Wireless Mesh Networks

Wireless Mesh Networks Anatolij Zubow (zubow@informatik.hu-berlin.de) Antennas and Propagation

Introduction • An antenna is an electrical conductor or system of conductors • Transmission - radiates electromagnetic energy into space • Reception - collects electromagnetic energy from space • In two-way communication, the same antenna can be used for transmission and reception (same characteristics) 2

Antenna • Radiation pattern • Performance of an antenna • Graphical representation of radiation properties of an antenna as a function of space coordinates • Depicted as two-dimensional cross section • Beam width (or half-power beam width) • Measure of directivity of antenna • Reception pattern • Receiving antenna’s equivalent to radiation pattern 3

Idealized Radiation Patterns • Distance from the antenna to each point on the radiation pattern is proportional to the power radiated from the antenna in that direction • Actual size of radiation pattern is arbitrary – important is relative distance (= relative power) from antenna in each direction 4

Types of Antennas • Isotropic antenna (idealized) • Radiates power equally in all directions • Dipole antennas • Half-wave dipole antenna (or Hertz antenna) • Quarter-wave vertical antenna (or Marconi antenna) • Parabolic Reflective Antenna 5

Radiation Patterns in Three Dimensions 6 Acoustics: http://www.kettering.edu/~drussell/Demos/rad2/mdq.html

Antenna Gain • Antenna gain • Measure of the directionality of an antenna • Power output, in a particular direction, compared to that produced in any direction by a perfect omnidirectional antenna (isotropic antenna) • Note: increased power is radiated in one direction by reducing the power radiated in other directions • E.g. antenna gain of 3 dB • Effective area • Related to physical size and shape of antenna 7

Propagation Modes • A signal radiated from an antenna travels along one of three routes: • Ground-wave propagation (GW) • Follows contour of the earth • Frequencies up to 2 MHz • Example: AM radio • Sky-wave propagation (SW) • Signal reflected from ionized layer of atmosphere back down to earth • Signal can travel a number of hops • Examples: Amateur radio, CB radio • Line-of-sight propagation (LOS) • Transmitting and receiving antennas must be within line of sight • Ground communication – antennas within effective line of site due to refraction 8

Fundamentals of Propagation Modeling 9

Fundamentals of Propagation Modeling (cont.) • … and would like to understand why the received power is like this: 10

Presupposed Basics • To really understand these phenomena, one needs a profound knowledge in Physics and Mathematics. • From the world of Physics: • Formulation of electromagnetic propagation • Reflection, scattering and diffraction • Many subsequent processes are random: • Notions of statistics (PDF, CDF) • Moments, mean, variance, etc. • Dependence, correlation, etc. • Many processes are in addition stochastic: • Notions of coherence, etc. 11

Presupposed Basics • Some revisions on statistics: • A random process (left) leads to a histogram (middle) and a mathematical abstraction in form of the probability density function, PDF (right) • The most important factors about the PDF are mean, std/variance, and shape • In nature, unbounded PDFs are Gaussian and bounded PDFs are uniform • Typical half-bounded PDFs: Rayleigh, Rice, Nakagami, lognormal, Gamma, etc. 12

Lognormal Gaussian Rayleigh Gamma 13

Presupposed Basics • Electromagnetic (EM) waves: • E & H are in-phase and occur together; hence, only E-field is considered normally • E-wave oscillates: in time with angular frequency ω = 2πf = 2π/T in space with spatial frequency k = 2π/λ • f is the frequency in [Hz], T the period in [s], and λ = c/f the wavelength in [m] • E = E0 cos(ωt – kr); for convenience, we write E = Re{ E0 ej‧(ωt – kr) } (Euler's formula ) 14

Sources of Signal Distortions • A useful signal can get distorted by: • Noise (thermal, shot): additive • Interference (self, other): additive • Wireless channel: multiplicative • Simplified, we can hence write for the received signal: • received = channel * transmitted + noise + interference • Note! • Noise and interference is always bad news, the channel not always (cf. MIMO) • Modern communication systems are dominated by interference and channel • For the additive components, important is the ratio between signal power and noise + interference powers (SNR, SIR, SINR) 15

