: dd ff = 2DD2 λλ D is the largest physical linear dimension of the antenna. Therefore, the received power in free space at a distance greater than d 0 is given by: PP rr (dd) = PP rr (dd 0 ) dd 0 dd 2 14

15 Free Space Propagation Model In mobile communication systems, P r may vary by many orders of magnitude, over a typical coverage area of several square kilometers often dbm or dbw units are used. If P r is in units of dbm: PP rr dd dbm = 10 log PP rr dd W log dd 0 dd The reference distance d 0 for practical systems using low-gain antennas in the 1-2 GHz region is typically: 1 m in indoor environment 100m or 1000m in outdoor environments 15

16 Example 1 solution Find the far-field distance for an antenna with maximum dimension of 1 m and operating frequency of 900 MHz. 16

17 Example 2 solution If a transmitter produces 50W of power, express the transmit power in units of: a) dbm, b) dbw. If 50W is applied to a unity gain antenna (for both base and mobile stations) with a 900 MHz carrier frequency, find: c) the received power in dbm at a free space distance of 100 m from the antenna. Find also P r (10km)? 17

18 Basic Propagation Mechanisms Reflection Diffraction Scattering In urban areas, there is no direct line-of-sight path between: the transmitter and the receiver, and where the presence of high- rise buildings causes severe diffraction loss. Multiple reflections cause multi-path fading. 18

19 Basic Propagation Mechanisms Multipath propagation: Signal arrives at receiver through different paths. Paths could arrive with different gains, phase & delays. Small distance variation can have large amplitude variation. Physical phenomena behind multipath propagation Reflection (R), Diffraction (D), Scattering (S) 19

20 Basic Propagation Mechanisms Reflections arise when the plane waves are incident upon a surface with dimensions that are very large compared to the wavelength. Diffraction occurs according to Huygens's principle when there is an obstruction between the transmitter and receiver antennas, and secondary waves are generated behind the obstructing body. Scattering occurs when the plane waves are incident upon an object whose dimensions are on the order of a wavelength or less, and causes the energy to be redirected in many directions. 20

21 Reflection from Smooth Surface 21

22 Typical Electromagnetic Properties 22

23 Reflection Coefficients 23

24 Power-Electric Field Relation In free space, power flux density P d is: PP dd = EEEEEEEE 4ππdd 2 = PP ttgg tt 4ππdd 2 = EE2 RR ffff = EE2 ηη W/m2 Equation to relate electric field (units of V/m) to received power (units of Watts): PP rr dd = PP dd AA ee = EE 2 120ππ AA ee = PP ttgg tt GG rr λλ 2 4ππ 2 dd 2 = EE 2 GG rr λλ 2 480ππ 2 W 24

25 Ground Reflection (Two-Ray) Model Friis free space equation is in most cases inaccurate when used alone. Hence, the more useful geometric optics-based propagation model is: 25

26 Ground Reflection (Two-Ray) Model Consider both direct and ground reflected propagation path between base and mobile stations. Reasonably accurate for predicting large-scale signal strength over distances of several km, especially for mobile radio systems that use tall towers (height 50m) and in LOS microcell channels in urban environments. 26

27 Ground Reflection (Two-Ray) Model 1. The total received E-field, E tot is the result of the direct LOS component, E LOS and the ground reflected component, E g. 2. If E 0 is the free space E-field at a reference distance d 0 from the transmitter, then for d>d 0, the free space propagating E-field is: EE dd, tt = EE 0dd 0 dd cos ωω cc tt dd cc 27

28 Ground Reflection (Two-Ray) Model 3. The direct wave that travels a distance d : EE LLLLLL dd, tt = EE 0dd 0 cos ωω dd cc tt dd cc 4. The reflected wave that travels a distance d : EE gg dd, tt = Γ EE 0dd 0 cos ωω dd cc tt dd cc 5. Laws of reflection in dielectrics θθ ii = θθ 0 EE gg = ΓEE ii EE tt = 1 + Γ EE ii 28

