Course Agenda
5G Overview
3. RAN II: Architecture
6. Operations
1. Fundamentals
4. Core I: Topology
7. Big Data and ML
2. RAN I: Interfaces
5. Core II: Flows
8. Edge and IoT
C. Larsson
Principles of 5G Network Design
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Fundamentals
Radio physics and information theory
• Radio communication, basic properties
• Modulation and multiple access
• The Nyquist rate and the Shannon limit
Graph theory
• Shortest paths and minimum spanning trees
• Problem complexity and solution methods
• Design, maximum flows and minimum cuts
Probability theory
• Queueing gains
• Self-similar traffic
• Effective bandwidth
C. Larsson
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Radio physics and information theory - motivation
Description and limitations of physical resources
• Radio communication is subject to environmental factors:
- fading
- reflection
- diffraction
- absorption
- polarization
- scattering
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio physics and information theory - motivation
Description and limitations of physical resources
• Radio communication is subject to environmental factors:
- fading
- reflection
- diffraction
- absorption
- polarization
- scattering
• Different frequency bands exhibit varying degrees of such effects
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
3 / 36
Radio physics and information theory - motivation
Description and limitations of physical resources
• Radio communication is subject to environmental factors:
- fading
- reflection
- diffraction
- absorption
- polarization
- scattering
• Different frequency bands exhibit varying degrees of such effects
• The carrier frequency sets a limit on achievable throughput
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
3 / 36
Radio physics and information theory - motivation
Description and limitations of physical resources
• Radio communication is subject to environmental factors:
- fading
- reflection
- diffraction
- absorption
- polarization
- scattering
• Different frequency bands exhibit varying degrees of such effects
• The carrier frequency sets a limit on achievable throughput
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
3 / 36
Radio physics and information theory - motivation
Description and limitations of physical resources
• Radio communication is subject to environmental factors:
- fading
- reflection
- diffraction
- absorption
- polarization
- scattering
• Different frequency bands exhibit varying degrees of such effects
• The carrier frequency sets a limit on achievable throughput
5G context
5G NR networks needs strong focus on efficient radio planning for cost
efficency, throughput, etc.
C. Larsson
Principles of 5G Network Design
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Graph theory - motivation
Description of flows, interactions and resource assignment
• Networks can be described by graphs (nodes and links)
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Graph theory - motivation
Description of flows, interactions and resource assignment
• Networks can be described by graphs (nodes and links)
• Most design tasks are very hard to solve optimally (NP-complete)
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Graph theory - motivation
Description of flows, interactions and resource assignment
• Networks can be described by graphs (nodes and links)
• Most design tasks are very hard to solve optimally (NP-complete)
• Consequence: there is no known algorithm solving such problems
exactly in "finite" time
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Graph theory - motivation
Description of flows, interactions and resource assignment
• Networks can be described by graphs (nodes and links)
• Most design tasks are very hard to solve optimally (NP-complete)
• Consequence: there is no known algorithm solving such problems
exactly in "finite" time
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
4 / 36
Graph theory - motivation
Description of flows, interactions and resource assignment
• Networks can be described by graphs (nodes and links)
• Most design tasks are very hard to solve optimally (NP-complete)
• Consequence: there is no known algorithm solving such problems
exactly in "finite" time
5G context
High transport reliability is a concern and a requirement: URLLC,
C-RAN, etc.
