Transcript The MIMO Channel

RF Propagation
Basic Track
Phil Ziegler
Principal Consultant
APRIL 4, 2016
4/4/16
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1
Agenda
•
•
•
•
RF Propagation Fundamentals
Coupling Loss and Antennas
Quick review of dB Math
Other Phenomena Effecting Propagation
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2
Wavelengths &
Frequencies
As we will see, RF Propagation is strongly
dependent on Wavelength
Propagation in the atmosphere (snow, rain,
…) is slightly slower (through glass, 1/3
slower) due to optical density of medium
Where:
Remember this number!
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C

f
= 3x108 m/s
C  299 792 458 m
S
f  frequency  Hz 
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= 300 m/ms
= 1 ft/ns
3
Radio Transmission in Free
Space
PR
F=
4p R 2
To go twice as far
requires 4x the power
F = Power Flux Density
Watts
F  
m2
To go three times as
far requires 9x the
power
Energy decay (dispersion) as surface area expands,
inversely with the square of the distance
Power is energy applied over time distributed over space
PR is radiated power
Etc, …
OmniCells.emf
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4
Friis Equation for Received Power
(not pathloss)
l
PT
F 
4 R 2
l
PG )
(
F=
T
T
4p R 2
PR
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OmniCells.emf
PG )A
(
=
T
T
4p R
é l ù
PR = PT GT GR ê
ú
ë 4p R û
2
e
2
Friis Transmission Equation
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5
Free-Space & dn Model of Path Loss
(not Rx Power)
é 4p d f ù2
LFS (d ) = ê
ú
ë c û
in dB:
 4 d f 
10log L (d )  20log 
 c 
FS
LFS (d ) = [-27.56 + 20log( f )]+ 20log(d )
The path loss equation is characterized by a constant term, frequency term and a distance term.
When the distance is 0 only coupling loss [….] remains.
When the environment is not free space, the rate of decay is other than it is in free space and the distance
term 20 log(d) becomes Nx10Log(d). Where n is the rate of decay relative to free space.
L(d ) = -27.56 + 20log( f ) + n ×10log(d )
Where: n = Propagation Constant; d = distance in meters; f = frequency in MHz
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6
Large-Scale Path Loss
Measurements
Various Environments
Will signals propagate farther indoors or outdoors?
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7
Review of
RF Mathematics Basics
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8
dB’s The Units of Choice for RF
Engineers
• Typical Power amps provide 1 watt of power.
• Typical Receivers can receive .00000000001 watts of power.
• The difference in these numbers require us to use a system of mathematics that keeps track of orders of
magnitude (groups of 10) rather than linear units
• dB math uses logarithmic units of Bels to measure power
»The relationship between watts and bels is given by Bels = Log (Watts)
»One decibel is one tenth of a bel, 1B = 10 dB
»One watt is 1000 milliwatts = 30 dBm
• We use milliwatts not watts and deciBels not Bels as our units of choice for discussions
• Path loss is a ratio -> dB,
• Signal strength is an amount of power -> dBm
dB ± dB = dB
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dBm ± dB = dBm;
dBm – dBm = dB
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9
Free-Space & dn Model of Path Loss
(not Rx Power)
é 4p d f ù2
LFS (d ) = ê
ú
ë c û
in dB:
 4 d f 
10log L (d )  20log 
 c 
FS
LFS (d ) = [-27.56 + 20log( f )]+ 20log(d )
The path loss equation is characterized by a constant term, frequency term and a distance term.
When the distance is 0 only coupling loss [….] remains.
When the environment is not free space, the rate of decay is other than it is in free space and the distance
term 20 log(d) becomes Nx10Log(d). Where n is the rate of decay relative to free space.
L(d ) = -27.56 + 20log( f ) + n ×10log(d )
Where: n = Propagation Constant; d = distance in meters; f = frequency in MHz
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10
In Linear Units of Distance
Initial
Power
Power
Decay
In Free Space it takes about
4 times the amount of power
to double the distance covered.
6dB
6dB
100-200 m
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Distance
2 km
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-
4 km
11
In Logrithmic Units of Distance
~ dB CL
Slope of these lines is the propagation
decay coefficient or “n”
700 MHz
1-10
0m
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10 -100
100-1000
1,000-10,000
Log(Distance in Meters)
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1900 MHz
800 MHz
12
Antenna Overview
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13
Isotropic Antennas
• An isotropic antenna is a hypothetical reference, to which all other antennas may
be compared
• Radiation pattern is uniform in all directions
• Used to calculate gain or directivity, usually expressed in dBi
• dB(isotropic) – is defined as the forward gain of an antenna compared with the hypothetical
isotropic antenna which uniformly distributes energy in all directions
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14
Understanding Gain
Geometrically
Example – a perfect antenna with a 60 degree horizontal beam
width and 10 degree vertical beam width vs.an isotropic antenna
radiating at the same power would have antenna gain in dBi equal
to the ratio of the surface area of the sphere divided by the surface
area of the covered by the directionality of the antenna
Geometrically, the antenna gain would be 20.33 dBi = 10log(2 * 6 * 9);
- Factor of 1/2 for bottom half of sphere
- Factor of 1/6 for 60 degree beam width
- Factor of 1/9 for 10 degrees
In reality the energy radiated from a directional antenna is not
restricted to the main beam, side lobes and back lobes reduce the
gain from the geometrically calculated conceptual solution.