29 Ground Reflection (Two-Ray) Model 6. The resultant electric field, is the vector sum of E LOS and E g. (Note: Assume perfect horizontal E- field polarization and ground reflection, i.e. Γ = - 1 and E t = 0.) EE TTTTTT = EE LLLLLL + EE gg EE TTTTTT dd, tt = EE 0dd 0 dd cos ωω cc tt dd cc + ( 1) EE 0dd 0 dd cos ωω cc tt dd cc 29

30 Ground Reflection (Two-Ray) Model 7. By image method, the path difference between the LOS and the ground reflected paths: Δ = dd dd = h tt + h rr 2 + dd 2 h tt h rr 2 + dd 2 8. When d is very large compared to h t +h r, the Δ can be simplified using a Taylor series approximation: Δ = dd dd 2h tth rr dd 9. Therefore: θθ Δ = 2ππΔ λλ = Δωω cc cc ττ dd = Δ cc = θθ Δ 2ππff cc 30

31 Image Method

32 Ground Reflection (Two-Ray) Model 10. The electric field (at the receiver) at a distance d from the transmitter (please refer reference pg ): 11. If it satisfies: EE tttttt (dd) = 2 EE 0dd 0 dd sin θθ Δ 2 dd > 20ππh tth rr 20h tth rr 3λλ λλ Then, the received E-field is: EE tttttt (dd) = 2EE 0dd 0 dd 2ππh tt h rr λλdd kk dd 2 V/m 32

33 Ground Reflection (Two-Ray) Model 13. The received power at a distance d from the transmitter for the two-ray ground bounce model : PP rr = PP tt GG tt GG rr h rr 2 h tt The path loss for the two-ray model (with antenna gains): dd 4 PPPP dddd = 40 log dd 10 log GG tt + 10 log GG rr + 20 log h tt + 20 log h rr 33

34 Example 3 solution Consider GSM900 cellular radio system with 20 W transmitted power from Base Station Transceiver (BTS). The gain of BTS and Mobile Station (MS) antenna are 8 db and 2 db respectively. The BTS is located 10 km away from MS and the height of the antenna for BTS and MS are 200 m and 3 m, respectively. By assuming two-ray ground reflection model between BTS and MS, calculate the received signal level at MS. 34

35 Example 4 solution A mobile is located 5 km away from a base station and uses a vertical quarter wavelength monopole antenna with a gain of 2.55 db to receive cellular radio signals. The E-field at 1km from the transmitter is measured to be 10-3 V/m. The carrier frequency of the system is 900 MHz. Find: a. Length and effective aperture of the receiving antenna. b. The received power at the mobile using the tworay ground reflection model assuming the transmitter s height is 50m, and receiver s height is 1.5 m above ground. 35

36 Diffraction Occurs when the radio path between sender and receiver is obstructed by an impenetrable body and by a surface with sharp irregularities (edges). 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. Diffraction explains how radio signals can travel in urban and rural environments without a LOS path. 36

37 Diffraction The phenomenon of diffraction from Huygen's principle - all points on a wave front can be considered as point sources for the production of secondary wavelets, and that these wavelets combine to produce a new wave front in the direction of propagation. 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. 37

38 Diffraction Due to diffraction: Difference between direct and diffracted path exist the excess path length: Δ h2 dd 1 + dd 2 2 dd 1 dd 2 The corresponding phase difference: φφ = 2ππΔ λλ 2ππ λλ h 2 2 dd 1 + dd 2 dd 1 dd 2 Diffraction parameter (Fresnel-Kirchoff) v : vv = h 2 dd 1 + dd 2 λλλλ 1 dd 2, which allows φφ = ππ 2 vv2 38