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Probability theory - motivation
Description of traffic, interactions and assignment problems
• Traffic and failure situations are largely unpredictable and can only
be described by probabilistic models
C. Larsson
Principles of 5G Network Design
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Probability theory - motivation
Description of traffic, interactions and assignment problems
• Traffic and failure situations are largely unpredictable and can only
be described by probabilistic models
• Network performance and QoS/QoE depends on random events
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Probability theory - motivation
Description of traffic, interactions and assignment problems
• Traffic and failure situations are largely unpredictable and can only
be described by probabilistic models
• Network performance and QoS/QoE depends on random events
• Aggregation of (modern) traffic sources shows self-similarity and
long-range dependence, leading to persistent congestion
situations
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Probability theory - motivation
Description of traffic, interactions and assignment problems
• Traffic and failure situations are largely unpredictable and can only
be described by probabilistic models
• Network performance and QoS/QoE depends on random events
• Aggregation of (modern) traffic sources shows self-similarity and
long-range dependence, leading to persistent congestion
situations
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
5 / 36
Probability theory - motivation
Description of traffic, interactions and assignment problems
• Traffic and failure situations are largely unpredictable and can only
be described by probabilistic models
• Network performance and QoS/QoE depends on random events
• Aggregation of (modern) traffic sources shows self-similarity and
long-range dependence, leading to persistent congestion
situations
5G context
Traffic flows require flexible routing for cost efficiency, network slicing,
etc.; Service Level Agreements need to be monitored
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
• The isotropic radiation is an idealized omni-directional radiation
from a point source
C. Larsson
Principles of 5G Network Design
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Radio basics - Friis’ equation
• The isotropic radiation is an idealized omni-directional radiation
from a point source
• By geometry, the power density at any point a distance R from the
PT
is transmitter is p = 4πR
2
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
• The isotropic radiation is an idealized omni-directional radiation
from a point source
• By geometry, the power density at any point a distance R from the
PT
is transmitter is p = 4πR
2
• At a distance (large R), the wave form approaches a plane wave
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
• The receiving antenna has an effective area (aperture) Ae
(lossless isotropic antenna)
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
• The receiving antenna has an effective area (aperture) Ae
(lossless isotropic antenna)
• The received power is proportional to the receiving antenna area,
PT
PR = 4πR
2 Ae
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
• The receiving antenna has an effective area (aperture) Ae
(lossless isotropic antenna)
• The received power is proportional to the receiving antenna area,
PT
PR = 4πR
2 Ae
• The effective area can be found to be Ae =
C. Larsson
Principles of 5G Network Design
λ2
4π
Aug 21. 2019
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Radio basics - Friis’ equation
• The receiving antenna has an effective area (aperture) Ae
(lossless isotropic antenna)
• The received power is proportional to the receiving antenna area,
PT
PR = 4πR
2 Ae
2
λ
• The effective area can be found to be Ae = 4π
• Modifying transmitting and receiving antenna properties give
multiplicative gains GT and GR
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
• The receiving antenna has an effective area (aperture) Ae
(lossless isotropic antenna)
• The received power is proportional to the receiving antenna area,
PT
PR = 4πR
2 Ae
2
λ
• The effective area can be found to be Ae = 4π
• Modifying transmitting and receiving antenna properties give
multiplicative gains GT and GR
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
7 / 36
Radio basics - Friis’ equation
• The receiving antenna has an effective area (aperture) Ae
(lossless isotropic antenna)
• The received power is proportional to the receiving antenna area,
PT
PR = 4πR
2 Ae
2
λ
• The effective area can be found to be Ae = 4π
• Modifying transmitting and receiving antenna properties give
multiplicative gains GT and GR
In a transmitting antenna, the gain describes how well the antenna
converts input power into radio waves headed in a specified direction
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
Suppose we have a radio communication between two points.
The power received at a point PR (idealised to free space and lossless
antennas) is given by Friis’ equation:
PR =
P T G T G R λ2
(4πR)2
(1)
where
• PR received power
• PT transmitted power
• GT antenna gain at transmitter
• GR antenna gain at receiver
• λ wavelength of (carrier) wave
• R distance between transmitting and receiving end points
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Friis’ equation
Suppose we have a radio communication between two points.
The power received at a point PR (idealised to free space and lossless
antennas) is given by Friis’ equation:
PR =
P T G T G R λ2
(4πR)2
(1)
where
• PR received power
• PT transmitted power
• GT antenna gain at transmitter
• GR antenna gain at receiver
• λ wavelength of (carrier) wave
• R distance between transmitting and receiving end points
Bottom line
The power is proportional to the squared ratio of the wavelength to the
distance L ∝ λ2 /R 2
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - path loss
• Reflection - an incident wave on a flat surface changes its path
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - path loss
• Reflection - an incident wave on a flat surface changes its path
• Diffraction - small slits in a conducting plane or sharp edges of
obstacles cause the wave to diverge
C. Larsson
Principles of 5G Network Design
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Radio basics - path loss
> Refraction - layers of different physical or chemical properties
changes the path (and speed) of propagation
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Principles of 5G Network Design
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Radio basics - path loss
> Refraction - layers of different physical or chemical properties
changes the path (and speed) of propagation
> Scattering - small objects cause spreading of the wave energy in
different directions
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - path loss
> Polarization
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Principles of 5G Network Design
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Radio basics - path loss
Bottom line
Multipath fading: Difference in path length and phase lead to local
signal amplification or cancellation. This is a major challenge in radio
communication.
