Radio link

Property of R. Struzak Radio transmission: 2 viewpoints

RF LINES & AUXILIARY EQUIPMENT RF LINES & AUXILIARY EQUIPMENT

EM wave Transmitter propagation path Receiver

Energy radiated Energy received

Input Signal Signal Output signal radiate received signal d Information EM wave Information source Transmitter propagation channel Receiver destination (Transmitting station) Signal transformations (Receiving station) Transmitter signal processing due to natural phenomena; Receiver signal processing attenuation, external noise/signals, fading, reflection, refraction, etc.

Property of R. Struzak 34 Radio Link model Original message/ data Man-made Transmitter Processing

T-antenna

Natural onment Propagation medium EM wave Propagation Envir Process

Other radio systems R-antenna Noise Receiver Man-made Processing Reconstructed message/ data

Property of R. Struzak 35 Why consider propagation? 1. Could my system operate correctly (wanted signal)? • Required signal intensity/ quality of service over required distance/ area/ volume, given the geographic/ climatic region and time period 2. Could my system coexist with other systems (unwanted signals)? • Degradation of service quality and/ or service range/ area due to potential radio interference? – Will my system suffer unacceptable interference? – Will it produce such interference to other systems?

Property of R. Struzak 36 Principal propagation effects 1. Basic energy spreading 2. Effects of obstructions (indoor, outdoor) 3. Effects of the ground 4. Tropospheric effects (outdoor) – clear air – non-clear air 5. Ionospheric effects (outdoor)

Generally, dependence on - Wavelength (frequency) & polarization - Environment/ climate/ weather - Time Property of R. Struzak 37 What is propagation model?

• Relation between the signal radiated and signal received as a function of distance and other variables • Different models – Various dominating propagation mechanisms • different environments (indoor-outdoor; land-sea-space; … ) • different applications (point-to-point, point-to-area, …) • different frequency ranges • … • Some models include random variability

Property of R. Struzak 38 Indoor propagation

Wall Reflected Scattered

Diffracted

Direct-attenuated

Wall

Property of R. Struzak 39 Outdoor propagation: long-term modes

Reflection

Property ofITU R. Struzak 40 Layers above the Earth

대류권, 성층권, 중간권, 열권

1

Outdoor propagation: short-term modes

Property of ITUR. Struzak 41 Waver Refraction and Ducting in Atmosphere

4

Ionospheric “reflections”

• The ionosphere is transparent for microwaves but reflects HF waves • There are various ionospheric layers (D, E, F1, F2, etc.) at various heights (50 – 300 km) • Over-horizon commu- nication range: several Ionospheric reflectivity depends on time, thousand km frequency of incident wave, electron • Suffers from fading density, solar activity, etc. Difficult to predict with precision. Property of R. Struzak 42 Waver Refraction in Ionosphere

2

Ionosphere Multi-Hop Propagation

3

Basic mechanisms

Property of R. Struzak Radio Wave Components

Component Comments Direct wave Free-space/ LOS propagation Attenuated wave Through walls etc. in buildings, atmospheric attenuation (>~10 GHz) Reflected wave Reflection from a wall, passive antenna, ground, ionosphere (<~100MHz), etc. Refracted wave Standard, Sub-, and Super-refraction, ducting, ionized layer refraction (<~100MHz) Diffracted wave Ground-, mountain-, spherical earth- diffraction (<~5GHz) Surface wave (<~30 MHz) Scatter wave Troposcatter wave, precipitation-scatter wave, ionized-layer scatter wave Property of R. Struzak 44 Reflection

• = the abrupt change in direction of a wave front at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. • Reflecting object is large compared to wavelength.

Property of R. Struzak 45 Scattering

• - a phenomenon in which the direction (or polarization) of the wave is changed when the wave encounters propagation medium discontinuities smaller than the wavelength (e.g. foliage, …) • Results in a disordered or random change in the energy distribution

Property of R. Struzak 46 Diffraction

• = the mechanism the waves spread as they pass barriers in obstructed radio path (through openings or around barriers) • Diffraction - important when evaluating potential interference between terrestrial/ stations sharing the same frequency.

Property of R. Struzak 47 Absorption

• = the conversion of the transmitted EM energy into another form, usually thermal. – The conversion takes place as a result of interaction between the incident energy and the material medium, at the molecular or atomic level. – One cause of signal attenuation due to walls, precipitations (rain, snow, sand) and atmospheric gases

Property of R. Struzak 48 Refraction

• = redirection of a wavefront passing through a medium having a refractive index that is a continuous function of position (e.g., a graded-index optical fibre, or earth atmosphere) or through a boundary between two dissimilar media – For two media of different refractive indices, the angle of refraction is approximated by Snell's Law known from optics

Property of R. Struzak 49 Super-refraction and ducting

Important when evaluating potential interference between terrestrial/ earth stations sharing the same frequency – coupling losses into duct/layer • geometry – nature of path (sea/ land) – propagation loss associated with duct/ layer • frequency • refractivity gradient • nature of path (sea, Standard atmosphere: -40 N units/km (median), temperate climates land, coastal) Super-refractive atmosphere: < -40 N units/km, warm maritime regions • terrain roughness Ducting: < -157 N units/km (fata morgana, mirage)

Property ofITU R. Struzak 50 Simplest models

Property of R. Struzak The simplest model: Free-space

PT = transmitted power [W] d = distance between antennas Tx and Rx [m] PR = received power [W] GT = transmitting antenna power gain

GR = receiving antenna power gain

PR/PT = free-space propagation Notes:(transmission) loss (gain) Time delay 1. Propagation of a plane EM wave in a homogeneous ideal absorption-less medium (vacuum) unlimited in all directions. 2. Doubling the distance results in four-times less power received; the frequency-dependence is involved (antenna gains vary with frequency) 3. Matched polarizations 4. Specific directions Avaya Property of R. Struzak 52 LOS model

• Power flow from T to R concentrates in the 1st Fresnel zone • LOS model approximates the free- space model if: – 1st Fresnel zone unobstructed – no reflections, Avaya absorption & other propagation effects

Property of R. Struzak 53 Fresnel Zone • Fresnel zones are loci of

T R points of constant path- length difference of λ/2 (1800 phase difference ) d1 d2 – The n-th zone is the region enclosed between the 2 ellipsoids giving path-length differences n (λ/2) and (n-1)(λ/2) • The 1st Fresnel zone Example: max. radius of the 1st Fresnel zone corresponds to n = 1 at 3 GHz (λ= 0.1m) with T – R distance of 4 km: = (1/2)sqrt(0.1*4000) = 10m Property of R. Struzak 54 Okumura-Hata model

Microwave transmission gain up to the radio horizon:

-n Gavrg = Kd

Long-term average K, n – constants Typically: 3≤ n≤ 5 n = 2: free space Free space n = 4: two-ray model

The best results – when the constants are determined experimentally for a given Open area (LOS) environment Signal strength (log)

Urban Suburban

Distance (log)

Property of R. Struzak 55 • MAPL = Max. Allowable Path Loss

MAPLdB = PTmax(dB) – PRmin(dB) • Max range:

Property of R. Struzak 56 MAPL & max range n PTdBm PRdBm MAPL 2.4 5 GHz dB GHz range range m m 2 0 -80 80 100 45

2 +20 -80 100 1000 450

4 0 -80 80 6 4

4 +20 -80 100 32 21 Property of R. Struzak 57 Power budget example

Parameters To access Peer to peer at different data rate point . 11 Mbps 5.5 Mbps 2 Mbps 1 Mbps Frequency (GHz) 2.45 2.45 2.45 2.45 Transmit power (W) 0.020 0.020 0.020 0.020 Transmit power (dBW) 16.9 16.9 16.9 16.9 Transmit antenna gain (dBi) 2.0 2.0 2.0 2.0 Polarization loss (dB) 3.0 3.0 3.0 3.0 EIRP (dBW) 21.9 21.9 21.9 21.9 Range (m) 25.1 37.3 60.6 90.1 Path loss exponent (dB) 3.5 3.5 3.5 3.5 Free-space path loss (dB) 84.7 90.7 98.1 104.1 Rec. antenna gain (dBi) 2.0 2.0 2.0 2.0 Cable loss (dB) 1.9 1.9 1.9 1.9 Rake equalizer gain (dB) 0.5 0.5 0.5 0.5 Diversity gain (dB) 5.5 5.5 5.5 5.5 Receiver noise figure (dB) 13.6 13.6 13.6 13.6 Data rate (Kbps) 11000 5500 2000 1000 Required Eb/No (dB) 8.0 5.0 2.0 1.0 Rayleigh fading (dB) 7.5 7.5 7.5 7.5 Receiver sensitivity (dBm) 80.1 86.1 93.5 99.5 Signal-to-noise ratio (dB) 8.0 5.0 2.0 1.0 Link margin (dB) 0.0 0.0 0.0 0.0 . Source: D. Liu et al.: Developing integrated antenna subsystems for laptop computers; IBM J. RES. & DEV. VOL. 47 NO. 2/3 MARCH/MAY 2003 p. 355-367

Property of R. Struzak 58

Non-LOS propagation

• – when the 1st Fresnel zone is obstructed and/ or the signal reached the receiver due to reflection, refraction, diffraction, scattering, etc. – An obstruction may lie to the side, above, or below the path. » Examples: buildings, trees, bridges, cliffs, etc. » Obstructions that do not enter in the 1st Fresnel zone can be ignored. Often one ignores obstructions up to ½ of the zone

Property of R. Struzak 59 Quiz

• A LOS link shown

T in the figure was R designed with positive link budget. After deployment, no signal was received • Why?

Property of R. Struzak 60 Reflection

Property of R. Struzak Reflection: what it does? • Changes the direction, magnitude, phase and polarization of the incident wave – Depending on the reflection coefficient, wave polarization, and shape of the interface • Reflection may be specular (i.e., mirror- like) or diffuse (i.e., not retaining the image, only the energy) according to the nature of the interface. • Demonstration (laser pointer)

Property of R. Struzak 62 • Boundary conditions – Tangential components of E (and H) at both sides of the border are equal to each other – With ideal conductor, tangential component of E is zero at the border

Property of R. Struzak 63 Reflection coefficient

• = The ratio of the complex amplitudes of the reflected wave and the incident wave

Property of R. Struzak 64 Property of R. Struzak 65 Property of R. Struzak 66 Brewster Angle

6

2 ray propagation model

T R

• The received direct and reflected waves differ due to – Path-lengths difference – Transmitting antenna (phase characteristics) – Receiving antenna (phase characteristics) • The antenna directive radiation pattern may have different magnitudes and phases for the direct ray and for the reflected ray

Property of R. Struzak 67 2 Rays: Path-length Difference h 1 h2

D h1

Property of R. Struzak 68 Quiz

• At what distance difference the phase of the direct ray differ from that of the reflected ray by 180 deg at – 3 MHz? – 300 MHz? – 3 GHz?