Wireless Channel Taxonomies • Propagation Mechanisms: • Free space propagation (distance dependent) • Reflection and refraction (from surfaces, into buildings) • Diffraction (from roof edges) • Scattering (from surrounding trees) • Propagation Conditions: • Line-of-sight (LOS) (great visibility between Tx & Rx) • Non LOS (nLOS) (no direct visibility between Tx & Rx) • Obstructed LOS (oLOS) (small obstacle in-between Tx & Rx) • Distortions: • Doppler effect (caused by mobility in the channel) • Multipath propagation (signals arriving via different paths) 16

Propagation Mechanisms – Overview • Note! • All 5 effects result from the same set of equations: Maxwell's Equations • The equations are very complicated and not useful for every problem • For different ratios between object size and wavelength, different effects occur • Occurrence (object size d and wavelength λ): • Free-space propagation: always occurs for any d and λ • Reflection/refraction: d >> λ • Diffraction: λ in the order of the curvature of the edge • Scattering: d ≈or< λ 17

Reflection of Waves from Boundaries Reflection from a HARD boundary Reflection from a SOFT boundary When a wave encounters a boundary which is neither rigid (hard) nor free (soft), part of the wave is reflected from the boundary and part of the wave is transmitted across the boundary. From high to low speed (low  high density) From low speed to high speed 18 Example: http://www.kettering.edu/~drussell/Demos/reflect/reflect.html

Propagation Mechanisms – Free-Space • Friis' Transmission Equation: assuming • PRxto be received and PTxtransmitted powers • GRxto be receive and GTxtransmit antenna gains • d the distance between Tx and Rx, and λ = c/f the wavelength • perfect matching of Tx and Rx antennas, no multipath and aligned polarisation • In dB, we hence get: PRx=PTx+GTx+GTx+ 20log(c/2π) – 20log(f) – 20log(d) • PRxdecreases with -20dB/dec: 19

Antenna Polarization • An antenna is a transducer that converts electric current to electromagnetic waves that are then radiated into space. • The electric field plane determines the polarization or orientation of the radio wave. • Most systems use either vertical, horizontal or circular polarization. • Vertical polarization is most commonly used when it is desired to radiate a radio signal in all directions over a short to medium range. 20

Propagation Conditions – Overview • LOS (opposite for nLOS) has the following properties: • Advantage: strong signal • Disadvantage LOS: strong interference • oLOS is something in-between LOS and nLOS 21

Distortions – Doppler Effect • Doppler Formula: , where • c = 3‧108 m/s is the speed of light, and • v is the summed speed of the Tx and/or Rx and/or (!) reflecting objects • E.g., little movement in the channel (left), more movement in the channel (right): 22

Doppler effect • C. Doppler, was first to describe how the observed frequency of sound waves is affected by the relative motion of the source and the detector (Doppler effect). • Doppler effect occurs for all type of waves! • Experiment: • Doppler hired a train and the trumpet section of an orchestra. • Half of the players got on the train and played a specific note, the other half did the same sitting at the station. • As the train passed by the train station, people listened to the difference between the notes played by the moving musicians and those sitting. It was possible to tell the difference between the notes! • Also possible to show that a moving observer will detect a different frequency from that of a stationary observer 23

Doppler effect (cont.) • Moving source, stationary observer • We always measure everything relative to the air (medium transporting wave) • Source of sound moves with vs, observer stationary • Speed of sound cw • Sound waves are generated T=1/f0 times apart • When source moves (and observer is stationary), the distance between the wavefronts will be (cw+/- vs)T • while for stationary source it is cwT. 24