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15
Isotropic Antenna in Free
Space
•
Transmitted power is amplifier output power less cable loss, plus
antenna gain.


Outdoors = BTS Power – Cable Loss + Antenna Gain
Indoors = BTS Power +DAS Impacts to the Remote Amplifier- Cable Loss + Antenna
Gain
• EIRP
(Effective Isotropic Radiated Power)
•EIRP = Pt – Losses + Antenna Gain
Note – ERP is sometimes used when antenna gain is measured in dBd or referenced from a dipole instead of an
isotropic point source. Think of this as a different choice of units such as Fahrenheit vs. Centigrade
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16
One More Confusing Item
Antenna Gain Units
Gain dBd
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ERP
+2.15dB
Gain dBi
Radiated Power
or
EiRP
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17
Dipole or OMNI Antenna in
Free Space
• Three-Dimensional
Pattern
Radiation
Position the 2 vertical elements in the “hole” of the
doughnut
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18
Directional Antennas
• Directional Antennas have radiation patterns described by horizontal and vertical beam
width and GAIN. The pattern and the associated gain are driven by antenna size.
GR 
4 Ae

2
• Here we see that the antenna gain is a function of the Area of the antenna element and
the wavelength of the radiation. Higher frequencies can use smaller antennas. Gain is simply
the ratio of input power to output power and is usually expressed in dB.
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19
Other Conditions that make up the RF Environment
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20
Multipath Concepts
Multipath 1
Direct path
Multipath 2
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21
Multipath & Fading
Large-Scale and Small-Scale
Statistical Accounting for Fading determines Design Confidence
Channel varies due to two fading effects:
- Rayleigh non-LOS lots of obstructions
- Rician LOS self interfering
•
•
•
•
Multipath fading is due to constructive and destructive interference of the transmitted waves (in air) 6-14dB of variance indoors
Channel varies when mobile moves a distance on the order of the carrier wavelength. This is about 0.3 m for 850 MHz cellular. (fades may
occur every ½ wavelength)
For vehicular speeds, this translates to channel variation of the order of 100 Hz. Pedestrian speeds see this variation on the order of 10 Hz
or less.
Primary driver behind wireless communications system design, especially coding and power control
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22
Multipath Rich Environments Allow
For MIMO Channel Conditions
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23
Communication Schemes
FACTS:
1. Current baseline ”1-TX-1-RX-antenna” wireless communications are
running out of improvement possibilities (we are indeed close to the
theoretical capacity bounds as defined by Shannon)
2. Multi-stream/MIMO based transmission schemes redefine those
bounds!
SISO
SIMO
3. Multi-stream/MIMO transmission schemes are realizable in cellular
systems & frequencies
MISO
4. Interference can be managed better in future/evolved wireless
systems
MIMO
This becomes increasingly critical as an increased utilization of Mobile Broadband increases network density
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24
Review: Shannon-Hartley Capacity
Formula
The basic Shannon Formula demonstrates that the main factors governing channel capacity (a.k.a throughput) are
channel bandwidth and the signal to noise plus interference ratio.
C = B*log2(1 + SNR)
Where
C is the channel capacity in bits per second;
B is the bandwidth of the channel in hertz;
SNR is the signal to noise ratio expressed as a unitless linear power ratio
Capacity increases linearly with Bandwidth but as the FCC mostly controls bandwidth allocations, the only
available parameters available for different vendors to increase the information capacity (or quality) of the channel
is to use:
 physics (by managing the physical radio isolation) and
 communications coding theory to virtually and substantially enhance the Signal to Noise ratio of
the channel.
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25
Theoretical Shannon
Capacity Formula
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26
MIMO Receive Side Spatial
Diversity Gain
In a fast fading (Raleigh) environment, independent fading characteristics
at each of the Receive antennas in a MIMO system are exploited to improve the
Tx
Rx
signal quality.
h11
1
1
Datastream A ->
h12
h21
2
2
Datastream B ->
h
22
In a 2 x 2 MIMO system,
- Multi-path effects are used to separate and extract the two data streams, A and B, at each receiver.