Property of R. Struzak 69 2 rays: resultant field strength

Edir δ

E

φR

Erefl

Property of R. Struzak 70 2-ray model: max signal

Property of R. Struzak 71 2-ray model: min signal

Property of R. Struzak 72 2 rays: R ≅ -1

Property of R. Struzak 73 Distance Dependence

Doubled power received!

6 dB 0 dB relative to free-space

Log. distance

Level relative to Free-space, dB d = 2πh1h2/λ Slope (absolute): -40 dB/dec d = 4h h / 1 2 λ Field-strength ~d-2 -4 d = 2h1h2/λ Power ~d

Property of R. Struzak 74 Simulated Experiments • Distance dependence • Height dependence • Frequency dependence

Property of R. Struzak 75 Example 1: distance

2 Variable: d = 500-1000m Step = 10m

2 Fixed parameters: F = 2.4 GHz H1 = 11m 1 H2 = 10m |R| = 1 Arg(R) = 1800 1

0 500 600 700 800 900 1.000 Property of R. Struzak 76 Example 2: height

3 Variable: 3 H2 = 2 - 3m 3 Step = 1 cm

3

3 Fixed 3 parameters: 2 F = 2.4GHz 2

2 H1 = 1m 2 D = 3m 2 0 1 1 2 2 |R| =1 Property of R. Struzak Arg(R) =77 1800 Example 3: frequency

2 Variable: F = 2.4 - 2.6 GHz Step = 2 2 MHz

1 Fixed parameters: H1 = 14 m 1 H2 = 12 m D = 104 m

0 |R| =1 -0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 Arg(R) = 1800

Property of R. Struzak 78 Quiz

• What precision of antenna location (ΔD, Δh) is required to assure

|E/Edirect| < 3 dB (assuming 2-rays propagation model) at frequency – 30 MHz? – 300 MHz? – 3 GHz?

Property of R. Struzak 79 Field-strength measurements

• The field strength strongly depends on local environment • Measurement results depend on the antenna location/ orientation, local cables, etc. • Measurement uncertainty can be reduced by statistical evaluation of many measurements at slightly changed antenna positions

Property of R. Struzak 80 Avoiding negative reflection effects

T R • Controlling the directive R antenna gain at the transmitter and/or receiver • Blocking the reflected ray at the transmitter-reflector path and/or reflector – T R receiver path • Combine constructively the signals using correlation- type receiver – Antenna diversity (~10 dB) – Dual antennas placed at λ/2 separation

Property of R. Struzak 81 Absorbing reflections

• Absorbing the reflected wave • Covering reflecting objects by absorbing material (Black- body in optics)

Source: Rohde & Schwarz Property of R. Struzak 82 Passive relaying

Property of R. Struzak 83 Multipath

Property of R. Struzak Multipath propagation

S

T D

R

R

Indoor Outdoor: reflection (R), diffraction (D), scattering (S)

Property of R. Struzak 85 • The effects of multipath include constructive and destructive interference, and phase shifting of the signal. This causes Rayleigh fading, with standard statistical distribution known as the Rayleigh distribution. • Rayleigh fading with a strong line of sight content is said to have a Rician distribution, or to be Rician fading. » http://en.wikipedia.org/wiki/Rayleigh_fading; http:// en.wikipedia.org/wiki/Lord_Rayleigh;

Property of R. Struzak 86 Time – Frequency Characteristics

• Radio channel can be treated as a linear two-terminal-pair transmission channel (input port: transmitting antenna; output port: receiving antenna).

Property of R. Struzak 87 Direct RF Pulse Sounding

Direct ray Detector Key BPF

Digital Storage Oscilloscope Pulse Generator

Reflected ray

Property of R. Struzak 88 Frequency Domain Sounding

Vector Network Analyzer & X( ) ω Swept Frequency Oscillator Y(ω)

Port 1 S-Parameter Test Set Port 2

S21(ω) ≈ H(ω) = [X(ω)] / [X(ω)]

Inverse DFT Processor

h(t)

h(t) = Inverse Fourier Transform of H(ω)

Property of R. Struzak X Time Response, 2 Rays

Transmitted signal Received signal Direct ray Reflected ray Amplitude Amplitude

Time Time y(t) x(t) a 1 + Δτ = c(dreflect – ddirect)

Light velocity a2 Δτ Path-length difference

Property of R. Struzak 89 Power Delay Profile Relative Power Time

• If an impulse is sent from transmitter in a multiple-reflection environment, the received signal will consist of a number of impulse responses whose delays and amplitudes depend on the reflecting environment of the radio link. The time span they occupy is known as delay spread • The dispersion of the channel is normally characterized using the RMS Delay Spread, or standard deviation of the power delay profile

Property of R. Struzak 90 Inter-symbol Interference

Symbols Sent Symbols Received • The delay spread limits the maximum data rate: no new impulse should reach the receiver before the last replica of the previous impulse has perished. • Otherwise the symbol spreads into its adjacent symbol slot, the two symbols mix, the receiver decision-logic circuitry cannot decide which of the symbols has arrived, and inter-symbol interference occurs.

Property of R. Struzak 91 Error Bursts

• When the delay spread becomes a substantial fraction of the bit period, error bursts may happen. • These error bursts are known as irreducible since it is not possible to reduce their value by increasing the transmitter power.

Property of R. Struzak 92 Error Reduction

• Elimination of reflections as discussed earlier, plus • Applying error- resistant modulations, codes, and communication protocols • Applying Automatic Repeat Request (ARQ) • Retransmission protocol for blocks in error

Property of R. Struzak 93 Microcell vs. Macrocell

Microcell Macrocell Cell radius 0.1-1 km 1-20 km Tx power 0.1-1 W 1-10 W Fading Ricean Rayleigh RMS delay spread 10-100 ns 0.1-10us Bit Rate 1 Mbps 0.3 Mbps

After R.H.Katz CS294-7/1996

Property of R. Struzak 94 Propagation effects

Property of R. Struzak Troposphere

• = the lower layer of atmosphere (between the earth surface and the stratosphere) in which the change of temperature with height is relatively large. It is the region where convection is active and clouds form. • Contains ~80% of the total air mass. Its thickness varies with season and latitude. It is usually 16 km to 18 km thick over tropical regions, and less than 10 km thick over the poles.

Property of R. Struzak 96 Troposphere effects (clear air) • absorption by atmospheric gases

– molecular absorption by water vapor and O2 – important bands at ~22 and ~60 GHz • refractive effects – ray bending – super-refraction and ducting – multipath – Scintillation » scintillation: a small random fluctuation of the received field strength about its mean value. Scintillation effects become more significant as the frequency of the propagating wave increases.

Property of R. Struzak 97 LOS – Radio Horizon

• Earth curvature •Optics: Snell’s law • Radio waves go behind the geometrical horizon due to refraction: the air refractivity changes with height, water vapor contents, etc.

• In standard conditions the radio wave travels approximately along an arc bent slightly downward. Radio horizon • K-factor is a scaling factor of the ray path curvature. K=1 means a straight line. For the standard atmosphere K=4/3. An equivalent Earth radius KRearth ‘makes’ the path straight

Geometrical horizon • Departure from the standard conditions may led to subrefraction, superrefraction or duct phenomena.

Property• ofStrong R. Struzak dependence on meteorological98 phenomena. Atmospheric Absorption

• Important at 10 frequencies >10 GHz • The atmosphere introduces attenuation

Attenuation dB/km due to interaction of 10 radio wave at

Specific molecular/ atomic

H2O level • Exploited in Earth- exploration passive applications

0.1 O • New wideband short- 2 distance systems

10 100 GHz Property of R. Struzak 99 Ground and obstacles • terrain (smooth Earth, hills and mountains) – diffraction, reflection and scattering • buildings (outside and inside) – diffraction, reflection and scattering • vegetation – attenuation – scattering

Property of R. Struzak 100 Obstacles & diffraction

Obstacles such as a mountain range or edge of a building are often modeled as knife-edge obstacle

Property of R. Struzak 101 Huygens principle

• Dutch physicist and astronomer Christiaan Huygens (1629 - 1695) offered an explanation of wave propagation near obstacles (diffraction) in the far field. • Each point of an advancing wave front acts as a source of secondary spherical waves. The advancing wave as a whole is the sum of all the secondary waves arising from points in the medium already traversed. When the wave front approaches an opening or barrier, only the wavelets approaching the unobstructed section can get past. They emit new wavelets in all directions, creating a new wave front, which creates new wavelets and new wave front, etc. - the process self-perpetuates. • Example: two rooms are connected by an open doorway and a sound is produced in a remote corner of one of them; in the other room the sound seems to originate at the doorway.

Property of R. Struzak 102 Effects of Buildings - inside • Important for the planning of indoor LAN’s and wireless private business exchanges for high data rate services – Reflection, multipath and diffraction from objects • delay spread 70 - 150 ns (~2 GHz; residential – commercial; compare with symbol length) • statistical or site-specific propagation models – Path loss through walls and floors • frequency re-use? – Channeling of energy along the building structures

Property of R. Struzak 103 Effects of Buildings - outside • Important in the planning of short-range mobile and personal communication systems, LAN’s and Wireless Local Loop systems – Wall/ roof attenuation if antennas located in the building – Line-of-sight path outside • Attenuation (free-space, atmospheric gases, rain, etc.) – Non line-of-sight path • reflection, diffraction and scatter – building height, density, street width, orientation – crossing streets, corner angle (street canyon) • Multipath delay spread e.g. 0.8 - 3 µs (urban - suburban)

Property of R. Struzak 104 Troposphere effects (non-clear air) • rain effects – attenuation – depolarization – scattering • cloud effects – attenuation • system availability considerations 99.9 % availability (rain at 0.1 % time) 90 % availability (cloud at 10 % time)

Property of R. Struzak 105 Effects of vegetation shadowing Pine tree Attenuation up to 20 dB

Depends on the species of tree, density and structure of foliage, movement of branches and Palm tree foliage, etc.

Important for the planning of microwave propagation path over wooded areas

Property ofITU R. Struzak 106 Fading

• Case of more than one propagation path (mode) exists between T and R • Fading = the result of variation (with time) of the amplitude or relative phase, or both, of one or more of the frequency components of the signal. • Cause: changes in the characteristics of the propagation path with time.