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Direct modes (line-of-sight)
Description and limitations of physical resources
• Line-of-sight refers to radio waves which travel directly in a line
from the transmitting antenna to the receiving antenna
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Direct modes (line-of-sight)
Description and limitations of physical resources
• Line-of-sight refers to radio waves which travel directly in a line
from the transmitting antenna to the receiving antenna
• It does not necessarily require a cleared sight path; at lower
frequencies radio waves can pass through buildings, foliage and
other obstructions
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Direct modes (line-of-sight)
Description and limitations of physical resources
• Line-of-sight refers to radio waves which travel directly in a line
from the transmitting antenna to the receiving antenna
• It does not necessarily require a cleared sight path; at lower
frequencies radio waves can pass through buildings, foliage and
other obstructions
• This is the most common propagation mode at VHF and above,
and the only possible mode at microwave frequencies and above
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Direct modes (line-of-sight)
Description and limitations of physical resources
• Line-of-sight refers to radio waves which travel directly in a line
from the transmitting antenna to the receiving antenna
• It does not necessarily require a cleared sight path; at lower
frequencies radio waves can pass through buildings, foliage and
other obstructions
• This is the most common propagation mode at VHF and above,
and the only possible mode at microwave frequencies and above
• On the surface of the Earth, line of sight propagation is limited by
the visual horizon to about 40 miles (64 km)
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - antennas
"The antenna launches energy from a transmitter into space or pulls it
in from a passing wave for a receiver. Without a suitable, properly
installed antenna, the best transmitter and receiver are useless"
C. Larsson
Principles of 5G Network Design
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Radio basics - modulation
Modulation by amplitude, phase or frequency
Modulation changes the carrier wave slightly in time to represent data.
C. Larsson
Principles of 5G Network Design
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Radio basics - Quadrature amplitude modulation
(QAM)
• QAM sends two digital bit streams, by changing (modulating) the
amplitudes of two carrier waves
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Quadrature amplitude modulation
(QAM)
• QAM sends two digital bit streams, by changing (modulating) the
amplitudes of two carrier waves
• The two carrier waves of the same frequency are out of phase
with each other by 90◦ , a condition known as orthogonality and as
quadrature
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Quadrature amplitude modulation
(QAM)
• QAM sends two digital bit streams, by changing (modulating) the
amplitudes of two carrier waves
• The two carrier waves of the same frequency are out of phase
with each other by 90◦ , a condition known as orthogonality and as
quadrature
• Being the same frequency, the modulated carriers add together,
but can be coherently separated (demodulated) because of their
orthogonality property
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - Quadrature amplitude modulation
(QAM)
• QAM sends two digital bit streams, by changing (modulating) the
amplitudes of two carrier waves
• The two carrier waves of the same frequency are out of phase
with each other by 90◦ , a condition known as orthogonality and as
quadrature
• Being the same frequency, the modulated carriers add together,
but can be coherently separated (demodulated) because of their
orthogonality property
• Another key property is that the modulations are
low-frequency/low-bandwidth waveforms compared to the carrier
frequency, which is known as the narrowband assumption
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - QAM constellations
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - QAM constellations
BPSK 1 bits/symbol ::
C. Larsson
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Radio basics - QAM constellations
BPSK 1 bits/symbol :: QPSK 2 bits/symbol (100%) ::
C. Larsson
Principles of 5G Network Design
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Radio basics - QAM constellations
BPSK 1 bits/symbol :: QPSK 2 bits/symbol (100%) ::
16-QAM 4 bits/symbol (100%) ::
C. Larsson
