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- 1. Radio Propagation CSCI 694 24 September 1999 Lewis Girod
- 2. 17 March 1999 Radio Propagation 2 Outline • Introduction and terminology • Propagation mechanisms • Propagation models
- 3. 17 March 1999 Radio Propagation 3 What is Radio? • Radio Xmitter induces E&M fields – Electrostatic field components 1/d3 – Induction field components 1/d2 – Radiation field components 1/d • Radiation field has E and B component – Field strength at distance d = E B 1/d2 – Surface area of sphere centered at transmitter
- 4. 17 March 1999 Radio Propagation 4 General Intuition • Two main factors affecting signal at receiver – Distance (or delay) Path attenuation – Multipath Phase differences Green signal travels 1/2 farther than Yellow to reach receiver, who sees Red. For 2.4 GHz, (wavelength) =12.5cm.
- 5. 17 March 1999 Radio Propagation 5 Objective • Invent models to predict what the field looks like at the receiver. – Attenuation, absorption, reflection, diffraction... – Motion of receiver and environment… – Natural and man-made radio interference... – What does the field look like at the receiver?
- 6. 17 March 1999 Radio Propagation 6 Models are Specialized • Different scales – Large scale (averaged over meters) – Small scale (order of wavelength) • Different environmental characteristics – Outdoor, indoor, land, sea, space, etc. • Different application areas – macrocell (2km), microcell(500m), picocell
- 7. 17 March 1999 Radio Propagation 7 Outline • Introduction and some terminology • Propagation Mechanisms • Propagation models
- 8. 17 March 1999 Radio Propagation 8 Radio Propagation Mechanisms • Free Space propagation • Refraction – Conductors & Dielectric materials (refraction) • Diffraction – Fresnel zones • Scattering – “Clutter” is small relative to wavelength
- 9. 17 March 1999 Radio Propagation 9 Free Space • Assumes far-field (Fraunhofer region) – d >> D and d >> , where • D is the largest linear dimension of antenna • is the carrier wavelength • No interference, no obstructions
- 10. 17 March 1999 Radio Propagation 10 Free Space Propagation Model • Received power at distance d is – where Pt is the transmitter power in Watts – a constant factor K depends on antenna gain, a system loss factor, and the carrier wavelength Watts)( 2 d P KdP t r
- 11. 17 March 1999 Radio Propagation 11 Refraction • Perfect conductors reflect with no attenuation • Dielectrics reflect a fraction of incident energy – “Grazing angles” reflect max* – Steep angles transmit max* r t • Reflection induces 180 phase shift *The exact fraction depends on the materials and frequencies involved
- 12. 17 March 1999 Radio Propagation 12 Diffraction • Diffraction occurs when waves hit the edge of an obstacle – “Secondary” waves propagated into the shadowed region – Excess path length results in a phase shift – Fresnel zones relate phase shifts to the positions of obstacles T R 1st Fresnel zone Obstruction
- 13. 17 March 1999 Radio Propagation 13 Fresnel Zones • Bounded by elliptical loci of constant delay • Alternate zones differ in phase by 180 – Line of sight (LOS) corresponds to 1st zone – If LOS is partially blocked, 2nd zone can destructively interfere (diffraction loss) Fresnel zones are ellipses with the T&R at the foci; L1 = L2+ Path 1 Path 2
- 14. 17 March 1999 Radio Propagation 14 Power Propagated into Shadow • How much power is propagated this way? – 1st FZ: 5 to 25 dB below free space prop. Obstruction of Fresnel Zones 1st 2nd 0 -10 -20 -30 -40 -50 -60 0o 90 180o dB Tip of Shadow Obstruction LOS Rappaport, pp. 97
- 15. 17 March 1999 Radio Propagation 15 Scattering • Rough surfaces – critical height for bumps is f( ,incident angle) – scattering loss factor modeled with Gaussian distribution. • Nearby metal objects (street signs, etc.) – Usually modelled statistically • Large distant objects – Analytical model: Radar Cross Section (RCS)
- 16. 17 March 1999 Radio Propagation 16 Outline • Introduction and some terminology • Propagation Mechanisms • Propagation models – Large scale propagation models – Small scale propagation (fading) models
- 17. 17 March 1999 Radio Propagation 17 Propagation Models: Large • Large scale models predict behavior averaged over distances >> – Function of distance & significant environmental features, roughly frequency independent – Breaks down as distance decreases – Useful for modeling the range of a radio system and rough capacity planning
- 18. 17 March 1999 Radio Propagation 18 Propagation Models: Small • Small scale (fading) models describe signal variability on a scale of – Multipath effects (phase cancellation) dominate, path attenuation considered constant – Frequency and bandwidth dependent – Focus is on modeling “Fading”: rapid change in signal over a short distance or length of time.