Property of R. Struzak 107 • Variations

Property of R. Struzak X Digital terrain model

Property of R. Struzak SISP

• SISP – Site Specific propagation models based on an analysis of all possible rays between the transmitter and receiver to account for reflection, diffraction & scattering • Requires exact data on the environment – Indoor: detailed 3D data on building, room, equipment – Outdoor: 3D data on irregular terrain infrastructure, streets, buildings, etc. (Fresnel-Kirchoff or Deygout theoretical constructions) – Large databases • Satellite/ aerial photographs or radar images,

Property of R. Struzak 109 Signal coverage map

• Example of computer- generated signal-level distribution superimposed on a terrain map – Light-blue = strong signal

Property of R. Struzak 110 DTM • Application of detailed propagation prediction models requires topographical information: Digital Terrain Model (DTM) or Digital Terrain Elevation Data (DTED)

Property of R. Struzak 111 DTM data base

Property of R. Struzak 112 • Production of 2-D profile from 3-D DTM

Property of R. Struzak 113 • Direct geodetic terrain measurements • Scanning/ digitizing paper maps/ plans • Scanning/ digitizing aerial photographs • Scanning/ digitizing satellite photographs • Direct stereoscopic satellite/ aerial radar/ lidar/ infrared measurements

Property of R. Struzak 114 DTM production

• Irregularly-distributed data (triangulation) • Regularly-distributed

data (xi, yi)

Property of R. Struzak 115 • DTM (height) produced from a ‘paper map’ as set of interpolated numerical values at intersections of grid lines

Property of R. Struzak 116 Digital terrain elevation maps

Most of DTM & DTED were created from paper maps Recently, they were also produced from radar data collected from satellite Best resolution: 1 arc- sec (~30 m) 30 times as precise as the best global maps in use today. First such maps were planned for 2004.

Source: NASA (http://www2.jpl.nasa.gov/srtm/)

Property of R. Struzak 117 Radar Topography

Radar interferometry compares two radar images taken at slightly different locations

Combining the two images produces a single 3-D image.

Shuttle Radar Topographic Mission (SRTM) used single-pass interferometry: the two images were acquired at the same time -- one from the radar antennas in the shuttle's payload bay, the other from the radar antennas at the end of a 60-meter mast extending from the shuttle.

Source: NASA

Property of R. Struzak 118 Shuttle Radar Topography Mission 2000

•Mission: 11-22 Feb. 2000 •Collected: 9 terabytes of raw data (~15,000 CDs) • More than 80 hours data recording

• Orbiter: Shuttle Endeavour (7.5km/ sec) • Nominal altitude: 233 km (with orbital adjustment once per day) • Inclination:57 degrees • 6-member crew • to activate payload, deploy and stow mast, align inboard and outboard structures, monitor payload flight systems, operate on-board computers & recorders, & handle contingencies

Source: NASA

Property of R. Struzak 119 Google Earth

• Download: http://earth.google.com/ download-earth.html

Property of R. Struzak 120 Summary

Property of R. Struzak What we have learned

• Radio propagation conditions decide on the system performance • The best transmitter, receiver, antennas, cables, etc. may not work as expected if the relevant propagation effects are ignored or incorrectly taken into consideration • The propagation mechanisms of the wanted signal and unwanted signals must be carefully analyzed

Property of R. Struzak 122 Selected references

• Some software available at ICTP: – MLINK – RadioMobile – ITS Irregular Terrain Model – SEAMCAT • International recommendations – ITU-R recommendations series SG3 – http://www.itu.int/; publications/main_publ/itur.html – Major propagation models & related computer programs: see ITU (www.itu.int) and ERO documents (e.g. www.ero.dk/seamcat - free!) • Books: – Shigekazu Shibuya: A basic atlas of radio-wave propagation; Wiley – Freeman RL: Radio System Design for Telecommunications, Wiley – Coreira LM: Wireless Flexible Personalised Communications, Wiley » Acknowledgment: Some of the material is based on Dr. Kevin Hughes’ presentations at previous ICTP Schools

Property of R. Struzak 123 Path Loss Expression in dB Free Space Propagation

2 ⎛ ⎡ λ ⎤ ⎞ − PL =10log PL =10log⎜ g g ⎟ dB () ⎜ 1 2 ⎢ ⎥ ⎟ ⎝ ⎣4π ⎦ ⎠

¾ For isotropic antennas, g1 = g2 = 1

¾ For frequency in GHz, λ = c/f = 0.3/fGHz

− PLdB = −32.4 − 20log fGH − 20log r

Wireless channel modeling 1

Two Ray Model for Propagation Above a Flat Earth (Antennas are assumed to be isotropic

2 2 ⎛ λ ⎞ 1 1 Pr = Pt ⎜ ⎟ exp()()− jkr1 + Γ α exp()− jkr2 ⎝ 4π ⎠ r1 r2 cosθ − a ε − sin 2 θ Γ()θ = r 2 cosθ + a ε r − sin θ

θ = 90 −α , a =1 ε r or 1 for vertical or horizontal polarization

Wireless channel modeling 2 Plane wave Reflection Coefficients for TE(Horizontal) and TM (Vertical) Polarizations at Plane Earth as a Function of the Angle of Incidence

Wireless channel modeling 3

Path Loss as a Function of Antenna Separation

h1 = 8.7 m and h2 = 1.8 m , f=900 Mhz

Wireless channel modeling 4 Measured Example

dipole Biconical

Wireless channel modeling 5

Fresnel Zones

¾ For n=1: ) Ray fields propagate within Fresnel zones ) objects placed outside Fresnel zone generate new rays. But have only small effect on direct ray fields ) Objects placed inside Fresnel zone change fields of direct ray

Wireless channel modeling 6 Fresnel Zone Interpretation of the Change in Dependence of Path Loss on Distance

nλ ¾ Fresnel zone definition r2 − r1 = 2 ¾ Horizontal antenna separation R for Fresnel Zone clearence

2 2 4 2 2 4h1h2 n ⎛ λ ⎞ n ⎛ λ ⎞ n ⎛ λ ⎞ R = 1− ⎜ ⎟ − ⎜ ⎟ + ⎜ ⎟ nλ 16 ⎝ h1 ⎠ 16 ⎝ h2 ⎠ 256 ⎝ h1h2 ⎠ 4h h ¾ Approximation for Fresnel Zone clearance R = 1 2 nλ

Wireless channel modeling 7

Two Slope regression Fit for 1st Fresnel Zone Clearance

break point Brewsters angle no interference

Wireless channel modeling 8 Two Slope Regression Fit for 1st Fresnel Zone Clearance

Wireless channel modeling 9

Flat Earth Path Loss Dependence for Large R

¾ If R>> h1, h2 ¾ Then 1 1 h h r = R2 + ()h ∓ h 2 ≈ R + ()h ∓ h 2 = R + ()h2 + h2 ∓ 1 2 1,2 1 2 2R 1 2 2R 1 2 R ¾ and Γ()θ ≈ −1 2 2 ⎛ λ ⎞ exp()− jkr1 exp()− jkr2 ¾ Received power PR = PT ⎜ ⎟ + Γ()θ ⎝ 4π ⎠ r1 r2

2 2 ⎛ λ ⎞ ⎛ h1h2 ⎞ ⎛ h1h2 ⎞ is approximated by PR ≈ PT ⎜ ⎟ exp⎜ jk ⎟ − exp⎜− jk ⎟ ⎝ 4πR ⎠ ⎝ R ⎠ ⎝ R ⎠

2 2 2 2 ⎛ λ ⎞ ⎛ h1h2 ⎞ ⎛ λ ⎞ ⎛ h1h2 ⎞ or PR ≈ PT ⎜ ⎟ 2sin⎜k ⎟ = PT 4⎜ ⎟ sin⎜2π ⎟ ⎝ 4πR ⎠ ⎝ R ⎠ ⎝ 4πR ⎠ ⎝ λR ⎠

2 2 h1h2 h1 h2 If << 1 , then PR ≈ PT λR R4

Wireless channel modeling 10 Diffraction Theory

¾ Kirchhoff-Huygens Approximation ¾ local Properties of radiation ¾ Plane Wave Diffraction by Edge ¾ Spherical Wave Diffraction by Edges

Wireless channel modeling 11

Kirchhoff-Huygen’s Approximation

¾ Scalar approximation for fields incident in the y-z plane jke− jkr E ()x, y, z ≈ E in (x',0, z' )(cosα + cosα' ) dx'dz' V ,H ∫∫ V ,H 4πr ) [Ref] Max Born and Emil Wolf, Principles of Optics, Pergammon Press, pp370-382

Wireless channel modeling 12 Example of Plnae Wave Incidence --To show that the Kirchhoff-Huygens method works correctly--

¾ For simplicity assume wave propagates along y (α’ =0): normal incidence in − jky E ()x, y, z = E0e ¾ Without loss of generality take the field point to be on the y axis (0,y,0) jke− jkr E()0, y,0 = E (1+ cosα ) dx'dz' ∫∫ 0 4πr − jkr jk 2π ∞ e = E0 ()1+ cosα ρ'dρ'dθ ' 4π ∫0 ∫0 r

Wireless channel modeling 13

Approximation for Integration Over ρ’

¾ For large ρ’, subsequent half cycles of integrand cancel ¾ Primary contribution to integral come from vicinity of ρ’=0

2π ().. dθ '= 2π For y >> ρ’, cosα≈1and ∫0

2 2 ∞ exp(− jk y + ρ' ) E()0, y,0 = jkE0 ρ'dρ' ∫0 2 2 y + ρ' ρ'dρ' Let u = jk y 2 + ρ '2 ,then du = jk y 2 + ρ'2

∞ −u − jky E()0, y,0 = E0 e du = E0e is the original incident field ∫jky

Wireless channel modeling 14 Local Properties of Propagation ¾ Quantify the region about a ray through which the fields propagate ¾ Source at (0,-d,0) e− jkr' E in = f ()α' r' ¾ Without loss of generality, take field point at (0,y,0) along y axis ¾ What region in the x-z plane is responsible for wave propagation from the source to observation point? ¾ To answer the question, assume plane y=0 is opaque with a transparent hole and examine the transmitted field. Question is then ) What location gives minimum distortion? ) What is the minimum size of the hole for a given distortion Wireless channel modeling 15

How to find the Hole Position and size

¾ By symmetry, hole must be centered on the y-axis and be circular ¾ To create the hole, assume the plane has transmission coefficient T(ρ’) where ρ ′ = x ′ 2 + z ′ 2 ; T(0) = 1 and T(∞)=0. ¾ To avoid diffraction that can confuse results, use a continuously varying function for T(ρ’) ¾ Simple dependence for T(ρ’) is

T ()ρ' = exp[− ρ'2 / w2 ]

¾ Then

− jkr' − jkr ∞ 2π e e E()0, y,0 = f ()()(α' T ρ' cosα + cosα' )jk dθ ' ρ'dρ'' ∫0 ∫0 r' 4πr

Wireless channel modeling 16 Evaluation of Integral for E(0,y,0)

¾ Integration over θ’gives 2π ¾ Ray optical regime when d, y >> λ ¾ primary contribution to integral comes from the vicinity of ρ’=0 cosα + cosα ' = 2 and f (α ' )= f (0)

) In exponent r = y 2 + ρ'2 ≈ y + ρ'2 / 2y r'= d 2 + ρ'2 ≈ d + ρ'2 / 2d ) In denominator r≈y and r’≈d

jk ∞ ⎧ ⎡ 1 d + y ⎤ ⎫ E()()0, y,0 = f 0 e− jk ()d + y exp − + jk ρ'2 ' ρ'dρ'' ∫0 ⎨ ⎢ 2 ⎥ ⎬ d ⋅ y ⎩ ⎣w 2d ⋅ y ⎦ ⎭

⎡ 1 d + y ⎤ 2 2 ) let ⎢ 2 + jk ⎥ρ' = u ⎣w 2dy ⎦

Wireless channel modeling 17

Evaluation of Integral for E(0,y,0) (cont.)