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Radio basics - QAM constellations
BPSK 1 bits/symbol :: QPSK 2 bits/symbol (100%) ::
16-QAM 4 bits/symbol (100%) :: 64-QAM 6 bits/symbol (50%) ::
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - QAM constellations
BPSK 1 bits/symbol :: QPSK 2 bits/symbol (100%) ::
16-QAM 4 bits/symbol (100%) :: 64-QAM 6 bits/symbol (50%) ::
256-QAM 8 bits/symbol (33%)
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - 16-QAM
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Principles of 5G Network Design
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Radio basics - inverse FFT
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Radio basics - modulation
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Principles of 5G Network Design
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Radio basics - signal quality
Signal-to-Noise Ratio (SNR) and Bit Error Rate (BER)
Bottom line
The lower the SNR, the more error correction is needed which
decreases the effective throughput
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Principles of 5G Network Design
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Radio basics - signal quality
Bottom line
Conversely, higher throughputs require a better Signal to noise ratio
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Radio basics - multiple access
Multiple access methods (orthogonal) for user capacity
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Principles of 5G Network Design
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Radio basics - OFDM
• Orthogonal Frequency Division Multiplexing (OFDM) is a method
of encoding digital data on multiple carrier frequencies
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Principles of 5G Network Design
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Radio basics - OFDM
• Orthogonal Frequency Division Multiplexing (OFDM) is a method
of encoding digital data on multiple carrier frequencies
• Several closely spaced orthogonal sub-carrier signals with
overlapping spectra are emitted to carry data
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - OFDM
• Orthogonal Frequency Division Multiplexing (OFDM) is a method
of encoding digital data on multiple carrier frequencies
• Several closely spaced orthogonal sub-carrier signals with
overlapping spectra are emitted to carry data
• Each sub-carrier (signal) is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or
phase-shift keying) at a low symbol rate
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - OFDM
• Orthogonal Frequency Division Multiplexing (OFDM) is a method
of encoding digital data on multiple carrier frequencies
• Several closely spaced orthogonal sub-carrier signals with
overlapping spectra are emitted to carry data
• Each sub-carrier (signal) is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or
phase-shift keying) at a low symbol rate
• This maintains total data rates similar to conventional
single-carrier
modulation
schemes
the same bandwidth
C. Larsson
Principles
of 5G Networkin
Design
Aug 21. 2019
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Radio basics - OFDM
C. Larsson
Principles of 5G Network Design
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Radio basics - OFDM
C. Larsson
Principles of 5G Network Design
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Radio basics - 5G throughput
C. Larsson
Principles of 5G Network Design
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Radio basics - 5G throughput (3GPP)
• Frequency Range FR1: 450 MHz - 6000 MHz or FR2: 24250 MHz
- 52600 MHz; 3GPP 38.104)
With values in square brackets or default/typical values: 292 MHz
C. Larsson
Principles of 5G Network Design
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Radio basics - 5G throughput (3GPP)
• Frequency Range FR1: 450 MHz - 6000 MHz or FR2: 24250 MHz
- 52600 MHz; 3GPP 38.104)
• Number of aggregated component carriers, J (max 16; 3GPP
38.802) [2]
With values in square brackets or default/typical values: 292 MHz
C. Larsson
Principles of 5G Network Design
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Radio basics - 5G throughput (3GPP)
• Frequency Range FR1: 450 MHz - 6000 MHz or FR2: 24250 MHz
- 52600 MHz; 3GPP 38.104)
• Number of aggregated component carriers, J (max 16; 3GPP
38.802) [2]
(j)
• Maximum number of MIMO layers νLayers (max 8 in DL; 3GPP
38.802) [2]
With values in square brackets or default/typical values: 292 MHz
C. Larsson
Principles of 5G Network Design
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Radio basics - 5G throughput (3GPP)