- 19. 17 March 1999 Radio Propagation 19 Large Scale Models • Path loss models • Outdoor models • Indoor models
- 20. 17 March 1999 Radio Propagation 20 Free Space Path Loss • Path Loss is a measure of attenuation based only on the distance to the transmitter • Free space model only valid in far-field; – Path loss models typically define a “close-in” point d0 and reference other points from there: 2 0 0 )()( d d dPdP rr dB dBr d d dPLdPdPL 0 0 2)()]([)( What is dB?
- 21. 17 March 1999 Radio Propagation 21 Log-Distance Path Loss Model • Log-distance generalizes path loss to account for other environmental factors • Choose a d0 in the far field. • Measure PL(d0) or calculate Free Space Path Loss. • Take measurements and derive empirically. dB d d dPLdPL 0 0 )()(
- 22. 17 March 1999 Radio Propagation 22 Log-Distance 2 • Value of characterizes different environments Environm ent Exponent Free Space 2 Urban area 2.7-3.5 Shadowed urban area 3-5 Indoor LOS 1.6-1.8 Indoor no LOS 4-6 Rappaport, Table 3.2, pp. 104
- 23. 17 March 1999 Radio Propagation 23 Log-Normal Shadowing Model • Shadowing occurs when objects block LOS between transmitter and receiver • A simple statistical model can account for unpredictable “shadowing” – Add a 0-mean Gaussian RV to Log-Distance PL – Markov model can be used for spatial correlation
- 24. 17 March 1999 Radio Propagation 24 Outdoor Models • “2-Ray” Ground Reflection model • Diffraction model for hilly terrain
- 25. 17 March 1999 Radio Propagation 25 2-Ray Ground Reflection • For d >> hrht, – low angle of incidence allows the earth to act as a reflector – the reflected signal is 180 out of phase – Pr 1/d4 ( =4) RT ht hr Phase shift!
- 26. 17 March 1999 Radio Propagation 26 Ground Reflection 2 • Intuition: ground blocks 1st Fresnel zone – Reflection causes an instantaneous 180 phase shift – Additional phase offset due to excess path length – If the resulting phase is still close to 180 , the gound ray will destructively interfere with the LOS ray. RT ht hr p1 p0 180
- 27. 17 March 1999 Radio Propagation 27 Hilly Terrain • Propagation can be LOS or result of diffraction over one or more ridges • LOS propagation modelled with ground reflection: diffraction loss • But if there is no LOS, diffraction can actually help!
- 28. 17 March 1999 Radio Propagation 28 Indoor Path Loss Models • Indoor models are less generalized – Environment comparatively more dynamic • Significant features are physically smaller – Shorter distances are closer to near-field – More clutter, scattering, less LOS
- 29. 17 March 1999 Radio Propagation 29 Indoor Modeling Techniques • Modeling techniques and approaches: – Log-Normal, <2 for LOS down corridor – Log-Normal shadowing model if no LOS – Partition and floor attenuation factors – Computationally intensive “ray-tracing” based on 3-D model of building and attenuation factors for materials
- 30. 17 March 1999 Radio Propagation 30 Outline • Introduction and some terminology • Propagation Mechanisms • Propagation models – Large scale propagation models – Small scale propagation (fading) models
- 31. 17 March 1999 Radio Propagation 31 Recall: Fading Models • Small scale (fading) models describe signal variability on a scale of – Multipath effects (phase cancellation) dominate, path attenuation considered constant – Frequency and bandwidth dependent – Focus is on modeling “Fading”: rapid change in signal over a short distance or length of time.
