Wiki for ITS

Radio propagation equation (A4,B1)

Course	UNIK4700, UNIK9700
Title	Radio propagation for mobile and wireless communications
Lecture date	2013/09/13 0915-1200
presented	by Josef Noll
Objective	The objective of this lecture is to explain the principles of radio propagation.
Learning outcomes	What will we learn today Modes of Propagation Free Space Propagation Transmit Power EIRP Permittivity Permeability Attenuation Reflection, Scattering, Diffraction
Pensum (read before)
References (further info)	References: http://wiki.unik.no/index.php/Courses/UNIK4700signal http://wiki.unik.no/index.php/Courses/UNIK4700?action=download&upname=PROPAGASJON.pdf http://wiki.unik.no/index.php/Courses/UNIK4700propagation Media:PropagationConstant.pdf
Keywords	Propagation, Free space attenuation, propagation equation, transmit power, Attenuation, Permittivity, Permeability, EIRP, Reflection, Diffraction, Scattering

this page was created by Special:FormEdit/Lecture, and can be edited by Special:FormEdit/Lecture/Radio propagation equation (A4,B1).

Test yourself, answer these questions

Convert to dB, dBm: Pr = Pt . Gt . Gr . L(free)
What is the exact difference between permeability and permittivity?
What is Relative permittivity? and Relative Permeability?
Define Propagation constant

Lecture notes

Discussions from earlier years

How much is 0 dB_m and 10 dB_m?

Convert dBm to mW is: mW = 10^(x/10), x = number of dBm
Convert mW to dBm is: dBm = 10*log10(y), y = number of mW

So you get:

0 dBm = 10^(0/10) = 1 mW
10 dBm = 10^(10/10) = 10 mW

Power received in an area in a distance R from transmitter:

area of a sphere is $A_s = 4*\pi*R^2$
power transmitted from isotropic antenna is $P_t$
antenna area of receiver is $A_r$
power received in A_r = P_r

$P_r = P_t * A_r / A_s = P_r = P_t * A_r / (4*\pi*R^2)$

Free space propagation Calculation: http://spreadsheets.google.com/pub?key=p0EyjWrbirGKJXK43uluJfg Josef, check numbers in spreadsheet

Slide Show

Title: UNIK4700/UNIK9700 Signal and Capacity
Author: Josef Noll,
Footer: Radio propagation equation (A4,B1)
Subfooter: UNIK4700/UNIK9700

⌘ UNIK 4700: Radio & Mobility

3rd lecture block

Radiowave propagation

⌘ Propagation

Main focus in this lecture is on propagation effect. We will first repeat the main conclusions from last lecture on electromagnetic signals, and then introduce the capacity of a system based on Shannon's theorem.

New literature:

J. Noll, K. Baltzersen, A. Meiling, F. Paint , K. Passoja, B. H. Pedersen, M. Pettersen, S. Svaet, F. Aanvik, G. O. Lauritzen. '3rd generation access network considerations'. selected pages from Unik/FoU R 3/99, Jan 1999 (.pdf]])
H. Holma, A. Toskala (eds.), "WCDMA for UMTS", John Wiley & sons, Oct 2000, selected pages

⌘ Left over discussions

Bandwidth separation between signals and adjacent channel separation (ACS) [Holma2000, p183]. ACS requirements 33 dB. Measurements performed by [Potman et.al. ]
E versus B: later today

Comments

Figure: Illustrating reduction of capacity in network A (top) and blinding of phones in cell (B)

More detailed discussions on these effects can be found in the literature indicated above.

⌘ Summary

radio wave propagation
Electromagnetic signals
Nyquist Theorem
Signal/noise ratio
Shannon Theorem
Signal strength

⌘ Nyquist Theorem

Shannon: If a function $f(t)$ contains no frequencies higher than $W$ [cycles/s], it is completely determinded by giving its ordinates at serires of points spaced $\frac{1}{2W}$ seconds apart

band-limitation versus time-limitation
Fourier transform

[source: Shannon, 1948]

⌘ Signal/noise ratio

$\mathrm{SNR} = {P_\mathrm{signal} \over P_\mathrm{noise}}$

$\mathrm{SNR (dB)} = 10 \log_{10} \left ( {P_\mathrm{signal} \over P_\mathrm{noise}} \right )$ ,

where P is average power

why talking about noise?
dB, $\fs2 \mbox{dB}_m,\ \mbox{dB}_a$
near-far problem

[source: Wikipedia]

⌘ Shannon Theorem

The fundamental theorem of information theory, or just Shannon's theorem, was first presented by Claude Shannon in 1948.
Given a noisy channel with channel capacity C and information transmitted at a rate R, then if R < C there exist codes that allow the probability of error at the receiver to be made arbitrarily small. This means that theoretically, it is possible to transmit information nearly without error at any rate below a limiting rate, C.

See File:LarsLundheim-Telektronikk2002.pdf: The channel capacity of a band-limited information transmission channel with additive white, Gaussian noise. This capacity is given by an expression often known as “Shannon’s formula”: $C = W\ \mathrm{log}_2(1+P/N)$ [bits/s]

with W as system bandwidth, and $P/N = \frac{P}{N_0 W}$ in case of interference free environment, otherwise $N_0 W + N_\mathrm{interference}$ , where $N_0 = k_B T_K$ with $k_B$ as Boltzmann constant and $T_K$ as temperature in Kelvin.

Exercises:

If the SNR is 20 dB, and the bandwidth available is 4 kHz, what is the capacity of the channel?
If it is required to transmit at 50 kbit/s, and a bandwidth of 1 MHz is used, what is the minimum S/N required for the transmission?