• Frequency Range FR1: 450 MHz - 6000 MHz or FR2: 24250 MHz
- 52600 MHz; 3GPP 38.104)
• Number of aggregated component carriers, J (max 16; 3GPP
38.802) [2]
(j)
• Maximum number of MIMO layers νLayers (max 8 in DL; 3GPP
38.802) [2]
(j)
• Modulation scheme Qm (max 256QAM - 8 bits; 3GPP 38.804) [6]
With values in square brackets or default/typical values: 292 MHz
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - 5G throughput (3GPP)
• Frequency Range FR1: 450 MHz - 6000 MHz or FR2: 24250 MHz
- 52600 MHz; 3GPP 38.104)
• Number of aggregated component carriers, J (max 16; 3GPP
38.802) [2]
(j)
• Maximum number of MIMO layers νLayers (max 8 in DL; 3GPP
38.802) [2]
(j)
• Modulation scheme Qm (max 256QAM - 8 bits; 3GPP 38.804) [6]
• Scaling factor f (j) (max 1.0; 3GPP 38.306)
With values in square brackets or default/typical values: 292 MHz
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Radio basics - 5G throughput (3GPP)
• Frequency Range FR1: 450 MHz - 6000 MHz or FR2: 24250 MHz
- 52600 MHz; 3GPP 38.104)
• Number of aggregated component carriers, J (max 16; 3GPP
38.802) [2]
(j)
• Maximum number of MIMO layers νLayers (max 8 in DL; 3GPP
38.802) [2]
(j)
• Modulation scheme Qm (max 256QAM - 8 bits; 3GPP 38.804) [6]
• Scaling factor f (j) (max 1.0; 3GPP 38.306)
• Rmax (parity check; max 948/1024 = 0.92578125; 3GPP 38.212)
With values in square brackets or default/typical values: 292 MHz
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Principles of 5G Network Design
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Radio basics - 5G throughput (3GPP)
• Numerology µ - carrier configuration (max 5; 3GPP 38.211) [0]
With values in square brackets or default/typical values: 292 MHz
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Principles of 5G Network Design
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Radio basics - 5G throughput (3GPP)
• Numerology µ - carrier configuration (max 5; 3GPP 38.211) [0]
BW (j),µ
• NPRB
Number of Physical Resource Blocks (PRB) based on
Bandwidth BW (j) and µ (max 100MHz for FR1; 3GPP 38.104)
[106]
With values in square brackets or default/typical values: 292 MHz
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Principles of 5G Network Design
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Radio basics - 5G throughput (3GPP)
• Numerology µ - carrier configuration (max 5; 3GPP 38.211) [0]
BW (j),µ
• NPRB
Number of Physical Resource Blocks (PRB) based on
Bandwidth BW (j) and µ (max 100MHz for FR1; 3GPP 38.104)
[106]
• Overhead for control channels OH (j) (typ. 0.14 DL; 3GPP 38.306)
With values in square brackets or default/typical values: 292 MHz
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Radio basics - 5G throughput (3GPP)
• Numerology µ - carrier configuration (max 5; 3GPP 38.211) [0]
BW (j),µ
• NPRB
Number of Physical Resource Blocks (PRB) based on
Bandwidth BW (j) and µ (max 100MHz for FR1; 3GPP 38.104)
[106]
• Overhead for control channels OH (j) (typ. 0.14 DL; 3GPP 38.306)
• Average OFDM symbol duration in a subframe Tsµ (71.4 · 10−6 s for
µ = 0)
With values in square brackets or default/typical values: 292 MHz
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Radio basics - 5G throughput (3GPP)
• Numerology µ - carrier configuration (max 5; 3GPP 38.211) [0]
BW (j),µ
• NPRB
Number of Physical Resource Blocks (PRB) based on
Bandwidth BW (j) and µ (max 100MHz for FR1; 3GPP 38.104)
[106]
• Overhead for control channels OH (j) (typ. 0.14 DL; 3GPP 38.306)
• Average OFDM symbol duration in a subframe Tsµ (71.4 · 10−6 s for
µ = 0)
• Slots allocated for DL in TDD mode (nDL /14; 3GPP 38.213)
[85.7%]
With values in square brackets or default/typical values: 292 MHz
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Information theory - Nyquist, Hartley and Shannon
The amount of information that can be sent per time unit in a
noisy environment
• How much information can be sent over a (radio) link?
C. Larsson
Principles of 5G Network Design
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Information theory - Nyquist, Hartley and Shannon
The amount of information that can be sent per time unit in a
noisy environment
• How much information can be sent over a (radio) link?
• The Nyquist rate gives an upper limit on the the symbol rate in a
passband channel
C. Larsson
Principles of 5G Network Design
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Information theory - Nyquist, Hartley and Shannon
The amount of information that can be sent per time unit in a
noisy environment
• How much information can be sent over a (radio) link?