Doppler effect (cont.) • Moving source, stationary observer • The arrival time at the listener is tin front = [(cw- vs)T]/cw • and tbehind= [(cw+ vs)T]/cw • In terms of frequency: • where (-) refers to the observer being ahead and (+) is behind the source, and f0= 1/T and f±=1/t± • Doppler shift is defined as: Δf = f - fo 25 Example: http://www.gmi.edu/~drussell/Demos/doppler/doppler.html

Distortions – Multipath Propagation • Assume we send two symbols of duration Ts; then, objects along the ellipses with Tx & Rx in the foci, yield same propagation delays: • Intra-symbol interference • Overlap of symbol replicas within symbol duration (same color) • This leads to mutual cancellation • Inter-symbol interference • Overlap of symbol replicas belonging to different symbols (grey shading) 26

Summed Contributions • Defining characteristic of the mobile wireless channel is the variations of the channel strength over time and over frequency. • The variations can be roughly divided into three types: • Large-scale Fading (e.g. free space) • Shadowing • Multi-path Fading (e.g. Rayleigh) Example of a frequency selective, fast changing (fast fading) channel. 27

Summed Contributions • The sum in dB (i.e. product in linear scale!) of pathloss (blue), shadowing (red), fading (green) is our total channel (black). 28

Pathloss – Overview • Pathloss has the following characteristics: • Function of distance (as well as frequency, environment, antenna heights) • It is a 'deterministic' effect • Is obtained by averaging over 1000 λ 29

Pathloss – Important Models • Free space • Two-Ray Ground • Diffraction Model • Hybrid models or too complex ;-) 30

Pathloss – Degrees of Modeling • Free-space pathloss model: • Loss of -20dB/decade distance • Very simple model, but not very realistic • Application in satellite channels and over short LOS distances • Single-slope pathloss model: • n = 1.5 (waveguides), n = 2…4 (LOS + clutter), n = 4…6 (nLOS + clutter) • Application in WLANs, interference power in cellular systems, etc. • Other models • Two-Ray Ground • Considers antenna height 31

Pathloss – Degrees of Modeling • Other models • Dual-slope pathloss model (hybrid model) • dgturnover distance • Simple and more accurate model, but correct reference point dg has to be found • Application in long-range WLANs and cellular systems 32

Pathloss – Other Propagation Models • Hata-Okumura Model (empirical model, 3GPP) • Walfish-Ikegami Model (radio propagation above roof tops) • Berg Model (pathloss calculation along streets) 33

Pathloss – Degrees of Modeling • Deterministically simulated pathloss behavior: • Ray-tracing type tools determine field behavior for given scenario • Very complex modeling approach, and not necessarily a better model • Empirically-fitted pathloss model: • Real measurements taken with P(d0) and n fitted to give best match • Difficult to obtain, very simple model and fairly realistic • Application in simulators, planning and optimization tools, etc • Really measured pathloss behavior: • Real measurements taken and used for planning and optimization tools • Complex and memory-consuming model, but very accurate • Used by all operators and within available commercial tools 34

Shadowing – Overview • Shadowing has the following characteristics: • Function of the environment (freq., distance, antenna heights) • Random effect due to randomly appearing and disappearing waves • Is obtained by averaging over 40 λ and subtracting the pathloss 35

Shadowing – Modeling Approach • The reasoning behind the distribution of shadowing is as follow: • Each arriving multipath component is the result of a random amount of multiple random reflections • Shadowing behavior: the (dis)appearance of waves • Shadowing has a lognormal distribution • Pathloss + Shadowing: • Local-mean power • Lognormal distribution has mean [dB] = and STD [dB] = σdB = σ* 10 / ln10 • Typical values are σdB = 4-10dB (microcell), 6-18dB (macrocell) 36

Fading – Overview • Fading has the following characteristics: • Function of the environment and frequency • Random effect due to randomly wave additions/cancellations • Is obtained by subtracting the pathloss and shadowing (no averaging!) Requires multi-path propagation 37

Fading – Overview • Interference of Waves • Superposition of waves y1 and y2 Two signals of different but nearly equal frequencies (f1 and f2) 38 Example: http://www.gmi.edu/~drussell/Demos/superposition/superposition.html

