Antenna Systems, - Chalmers...Ericsson research areas Broadband and transport networks SW research...

Björn JohannissonAntenna Research Center

Ericsson Research

([email protected])

Antenna Systems,Development Based on Mathematics

© Ericsson AB 2007 Commercial in confidence Antenna Systems, Development Based on Mathematics 2007-11-17

Agenda

Ericsson Research introductionAntenna fundamentalsRequirments for antenna systemAntenna design and radiation pattern representation


With future in sightEricsson research areas

Broadband and transport networksSW researchService layer technologiesMultimedia technologiesIP networksWireless access networksAccess technologies & signal processingEMF health and safety


R&D long-term & short-term

Strategic Direction

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Agenda



Antennas in wireless systemsThe task of antennas are to transform cable-bound information to wireless electro-magnetic waves

– Send (or receive) energy in directions where it is useful– High efficiency, high gain– No distorsion of the signal

010001101001Basestation


Antenna beamwidth

d θ3dB θ3dB [ ] 50λd

The half-power beamwidth of an antenna with uniform taper exitation is inveresly proportional to the dimension of the antenna

o


Mobile system deployment

Mobile base stations are commonly deployed as 3-sector sites in a hexagonal grid

The half-power beamwidth required to cover each sector is approximately 65o


Typical antenna characteristics

65o

10o

1,65 m

25 cm

GSM 900 MHzantenna


Different antennas for different purposes

Every antenna is designed and optimized for a specific purpose

NASA


Antenna system mathematicsDuring design of antenna systems many different aspects

of mathematics are being used. Some examples:

Complex Numbers and Trigonometry– General tools

Partial Differential Equations– Radio waves, Eigenmodes, Diffraction

Matrix Theory (System of equations)– Radio systems, Data fitting, General tool

Fourier Transforms– Spatial and temporal spectrum

Special Functions (Bessel, Hankel etc.)– Field decomposition

Statistics– Tolerances, Capacity


Agenda



Example 1: Communication SystemEquation system for calculating power to mobile phone


Power allocation for mobile phoneSignal quality measure

Signal S

Bit-rate relates to SIR (signal-to-interference ratio):Higher data-rates (surfing, downloading, streaming) require higher SIRVoice (speech) requires lower SIR

Thermal noise N0 in phone (due to random motion of electrons) sets a required signal level

Noise N0 (in phone receiver)

SIR =SN0


S = P/L

Power allocation for mobile phoneIsolated phone

Received signal power S depends onP, the output power from base stationL, loss between base station and phone

So, SIR can be written

S = P/L

SIR = =SN0

P/LN0

S


Power allocation for mobile phoneMultiple phones in network

Signal S1 Signal S2

InterferenceI12I21


Power allocation for mobile phoneMultiple phones in network

Signal S1

I12

Interference I12

affects user 1due to user 2

I12 = P2/L12


Power allocation for mobile phoneDesired signal quality (SIR) maintained for all phones

SIR1 = =S1

I2 + N0

P1/L11

P2/L12 + N0

SIR2 = =S2

I1 + N0

P2/L22

P1/L21 + N0

One SIR expression for each phone:

Power values are interdependent!


Power allocation for mobile phoneDesired signal quality (SIR) maintained for all phones

In matrix form:

1/L11

1/L22

-SIR1/L12

-SIR2/L21(( ()) ) P1

P2

SIR1

SIR2

N0 =

N0 SIR = A · P

matrix

vector

N0 SIR= A-1P


Power allocation for mobile phoneMoving user with fixed service (streaming video)

User 1 moving from one basestation toward other basestation

1 2

1000 m

250 m


Power allocation for mobile phoneMoving user with fixed service (streaming video)

Power for user 1 increases with distancePower for user 2 (connected to other basestation) also

increases due to changing interference

User #1 distance from basestation #1 (m)

Log

of P

ower

User 1

User 2

No solution forthese distances; negative power!

det(A) = 0,P → ∞


Power allocation for mobile phoneAntenna application

Tilt (rotate) antenna to reduce power requirementsDirect energy in desired directions (close to basestation)Suppress interference toward unintended users (less interdependence)

S2

I12I21

S1


Power allocation for mobile phoneConclusion

Required power greatly reduced with antenna tiltUser #1 needs less power for all distances closer to basestation #1User #2 needs a factor of 10 less power for almost all distances

Interference situation is key property of wireless networks!

User #1 distance from basestation #1 (m)

Log

of P

ower

User 1

User 2


Agenda



Electro-Magnetic Radiation- All you need to know...

James Clerk Maxwell(13/6 1831 – 5/11 1879)Scottish mathematician

and theoretical physicist

Aggregated a setof equationsfor electricity,magnetismand inductance

Maxwells equations


Antenna RadiationBased on Maxwells equations, antenna radiation and wave propagation can be calculated for structures of different size and complexity

Much effort has been put into analytical calculations for different type of transmission lines and basic antennas

– Coaxial cables, waveguides, striplines, dipoles, monopoles, microstrip patches, reflectors, etc...

One example is the electrical dipole antenna that is formed by two quarter wavelength conductors placed back to back for a total length of λ/2. Assuming a sinusoidal distribution, the current impressed is given by:

For the far-field case, the formula for the electric field of a radiating electromagnetic wave is:

λ/2

I = Io ejωt cos (kd)

Eθ = ej(ωt-kr)2πεocr sin(θ)

-jIo cos( cos(θ))π2


-25

-20

-15

-10

-5

0

5

10

15

20

-180

-160

-140

-120

-100 -80 -60 -40 -20 0 20 40 60 80 100

120

140

160

180

Azimuth angle [o]

Gai

n [d

Bi]

Radiated field from antenna

For more complex strucures, where no analytical description is derived, numerical calculations are needed, using a number of different numerical methods

– Finite elements, Method of moments, Finite difference time domain (FDTD), Ray tracing, etc ...


Radiation Pattern for an AntennaThe radiation from an antenna follows Maxwells equations, but wealso need ways to describe it and store the dataRadiation patterns are descriptions that characterize the relative signal (amplitude and phase) at any point outside the antennaTo store data for every point in space requires a lot of data storage and data processing

Are there any better way?

150 100 50 0 50 100 150

0

0

0

0

0

0

0

0

0

0

Ele

vatio

n an

gle

Azimuth angle


Spectral methods (Fourier)

Standing waves (confined region)

Guitar E-string modes (first six)

Boundary condition

Boundary condition

Wave equation (inertia vs string tension)

E0

E1

H1E2

G#2

H2

E major chord


Antenna modes on a sphere

Maxwell Eqs (inductance vs capacitance) and periodic boundary conditions


Field decomposition

The field on a sphere can be described as a sum of spherical modesWhen changing the radius of the sphere the new field distribution can be evaluated using the same modes at the new radius

Field on a single sphere => Field on any sphere (Huygens principle in spherical geometry)


Field and spectrum (infinite radius)

150 100 50 0 50 100 150

0

0

0

0

0

0

0

0

0

0

10 20 30 40

-10

0

10

20 40

-10

0

10

dB

-70-60-50-40-30

M-modes

E-modes

Ele

vatio

n an

gle

Azimuth angle


Field propagation0

0

0

0

0

0

10 20 30 40

R=1 m

R=5 m

R=50 m

R=infinity

E-field M-modes E-modes

150 100 50 0 50 100 150


Iso-surfaces

Interpolation in 3D data

Antenna Systems, - Chalmers...Ericsson research areas Broadband and transport networks SW research...

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