3rd lecture block

• Free space propagation equation, what is the power level at a receive antenna, see Media:PropagationConstant.pdf for a more detailed explanation of the terms being used here
• Capacity of mobile and wireless propagation,

Main focus in the previous lectures was on propagation effects. 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 FoU R 3/99, Jan 1999
• H. Holma, A. Toskala (eds.), "WCDMA for UMTS", John Wiley & sons, Oct 2000, selected pages

,

where P is average power

• why talking about noise?
• dB,
• near-far problem

[source: Wikipedia]

• 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”: [bits/s]

with W as system bandwidth, and in case of interference free environment, otherwise , where with as Boltzmann constant and as temperature in Kelvin.

[bits/s]

Exercises

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

UMTS has already good spectrum efficiency with respect to Shannon.

• Modulation schemes like QPSK and 16-QAM are applied to achieve higher bandwidth.
• Higher modulation schemes need a higher signal to noise ration, Why?

Using multiple paths (wave propagation) in a MIMO system to enhance the bandwidth of the system.

Figure: A MIMO equipped laptop (Source:Valenzuela, BLAST project)

Source free environment and free space:

where div is a scalar function

and curl is a vector function

[Source: Wikipedia]

Taking the curl of Maxwell's equation

yields the wave equation:

with m/s

[Source: Wikipedia]

A single frequency electro (E)-magnetic (B) wave is described by

,

,

[Source: Wikipedia]

where

• and so?
• is the imaginary unit
• is the angular frequency, [rad/s]
• is the frequency [1/s]
• is Euler's formula

with the group velocity (free space = speed of light) and
the refraction index

• What is the difference between a static and a dynamic field

• Develop the relations for a plain wave

• Assume a plane wave: . Show that

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

• area of a sphere is
• power transmitted from isotropic antenna is
• antenna area of receiver is
• power received in A_r = P_r

thus

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

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

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

Free space attenuation