− jk (d + y ) jk e ∞ E()()0, y,0 = f 0 exp()− u 2 udu d ⋅ y ⎡ 1 d + y ⎤ ∫0 ⎢ 2 + jk ⎥ ⎣w 2d ⋅ y ⎦

⎧ ⎫ ⎧e− jk ()d + y ⎫⎪ 1 ⎪ E()()0, y,0 = f 0 ⎨ ⎬⎨ ⎬ ⎩ d + y ⎭⎪ 2yd ⎪ 1− j 2 ⎩⎪ kw ()y + d ⎭⎪ Field at (0,y,0) in the absence of Correction due to the the window (w=∞) presence of the window 2yd λyd ¾ Letε = 2 = 2 be a measure of error. Then for kw ()y + d πw ()y + d w large, ε will be small and correction will be ~ 1+j ε

Wireless channel modeling 18 Interpretation of Window Size in Terms of Fresnel Zones

Definition of Fresnel ellipse (r'+r)(− d + y )= nλ 2

2 2 2 2 2 2 ¾ For d, y >> λ, r'= d + wFn ≈ d + wFn 2d r = y + wFn ≈ y + wFn 2y

2 wFn ⎛ 1 1 ⎞ nλ ¾ Fresnel Zone ellipse is approximately ⎜ + ⎟ = 2 ⎝ d y ⎠ 2 2 or w Fn = n λ yd () d + y . Substituting into the expression for ε gives 2 1 ⎛ w ⎞ If w=w , then ε=1/nπ and the amplitude ε = ⎜ Fn ⎟ Fn nπ ⎝ w ⎠ 1 correction is 1+ jε = 1+ ε 2 ≈1+ 2n2π 2

Wireless channel modeling 19

Size of the Fresnel zone at Cellular Frequencies

y+d = R

2 wFn = nλyd ()d + y

¾ Maximum width when d=y=R/2, in which case the full width

2 is wFn = nλyd ()d + y

¾ At f= 900 MHz, λ=1/3 m. If R=1 km, then 2wFn=18.3 m.

¾ At f= 1.8 GHz, λ=1/6 m. If R=1 km, then 2wFn=12.9 m.

Wireless channel modeling 20 Fresnel Zone for Plane Waves (Distance Source)

2 ¾ For d>>y, then w Fn = n λ yd () d + y ≈ n λ y and

2wFn = 2 nλy

Wireless channel modeling 21

Plane Wave Diffraction by an Absorbing Half- Plane

− jkr jk ∞ ∞ e E()0, y,0 = E0 ()1+ cosα dx'dz' 4π ∫0 ∫−∞ r

where r = x'2 + y 2 + ()z − z' 2

Wireless channel modeling 22 RADIO PROPAGATION MODELS

1 Radio Propagation Models

1 Path Loss • Free Space Loss • Ground Reflections • Surface Waves • Diffraction • Channelization

2 Shadowing

3 Multipath Reception and Scattering • Dispersion • Time Variations

2 Key Questions about Propagation

• Why may radio reception vanish while waiting for a traffic light? • How does path loss depend on propagation distance? • What are the consequences for cell planning? • Why has the received amplitude a ‘Rician’ amplitude? • What can we do to improve the receiver?

Key Terms

• Antenna Gain; Free-Space Loss; Ground Reflections; Two-Ray Model; "40 Log d"; Shadowing; Rician

Fading; Bessel Function I0(.); Rician K-Ratio; Rayleigh Fading

3 Free Space Loss

Isotropic antenna: power is distributed homogeneously over surface area of a sphere.

The power density w at distance d is

w = PT 4πd 2 where PT is the transmit power.

The received power is

= A w PT 4πd 2 with A the `antenna aperture' or the effective receiving surface area.

4 FREE SPACE LOSS, continued

The antenna gain GR is related to the aperture A according to

π G = 4 A R λ2 Thus the received signal power is λ21 PRTR = PG•• 4ππ4 d2 -2 • The received power decreases with distance, PR :: d -2 • The received power decreases with frequency, PR :: f

Cellular radio planning Path Loss in dB:

Lfs= 32.44 + 20 log (f /1 MHz) + 20 log (d / 1 km)

Broadcast planning (CCIR)

Field strength and received power: E0 = √(120 π PR)

30 PGTT In free space: E0 = 4dπ

5 Antenna Gain

A theorem about cats: An isotropic antenna can not exist.

Antenna Gain

GT (φ,θ) is the amount of power radiated in direction (φ,θ), relative to an isotropic antenna.

Definition: Effective Radiated Power (ERP) is PT GT

Half-Wave Dipole: A half-wave dipole has antenna gain  π  2 cos cosθ   2  G(θφ , ) = 1.64    sinθ   

6 Law of Conservation of Energy

Total power at distance d is equal to PT

∫ G(φθ , ) dA = 1 4π

⇒ A directional antenna can amplify signals from one

direction {GR (φ,θ) >> 1}, but must attenuate signals

from other directions {GR (φ,θ) < 1}.

7 Groundwave loss:

Waves travelling over land interact with the earth's surface.

Norton: For propagation over a plane earth,

()jj∆∆•••• Ei =E0i 1+ Recc+ (1-R ) F( )e + , where

Rc is the reflection coefficient,

E0i is the theoretical field strength for free space F(⋅) is the (complex) surface wave attenuation ∆ is the phase difference between direct and ground- reflected wave

Bullington: Received Electric Field = direct line-of-sight wave + wave reflected from the earth's surface + a surface wave. Space wave The (phasor) sum of the direct wave and the ground-reflected wave is called 'space wave'

8 Space-wave approximation for UHF land-mobile communication:

• Received field strength ≈ LOS + Ground-reflected wave.

Surface wave is negligible, i.e., F(⋅) << 1, for the usual values of ht and hr.

2 2 {(ht - hr) +d } hr ht

2 2 {(ht + hr) +d }

The received signal power is

λ 2 + j∆ PR =  1 Re  PGGTTR 4dπ  The phase difference ∆ is found from Pythagoras. Distance

2 2 between TX and RX antenna = √{( ht - ht) + d } Distance between TX and mirrored RX antenna =

2 2 √{( ht + ht) + d }}

9 Space-wave approximation

The phase difference ∆ is 2π ∆=()2+( + )2- 2+( - )2 λdhtrh d htrh

At large a distance, d >> 5ht hr, π ∆≈4 hhrt λd so, the received signal power is

λ π 2 + 4jhhrt PR =  1 Rexp  PGGTTR 4dπ λd 

The reflection coefficient approaches Rc → -1 for • large propagation distances • low antenna heights

For large distances d → ∞: ∆ → 0 and Rc → -1. In this case, LOS and ground-reflected wave cancel!!

10 Two-ray model (space-wave approximation)

d-2

d-4 Received Power[dB]

ln(Distance)

For Rc = -1 and approximate ∆, the received power is λ2 π  = 2 2 hhrt PR   4sin   GRTT GP 4dπ  λd 

N.B. At short range, Rc may not be close to -1. Therefor, nulls are less prominent as predicted by the above formula.

11 Macro-cellular groundwave propagation

For dλ >> 4 hr ht, we approximate sin(x) ≈ x:

2 2 hhr t PR _ PGGTRT d4

Egli [1957]: semi-empirical model for path loss

 f c  L = 40log d + 20 log  -20loghhrt .  40MHz • Loss per distance:...... 40 log d • Antenna height gain:...... 6 dB per octave • Empirical factor:...... 20 log f • Error: standard deviation...... 12 dB

12 Generic path-loss models •p is normalized power •r is normalized distance

Free Space Loss: "20 log d" models p = r -2

Groundwave propagation: "40 log d" models p = r -4

Empirical model: p = r -β, β ≈ 2 ... 5 β ≈ 3.2

Micro-cellular models

VHF/UHF propagation for low antenna height (ht = 5 ⋅⋅ 10 m)

β   - 2 β r p = r- 1 1 +   r g

13 Diffraction loss

The diffraction parameter v is defined as

211 v = + , hm   λdtrd where

hm is the height of the obstacle, and

dt is distance transmitter - obstacle

dr is distance receiver - obstacle

The diffraction loss Ld, expressed in dB, is approximated by +−2 << =69vv 127.. 0 v 24 Ld 13+> 20logvv 2 . 4

14 How to combine ground-reflection and diffraction loss?

Obstacle gain: • The attenuation over a path with a knife edge can be smaller than the loss over a path without the obstacle! • "Obstacles mitigate ground-reflection loss"

Bullington: "add all theoretical losses"

LKfsdR = L + L + L ,

Blomquist:

22 LKfsd = L + L +LR ,

15 Statistical Fluctuation: Location Averages Received Power [dB] Received

ln(Distance) • Area-mean power · is determined by path loss · is an average over 100 m - 5 km • Local-mean power · is caused by local 'shadowing' effects · has slow variations · is an average over 40 λ (few meters) • Instantaneous power

· fluctuations are caused by multipath reception · depends on location and frequency · depends on time if antenna is in motion · has fast variations (fades occur about every half a wave length)

16 Shadowing

Local obstacles cause random shadow attenuation

Model: Normal distribution of the received power PLog in logarithmic units (such as dB or neper),

Probability Density:

1  12  f ()p = exp- p pLog Log2πσ  2σ2 Log where σ is the 'logarithmic standard deviation' in natural units.

PLog = ln [local-mean power / area-mean power ]

The standard deviation in dB is found from s = 4.34 σ

17 The log-normal distribution

Convert 'nepers' to 'watts'. Use

p p = ln Log p and

f (pdp=) f ()pdp   ppLog Log =  p pLog ln    p The log-normal distribution of received (local-mean) power is

1  1 p f ( p=) exp- 2  , p π 2 ln 2pσσs  2  p

18 Area-mean and local-mean power

• The area-mean power is the logarithmic average of the local-mean power

• The linear average and higher-order moments of local- mean power are

∞  2 mmm2σ Eexp[]p _ ∫ p f p()p dp = p m  . 0  2

N.B. With shadowing, the interference power accumulates rapidly!! Average of sum of 6 interferers is larger than sum of area means.