• The Nyquist rate gives an upper limit on the the symbol rate in a
passband channel
• Hartley’s law states the maximum line rate of a channel
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Information theory - Nyquist, Hartley and Shannon
The amount of information that can be sent per time unit in a
noisy environment
• How much information can be sent over a (radio) link?
• The Nyquist rate gives an upper limit on the the symbol rate in a
passband channel
• Hartley’s law states the maximum line rate of a channel
• The Shannon limit relates the line rate to a noisy environment
C. Larsson
Principles of 5G Network Design
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Information theory - The Nyquist rate
The Nyquist rate
The Nyquist rate is an upper bound for the symbol rate fS across a
bandwidth-limited baseband channel as twice its bandwidth B,
fS = 2B.
• The carrier wave is a sine wave for almost any communication
system, which exists at only one frequency and therefore occupies
zero bandwidth
C. Larsson
Principles of 5G Network Design
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Information theory - The Nyquist rate
The Nyquist rate
The Nyquist rate is an upper bound for the symbol rate fS across a
bandwidth-limited baseband channel as twice its bandwidth B,
fS = 2B.
• The carrier wave is a sine wave for almost any communication
system, which exists at only one frequency and therefore occupies
zero bandwidth
• As soon as the signal is modulated to transmit information,
however, the bandwidth increases. A detailed knowledge of the
bandwidth of various types of modulated signals is essential to the
understanding of the communication systems
C. Larsson
Principles of 5G Network Design
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Information theory - The Nyquist rate
The Nyquist rate
The Nyquist rate is an upper bound for the symbol rate fS across a
bandwidth-limited baseband channel as twice its bandwidth B,
fS = 2B.
• The carrier wave is a sine wave for almost any communication
system, which exists at only one frequency and therefore occupies
zero bandwidth
• As soon as the signal is modulated to transmit information,
however, the bandwidth increases. A detailed knowledge of the
bandwidth of various types of modulated signals is essential to the
understanding of the communication systems
• In addition, the degrading effect of noise on signals increases with
bandwidth. Therefore, in most communication systems it is
important to conserve bandwidth to the extent possible.
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Information theory - The Nyquist rate
• Frequency division multiplexing (FDM) - move the frequency of the
individual signals up to different frequencies, which share the
channel
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
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Information theory - The Nyquist rate
• Frequency division multiplexing (FDM) - move the frequency of the
individual signals up to different frequencies, which share the
channel
• FDM allows many channels at the same time because each one is
given a different frequency, so they don’t interfere with one another
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
32 / 36
Information theory - The Nyquist rate
• Frequency division multiplexing (FDM) - move the frequency of the
individual signals up to different frequencies, which share the
channel
• FDM allows many channels at the same time because each one is
given a different frequency, so they don’t interfere with one another
• Upconverters convert each baseband signal to a new, higher
frequency by mixing the signal frequency, fCH with a local
oscillator at a much higher frequency fLO , creating a passband
signal at the sum fCH + fLO
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
32 / 36
Information theory - The Nyquist rate
• Frequency division multiplexing (FDM) - move the frequency of the
individual signals up to different frequencies, which share the
channel
• FDM allows many channels at the same time because each one is
given a different frequency, so they don’t interfere with one another
• Upconverters convert each baseband signal to a new, higher
frequency by mixing the signal frequency, fCH with a local
oscillator at a much higher frequency fLO , creating a passband
signal at the sum fCH + fLO
• Downconverters at the receiver mixes the incoming signal at
frequency fCH + fLO with the same local oscillator frequency fLO
C. Larssonthe differencePrinciples
of 5G
Aug 21. 2019
creating
(f +
f Network
) −Design
f = f , converting
the 32 / 36
Radio basics - the Nyquist rate
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
33 / 36
Information theory - Hartley’s law
Hartley’s law
The maximum number of distinguishable pulse levels that can be
transmitted and received reliably over a communications channel is
limited by the dynamic range of the signal amplitude and the precision
with which the receiver can distinguish amplitude levels.
Specifically, if the amplitude of the transmitted signal is restricted to the
range of [−A . . . + A] volts, and the precision of the receiver is ±∆V
volts, then the maximum number of distinct pulses (messages) M is
given by
A
.