- 32. 17 March 1999 Radio Propagation 32 Factors Influencing Fading • Motion of the receiver: Doppler shift • Transmission bandwidth of signal – Compare to BW of channel • Multipath propagation – Receiver sees multiple instances of signal when waves follow different paths – Very sensitive to configuration of environment
- 33. 17 March 1999 Radio Propagation 33 Effects of Multipath Signals • Rapid change in signal strength due to phase cancellation • Frequency modulation due to Doppler shifts from movement of receiver/environment • Echoes caused by multipath propagation delay
- 34. 17 March 1999 Radio Propagation 34 The Multipath Channel • One approach to small-scale models is to model the “Multipath Channel” – Linear time-varying function h(t, ) • Basic idea: define a filter that encapsulates the effects of multipath interference – Measure or calculate the channel impulse response (response to a short pulse at fc): h(t, ) t
- 35. 17 March 1999 Radio Propagation 35 Channel Sounding • “Channel sounding” is a way to measure the channel response – transmit impulse, and measure the response to find h( ). – h( ) can then be used to model the channel response to an arbitrary signal: y(t) = x(t) h( ). – Problem: models the channel at single point in time; can‟t account for mobility or environmental changes h(t, ) SKIP
- 36. 17 March 1999 Radio Propagation 36 Characterizing Fading* • From the impulse response we can characterize the channel: • Characterizing distortion – Delay spread ( d): how long does the channel ring from an impulse? – Coherence bandwidth (Bc): over what frequency range is the channel gain flat? – d 1/Bc *Adapted from EE535 Slides, Chugg „99 In time domain, roughly corresponds to the “fidelity” of the response; sharper pulse requires wider band
- 37. 17 March 1999 Radio Propagation 37 Effect of Delay Spread* • Does the channel distort the signal? – if W << Bc: “Flat Fading” • Amplitude and phase distortion only – if W > Bc: “Frequency Selective Fading” • If T < d, inter-symbol interference (ISI) occurs • For narrowband systems (W 1/T), FSF ISI. • Not so for wideband systems (W >> 1/T) For a system with bw W and symbol time T...
- 38. 17 March 1999 Radio Propagation 38 Qualitative Delay Spread RMS Delay spread ( ) Mean excess delay Noise threshold Delay Power(dB) Typical values for : Indoor: 10-100 ns Outdoor: 0.1-10 s
- 39. 17 March 1999 Radio Propagation 39 Characterizing Fading 2* • Characterizing Time-variation: How does the impulse response change with time? – Coherence time (tc): for what value of are responses at t and t+ uncorrelated? (How quickly is the channel changing) – Doppler Spread (fd): How much will the spectrum of the input be spread in frequency? – fd 1/tc
- 40. 17 March 1999 Radio Propagation 40 Effect of Coherence Time* • Is the channel constant over many uses? – if T << tc: “Slow fading” • Slow adaptation required – if T > tc: “Fast fading” • Frequent adaptation required • For typical systems, symbol rate is high compared to channel evolution For a system with bw W and symbol time T...
- 41. 17 March 1999 Radio Propagation 41 Statistical Fading Models • Fading models model the probability of a fade occurring at a particular location – Used to generate an impulse response – In fixed receivers, channel is slowly time-varying; the fading model is reevaluated at a rate related to motion • Simplest models are based on the WSSUS principle
- 42. 17 March 1999 Radio Propagation 42 WSSUS* • Wide Sense Stationary (WSS) – Statistics are independent of small perturbations in time and position – I.e. fixed statistical parameters for stationary nodes • Uncorrelated Scatter (US) – Separate paths are not correlated in phase or attenuation – I.e. multipath components can be independent RVs • Statistics modeled as Gaussian RVs
- 43. 17 March 1999 Radio Propagation 43 Common Distributions • Rayleigh fading distribution – Models a flat fading signal – Used for individual multipath components • Ricean fading distribution – Used when there is a dominant signal component, e.g. LOS + weaker multipaths – parameter K (dB) defines strength of dominant component; for K=- , equivalent to Rayleigh
- 44. 17 March 1999 Radio Propagation 44 Application of WSSUS • Multi-ray Rayleigh fading: – The Rayleigh distribution does not model multipath time delay (frequency selective) – Multi-ray model is the sum of two or more independent time-delayed Rayleigh variables s(t) R1 R2 r(t) Rappaport, Fig. 4.24, pp. 185.