19 Depth of shadowing: sigma = 3 .. 12 dB

"Large-area Shadowing": · Egli: Average terrain: 8.3 dB for VHF and 12 dB for UHF · Marsan, Hess and Gilbert: Semi-circular routes in Chicago: 6.5 dB to 10.5 dB, with a median of 9.3 dB.

"Small-area shadowing" · Marsan et al.: 3.7 dB · Preller & Koch: 4 .. 7 dB

Combined model by Mawira (PTT Research): Two superimposed Markovian processes: 3 dB with coherence distance over 100 m, plus 4 dB with coherence distance 1200 m

20 Rician multipath reception reflections line of sight TX RX

Narrowband propagation model:

• Transmitted carrier

s(t) = cosω c t • Received carrier

N ω ∑ ρ ω φ v(t)= Ccosc t + n cos (c t +n ) , n=1 where C is the amplitude of the line-of-sight component

ρn is the amplitude of the n-th reflected wave

φn is the phase of the n-th reflected wave

Rayleigh fading: C = 0

21 Rician fading: I-Q Phasor diagram

Received carrier:

N ω ∑ ρ ω φ v(t)= Ccosc t + n cos (c t +n ) , n=1 where ζ is the in-phase component of the reflections ξ is the quadrature component of the reflections. I is the total in-phase component (I = C + ζ) Q is the total quadrature component (Q = ξ)

22 Central Limit Theorem

ζ and ξ are zero-mean independently identically distributed (i.i.d.) jointly Gaussian random variables

PDF:

1  i2 +(q-C )2  f (i,q) = exp-  I,Q 2πσσ2  2 2  Conversion to polar coordinates: • Received amplitude ρ: ρ2 = i2 + q2 . • i = ρ cos φ; q = ρ sin φ,

2 ρ  ρ +C2-2ρφ Ccos  fΡΦ(,)ρφ = exp-  , 2πσ2  2σ2 

23 Rician Amplitude

Integrate joint PDF over φ from 0 to 2π: Rician PDF of ρ

ρ  ρ2 2  ρ  ρ +C C f ρ ( ) = exp-  I0   , q  2q   q  where

I0(⋅) is the modified Bessel function of the first kind and zero order is the total scattered power ( = σ2).

Rician K-ratio K = direct power C2/2 over scattered power

Measured values K = 4 ... 1000 (6 to 30 dB) for micro-cellular systems

24 Light fading (K → ∞) • Very strong dominant component • Rician PDF → Gaussian PDF

Severe Fading: Rayleigh Fading

• Direct line-of-sight component is small (C → 0, K → 0). • The variances of ζ and ξ are equal to local-mean power • PDF of amplitude ρ is Rayleigh ρ  ρ2  f Ρ (ρ) = exp-  .• p  2p

1 2 1 2 1 2 • The instantaneous power p (p = /2ρ = /2ζ + /2ξ ) is exponential dρ 1  p f ()p =fρ ()ρ = exp-  . p dp p  p

25 Nakagami fading

• The sum of m exponentially distributed powers is Gamma distributed. m-1 1 p  p fp()=  tt exp-  . ptt p(m)Γ  p  p where Γ(m) is the gamma function; Γ(m+1) = m! m is the 'shape' factor

• The local-mean power E [pt ] = m. • The amplitude is Nakagami m-distributed ρρ2m-1  2  ()ρ   fρ =m exp - Γ(m)2m-1 p  2p • Application of this model: - Joint interference signal (not constant envelope!!) - Dispersive fading; self interference

N.B. The sum of m Rayleigh phasors is again a Rayleigh phasor.

26 Now, what’s tomorrow’s challenge? APN-008 Rev 1 February 3, 2000 Discussions on RF Signal Propagation and Multipath

Radio frequency (RF) signal multipathing is a phenomenon common to virtually all types of radio communications and navigation systems. It affects the complete radio spectrum ranging from low frequency (LF) channels in the kiloHertz range up to and beyond microwave channels in the gigaHertz range. This document provides a brief overview of multipath and why it is an important consideration in radio wave propagation, followed by solutions provided by NovAtel Inc. as related to GPS positioning systems.

Radio Wave Propagation It is generally the objective of a radio service to relay information from one location to another by the use of a radio transmitter at the origin and one or more receivers at the remote destination points. The link between these points includes the origin transmitting antenna, propagation medium (free space or the earth’s atmosphere), and the destination receiving antenna. Radio waves (electromagnetic radiation) propagate from the transmitting antenna to the receiving antenna utilizing the propagation medium between them. We will assume that the earth’s atmosphere (ionosphere and troposphere) is the primary propagation medium. To understand multipath, it is helpful to understand the nature of these waves and their behavior in the propagation medium. As the subject of radio wave propagation is a field of study in its own right, only enough subject matter is covered here to provide some background for multipath discussions. Radio waves, also called radio frequencies, (or, the RF signal), propagate through free space (vacuum) at the speed of light (299,792,458 metres/second). The frequency of the RF signal is expressed as the number of complete polarity reversal cycles that occur during a period of one second. Thus a frequency of 10 MHz indicates that the signal experiences 10,000,000 polarity reversal cycles every second. Wavelength is the distance the RF signal travels during the period of one RF cycle. Thus wavelength = c/f, where c is velocity of electromagnetic waves expressed in metres per second and f is frequency expressed in cycles per second. A frequency of 1575.42 MHz will have a wavelength of approximately 19 cm whereas a frequency of 1 MHz will have a wavelength of approximately 300 metres. Wavelength plays an important role in RF signal propagation and reflection characteristics. The rate of signal propagation changes if the signal passes through different mediums of different dielectric constants, such as the various layers of the earth’s atmosphere and differing temperature zones. When this occurs, the velocity of propagation as well as the direction are altered somewhat. The degree of alteration depends on the degree of change in medium dielectric constants as the signal passes from medium to medium. This is the same phenomenon that causes light to reflect off mirrors and why objects immersed in water appear distorted when viewed from above the waterline. Just as light waves are subject to refraction and reflection phenomena, so are RF signals (both are electromagnetic waves). RF signals generally propagate between the transmitting antenna and the receiving antenna in one of the following most common methods: line of sight (space waves), refraction, or reflection. Dominant propagation characteristics vary with the frequency (or wavelength) of the transmitted signal involved. As well, these characteristics are also variable depending on changing conditions in the earth’s atmosphere (primarily the ionosphere and troposphere) which cause varying degrees of signal refraction and even reflection. Natural and man-made objects can influence wave propagation as well. Metals and fluids tend to be highly reflective surfaces for electromagnetic waves and thus influence the path of propagation. Low and medium frequencies (LF or long waves, and MF or medium waves) ranging from about 30 kilohertz up to a few megahertz propagate primarily by surface waves. Surface waves tend to follow the earth’s surface and are capable of dependable non-line-of-sight propagation of up to about 150 kilometres. Surface wave propagation distances are greater over the ocean than over land and may extend up to a few hundred kilometres. Because of the long wavelengths involved in the

1 of 15 LF/MF range, radio signal reflections are of little consequence. (Periodically conditions may exist which cause some atmospheric refraction.) High frequencies (HF or short wave) range from about 3 MHz up to about 30 MHz and propagate by combinations of line of sight, refraction, and reflection. Propagation characteristics tend to vary from day to night, summer to winter. This is because the dominant propagation of short waves is dependent upon the earth’s ionosphere, and as the ionosphere’s characteristics change through day, night, summer, and winter, so do its propagation characteristics. Because of susceptibility to changing conditions, HF radio navigation and communications reliability can be highly variable. Propagation ranges thus can vary from line of sight (50 km) during poor conditions or up to thousands of kilometres during optimal conditions. These long distance propagations are possible because of ionized particles in the ionosphere causing the RF signals to refract or reflect back down to the earth’s surface. And when the earth’s surface is highly reflective (such as over water bodies) multiple reflections between the earth and ionosphere occur allowing long distance propagation (multi-hop). Very high frequencies (VHF) range from about 30 MHz up to about 300 MHz and propagate primarily by line of sight. For most applications this limits reliable propagations to about 30 - 50 km. However, these distances can be increased by raising the transmitter and receiver antennas as high as possible above the terrain. Obviously, aircraft may have line of sight capabilities of 200 km or more. VHF occasionally experiences special atmospheric conditions known as tropospheric ducting where temperature inversions in the atmospheric layers cause signal refraction due to sudden changes in the air mass dielectric constants, thus causing the signal to follow the inversion duct. Ducting can extend the propagation distance to hundreds of kilometres. At VHF frequencies, many natural and man-made objects become fairly good RF signal reflectors. For ultra high frequencies (UHF) ranging from 300 MHz up to about 3000 MHz (3 GHz) where the signal wavelengths are submetre, line of sight is the primary mode of propagation. Thus, signal propagation distances on the earth are generally limited to 50 km. Aircraft can achieve hundreds of kilometres depending on their altitude above the earth’s surface. Natural terrain as well as man-made objects can have great influence on the signal as it travels along the propagation route. Because of the small wavelengths in this frequency range, reflections occur off almost any metal structure larger than a few centimetres in size. This frequency range is the primary segment used for satellite communications and navigation systems including TRANSIT and GPS.

The GPS RF Signal The GPS satellite constellation maintains precise orbit patterns at approximately 10,898 nautical miles above the earth’s surface. Each of the 24 orbiting satellites (exact number may vary) broadcast continuous PRN code as well as precise orbit data on the GPS L1 channel (1575.42 MHz carrier) and L2 channel (1227.60 MHz carrier). Each satellite transmits these signals using a right hand circular polarized (RHCP) antenna. As the GPS signal must travel approximately 10,898 nmi, some refraction and delay of the signal does occur as it travels through the changing propagation mediums (ionospheric layers and troposphere). Some GPS receivers, such as the NovAtel GPSCard, model out much of the ionospheric and tropospheric delays. However, the most successful method for cancelling the effects of atmospheric refraction and delays is to use a dual frequency GPS receiver (L1/L2). These two frequencies have a special ralationship which, when combined with special down-conversion and mixing techniques, allows them to be combined in such a way as the effects of atmospheric delay are almost completely cancelled. Because GPS is a radio ranging and positioning system, it is imperative that ground station signal reception from each satellite be of direct line of sight. This is critical to the accuracy of the ranging measurements. Obviously anything other than direct line of sight will skew and bias the range measurements and thus the positioning triangulation (or more correctly, trilateration).