39 Knife-edge Diffraction Geometry 39

40 Knife-edge Diffraction Geometry αα = h dd 1 + dd 2 dd 1 dd 2 40

41 Fresnel Zone Geometry The concept of diffraction loss as a function of the path difference around an obstruction is explained by Fresnel zones. Fresnel zone successive regions where secondary waves have a path length from the transmitter to receiver which are nλ/2 greater than the total path length of a LOS. 41

42 Fresnel Zone Geometry Fresnel zones concentric circles on the plane with loci of the origins of secondary wavelets which propagate to the receiver, such that the total path length increases by λ/2 for successive circles. Alternately constructive and destructive interference to the total received signal. The radius of the n-th Fresnel zone circle is: rr nn = nnλλλλ 1dd 2 dd 1 + dd 2 Smallest circle, n = 1, so excess path length is λ/2 as compared to LOS path. Circle n = 2, 3,etc have an excess path length of λ, 3λ/2, etc. 42

43 Fresnel Zone Geometry Maximum radii if the plane is midway between the transmitter and receiver. Radii becomes smaller when the plane is moved toward either the transmitter or receiver. Shadowing is sensitive to the frequency and location of obstruction with relation to the transmitter or receiver. 43

44 Fresnel Zone Considerations In mobile communication systems, diffraction loss occurs from the blockage of secondary waves, such that only a portion of the energy is diffracted around the obstacle blockage of energy from some of Fresnel zones only allows some energy to reach the receiver. Depending on geometry of obstruction, the received energy is vector sum of the energy contributions from all unobstructed Fresnel zones. If an obstruction does not block the volume contained within the first Fresnel zone diffraction loss is minimal, and diffraction effects can be neglected. E.g. for the design of LOS microwave link, 55% of the first Fresnel zone is kept clear. 44

45 Fresnel Zones for Different Knifeedge Diffraction Figure 4.12 Illustration of Fresnel zones for different knife-edge diffraction scenarios. 45

46 Multiple Knife-edge Diffraction 46

47 Example 5 solution Compute the diffraction loss for the three cases shown in Fig Assume λ=1/3m, d 1 = 1km, d 2 = 1km, and height is: a. 25m b. 0 c. -25m For each of the cases, identify the Fresnel zone within which the tip of the obstruction lies. 47

48 Scattering The medium which the wave travels consists of objects with dimensions smaller or comparable to the wavelength and where the number of obstacles per unit volume is large rough surfaces, small objects, foliage, street signs, lamp posts. The actual received signal in a mobile radio environment is often stronger than what is predicted by reflection and diffraction models alone. This is because when a radio wave impinges on a rough surface, the reflected energy is spread out (diffused) in all directions due to scattering. Objects such as lamp posts and trees tend to scatter energy in all directions, thereby providing additional radio energy at a receiver. 48

49 Scattering How about rain drops? 49

50 Practical Link Budget Design using Path Loss Models Most propagation models are derived using a combination of analytical and empirical methods. Empirical model fitting curves or analytical expressions that recreate a set of measured data advantage since takes into account all known and unknown propagation factors, through actual field measurements. By using path loss to estimate received signal level as a function of distance possibly to predict SNR for mobile communication system. 50

51 Log-distance Path Loss Model The average path loss for an arbitrary transmitreceive separation is expressed by: PPPP(dd) dd dd 0 nn or PPPP(dB) PPPP dd nn log dd dd 0 51

52 Log-normal Shadowing Model Previous model does not consider the fact that the surrounding environmental clutter may be vastly different at two different locations having the same transmit-receive separation. PL at a particular location is random and distributed log-normally about the mean distancedependent value, i.e. PPPP(dd)[dB] = PPPP dd 0 + XX σσ = PPPP dd nn log dd dd 0 + XX σσ and PP rr (dd)[dbm] = PP tt [dbm] PPPP (dd)[db] X σ is a zero-mean Gaussian distributed random variable (db) with standard deviation σ (in db) 52