- 45. 17 March 1999 Radio Propagation 45 Saleh & Valenzuela (1987) • Measured same-floor indoor characteristics – Found that, with a fixed receiver, indoor channel is very slowly time-varying – RMS delay spread: mean 25ns, max 50ns – With no LOS, path loss varied over 60dB range and obeyed log distance power law, 3 > n > 4 • Model assumes a structure and models correlated multipath components. Rappaport, pp. 188
- 46. 17 March 1999 Radio Propagation 46 Saleh & Valenzuela 2 • Multipath model – Multipath components arrive in clusters, follow Poisson distribution. Clusters relate to building structures. – Within cluster, individual components also follow Poisson distribution. Cluster components relate to reflecting objects near the TX or RX. – Amplitudes of components are independent Rayleigh variables, decay exponentially with cluster delay and with intra-cluster delay
- 47. 17 March 1999 Radio Propagation 47 References • Wireless Communications: Principles and Practice, Chapters 3 and 4, T. Rappaport, Prentice Hall, 1996. • Principles of Mobile Communication, Chapter 2, G. Stüber, Kluwer Academic Publishers, 1996. • Slides for EE535, K. Chugg, 1999. • Spread Spectrum Systems, Chapter 7, R. Dixon, Wiley, 1985 (there is a newer edition). • Wideband CDMA for Third Generation Mobile Communications, Chapter 4, T. Ojanpera, R. Prasad, Artech, House 1998. • Propagation Measurements and Models for Wireless Communications Channels, Andersen, Rappaport, Yoshida, IEEE Communications, January 1995.
- 48. 17 March 1999 Radio Propagation 48 The End
- 49. 17 March 1999 Radio Propagation 49 Scattering 2 • hc is the critical height of a protrusion to result in scattering. • RCS: ratio of power density scattered to receiver to power density incident on the scattering object – Wave radiated through free space to scatterer and reradiated: )sin( θ8 λ i c h )log(20)log(20)π4log(30 ]dB[)λlog(20)dBi()dBm()dBm( 2 RT TTR dd mRCSGPP
- 50. 17 March 1999 Radio Propagation 50 Free Space 2a • Free space power flux density (W/m2) – power radiated over surface area of sphere – where Gt is transmitter antenna gain • By covering some of this area, receiver‟s antenna “catches” some of this flux 2 π4 d GP P tt d
- 51. 17 March 1999 Radio Propagation 51 Free Space 2b • Fraunhofer distance: d > 2D2/ • Antenna gain and antenna aperture – Ae is the antenna aperture, intuitively the area of the antenna perpendicular to the flux – Gr is the antenna gain for a receiver. It is related to Ae. – Received power (Pr) = Power flux density (Pd) * Ae 2 λ π4 e A G π4 λ 2 G Ae
- 52. 17 March 1999 Radio Propagation 52 Free Space 2c – where L is a system loss factor – Pt is the transmitter power – Gt and Gr are antenna gains – is the carrier wavelength Watts )π(4 λ1 )( 2 2 2 L GGP d dP rtt r
- 53. 17 March 1999 Radio Propagation 53 LNSM 2 • PL(d)[dB] = PL(d0) +10nlog(d/d0)+ X – where X is a zero-mean Gaussian RV (dB) • and n computed from measured data, based on linear regression
- 54. 17 March 1999 Radio Propagation 54 Ground Reflection 1.5 • The power at the receiver in this model is – derivation calculates E field; – Pr = |E|2Ae; Ae is ant. aperture • The “breakpoint” at which the model changes from 1/d2 to 1/d4 is 2 hthr/ – where hr and ht are the receiver and transmitter antenna heights 4 22 d hh GGPP rt rttr
- 55. 17 March 1999 Radio Propagation 55 Convolution Integral • Convolution is defined by this integral: τ)τ()τ()( )()()( dthxty thtxty Indexes relevant portion of impulse response Scales past input signal