M =1+
∆V
• Zero is always one level
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
34 / 36
Information theory - Hartley’s law
Hartley’s law
The maximum number of distinguishable pulse levels that can be
transmitted and received reliably over a communications channel is
limited by the dynamic range of the signal amplitude and the precision
with which the receiver can distinguish amplitude levels.
Specifically, if the amplitude of the transmitted signal is restricted to the
range of [−A . . . + A] volts, and the precision of the receiver is ±∆V
volts, then the maximum number of distinct pulses (messages) M is
given by
A
.
M =1+
∆V
• Zero is always one level
• The alternating current implies that the only the absolute value of
the amplitude can be used
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
34 / 36
Information theory - Hartley’s law
Hartley’s law
The maximum number of distinguishable pulse levels that can be
transmitted and received reliably over a communications channel is
limited by the dynamic range of the signal amplitude and the precision
with which the receiver can distinguish amplitude levels.
Specifically, if the amplitude of the transmitted signal is restricted to the
range of [−A . . . + A] volts, and the precision of the receiver is ±∆V
volts, then the maximum number of distinct pulses (messages) M is
given by
A
.
M =1+
∆V
• Zero is always one level
• The alternating current implies that the only the absolute value of
the amplitude can be used
• The precision of the receiver limits the number of detectable levels
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
34 / 36
Information theory - Hartley’s law
• By taking information per pulse in bit/pulse to be the
base-2-logarithm of the number of distinct messages M that could
be sent, Hartley constructed a measure of the line rate R as:
R = fp log2 (M),
where fp is the pulse rate, also known as the symbol rate, in
symbols/second or baud.
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
35 / 36
Information theory - Hartley’s law
• By taking information per pulse in bit/pulse to be the
base-2-logarithm of the number of distinct messages M that could
be sent, Hartley constructed a measure of the line rate R as:
R = fp log2 (M),
where fp is the pulse rate, also known as the symbol rate, in
symbols/second or baud.
• Hartley then combined the above quantification with Nyquist’s
observation that the number of independent pulses that could be
put through a channel of bandwidth B hertz was 2B pulses per
second, to arrive at his quantitative measure for achievable line
rate.
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
35 / 36
Information theory - Hartley’s law
• By taking information per pulse in bit/pulse to be the
base-2-logarithm of the number of distinct messages M that could
be sent, Hartley constructed a measure of the line rate R as:
R = fp log2 (M),
where fp is the pulse rate, also known as the symbol rate, in
symbols/second or baud.
• Hartley then combined the above quantification with Nyquist’s
observation that the number of independent pulses that could be
put through a channel of bandwidth B hertz was 2B pulses per
second, to arrive at his quantitative measure for achievable line
rate.
• Hartley’s law is sometimes quoted as just a proportionality
between the analog bandwidth, B, in Hertz and what today is
called the digital bandwidth, R, in bit/s or the achievable line rate
of R bits per second
R ≤ 2B log2 (M).
C. Larsson
Principles of 5G Network Design
Aug 21. 2019
35 / 36
Information theory - Hartley’s law
• By taking information per pulse in bit/pulse to be the
base-2-logarithm of the number of distinct messages M that could
be sent, Hartley constructed a measure of the line rate R as:
R = fp log2 (M),
where fp is the pulse rate, also known as the symbol rate, in
symbols/second or baud.
• Hartley then combined the above quantification with Nyquist’s
observation that the number of independent pulses that could be
put through a channel of bandwidth B hertz was 2B pulses per
second, to arrive at his quantitative measure for achievable line
rate.
• Hartley’s law is sometimes quoted as just a proportionality
between the analog bandwidth, B, in Hertz and what today is
called the digital bandwidth, R, in bit/s or the achievable line rate
of R bits per second
R ≤ 2B log2 (M).
C. Larsson
Principles
of 5G Network
Aug 21. 2019
35 / 36
• Hartley
did not work out
exactly
howDesign
the number M should
depend
Information theory - The Shannon-Hartley equation
The Shannon-Hartley equation
The Shannon-Hartley equation relates the maximum capacity
(transmission bit rate) that can be achieved over a given channel with
certain noise characteristics and bandwidth. For an AWGN the
maximum capacity is given by
C = B log2 (1 + S/N),
where S/N is the signal to noise ratio.
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Principles of 5G Network Design
Aug 21. 2019
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