53 Log-normal Shadowing Model The log-normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same transmit-receive separation, but different levels of clutter on the propagation path log-normal shadowing! Next figure illustrates actual measured data in several cellular radio systems and demonstrates the random variations about the mean path loss due to shadowing at specific transmit-receive separation. 53

54 Log-normal Shadowing Model 54

55 Outdoor Propagation Models Radio transmission in mobile communication system often takes place over irregular terrains: Simple curved earth profile? Highly mountainous profile? Presence of trees, buildings, and other obstacles? Several models used for prediction vary in terms of approach, complexity and accuracy. 55

56 Outdoor Propagation Models The Longley-Rice model: Point to point communication systems (40 MHz to 100 GHz). Use models of two-ray ground reflection, Fresnel-Kirchoff knife-edge, forward scatterer, far-field diffraction loss. Two modes with or without terrain path profile. No corrections for environmental factors in the immediate vicinity of the receiver, and multipath is not considered. Durkin s model: Reads digital elevation map and perform site-specific propagation computation. Produces signal strength contour. Cannot predict propagation effects due to foliage, buildings, man-made structures. Not account for multipath other than ground reflection. 56

57 Okumura Model One of the most widely used models for signal prediction in urban areas. Applicable for: frequencies ranging from 150MHz to 1920MHz. frequencies can be extrapolated to 3GHz. distances from 1km to 100km. base station antenna heights from 30m-1000m. Wholly based on measured data - no analytical explanation Among the simplest & best for in terms of path loss accuracy in cluttered mobile environment. Disadvantage: slow response to rapid terrain changes Common standard deviations between predicted and measured path loss 10dB - 14dB. 57

58 Okumura Model Okumura developed a set of curves in urban areas with quasi-smooth terrain. Developed from extensive measurements using vertical omni- directional antennas at base and mobile stations. It gives median attenuation relative to free space (A mu ). The model can be expressed as: LL 50 [db] = LL FF + AA mmmm (ff, dd) GG(h tttt ) GG(h rrrr ) GG AAAAAAAA 58

59 Okumura Model L 50 = 50 th percentile (median) value of propagation loss. L F = free space propagation loss. A mu = median attenuation relative to free space G(h te ) = base station antenna height gain factor. G(h re ) = mobile station antenna height gain factor. G AREA = gain due to the type of environment. G(h te ) = G(h re ) = h log 200 h log 3 20 te 10 re 1000 m > h te > 30m h re 3m G(h re ) = h log 3 20 re 10m h re 3m 59

60 Okumura Model A mu (f,d) Figure 4.23 Median attenuation relative to free space (A mu (f,d)), over a quasi-smooth terrain 60

61 Okumura Model - G AREA 61

62 Okumura Model Calculation a) calculate free-space path loss at the considered distance and carrier frequency. b) add median attenuation at the considered distance and carrier frequency. c) subtract the base and mobile station antenna gains (see previous antenna gains formula page 59). d) subtract the gain due to the specific environment. The values of A mu (f c,d) and G AREA are obtained from Okumura empirical plots. 62

63 Example 6 solution Find the median path loss using Okumura s model for d = 50 km, h te = 100 m, h re = 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 the power at the receiver (assume a unity gain receiving antenna). 63

64 Hata Model Empirical formulation of the graphical path loss data provided by Okumura, and valid from 150 MHz to 1500 MHz. Standard formula for urban environment: LL 50 (uuuuuuuuuu)[db = log ff cc log h tttt aa h rrrr + ( log h tttt ) log dd Correction factor, a(hre) is a function of the size of the coverage area. Prediction from Hata compare very closely to Okumura, as long as d exceeds 1 km. 64

65 Hata Model For small to medium sized city, the correction factor is: a(h re ) Comment (1.1log 10 f c - 0.7)h re (1.56log 10 f c - 0.8) db Medium City 8.29(log h re ) db Large City (f c 300MHz) 3.2(log h re ) db Large City (f c > 300MHz) For Suburban and Rural Regions L 50 (db) L 50 (urban) - 2[log 10 (f c /28)] L 50 (urban) (log 10 f c ) log 10 f c Comment Suburban Area Rural Area 65