The Role of Receiving Antennas The role of a receiving antenna is to intercept electromagnetic waves as they propagate through space (or the earth’s atmosphere). In order for an antenna to efficiently intercept a desired frequency or band of frequencies, it must be “tuned” to the frequency band where optimal reception is desired. Tuning helps reject out-of-band signals as well. Once intercepted, the electromagnetic wave induces alternating currents in the receiving antenna that accurately duplicate the RF signal as transmitted from the transmitting antenna. Once intercepted, the signal can be further amplified, filtered, downconverted, and demodulated or decorrelated by the receiver circuitry. Radio waves exhibit polarity characteristics based on the transmitting antenna design. For example, vertical (or whip) antennae are considered as vertically polarized, whereas dipole and other horizontally oriented antennae are considered horizontally polarized. Space radio systems such as GPS tend to use antennae that are circular polarized. For optimum signal transfer, radio links require that the receiving antennae polarization match that of the transmitting antenna. If cross polarization occurs between the two systems, the receiving system may lose anywhere from 10 to 30 dB of the available

2 of 15 signal. GPS earth stations require RHCP polarization to match the polarization of the satellite transmitted signal for optimal signal reception. GPS earth stations require that the receiving antenna radiation pattern possesses omnidirectional characteristics. An omnidirectional antenna is required to provide optimal reception of all GPS signals within the antenna’s reception hemisphere (from horizon to horizon at all bearings and elevations). As the signal wavelength of L1/L2 signals is quite short (about 19 cm L1/24.4 cm L2), this allows for the small and efficient antenna design. Further to this, antenna designs in general tend to be most efficient and practical using quarter wavelength and half wavelength construction. This means that practical GPS antenna construction dimensions can be as small as 4 to 5 centimetres in size. The two most commonly used GPS antennae use quadrifilar and microstrip construction techniques. Both types are optimized for RHCP polarization. Due to the physical characteristics of a quadrifilar antenna (relatively high profile vertical structure), they generally have very good low angle reception. As GPS signals tend to be weaker at low angles (the horizon), this can be an asset for early signal acquisition for rising satellites. Low angle antenna radiation patterns can also be an asset for craft that are subject to pitch and roll conditions. On the negative side, undesired multipath reflections off water bodies are also strongest at low angles. Microstrip (or patch) antennae, on the other hand, are generally very low profile structures (essentially a tuned flat plate separated by dielectric material from the ground plane). This type of antenna, by nature, tends to favor high elevation reception over low angles. Thus, low angle multipath reception off water bodies is less of a problem than for quadrifilar antennae. However, on the other hand, flat-plate patch antennae perform less favorably at the horizon when the craft is subject to pitch and roll conditions. In recent years, microstrip antenna construction techniques have evolved such that dome shapes are possible that enhance the low angle reception capabilities. The NovAtel GPSAntenna model 501 is an example where special construction techniques are used to enhance the low angle performance over traditional flat plate patch antennae. Each type of antenna has its advantages and disadvantages. Whatever type of antenna is chosen for the GPS receiver, multipath reception will still have to be dealt with as a common problem. In most radio systems, the shortest direct propagation route is generally the preferred route (with the exception of short-wave multihop used to achieve long distance radio communications on the earth). However, in practice, the RF signals may arrive at the receiving antenna from more than one propagation route. This is where problems may arise at the receiving antenna and leads us into the important topic of multipath reception and its associated problems and solutions.

3 of 15 What Is Multipath? Multipath occurs when an RF signal arrives at the receiving antenna from more than one propagation route (multiple propagation paths - thus multipath).

Figure 1 Illustration of GPS Signal Multipath

What Causes Multipath? When radio waves (electromagnetic radiation) are emitted from a radio transmitter antenna, the RF signal propagates in all directions from the antenna. Because the RF signal is emitted in many directions simultaneously and is travelling different paths, these signals encounter various and differing natural and man-made objects along the various propagation routes. Whenever a change in medium is encountered, the signal is either absorbed, attenuated, refracted, or reflected. Refraction and reflection cause the signals to change direction of propagation. This change in path directions often results in a convergence of the direct path signal with one or more of the reflected signals. When the receiving antenna is the point of convergence for these multipath signals, the consequences are generally not favorable. Whenever a signal is refracted, some signal polarity shifting takes place. And when full reflection occurs, full polarity reversal results in the propagating wave. The consequences of signal polarity shifting and reversal at the receiving antenna vary from minor to significant. As well, refracted and reflected signals generally sustain some degree of signal amplitude attenuation. Take, for example, some common occurrences we are all familiar with, such as commercial AM radio and television. Especially at night, it can be observed that AM radio signals “fade” in and out resulting in momentary loss of reception. Or in the case of television reception we see “ghost” images on the screen, or “flutter” when aircraft fly overhead. These are all effects of signal multipath. In the case of radio ranging systems, such as GPS, multipath reception can cause serious errors in the range measurements and thus position accuracy. It is generally understood that, in multipath conditions, both the direct and reflected signals are present at the antenna. However, in some situations, the direct signal may be obstructed or greatly attenuated to a level well below that of the received multipath signal. Obstruction of direct path signals is very common in city environments where many tall buildings block the line of sight to the satellites. As buildings generally contain an abundance of metallic materials, GPS signal reflections are abundant (if not overwhelming) in these settings. Obstruction of direct path signals can occur in wilderness settings as well. If the GPS receiver is in a valley with nearby hills, mountains and heavy vegetation, signal obstruction and attenuation is also very common.

Consequences Of Multipath Reception When a GPS multipath signal converges at the GPS antenna, there are two primary problems that occur: 1) a multiple signal with amplitude and phase shifting

4 of 15 2) a multiple signal with differing ranges. 1) Earlier it was mentioned that receiving antennae need to be polarized to match that of the transmitted signal – in the case of GPS, right hand circular polarization (RHCP). The problem arises that when the multipath signal reverses polarity (to left hand or LHCP), the direct and reflected signals will cancel each other when induced at the receiving antenna. The amount of signal cancellation varies with the degree of signal polarity shift and relative amplitude of the direct vs. multipath signal. On the other hand, if the multipath signal converges at the antenna inphase (through multiple reflections), the induced direct and multipath signals will actually sum together causing the receiver signal to significantly increase in amplitude. This inphase and out-of-phase signal reception can play havoc with the receiver automatic gain control circuitry (AGC) as it struggles to maintain constant signal levels for the receiver correlator. 2) Because a multipath signal travels a greater distance to arrive at the GPS antenna, the two C/A code correlations are, by varying degrees, displaced in time, which in turn causes distortion in the correlation peak and thus ambiguity errors in the range measurements. As mentioned in the previous subsection, it is possible that the received multipath signal has greater amplitude than the direct path signal. In such a situation the multipath signal becomes the dominant signal and receiver pseudorange errors become significant due to multipath biases and may exceed 150 metres. In single point positioning, the biases caused by multipath are not generally of great concern. Largely, this is because single point nominal positioning accuracies are influenced by a wide range of systematic biases that limit repeatable accuracies to about 100 metres CEP. The sources of these biases can be attributed to: Satellite orbit prediction Satellite clock drift Selective Availability (SA) Ionospheric delay Tropospheric delay Receiver clock offset Signal multipath

The majority of the above biases can be cancelled if pseudorange differential techniques are incorporated. When real-time differencing techniques are used, nominal accuracies of about 5 metres CEP (standard correlators) and about 0.75 metre CEP with NovAtel’s Narrow Correlator tracking technology are easily achievable. (These figures assume a relatively low multipath environment and using a multipath reduction antenna choke ring). However, multipath is one bias that is normally uncorrelated between the monitor and remote differential stations antennas (especially under kinematic situations) due to unknown or complex signal multipath occurrences. Now, with pseudorange C/A code differential accuracies achievable in the one to five metre range, multipath becomes a major concern, and may significantly bias users’ position accuracy expectations. Further to this discussion, when pseudorange and carrier phase double differencing techniques are used, biases are further reduced to achieve accuracies below 20 cm CEP range (such as with NovAtel’s RT-20 technology). But once again, multipath is a major obstacle in maintaining these accuracies with certainty. If a differential monitor station is subject to significant multipath conditions, this in turn will bias the range corrections transmitted to the differential remote receivers. And in turn, if the remote receivers also experience a high level of multipath, the remote receiver position solutions will be significantly biased by multipath from both stations.

Some Hardware Solutions For Multipath Reduction A few options exist by which GPS users may reduce the level of multipath reception. Among these include: antenna site selection, special antenna design, and ground plane options. Antenna Site Selection Multipath reception is basically a condition caused by environmental circumstances. Some of these conditions you may have a choice about and some you may not. Many GPS reception problems can be reduced to some degree by careful antenna site selection. Of primary importance is to place the antenna so that unobstructed line-of-sight reception is possible from horizon to horizon and at all bearings and elevation angles from the antenna. This is, of course, the ideal situation, which may not be possible under actual operating conditions.

5 of 15 Try to place the antenna as far as possible from obvious reflective objects, especially reflective objects that are above the antenna’s radiation pattern horizon. Close-in reflections will be stronger, and typically have a shorter propagation delay allowing for autocorrelation of signals with a propagation delay of less than one C/A code chip (300 m). When the antenna is in an environment with obstructions and reflective surfaces in the vicinity, it is advantageous to mount the antenna as high as possible to reduce the obstructions and should be placed above reflective surfaces as much as possible. Water bodies are extremely good reflectors of RF signals and are most troublesome for reception of low angle satellites. The best solution here is to avoid these locations. However, for marine vessels, that is not a viable solution, and the water reflections are a source of constant multipath errors.

Figure 2 Illustration of GPS Signal Multipath vs. Increased Antenna Height

Antenna Designs Low angle reflections, such as from water bodies, can be reduced by careful selection of the antenna design. For example, flat plate microstrip patch antennas have relatively poor reception properties at low elevation angles near their radiation pattern horizon. Quadrifilar helix antennas and other similar vertically high profile antennas tend to have high radiation gain patterns at the horizon. These antennas, in general, are more susceptible to the problems resulting from low angle multipath reception. So, for marine vessels, this type of antenna encourages multipath reception. However, the advantages of good low angle reception also means that satellites can be acquired more easily while rising in the horizon. As well, vessels subject to pitch and roll conditions will experience fewer occurrences of satellite loss of lock. A good antenna design will also incorporate some form of left hand circular polarization (LHCP) rejection. Multipath signals change polarization during the refraction and reflection process. This means that generally, multipath signals may be LHCP oriented. This property can be used to advantage by GPS antenna designers. If a GPS antenna is well designed for RHCP polarization, then LHCP multipath signals will automatically be attenuated somewhat during the induction into the antenna. To further enhance performance, antennas can be designed to increase the rejection of LHCP signals. NovAtel’s GPSAntenna model 501 is an example of an antenna optimized to further reject LHCP signals by more than 10 dB. The Model 600 GPSAntenna is an active antenna designed to operate at the GPS L1 and L2 frequencies, 1575.42 and 1227.60 MHz. The microstrip receiving elements are coupled to filters and a low-noise amplifier (LNA). The unit is optimized to receive right-hand-circularly-polarized signals, and its radiation pattern is shaped to reduce signals arriving at low elevation angles; these features decrease the errors associated with electromagnetic interference and multipath. Also, the model 600 roll-off compares well to a patch antenna roll-off mounted on a large choke ring ground plane. This antenna has a major advantage above the choke ring ground plane antenna - it is lighter by several pounds and much smaller.