[source: Wikipedia, Telektronikk 2002]

Comments

Shannon theorem and application to radio propagation

⌘ Hartley's law

The amount of information that may be transmitted over a system is proportional to the bandwidth of that system.

$\mbox{Amount of information} = const \cdot BT \cdot \mathrm{log} m$

where m is the “number of current values”, which in modern terms would be called “the size of the signalling alphabet”

Why did it take twenty years to fill the gap between Hartley’s law and Shannon’s formula? The only necessary step was to substitute 1+C/N for m in Hartley's law. Why, all of a sudden, did three or more people independently “see the light” almost at the same time? Why did neither Nyquist, nor Hartley or Küpfmüller realize that noise, or more precisely the signal-to-noise ratio play as significant a role for the information transfer capacity of a system as does the bandwidth?

[source: L. Lundheim, Telektronikk 2002]

⌘ Shannon - examples

$C = W\ \mathrm{log}_2(1+P/N)$ [bits/s]

Examples

calculate capacity for W= 200 kHz, 3.8 Unik/MHz, 26 Unik/MHz, (all cases P/N = 0 dB, 10 dB, 20 dB)

Comments

Figure: Calculation of Shannon capacity for GSM (GPRS, EDGE), UMTS (packet data, HSDPA) and 802.11b

Figure: Log_10 funtion and related power. The power expressed in dB is 10 times the log_10 of the normalised power.

There are also the abbreviations

$dB_m$ stands for power with respect to 1 mW. How much is 0 dB_m and 10 dB_m?
$dB_a$ Power of a sound (or music).

⌘ Cell capacity in UMTS

UMTS has good efficiency with respect to Shannon

⌘ Range versus SNR

$R_\mathrm{max}=\mathrm{log}_2(1 + SNR)$ [Source:Valenzuela, BLAST project]

Comments

[Source Valenzuela, BLAST project]

why is there no relation to frequency?

Relation between bit error rate (BER) and SNR

⌘ Coding and Modulation

A modulated radio signal can be written in a general form: $C(t) = A(t) cos(2\pi f(t) t + \varphi(t))$ Any of these three parameters can be varied: amplitude-, frequency- or phase-modulation.

Channel-coding is used to reduce bit-error-rate, e.g. through forward error correction.
Multiplexing is used to split the total amount of radio into smaller pieces. Typical: time, frequency or code multiplex. examples

[Source:K.E. Walter, Basics of Mobile Communications]

Comments

Figure: A frequency band consists of n channels.

Example GSM: the upload band is from 880-915 Unik/MHz, which is 35 Unik/MHz. With a carrier of 200 kHz we have 175 channels, which have to be divided between the various operators.

⌘ Modulation types

Amplitude shift keying (ASK)
Frequency shift keying (FSK)
Phase shift keying (PSK)

[Source:K.E. Walter, Basics of Mobile Communications]

⌘ Frequency and time division multiplexing

Time domain, e.g. 8 slots in GSM
Frequency domain, e.g. up- and downlink in specific bands
Code division (CDM), specific codes

[Source:K.E. Walter, Basics of Mobile Communications]

⌘ Code division multiple access

UMTS as an example (in one of the future lectures)

room for Comments

⌘ Propagation and absorption

Free space loss
Antenna types
Radiation patterns
Antenna gain
basic propagation models (ground wave, sky wave and line of sight (Unik/LoS) propagation)
optical vs radio Unik/LoS
attenuation (free space)
Noise (thermal, intermodulation, crosstaal, impulse noise)
Atmospheric absorption
Multipath propagation
refraction, reflection, diffraktion and scattering
fading (fast, slow, flat, selective, rayleigh, rician,..)

⌘ Recall: Plane wave propagation

Assume a plane wave: $E_x, H_y$ . Show that $\frac{E_x}{H_y}=Z_0 = \sqrt{\mu_0/\varepsilon_0}$

What is the relation between a plane wave and an omnidirectional wave?

Comments

Calculation of a plane wave, proove that Z_0 = ... = E_x/H_y

⌘ Free space propagation

develop propagation equation, see (http://www.antenna-theory.com/basics/friis.php)

$P_r = P_t \ G_t\ G_r\ \left (\frac{\lambda}{4\pi r} \right )^2\cdot$

convert into dB
provide examples for f = 10 MHz, 1 GHz, 100 GHz
discuss influences on radiation pattern

Free space attenuation $L = 92,4 + 20 \log(d \mathrm{[km]}) + 20 \log(f \mathrm{[GHz]})$

Comments

Figure: Free space propagation from a transmit (t) to a receive (R) station.

⌘ Antennas

Antennas and propagation models in next lecture

Radio propagation equation (A4,B1)

Test yourself, answer these questions

Lecture notes

Discussions from earlier years

⌘ UNIK 4700: Radio & Mobility

⌘ Propagation

⌘ Left over discussions

Comments

⌘ Summary

⌘ Nyquist Theorem

⌘ Signal/noise ratio

⌘ Shannon Theorem

Comments

⌘ Hartley's law

⌘ Shannon - examples

Comments

⌘ Cell capacity in UMTS

⌘ Range versus SNR

Comments

⌘ Coding and Modulation

Comments

⌘ Modulation types

⌘ Frequency and time division multiplexing

⌘ Code division multiple access

room for Comments

⌘ Propagation and absorption

⌘ Recall: Plane wave propagation

Comments

⌘ Free space propagation

Comments

⌘ Antennas

Navigation menu

Search