66 Other Outdoor Propagation Models PCS extension to Hata Model :- Extended version of Hata Model to 2 GHz. Walfisch and Bertoni Model :- Considers the impact of rooftops and building height by using diffraction to predict average signal strength at street level. Wideband PCS Microcell Model :- Statistics for path loss, multipath and coverage area were developed based on extensive measurements made in LOS and obstructed environments. 66

67 Indoor Propagation Models The indoor radio channel differs from the traditional mobile radio channel: Distances covered are much smaller Variability of the environment is much greater for a much smaller range of transmit-receive separation. Propagation within buildings is strongly influenced by Layout of the building Construction material Building type Same mechanisms as outdoor: reflection, diffraction and scattering but much more variable. 67

68 Partition Losses (same floor) 68

69 Partition Losses (between floors) Floor attenuation factors (FAF) between one floor of the building is greater than the incremental attenuation caused by each additional floor. 69

70 Partition Losses (between floors) After about five or six floor separations, very little additional path loss is experienced. 70

71 Log-distance Path Loss Model PPPP[dB] = PPPP dd nn log dd dd 0 + XX σσ n depends on the surroundings and building types. 71

72 Ericsson Multiple Breakdown Model Measurements in a multiple floor office building. Four breakpoints also gives upper and lower bound on the path loss. 72

73 Signal Penetration into Buildings Limited number of experiments difficult to examine exact models for penetration and difficult to compare. Generalizations have been made: Signal strength received inside a building increases with height. At lower floor, the urban clutter induces high great attenuation and reduces the level of penetration. At higher floor, a LOS path may exist, causing stronger incident signal at the exterior wall of the building. RF penetration changes as a function of frequency and height within the building. Antenna elevation pattern is also important for signal penetration from outside the building. Amount of windows compared to building surface area, presence of tinted metal in windows and angle of incidence have strong impact on penetration loss. 73

74 Ray Tracing and Site Specific Modeling New methods of predicting radio signal coverage: Site Specific propagation models : Deterministically modelling any indoor or outdoor propagation environment. Graphical Information System database : Building database can be drawn or digitized using graphical software packages able to include accurate representation of building and terrain features. 74

75 Small-Scale Fading and Multipath Small-scale fading (or simply fading) rapid fluctuations of the amplitudes, phases, or multipath delays of radio signal short period of time / travel distance. Fading interference between two or more versions of the transmitted signal arrived at the receiver at slightly different times. 75

76 Small-Scale Multipath Propagation Multipath in radio channel creates small-scale fading effects: Rapid changes in signal strength over small travel distance or time interval. Random frequency modulation due to varying Doppler shifts on different multipath signals. Time dispersion (echoes) due to multipath propagation delays. 76

77 Signal Interference Power P T d (Km) Frequency 77

78 Large-Scale Parameters Distance Pathloss Signal Interference Power P T P T +PL(d) d (Km) Frequency 78

79 Large-Scale Parameters Distance Pathloss Lognormal Shadowing Signal Interference Power P T P T +PL(d) d (Km) Frequency 79

80 Large-Scale Parameters Distance Pathloss Lognormal Shadowing Signal Interference Power P T P T +PL(d) d (Km) Frequency 80

81 Large-Scale Parameters Distance Pathloss Lognormal Shadowing Signal Interference Power P T P T +PL(d) d (Km) Frequency 81

82 Large-Scale Parameters Distance Pathloss Lognormal Shadowing Signal Interference Power P T P T +PL(d) P T +PL(d)+X d (Km) Frequency 82

83 Large-Scale Parameters Distance Pathloss Lognormal Shadowing Signal Interference Small-Scale Parameters Multi-Path Fading Power P T P T +PL(d) P T +PL(d)+X d (Km) Frequency 83