6 of 15 Figure 3 Illustration Of Quadrifilar vs. Microstrip Patch Antennae

Antenna Ground Planes Nearby objects can influence the radiation pattern of an antenna. Thus, one of the roles of the antenna ground plane is to create a stabilizing artificial environment on which the antenna rests and which becomes a part of the antenna structure and its resultant radiation pattern. A small ground plane (relative to one wavelength at the operating frequency) may have minimal stabilizing effect, whereas a large ground plane (multiple wavelengths in size) will have a highly stabilizing effect. Large ground planes also exhibit a shielding effect against RF signal reflections originating below the antenna’s radiation pattern horizon. This can be a very effective low angle shield when the antenna is elevated on a hill or other structure above other reflecting surfaces such as vehicles, railway tracks, soil with high moisture content, water bodies, etc. One of the drawbacks of a "flat plate" ground plane is that it gives a “hard boundary condition”, ie. allowing electromagnetic waves to propagate along the ground plane and diffract strongly from its edge. The “soft boundary” condition, on the other hand, will prevent the wave from propagating along the surface of the ground plane and thereby reducing the edge diffraction effects. As a result the antenna will exhibit a completely different radiation pattern. The “soft boundary” condition is typically achieved by a quarter wavelength deep, transversely corrugated ground plane surface (denoted as “choke ring ground plane”). When the depth of the corrugation (choke rings) is equal to a quarter wavelength, the surface wave vanishes, and the surface impedance becomes infinite and hence provides the “soft boundary” condition for the electromagnetic field. This results in modifications to the antenna radiation pattern that is characterized by low back lobe levels, no ripples in the main lobe, sharper amplitude, roll-off near the horizon and better phase center stability (there are smaller variations in 2 axes). This is what makes NovAtel's GPS antennas so successful when used with the NovAtel GPSAntenna choke ring ground plane.

NovAtel’s Internal Receiver Solutions For Multipath Reduction The multipath antenna hardware solutions described in the previous paragraphs are capable of achieving varying degrees of multipath reception reduction. These options, however, require specific conscious efforts on the part of the GPS user. In many situations, especially kinematic, few if any of the above solutions may be effective or even possible to incorporate. By far, the best solutions are those which require little or no special efforts in the field on the part of the GPS user. This is what makes internal receiver solutions so desirable and practical. NovAtel has placed long term concerted effort into the development of internal receiver solutions and techniques that achieve multipath reduction, all of which are transparent to the GPSCard user. These achievements have led to three patented technologies: • Narrow Correlator tracking technology • MET • MEDLL

Each of the above listed solutions utilizes innovative correlator delay lock loop techniques. As the correlator is the heart of the GPS receiver C/A code tracking loop, further discussions on the correlator are provided to give just enough background to

7 of 15 grasp the basic concepts of NovAtel’s Narrow Correlator tracking technology, MET, and MEDLL multipath reduction technologies.

The Role of the GPS Receiver Correlator Each GPS satellite transmits a unique pseudorandom noise (PRN) C/A code (coarse/acquisition) and P code (precision). As the P code is generally for military and special authorized use only, it is denied general access by means of “anti-spoofing” (A-S), which is an encryption of the P code and referred to as the Y code. (As commercial GPS users are generally restricted to C/A code use, this discussion is limited to C/A code.) The C/A code has a clocking rate (chipping rate) of approximately 1.023 MHz. This chipping rate causes the GPS RF signal to have a main lobe (90% power) spread spectrum of approximately 2.046 MHz. As each satellite transmits on the same L1 carrier frequency, they are differentiated only by their respective PRN codes. To receive each GPS satellite PRN signal, the earth station receivers have C/A code generators that can match each of the satellite PRN codes. As well, the internal code generator must be clocked at a chipping rate that is as close as practical to that of the satellite’s clock. It is in the “matching” of the individual received C/A codes against those generated by the local receiver code generator that the correlator becomes of crucial importance. As the name “correlator” implies, it must be able to “correlate” a match between two PRN codes. Unless correlation can be achieved, the received signals only appear as random noise.

Figure 5 Example of C/A Code Correlation

t

C/A Code Propagation Ranging Delay (Pseudorange)

Satellite Received Code +1 –1 +1 –1+1 +1 –1 –1 +1 –1 –1 +1 +1 –1 +1 +1 –1 +1 –1 –1

Locally Generated Code +1 –1 +1 –1+1 +1 –1 –1 +1 –1 –1 +1 +1 –1 +1 +1 –1 +1 –1 –1

0.4 Chip Offset

Auto-correlation match

–1 +1 Negative pulse represents Positive pulse represents no correlation correlation

The GPS receiver measures its distance from each satellite by measuring the time it takes the GPS signal to propagate from the satellite to the receiver antenna. The GPS receiver determines its position by means of trilateration of the range measurements of at least four measured satellite ranges. The receiver’s ability to accurately correlate and phase lock on each PRN code directly influences the accuracy of the receiver’s range measurements accuracy, which in turn affects the accuracy of the computed position. NovAtel’s GPSCard has twelve parallel channels that can simultaneously correlate and track up to 12 satellites.

The Autocorrelation Function The ideal GPS receiver would have an infinitely wide receiver BW which would allow the receiver to capture 100% of the GPS spread spectrum signal. The normalized autocorrelation function for an infinately wide BW is generally illustrated as shown in Figure 6 below.

8 of 15 Figure 6 Theoretical Normalized Auto-correlation Function

Auto-correlation peak Pre-correlation BW assumed to be infinite 1.0

0.5 Early slope Late slope

-1.0 0 +1.0 Code Correlation Offset in Chips

The auto-correlation peak is maintained by continually adjusting the locally generated code for peak correlator output. The unlimited BW provides a sharp correlation peak and steep early/late slope which facilitates accurate error correction for the code-lock-loop (also called Delay Lock Loop). In reality, a GPS receiver would need a brick wall bandpass filter with a BW of at least ten times the code C/A code chipping rate to be capable of capturing > 99% of the GPS spread spectrum signal. For most GPS receivers this is generally not practical to achieve. The Standard Correlator For most general purpose GPS receivers a 2.046 MHz BW is easier to achieve and is typically adequate to capture approximately 90% of the GPS C/A code spread spectrum RF signal. However, this BW limiting has its tradeoffs which causes rounding of the autocorrelation function. The narrower the receiver BW, the greater will be the rounding of the correlation function. Figure 7 below illustrates the degree of autocorrelation rounding and flattening at the peak caused by 2 MHz BW limiting.

Figure 7 Typical Bandwidth Limited Correlation Function

Conventional Correlator with BW Auto-correlation peak limited to approximately 2 MHz

1.0

Early slope0.5 Late slope

-1.0 0 +1.0

Code Correlation Offset in Chips

There are various problems associated with single correlator sampling, especially for a 2 MHz BW limited receiver as illustrated in Figure 7 above. As can be seen, the BW limited correlation function is almost flat at the peak. This creates “wandering” at the peak resulting in significant ambiguity in determining the actual correlation peak as well as sensing the early/late slope for error correction. This correlation ambiguity directly translates into range measurement ambiguity. To help reduce the correlation peak ambiguity, one commonly adopted solution is to utilize three correlation samples per satellite channel (called Punctual, Early, and Late). The Early (E) and Late (L) correlators are generally spaced 1 chip apart from each other, while the Punctual (P) is centred between them (P - 0.5 chip = Early, and P + 0.5 chip = Late).

9 of 15 Figure 8 Standard Correlator with Punctual, Early and Late Correlator Sampling (PEL)

Auto-correlation peak – Punctual (P) Conventional Correlator BW limited to approximately 2 MHz 1 chip E/L spacing 1.0

Early sample Late sample (E) (L) 0.5

-1.0 0 +1.0 Code Correlation Offset in Chips

As the E and L correlator samples are spaced 1 chip apart, this places them on the steepest part of the autocorrelation E and L slopes. This placement provides greater sensitivity to changes in the correlation delay-lock-loop (DLL). The E and L samples are differenced to create the appropriate DLL loop feedback for maintaining code lock. Thus, when the E-L difference is zero, the P correlation will be at its peak. This correlator technique is generally referred to as a “Standard Correlator” and is the most common method in use (especially with low-cost general accuracy receivers). Because of its relatively flat correlation peak combined with the wide E-L sample width, Standard Correlators tend to be highly susceptible to multipath correlation distortion which may significantly skew the correlation function, thus resulting in skewed position solutions. Standard Correlator spacing can typically achieve C/A code range measurement accuracies of 100 cm RMS (not including multipath bias). A high multipath environment can potentially skew the ranges by as much as 80 metres. When used in differential mode, the Standard Correlator receiver can achieve nominal position accuracies of two to five metres CEP (low multipath environment) while using a multipath reduction antenna choke ring ground plane. However, once again, in a high multipath environment, this level of position accuracy may be significantly degraded. The Narrow Correlator Tracking Technology NovAtel has patented a correlation technique, which sharpens the autocorrelation peak and narrows the Early and Late spacing from 1 chip to 0.1 chip. A sharper correlation peak is achieved by broadening the receiver BW while using a filter with flat response over the pass- band and sharp cutoff rejection for out-of-band signals. The broader BW allows the receiver to capture a greater portion of the GPS signal spread spectrum. This increased BW reduces the amount of receiver-induced distortion on the GPS C/A code, which in turn allows for more accurate correlation. As well, a high sampling frequency of approximately 20 MHz contributes to the narrow correlator’s performance.