- 56. 17 March 1999 Radio Propagation 56 Partition Losses • Partition losses: same floor – Walls, furniture, equipment – Highly dependent on type of material, frequency • Hard partitions vs soft partitions – hard partitions are structural – soft partitions do not reach ceiling • “open plan” buildings
- 57. 17 March 1999 Radio Propagation 57 Partition Losses 2 • Partition losses: between floors – Depends on building construction, frequency – “Floor attenuation factor” diminishes with successive floors – typical values: • 15 dB for 1st floor • 6-10 dB per floor for floors 2-5 • 1-2 dB per floor beyond 5 floors
- 58. 17 March 1999 Radio Propagation 58 Materials • Attenuation values for different materials M aterial Loss (dB) Frequency Concrete block 13-20 1.3 GHz Plywood (3/4”) 2 9.6 GHz Plywood (2 sheets) 4 9.6 GHz Plywood (2 sheets) 6 28.8 GHz Alum inum siding 20.4 815 M Hz Sheetrock (3/4”) 2 9.6 GHz Sheetrock (3/4”) 5 57.6 GHz Turn corner in corridor 10-15 1.3 GHz
- 59. 17 March 1999 Radio Propagation 59 What does “dB” mean? • dB stands for deciBel or 1/10 of a Bel • The Bel is a dimensionless unit for expressing ratios and gains on a log scale • Gains add rather than multiply • Easier to handle large dynamic ranges ))log()(log(10log10 P P 12 1 2 10 dB1 2 PP P P
- 60. 17 March 1999 Radio Propagation 60 dB 2 • Ex: Attenuation from transmitter to receiver. – PT=100, PR=10 – attenuation is ratio of PT to PR – [PT/PR]dB = 10 log(PT/PR) = 10 log(10) = 10 dB • Useful numbers: – [1/2]dB -3 dB – [1/1000]dB = -30 dB
- 61. 17 March 1999 Radio Propagation 61 dB 3 • dB can express ratios, but what about absolute quantities? • Similar units reference an absolute quantity against a defined reference. – [n mW]dBm = [n/mW]dB – [n W]dBW = [n/W]dB • Ex: [1 mW]dBW = -30 dBW
- 62. 17 March 1999 Radio Propagation 62 Channel Sounding 2 • Several “Channel Sounding” techniques can measure the channel response directly: – Direct RF pulse (we hinted at this approach) – Sliding correlator – Frequency domain sounding
- 63. 17 March 1999 Radio Propagation 63 Channel Sounding 3 • Direct RF Pulse – Xmit pulse, scope displays response at receiver – Can be done with off-the-shelf hardware – Problems: hard to reject noise in the channel – If no LOS • must trigger scope on weaker multipath component • may fail to trigger • lose delay and phase information
- 64. 17 March 1999 Radio Propagation 64 Channel Sounding 4 • Sliding correlator – Xmit PseudoNoise sequence – Rcvr correlates signal with its PN generator – Rcvr clock slightly slower; PN sequences slide – Delayed components cause delayed correlations – Good resolution, good noise rejection
- 65. 17 March 1999 Radio Propagation 65 Channel Sounding 5 • Frequency domain sounding – Sweep frequency range – Compute inverse Fourier transform of response – Problems • not instantaneous measurement • Tradeoff between resolution (number of frequency steps) and real-time measurement (i.e. duration as short as possible)
- 66. 17 March 1999 Radio Propagation 66 Digression: Convolutions • The impulse response “box” notation implies the convolution operator, – Convolution operates on a signal and an impulse response to produce a new signal. – The new signal is the superposition of the response to past values of the signal. – Commutative, associative
- 67. 17 March 1999 Radio Propagation 67 y(t) y(t) Convolutions 2 • y(t) is the sum of scaled, time-delayed responses x(t) h(t) = + h(t) Each component of the sum is scaled by the x(t)dt at that point; in this example, the response is scaled to 0 where x(t) = 0.