84 100 Distance Pathloss Mobile Speed 3 Km/hr PL= log 10 (D KM ) d Lognormal Shadowing Mobile Speed 3 Km/hr ARMA Correlated Shadow Model Rapid changes in signal strength over a small traveling distances d Small-Scale Fading Mobile Speed 3 Km/hr Jakes s Rayleigh Fading Model d

85 Multipath Propagation Modeling Power Multi-Path Components τ 0 τ 1 τ 2 Time Multi-path results from reflection, diffraction, and scattering off environment surroundings Note: The figure above demonstrates the roles of reflection and scattering only on multi-path 85

86 Multipath Propagation Modeling Power Multi-Path Components τ 0 τ 1 τ 2 Time As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies 86

87 Multipath Propagation Modeling Power Multi-Path Components τ 0 τ 1 τ 2 Time As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies 87

88 Small-Scale Multipath Propagation Fading signals occur due to reflections from ground & surrounding buildings (clutter) as well as scattered signals from trees, people, towers, etc. often an LOS path is not available so the first multipath signal arrival is probably the desired signal (the one which traveled the shortest distance) allows service even when Rx is severely obstructed by surrounding clutter 88

89 Small-Scale Multipath Propagation Even stationary Tx/Rx wireless links can experience fading due to the motion of objects (cars, people, trees, etc.) in surrounding environment off of which come the reflections. Multipath signals have randomly distributed amplitudes, phases, & direction of arrival vector summation of (A θ) at Rx of multipath leads to constructive/destructive interference as mobile Rx moves in space with respect to time 89

90 Small-Scale Multipath Propagation Received signal strength can vary by small-scale fading over distances of a few meter (about 7 cm at 1 GHz)! This is a variation between, say, 1 mw and 10-6 mw. If a user stops at a deeply faded point, the signal quality can be quite bad. However, even if a user stops, others around may still be moving and can change the fading characteristics. And if we have another antenna, say only 7 to 10 cm separated from the other antenna, that signal could be good. 90

91 Factors influencing Small-Scale Fading 1) Multipath Propagation # and strength of multipath signals. time delay of signal arrival : large path length differences large differences in delay between signals. urban area with many buildings distributed over large spatial scale : large # of strong multipath signals with only a few having a large time delay. suburb with nearby office park or shopping mall moderate # of strong multipath signals with small to moderate delay times. rural few multipath signals (LOS + ground reflection). 91

92 Factors influencing Small-Scale Fading 2) Speed of Mobile relative motion between base station & mobile causes random frequency modulation due to Doppler shift (f d ) Different multipath components may have different frequency shifts. 3) Speed of Surrounding Objects also influence Doppler shifts on multipath signals dominates small-scale fading if speed of objects > mobile speed: otherwise ignored 92

93 Factors influencing Small-Scale Fading 4) Transmission bandwidth of the signal (B s ) The mobile radio channel (MRC) is modeled as filter with specific bandwidth (BW) The relationship between the signal BW & the MRC BW will affect fading rates and distortion, and so will determine: a) if small-scale fading is significant. b) if time distortion of signal leads to intersymbol interference (ISI). An MRC can cause distortion/isi or small-scale fading, or both. But typically one or the other. 93

94 Doppler Shift Doppler shift of the carrier frequency: relative motion of the receiver and transmitter causes Doppler shifts, f d. yields random frequency modulation due to different frequency shifts on the multipath components. A mobile moving with constant velocity v Along path between X and Y Receive signals remotely from S The difference in path length travelled by the wave from S to mobile at points X and Y is Δl = d cosθ = vδt cosθ 94

