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 Aug 21. 2019 1 / 36 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 Principles of 5G Network Design Aug 21. 2019 2 / 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 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 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 Aug 21. 2019 3 / 36 Graph theory - motivation Description of flows, interactions and resource assignment • Networks can be described by graphs (nodes and links) 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) 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 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 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 4 / 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 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 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 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 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 5 / 36 Radio basics - Friis’ equation • The isotropic radiation is an idealized omni-directional radiation from a point source C. Larsson Principles of 5G Network Design Aug 21. 2019 6 / 36 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 6 / 36 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 6 / 36 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 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 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 • The effective area can be found to be Ae = C. Larsson Principles of 5G Network Design λ2 4π 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 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 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 7 / 36 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 8 / 36 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 8 / 36 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 9 / 36 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 Aug 21. 2019 9 / 36 Radio basics - path loss > Refraction - layers of different physical or chemical properties changes the path (and speed) of propagation C. Larsson Principles of 5G Network Design Aug 21. 2019 10 / 36 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 10 / 36 Radio basics - path loss > Polarization C. Larsson Principles of 5G Network Design Aug 21. 2019 11 / 36 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 12 / 36 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 13 / 36 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 13 / 36 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 13 / 36 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 13 / 36 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 Aug 21. 2019 14 / 36 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 Aug 21. 2019 15 / 36 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 16 / 36 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 16 / 36 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 16 / 36 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 16 / 36 Radio basics - QAM constellations C. Larsson Principles of 5G Network Design Aug 21. 2019 17 / 36 Radio basics - QAM constellations BPSK 1 bits/symbol :: C. Larsson Principles of 5G Network Design Aug 21. 2019 17 / 36 Radio basics - QAM constellations BPSK 1 bits/symbol :: QPSK 2 bits/symbol (100%) :: C. Larsson Principles of 5G Network Design Aug 21. 2019 17 / 36 Radio basics - QAM constellations BPSK 1 bits/symbol :: QPSK 2 bits/symbol (100%) :: 16-QAM 4 bits/symbol (100%) :: C. Larsson Principles of 5G Network Design Aug 21. 2019 17 / 36 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 17 / 36 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 17 / 36 Radio basics - 16-QAM C. Larsson Principles of 5G Network Design Aug 21. 2019 18 / 36 Radio basics - inverse FFT C. Larsson Principles of 5G Network Design Aug 21. 2019 19 / 36 Radio basics - modulation C. Larsson Principles of 5G Network Design Aug 21. 2019 20 / 36 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 C. Larsson Principles of 5G Network Design Aug 21. 2019 21 / 36 Radio basics - signal quality Bottom line Conversely, higher throughputs require a better Signal to noise ratio C. Larsson Principles of 5G Network Design Aug 21. 2019 22 / 36 Radio basics - multiple access Multiple access methods (orthogonal) for user capacity C. Larsson Principles of 5G Network Design Aug 21. 2019 23 / 36 Radio basics - OFDM • Orthogonal Frequency Division Multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies C. Larsson Principles of 5G Network Design Aug 21. 2019 24 / 36 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 24 / 36 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 24 / 36 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 24 / 36 Radio basics - OFDM C. Larsson Principles of 5G Network Design Aug 21. 2019 25 / 36 Radio basics - OFDM C. Larsson Principles of 5G Network Design Aug 21. 2019 26 / 36 Radio basics - 5G throughput C. Larsson Principles of 5G Network Design Aug 21. 2019 27 / 36 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 Aug 21. 2019 28 / 36 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 Aug 21. 2019 28 / 36 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 Aug 21. 2019 28 / 36 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 28 / 36 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 28 / 36 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 C. Larsson Principles of 5G Network Design Aug 21. 2019 28 / 36 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 C. Larsson Principles of 5G Network Design Aug 21. 2019 29 / 36 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 C. Larsson Principles of 5G Network Design Aug 21. 2019 29 / 36 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 C. Larsson Principles of 5G Network Design Aug 21. 2019 29 / 36 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 C. Larsson Principles of 5G Network Design Aug 21. 2019 29 / 36 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 C. Larsson Principles of 5G Network Design Aug 21. 2019 29 / 36 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 Aug 21. 2019 30 / 36 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 Aug 21. 2019 30 / 36 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 30 / 36 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 Aug 21. 2019 30 / 36 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 Aug 21. 2019 31 / 36 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 Aug 21. 2019 31 / 36 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 31 / 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 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 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. C. Larsson Principles of 5G Network Design Aug 21. 2019 36 / 36