|
|
| Line 74: |
Line 74: |
| | Radiowave propagation | | Radiowave propagation |
| | | | |
| − | =⌘ Propagation =
| + | {{:BMWN: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'': <span style="color:#000B80">later today
| + | |
| − | | + | |
| − | == Comments ==
| + | |
| − | [[File:F3-1.png|450px|right]]
| + | |
| − | 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 =
| + | |
| − | * <span style="color:#000B80"> radio wave propagation
| + | |
| − | * <span style="color:#000B80"> Electromagnetic signals
| + | |
| − | * <span style="color:#0B0080"> Nyquist Theorem
| + | |
| − | * <span style="color:#0B0080"> Signal/noise ratio
| + | |
| − | * <span style="color:#0B0080"> Shannon Theorem
| + | |
| − | * <span style="color:#0B0080"> Signal strength
| + | |
| − | | + | |
| − | =⌘ Nyquist Theorem =
| + | |
| − | [[File:BandlimitedSignals.png|450px|right]]
| + | |
| − | * Shannon: If a function <math> f(t) </math> contains no frequencies higher than <math> W </math> [cycles/s], it is completely determinded by giving its ordinates at serires of points spaced <math> \frac{1}{2W} </math> seconds apart
| + | |
| − | | + | |
| − | [[File:InsufficientlySampled.png|450px|right]]
| + | |
| − | * <span style="color:#000B80"> band-limitation versus time-limitation
| + | |
| − | * <span style="color:#000B80"> Fourier transform
| + | |
| − | | + | |
| − | [source: Shannon, 1948]
| + | |
| − | | + | |
| − | =⌘ Signal/noise ratio =
| + | |
| − | <math> \mathrm{SNR} = {P_\mathrm{signal} \over P_\mathrm{noise}} </math>
| + | |
| − | | + | |
| − | <math> \mathrm{SNR (dB)} = 10 \log_{10} \left ( {P_\mathrm{signal} \over P_\mathrm{noise}} \right ) </math>,
| + | |
| − | | + | |
| − | where ''P'' is average power
| + | |
| − | | + | |
| − | * <span style="color:#000B80"> why talking about noise?
| + | |
| − | * <span style="color:#000B80"> dB, <math>\fs2 \mbox{dB}_m,\ \mbox{dB}_a </math>
| + | |
| − | * <span style="color:#000B80"> 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”: <math> C = W\ \mathrm{log}_2(1+P/N) </math> [bits/s]
| + | |
| − | | + | |
| − | with ''W'' as system bandwidth, and <math> P/N = \frac{P}{N_0 W} </math> in case of interference free environment, otherwise <math> N_0 W + N_\mathrm{interference} </math>, where <math>N_0 = k_B T_K</math> with <math>k_B</math> as Boltzmann constant and <math>T_K</math> 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==
| + | |
| − | [[File:F3-2.png|450px|right|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.
| + | |
| − | | + | |
| − | <math> \mbox{Amount of information} = const \cdot BT \cdot \mathrm{log} m </math>
| + | |
| − | * 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=
| + | |
| − | | + | |
| − | <math> C = W\ \mathrm{log}_2(1+P/N) </math> [bits/s]
| + | |
| − | | + | |
| − | Examples
| + | |
| − | * <span style="color:#000B80"> calculate capacity for ''W''= 200 kHz, 3.8 Unik/MHz, 26 Unik/MHz, (all cases P/N = 0 dB, 10 dB, 20 dB)
| + | |
| − | | + | |
| − | == Comments==
| + | |
| − | [[File:F3-3.png|500px|right]]
| + | |
| − | Figure: ''Calculation'' of Shannon capacity for GSM (GPRS, EDGE), UMTS (packet data, HSDPA) and 802.11b
| + | |
| − | | + | |
| − | | + | |
| − | [[File:F3-4.png|450px|right]]
| + | |
| − | 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
| + | |
| − | * <math>dB_m</math> stands for power with respect to 1 mW. <span style="color:#000B80">How much is 0 dB_m and 10 dB_m?
| + | |
| − | * <math>dB_a</math> Power of a sound (or music).
| + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | =⌘ Cell capacity in UMTS =
| + | |
| − | [[File:CapacityUMTS.png|450px|right]]
| + | |
| − | | + | |
| − | UMTS has good efficiency with respect to Shannon
| + | |
| − | | + | |
| − | =⌘ Range versus SNR =
| + | |
| − | [[File:RangeShannon.png|400px|right]]
| + | |
| − | | + | |
| − | <math> R_\mathrm{max}=\mathrm{log}_2(1 + SNR) </math>
| + | |
| − | [Source:Valenzuela, BLAST project]
| + | |
| − | | + | |
| − | == Comments ==
| + | |
| − | [[File:F3-6.png|450px|Range in wireless systems ]]
| + | |
| − | | + | |
| − | [Source Valenzuela, BLAST project]
| + | |
| − | | + | |
| − | <span style="color:#0B0080">why is there no relation to frequency?
| + | |
| − | | + | |
| − | [[File:F3-5.png|200px|right|Relation between bit error rate (BER) and SNR]]
| + | |
| − | | + | |
| − | | + | |
| − | =⌘ Coding and Modulation=
| + | |
| − | A modulated radio signal can be written in a general form:
| + | |
| − | <math> C(t) = A(t) cos(2\pi f(t) t + \varphi(t)) </math>
| + | |
| − | 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. <span style="color:#000B80">examples
| + | |
| − | | + | |
| − | [Source:K.E. Walter, Basics of Mobile Communications]
| + | |
| − | | + | |
| − | == Comments ==
| + | |
| − | [[File:F3-7.png|550px|right]]
| + | |
| − | 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 =
| + | |
| − | [[File:WalterModulation.png|450px|right]]
| + | |
| − | | + | |
| − | * 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 =
| + | |
| − | [[File:WalterMultiplexing.png|450px|right]]
| + | |
| − | | + | |
| − | [[File:WalterGSM.png|450px|right]]
| + | |
| − | | + | |
| − | * 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 =
| + | |
| − | | + | |
| − | <span style="color:#0B0080"> 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 =
| + | |
| − | | + | |
| − | <span style="color:#000B80">Assume a plane wave: <math>E_x, H_y</math>. Show that <math>\frac{E_x}{H_y}=Z_0 = \sqrt{\mu_0/\varepsilon_0}</math>
| + | |
| − | | + | |
| − | <span style="color:#000B80">What is the relation between a plane wave and an omnidirectional wave?
| + | |
| − | | + | |
| − | == Comments ==
| + | |
| − | | + | |
| − | [[File:f3-8.png|450px|right|Calculation of a plane wave, proove that Z_0 = ... = E_x/H_y]]
| + | |
| − | | + | |
| − | | + | |
| − | [[File:f3-9.png|450px|right|Cylindrical, plane and spherical wave]]
| + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | =⌘ Free space propagation=
| + | |
| − | <span style="color:#000B80"> develop propagation equation</span>, see (http://www.antenna-theory.com/basics/friis.php)
| + | |
| − | | + | |
| − | <math> P_r = P_t \ G_t\ G_r\ \left (\frac{\lambda}{4\pi r} \right )^2\cdot </math>
| + | |
| − | | + | |
| − | * <span style="color:#000B80"> convert into dB
| + | |
| − | * <span style="color:#000B80"> provide examples for ''f = ''10 MHz, 1 GHz, 100 GHz
| + | |
| − | * <span style="color:#000B80"> discuss influences on radiation pattern
| + | |
| − |
| + | |
| − | Free space attenuation
| + | |
| − | <math> L = 92,4 + 20 \log(d \mathrm{[km]}) + 20 \log(f \mathrm{[GHz]}) </math>
| + | |
| − | | + | |
| − | == Comments ==
| + | |
| − | [[File:f3-11.png|450px|right]]
| + | |
| − | Figure: Free space propagation from a transmit (''t'') to a receive (''R'') station.
| + | |
| | | | |
| | | | |
| | = Next lecture: [[BMWN:Antennas|Antennas]] = | | = Next lecture: [[BMWN:Antennas|Antennas]] = |