95 Doppler Shift The phase change in the received signal due to difference in path lengths: 2π l 2πv l φ = = cosθ λ λ The apparent change in frequency, or Doppler shift is given by: 1 φ f. v d = = cos( θ ) 2π t λ If mobile moving toward S, the Doppler shift is positive, that is the apparent received frequency is increased. If mobile moving away from the direction of arrival of the wave, the Doppler shift is negative, that is the apparent received frequency is decreased. 95

96 Doppler Shift Two Doppler shifts to consider above : The Doppler shift of the signal when it is received at the car. The Doppler shift of the signal when it bounces off the car and is received somewhere else. Multipath signals will have different f d s for constant v because of random arrival directions!! Note: What matters with Doppler shift is not the absolute frequency, but the shift in frequency relative to the bandwidth of a channel : For example: A shift of 166 Hz may be significant for a channel with a 1 khz bandwidth. In general, low bit rate (low bandwidth) channels are affected by Doppler shift. 96

97 Example 7 Consider a transmitter which radiates a sinusoidal carrier frequency of 1850 MHz. For a vehicle moving 60 mph, compute the received carrier frequency if the mobile is moving: (a) Directly towards the transmitter. (b) Directly away from the transmitter. (c) In a direction which is perpendicular to the direction of arrival of the transmitted signal. 97

98 Parameters of Mobile Multipath Channels Many multipath channel parameters are derived from power delay profiles (Eq. 5-18) : P (τ k ) : relative power amplitudes of multipath signals (absolute measurements are not needed) Relative to the first detectable signal arriving at the Rx at τ 0 use ensemble average of many profiles in a small localized area typically 2 6 m spacing of measurements to obtain average small-scale response. 98

99 Power Delay Profile The power delay profile depicts the spatial average of received power within the multi-path channel over a radius that is comparable to the signal wavelength. 99

100 Parameters of Mobile Multipath Channels The power delay profile is used to derive some parameters that can help characterize the effect of the wireless channel on signal communication Time dispersion parameters: Mean excess delay RMS delay spread Excess delay spread (X db) Coherence bandwidth Frequency dispersion parameters: Doppler spread Coherence time 100

101 Time Dispersion Parameters τ Mean Excess Delay = k k P ( τ ) P k ( τ ) k τ k P(t) RMS Delay Spread ( ) 2 στ = τ τ τ 2 = k k P ( τ ) P k ( τ ) k 2 τ 2 k τ 0 τ 1 τ 2 τ 3 τ N Power Delay Profile t Note: These delays are measured relative to the first detectable signal (multi-path component) arriving at the receiver at τ 0 =0 Maximum Excess Delay (XdB) or Excess Delay Spread (XdB): Time delay during which multi-path energy falls to X db below the maximum (Note that the strongest component does not necessarily arrive at τ 0 ) 101

102 Time Dispersion Parameters 102

103 Time Dispersion Parameters τ and σ τ provide a measure of propagation delay of interfering signals: Then give an indication of how time smearing might occur for the signal. A small σ τ is desired. The noise threshold is used to differentiate between received multipath components and thermal noise. 103

104 Time Dispersion Parameters 104

105 Coherence Bandwidth Analogous to the delay spread parameters in the time domain, coherence bandwidth is used to characterize the channel in the frequency domain. The RMS delay spread and coherence bandwidth are inversely proportional to each other. A statistical measure of the range of frequencies over which the channel is can be considered to be flat (i.e., a channel which passes all spectral components with approximately equal gain and linear phase) Coherence Bandwidth over which the frequency correlation function is 0.9 B C 1 = C 50σ τ Coherence Bandwidth over which the frequency correlation function is 0.5 B = 1 5σ τ 105

106 Coherence Bandwidth Amplitude correlation multipath signals have close to the same amplitude if they are then out-of-phase they have significant destructive interference with each other (deep fades). A flat fading channel is both good and bad : Good: The mobile radio channel is like a band-pass filter and passes signals without major attenuation from the channel. Bad: Deep fading can occur. So, the coherence bandwidth is the range of frequencies over which two frequency components have a strong potential for amplitude correlation. 106