Fading – Overview • Interference of Waves • Superposition of signals with different phasing 39

Travelling wave over “Singlepath” • Signal at source: s(t) = cos 2πft • Signal at destination: s(t) = cos 2πf(t-Δt) • Time to reach destination: Δt=Δd/c • Over single path: • Oversimplification of EM Wave:“Modeling” cos 2πf(t-Δt) cos 2πft Δt=Δd/c 40

Travelling wave over “Multipath” • Path 1: Δt1=Δd1/c • Path 2: Δt2=Δd2/c • Path 3: Δt3=Δd3/c • Over multiple path: cos 2πf(t-Δt1) +cos 2πf(t-Δt2) +cos 2πf(t-Δt3) cos 2πft 41

Phasors to visualize “Multipath” • How to visualize the sum of “shifted cosines” • We need some “convenient” representation of cosines and its shifted versions • We will use the “complex numbers” and the “phasors” cos 2πf(t-Δt1) + cos 2πf(t-Δt2) + cos 2πf(t-Δt3) 42

Phase Vector (Phasor) • Is a representation of a sine wave whose amplitude (A), phase (θ), and frequency (ω) are time-invariant. • Simplifies certain kinds of calculations • Definition: • Euler's formula indicates that sine waves can be represented mathematically as the real part of a complex-valued function: A cos(ωt+ θ) = Re{A ∙ ei(ωt+ θ)} = Re{Aeiθ∙ eiωt} • A phasor can refer to either Aeiθ∙ eiωt or just the complex constant, Aeiθ(encoding the amplitude + phase of the sinusoid) • The sine wave can be understood as the projection on the real axis of a rotating vector on the complex plane. 43

Phase Vector (Phasor) Animated phasor showing shadow (or projection) oscillating back and forth, simulating an oscillation. The angle θ = ωt + ϕ is shown by the angle numbers around the edge. The position of the tip of the shadow on the ruler is equal to x = r cos (ωt + ϕ). 44

Travelling wave –moving source • Recall Δt=Δd/c cos 2πft = cosθ Z = cos 2πf(t-Δt) = cos(2πft - 2πfΔt) = cos(θ-φ), If the source moves, received cosine Z is a “randomly” rotating phasor and rotates at a rate at which the received phase changes 45

Constructive-Destructive multipath sum cos 2πf(t-Δt1) +cos 2πf(t-Δt2) +cos 2πf(t-Δt3) • Recall: • Each path changes independently over time: 3 random vectors sum up at the dst. cos 2πft 46

Constructive-Destructive multipath sum (cont.) An animated phasor diagram showing phasor addition of two oscillations, that of the woman and that of the man suspended on bungy cords. Like before, the animation shows the relation between the phasor diagram, the actual oscillation, and a graph of the oscillations. 47

Constructive-Destructive multipath sum (cont.) An animated phasor diagram showing phasor addition of two oscillations when the frequencies of the two oscillations are different. This allows one of the rotating phasor vectors to rotate faster than the other, continuously changing the phase angle difference between the two. At times, the two phasors will add up in the maximum way, demonstrating constructive interference. At other times, they will subtract, demonstrating destructive interference. The result is that the amplitude of the sum varies with time in a repetitive way. 48

Multiplication of an oscillation by a complex constant An animated diagram showing the multiplication of a complex oscillation by the complex constant B. The value (amplitude and phase) of B, the multiplying complex constant is given in black at the top left of the animation. The yellow vector represent the initial oscillation, and the orange vector represents the product of the yellow vector (or oscillation) multiplied by B. 49

Fading – Modeling Approach • Typical distributions (usually referred to envelope): • Rayleigh (fits well under nLOS) • Nakagami (fits well under weak LOS) • Rice (fits well under strong LOS) • Fading Models • Consider Pathloss, Shadowing and Fading • Rayleigh Fading: • Rician Fading: 50

Wireless Mesh Networks