- SNR power gain is realized from multiple copies received (since SNR is additive) and combined using
various combining techniques such as Maximal Ratio Combining (MRC)
- Diversity Gain is calculated by the product of NT x NR. For a 2 x 2 MIMO system, the maximum diversity
gain achievable is 4.
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27
MIMO Spatial Multiplexing
Techniques
•
•
The basic idea of how MIMO increases data throughput to extend the Shannon limit is to view the
MIMO channel as a set of uncorrelated data streams in the downlink direction.
This technique, known as spatial multiplexing, increases the bandwidth by using multiple channels.
• Spatial multiplexing uses multipath fading as an asset by taking advantage of how the fading
environment changes the signal at each receiver to use the delay spread across multiple antennas
to create unique channels. The environment in effect becomes the “code” which spreads the signal
in the frequency.
• Using the knowledge of the communications channel, a receiver recovers independent streams
from each of the transmitter's antennas.
• The overall capacity increase can then be viewed as the sum of the individual capacities.
• Spatial Multiplexing Gain is the min(NT, NR). For a 2 x 2 MIMO system, the maximum SMG
achievable is 2.
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28
The MIMO Channel – How Does
it Work?
To illustrate how the MIMO channel uses multi-path to be able to discriminate among
differing data streams and improve signal throughput, consider a 2 x 2 MIMO channel.
Let’s use the analogy of a piano player striking (and sustaining) playing a chord consisting
of 5 notes with the left hand and another chord consisting of another 5 different notes with
the right hand at the same time.
• Think of the individual notes as resource elements and each chord as a symbol.
• The chord played by the left hand is transmitted from transmit antenna A.
• The chord played by the left hand is transmitted from transmit antenna B.
• Assume that the propagation path from transmit antenna A results in 3 multi-paths
• Assume that the propagation path from transmit antenna B results in 4 multi-paths
The following animation illustrates how the arrival of each multi-path results in a
detectable power change for either symbol through constructive or destructive
interference
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Multi-Path Animation
Initially, each receiver hears all the notes and
is unable to determine which chord (symbol)
each belongs to
Relative signal strength
Based on the changes to the signal strength of the notes,
the receiver is able to separate out the notes into
individual chords (symbols)
T1 direct path
T2 Multi-path A1 arrives
T3 Multi-path B1 arrives
T4 Multi-path A2 arrives
T5 Multi-path B2 arrives
T6 Multi-path B3 arrives
(deconstr.)
T7 Multi-path A3 arrives
T8 Multi-path B4 arrives
Frequency
F1
F1
F2
F2
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F3
F3
F4
F4
F5
F5
F6
F6
F7
F7
F8
F8
F9
F9
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F10
F10
F1, F3, F6, F8 and F10 are parts of
symbol 1
F2, F4, F5, F7 and F9 are parts of
symbol 2
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Conclusions
•
•
•
•
•
•
Shannon’s law still applies, even for MIMO; MIMO extends Shannon due to channel gain characteristics
which support multiple uncorrelated spatial transmission modes by exploiting transmission
environments rich in fading, multipath and scattering.
Transmission environments rich in fading, multipath and scattering offer the most channel gain
whereas environments with a strong line-of-sight (direct) path will exhibit limited MIMO channel
gains.
MIMO systems offer a combination of both diversity and spatial multiplexing gains to increase system
reliability and data throughput.
MIMO is unique in that it can support multiple uncorrelated data streams.
Spatial Multiplexing Gains offer a linear increase (ignoring channel overhead) in the transmission
rate based on the min(NT, NR) for the same bandwidth and with no additional power.
In particular, a 2 x 2 MIMO system produces two spatial streams to effectively double the maximum
data rate of what might be achieved in a traditional SISO communications channel
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31
Radio Wave Reflection & Scattering
•Reflection occurs when radio waves hit an object with large dimensions compared to size of one
wavelength
–Similar to optical reflection from a mirror
–Typical examples are reflections from the earth’s surface, buildings and walls
•Scattering occurs when the area through which a radio wave travels contains objects whose dimensions
are small compared to the size of a wavelength
–Caused by rough surfaces and small objects
–Examples are foliage, street signs, lamp posts
–Scattering may be caused by non-metallic objects
•Penetration Loss occurs when a signal passes through a medium other than air. Loss through many
solid materials as well as apertures are very frequency dependent.
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Radio Wave Diffraction
• May occur when an
object with sharp edges
obstructs the radio path
between a transmitter
and receiver
• Causes bending of the
waves around the
obstruction
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In the real world path loss curves are not strictly
decreasing function. Diffraction and the emergence
from a shadow will sometimes cause signal levels to
rise as distance grows.
Obstruction Diffraction Line of Site
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