107 Example 8 Calculate the mean excess delay, RMS delay spread, and the maximum excess delay (10 db) for the multipath profile given. Estimate the 50% coherence bandwidth of the channel. Would this channel be suitable for GSM service without the use of an equalizer? P r (τ) 0 db db db db τ (μs) 107

108 Frequency Dispersion Parameters Doppler spread and coherence time are parameters which describe the time varying nature of the channel. Doppler spread B D is a measure of spectral broadening due to the Doppler shift associated with mobile motion. Coherence time is a statistical measure of the time duration over which the channel impulse response is essentially invariant. Coherence Time is inversely proportional to Doppler spread T C f 1 m Coherence Time over which the time correlation function is TC 16πf m where f m is the maximum Doppler shift given by f m =v/λ A Common Rule: T C = = 16πf f f m m m 108

109 109

110 Fading Effects due to Multipath Time Delay Spread Time dispersion due to multipath causes the transmitted signal to undergo either flat or frequency selective fading. 110

111 Flat fading vs Freq. Selective fading Flat Fading P(t) Power Delay Profile B S << BC TS >> στ A Common Rule of Thumb: T S > 10 σ t Flat fading τ 0 τ 1 τ N Symbol Time (Digital Communication) T S t Wireless Channel + Minimal ISI τ 0 τa τn 111

112 Flat fading

113 Flat fading vs Freq. Selective fading Frequency Selective Fading B S > BC TS < στ A Common Rule of Thumb: T S < 10 σ t Freq. Selective Fading P(t) Power Delay Profile τ 0 τ 1 τ 2 τ 3 τ N Symbol Time (Digital Communication) T S t Wireless Channel + Significant ISI τ 0 τ a τ N 113

114 Frequency Selective fading

115 Flat fading vs Freq. Selective fading A channel is called frequency selective fading because different frequencies within a signal are attenuated differently by the mobile radio channel. Note: The definition of flat or frequency selective fading is defined with respect to the bandwidth of the signal that is being transmitted. B c and σ τ are related quantities that characterize time-varying nature of the mobile radio channel for multipath interference from frequency and time domain perspectives. However, B c and σ τ do NOT characterize the timevarying nature of the mobile radio channel due to the mobility of the mobile and/or surrounding objects. 115

116 Fading Effects due to Doppler Spread Depending on how rapidly the transmitted baseband signal changes as compared to the rate of change of the channel. 116

117 Slow fading vs Fast fading Power Delay Profile P(t) P(τ 0,t) P(τ 0,T C ) P(τ0,2T C ) P(τ 0,3T C ) P(τ 0,KT C ) τ 0 t 0 T C 2T C 3T C KT C t Consider a wireless channel comprised of a single path component. The power delay profile reflects average measurements P(τ 0 ) shall vary as the mobile moves Fast Fading Slow Fading T S B < B > TC S D T S B >> B << TC S D Frequency dispersion (time selective fading) 117

118 Two Independent Fading Issues 118

119 Assignment 2 Q1 If a particular modulation provides suitable BER performance whenever σ τ / T S 0.1, determine the smallest symbol period T S that maybe sent through RF channels in (a) indoor and (b) outdoor, without using equalizer. Estimate the 90% and 50% correlation coherence bandwidth for both channels. P r (τ) P r (τ) 0 db - (a) indoor 0 db - (b) outdoor -10 db db db db db τ (ns) -30 db τ (μs) 119

120 Assignment 2 Q2 If a baseband binary message with a bit rate R b = 100 kbps is modulated by an RF carrier using BPSK, (a) Find the range of values required for the rms delay spread of the channel, such that the received signal is a flat-fading signal (Note: T s = 1 / R b ) (b) If the modulation carrier frequency is 5.8 GHz, what is the coherence time of the channel, assuming a vehicle speed of 13 m/s? (c) Is the channel in (b) is fast or slow fading? 120