- 68. 17 March 1999 Radio Propagation 68 Flip & Slide: h(t- )h(t- ) Flip & Slide: h(t- )h(t- ) Flip & Slide: h(t- )h(t- ) Convolutions 3 • Graphical method: “Flip & Slide” x(t) x( ) h(t) = Pairwise multiply x*h and integrate over and Store y(t) y(t) y(t) Flip & Slide: h(t- )h(t- ) Flip & Slide: h(t- )h(t- )
- 69. 17 March 1999 Radio Propagation 69 Frequency and Time Domains • The channel impulse response is f(time) – It describes the channel in the “time domain” • Functions of frequency are often very useful; – Space of such functions is “frequency domain” • Often a particular characteristic is easier to handle in one domain or the other.
- 70. 17 March 1999 Radio Propagation 70 Frequency Domain • Functions of frequency – usually capitalized and take the parameter “f” – where f is the frequency in radians/sec – and the value of the function is the amplitude of the component of frequency f. • Convolution in time domain translates into multiplication in the frequency domain: – y(t) = x(t) h(t) Y(f) = X(f)H(f)
- 71. 17 March 1999 Radio Propagation 71 Frequency Domain 2 • Based on Fourier theorem: – any periodic signal can be decomposed into a sum of (possibly infinite number of) cosines • The Fourier Transform and inverse FT – Convert between time and frequency domains. – The frequency and time representations of the same signal are “duals”
- 72. 17 March 1999 Radio Propagation 72 Flat Fading • T >> d and W << BC minimal ISI 0 Ts 0 0 Ts+ fc fcfc t t t f f f s(t) r(t)h(t, ) Time domain (convolve) Freq domain (filter) = = Delay spread Coherence BW
- 73. 17 March 1999 Radio Propagation 73 Frequency Selective Fading • T << d and W >> BC ISI 0 Ts 0 0 Ts+ fc fcfc t t f f f s(t) r(t)h(t, ) Time domain (convolve) Freq domain (filter) = = Delay spread Coherence BW Ts
- 74. 17 March 1999 Radio Propagation 74 Review • Object of radio propagation models: – predict signal quality at receiver • Radio propagation mechanisms – Free space (1/d2) – Diffraction – Refraction – Scattering
- 75. 17 March 1999 Radio Propagation 75 Review 2 • Factors influencing received signal – Path loss: distance, obstructions – Multipath interference: phase cancellation due to excess path length and other sources of phase distortion – Doppler shift – Other radio interference
- 76. 17 March 1999 Radio Propagation 76 Review 3 • Approaches to Modelling – Models valid for far-field, apply to a range of distances – large scale models: concerned with gross behavior as a function of distance – small scale (fading) models: concerned with behavior during perturbations around a particular distance
- 77. 17 March 1999 Radio Propagation 77 Relevance to Micronets • Micronets may require different models than most of the work featured here – Smaller transmit range – Likely to be near reflectors: on desk or floor. • On the other hand, at smaller scales things are less smooth: “ground reflection” may turn into scattering – Outdoors, throwing sensors on ground may not work. Deployable tripods?
- 78. 17 March 1999 Radio Propagation 78 Relevance 2 • Consequences of “Fading” – You can be in a place that has no signal, but where a signal can be picked up a short distance away in any direction • Ability to move? Switch frequencies/antennas? Call for help moving or for more nodes to be added? • If stuck, may not be worth transmitting at all – Reachability topology may be completely irrelevant to location relationships
- 79. 17 March 1999 Radio Propagation 79 Relevance 3 • Relevant modelling tools: – Statistical models (Rice/Rayleigh/Log Normal) • Statistical fading assumes particular dynamics, this depends on mobility of receivers and environment – CAD modelling of physical environment and ray tracing approaches. • For nodes in fixed positions this is only done once.
- 80. 17 March 1999 Radio Propagation 80 Relevance 4 • An approach to modelling? – Characterize wireless system interactions with different materials, compare to published data – Assess the effect of mobility in environment on fixed topologies, relate to statistical models – Try to determine what environmental structures and parameters are most important: • Scattering vs. ground reflection? • can a simple CAD model help?

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