Figure 9 Example of Narrow Correlator Sampling (PEL)

Correlator function resulting from Punctual (P) 8 MHz precorrelation BW 0.1 chip E/L spacing 1.0 E L

0.5

-1.0 0 +1.0 Code Correlation Offset in Chips

10 of 15 NovAtel’s Narrow Correlator tracking technology is “dynamically adjustable”. This means that the correlator spacing is initially wide for fast acquisition and reacquisition purposes (1 chip spacing), followed by a narrowing down to 0.1 chip spacing for higher accuracy tracking and multipath rejection. The advantages of Narrow Correlator tracking technology are substantial over the Standard Correlator. Because of the narrower correlation peak and narrower correlator spacing, there is less floating or ambiguity about the correlation peak resulting in greater code correlation accuracy and stability. This directly translates into less noisy and more accurate range measurements. As well, the Narrow Correlator tracking technology achieves less susceptibility to multipath signals that arrive with delays of greater than the 0.1 chip E-L spacing. Because of the sharper correlator peak combined with the smaller 0.1 chip E-L spacing, the Narrow Correlator tracking technology can achieve C/A code range measurement accuracies of 10 cm rms. This is a ten fold gain over the Standard Correlator. However, multipath can still bias these measurements by as much as 10 metres. The benefits of operating NovAtel’s Narrow Correlator tracking technology receiver in single differencing DGPS mode results in position accuracies of 0.75 metre CEP (low multipath environment) while using a multipath reduction antenna choke ring ground plane. This yields significant accuracy improvement over the Standard Correlator. Narrow Correlator vs. Multipath The Narrow Correlator tracking technology is inherently less susceptible to multipath correlation biases than the Standard Correlator, by virtue of the 0.1 chip E-L sampling. This does achieve improvements in the C/A code pseudorange measurements, but does little for the reduction of carrier phase multipath biases. Under high multipath conditions, Narrow Correlator tracking technology range measurements can be skewed by as much as 10 metres. This is why the GPSAntenna model 501 and choke ring ground plane are still recommended for maximum Narrow Correlator performance. For the remainder of the discussions in this document about multipath, assumptions will be made concerning the characteristics of the received GPS signals and the GPS receiver being used: • that the direct path and multipath signals are both being received; • that the multipath signal is assumed to be weaker than the direct path signal; • multipath signal delays of less than 1 code chip are of greatest concern, and delays greater than 1 code chip are of little or no consequence.

If the autocorrelation graph of the direct path and multipath signals are simultaneously represented and then combined, the results can be illustrated in Figure 10 below.

Figure 10 Direct Path, Multipath (InPhase), and Resultant Correlation Function

Normalized Amplitude 1.6 Composite Direct + Multipath

1.4 Direct Path Signal Multipath Signal Correlation: Correlation 1.2 • 0 deg. inphase with direct signal 1 • Delay of 0.2 chip from direct signal 0.8 • Amplitude of 0.5 relative to direct signal

0.6

0.4 0.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Offset (C/A Code Chips)

In this example, the multipath signal has a delay of 0.2 chips, an amplitude of 0.5 relative to the direct path signal, and is inphase with the direct path signal. As can be seen by the composite correlation, signal magnitude increases, and more

11 of 15 importantly, distortion of the autocorrelation curve results. The distortion of the autocorrelation curve skews the E-L sampling and thus the Punctual resolution, resulting in tracking errors. It should be noted that inphase multipath signals typically result from an even number of reflections. If we recall that any time a signal is reflected, it will experience polarity reversal. Therefore, the GPS multipath signal must undergo two reflections to arrive at the antenna inphase with the direct path signal. (It is assumed that 180 degree phase shift results from each reflection; however, lower angles of incidence will result in something less than 180 degrees.) Figure 11 below illustrates the effects on autocorrelation when the multipath signal is 180 degrees out-of-phase with the direct path signal.

Figure 11 Direct Path, Multipath (Out-of-Phase), and Resultant Correlation Function

Normalized Amplitude 1 Direct Path Signal Correlation 0.8 Composite Direct + Multipath

0.6

0.4

0.2

-1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1 -0.2 Offset (C/A Code Chips)

-0.4

Multipath Signal Correlation: -0.6 • 180 deg. out-of-phase with direct signal • Delay of 0.2 chip from direct signal • Amplitude of 0.5 relative to direct signal

For signals arriving 180 degrees out-of-phase, distortion of the autocorrelation function can be even more substantial than for inphase multipath signals. It should also be noted that multipath signals arriving at the antenna 180 degrees out-of-phase are generally the result of a single reflection or odd multiple of reflections. Obviously, single reflections are of greatest concern because these will generally have greater amplitude and less propagation delay than multiple reflection signals (recalling that delays of less than one chip are of greatest concern). Another problem with 180º out-of-phase multipath signals is that they directly cancel out the direct path signal. This can cause substantial reduction and distortion to the autocorrelation function, or even cause loss of lock in the receiver tracking loops.

12 of 15 Figure 12 below further illustrates the effects of multipath to the autocorrelation function on a normal dot-product or early minus late delay-lock-loop (DLL). As a normal DLL is designed to feedback to the hardware in such a way as to keep the power of the early and late correlators equal, a distorted correlation function will bias this process.

Figure 12 Tracking Error Due to Multipath

Normalized Amplitude

1.5 Tracking Error

Late Early 1.4

1.3 Punctual

-0.2 -0.1 0 0.1 0.2 0.3 0.4 Offset (C/A Code Chips)

The above paragraphs have briefly covered the performance gains of the Narrow Correlator tracking technology referenced against Standard Correlator code tracking techniques. It has been discussed and illustrated that NovAtel’s Narrow Correlator tracking technology is capable of significant performance improvement over the Standard Correlator. However, multipath continues to be the dominant limiting factor in the accuracy performance of the Narrow Correlator tracking technology when used in single-differencing DGPS modes of operation. Maximum performance of the Narrow Correlator receiver can be achieved when combined with NovAtel’s model 501 GPSAntenna mounted on the NovAtel choke ring ground plane.

MET™ Overview It has been recognized that the use of a choke ring ground plane is highly effective in reducing reception of low angle multipath signals However, installation and usage of the choke ring is not always practical (or desirable) for many types of installations such as on aircraft and other high dynamics types of installations. To alleviate the necessity of a choke ring ground plane, NovAtel has developed a new technology called MET (Multipath Elimination Technology). MET is currently available as the “M” option to the GPSCard Series. MET is a further enhancement of NovAtel’s Narrow Correlator tracking technology whereby multiple correlators are spaced symmetrically, as closely as possible, at the top of the correlation peak. By means of software manipulation, the multiple correlator samples are used to model the shape and slope (Early and Late slopes) near the peak of the direct path correlation function, and thus model out the multipath distortions. In practice, a GPSCard utilizing MET technology can typically achieve multipath error reductions of up to 50% and does not require the use of a GPSAntenna choke ring ground plane. This 50% multipath error reduction will provide significant confidence improvement and flexibility when used at both the monitor and remote DGPS stations. Refer to Figure 13 for an illustration of comparisons between multipath error envelopes between NovAtel’s Narrow Correlator tracking technology and MET.

13 of 15 Figure 13 Multipath Error Envelopes for Narrow Correlator vs. MET

15 Narrow Corr. 0 degrees inphase envelope Multipath Signal Amplitude 10 = 0.5 relative to direct signal

5 MET 0 degrees inphase envelope

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

-5 Multipath Delay (C/A Chips) MET 180 degrees out-of-phase envelope

-10 Narrow Corr. 180 degrees out-of-phase envelope -15

MEDLL™ Overview NovAtel has developed a multipath reduction technology that approaches the theoretical limits of multipath-free GPS signal reception. This new patented technology, called “Multipath Estimation Delay-Lock-Loop” (MEDLL), utilizes a combination of hardware and software techniques that are capable of reducing the combined effects of pseudorange multipath errors by as much as 90% compared to a system using a Narrow Correlator. As well, MEDLL does all this without the need to mount the antenna on a choke ring ground plane. The MEDLL technology takes further advantage of NovAtel’s parallel channel Narrow Correlator sampling techniques. It is unique in that it utilizes an “array” of narrowly-spaced correlators distributed about the autocorrelation function whereby each satellite tracking channel is sampled by a dedicated correlator array. Currently, MEDLL is a 12 channel receiver (configuring for more channels is possible). This array distribution of correlator sampling allows the receiver to measure the shape of the received correlation function. Using a “maximum likelihood estimation” technique, MEDLL deconvolves the received signals into their direct path and multipath components by determining the amplitude, delay, and phase angle of each of the composite signals. Once the composite signal has been broken down into its components, the signal with the least delay is determined to be the direct signal, and all other signals with greater delay are considered to be the multipath components (assuming the direct path signal is available and unobstructed). MEDLL can effectively remove all multipath signals that have a propagation delay of greater than 0.1 chip relative to the direct path signal. The remaining multipath effect on the C/A code pseudorange measurements is now in the same order of magnitude as a P code GPS receiver.

Figure 14 Multipath Error Envelopes for Narrow Correlator vs. MET vs. MEDLL

14 of 15 Conclusion It has been discussed in this paper that the influences on radio wave propagation depend on the frequency and propagation mediums through which the RF signal travels. UHF signals such as GPS are highly susceptible to reflections because of the short wavelengths at the L1 channel. As GPS is a radio navigation ranging system, the direct path signal is of primary interest. Any propagation delays or multipath reception causes biases to the ranging measurements that cannot be differenced by traditional DGPS single differencing techniques. Multipath is the greatest source of errors to a system operating in single differencing mode. It has been concluded that careful site selection and the GPSAntenna model 600, or good antenna design combined with a choke ring ground plane are very effective in reducing multipath reception. The role of correlators was discussed to provide some insight into how multipath influences the correlation function required for satellite tracking and ranging. This led to the advantages of using a Narrow Correlator™ tracking technology versus the Standard Correlator and how this relates to reductions in pseudorange multipath biases. It was then discussed how MET™ technology is an enhancement of the Narrow Correlator tracking technique used by the GPSCard that provides up to 50% multipath reduction without the need of an antenna choke ring ground plane. Finally, the topic of MEDLL™ was discussed to describe a multi-correlator array technology whereby a multi-card system is used to sample the multipath signals as well as the direct path signals, recognizing the difference between them, then rejecting the multipath signals, leaving only the desired direct path signal. MEDLL is the most effective receiver technology available that reduces the combined effects of GPS L1 C/A code and carrier phase multipath by as much as 90% (without the need for a choke ring ground plane).

References • “Theory and Performance of Narrow Correlator Spacing in a GPS Receiver” – by A.J. Van Dierendonck, Pat Fenton, and Tom Ford • “A Practical Approach to the Reduction of Pseudorange Multipath Errors in a L1 GPS Receiver” – by Bryan Townsend and Patrick Fenton • “A Multipath Estimating Delay Lock Loop: Approaching Theoretical Accuracy Limits”, – by Richard D.J. van Nee, Jaap Siereveld, Patrick C. Fenton, and Bryan R. Townsend. For more information: Write to: NovAtel Inc., 1120 – 68 Ave N.E., Calgary, Alberta, Canada, T2E 8S5 Phone: 1-800-NOVATEL (in the U.S. and Canada) or +1-403-295-4500 Fax: 403-295-4501 E-mail: [email protected] Website: www.novatel.ca

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