Mob 2 wireless transmission 2010

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Wireless Transmissions       frequencies & regulations signals   Signal   Signal propagation   Antennas,   Link budget multiplexing, modulation, spread spectrum, cellular systems Analog and Digital Message     Message = data that a user wants to transmit Analog message –  –  Set of continuous values and time ex : voice, video, sensor collected data x(t) t   Digital message –  –  Discrete time, set of discret values ex : text, integer 010001100… 2 Internet & Mobile Communications - 2009 Analog versus Digital Signal   Signals are the physical representations of the message to transmit. –  –  –  They usually exist as an electrical value (voltage, intensity) that can then be converted into an electric or electromagnetic form for transmission Analog signal: signal that represents a analog message Digital signal: signal resulting from a digital message   It is represented as a succession of wave forms that can take one value among a given and finite set of possibilities 3 Internet & Mobile Communications - 2009 Signal transmission any signal is composed of several frequential components. For a periodic signal these components are all multiple of the fundamental frequency f.. –  Example : s(t ) = sin(2πft )+ s1(t) = sin(2Πft) 1 sin 2π (3 f )t 3 s2(t) = 1/3 sin(2Π(3f)t) ( ) s(t) = s1(t) +s2(t) 4 Internet & Mobile Communications - 2009 Signal transmission   19th century : Fourier shows that a simple periodic function g(t) can be decomposed into a sum of sine and cosine with q fundamental freauency of f= n/T ∞ ∞ 1 g (t ) = c + ∑ an sin (2π n f t )+ ∑ bn cos(2π n f t ) 2 n =1 n =1 –  5 an and bn are the sine and cosine of the nth harmonics (terms). T 2 an = g (t ) sin( 2π n f t ) dt The amplitudes of T ∫ 0 an,bn and c for a given T 2 bn = g (t ) cos( 2π n f t ) dt ∫ function g(t) are : T 0 2 c = T T ∫ g (t )dt 0 Internet & Mobile Communications - 2009 Signal transmission   Example : –  Let’s consider the transmission of “b” coded with the following 8 bits : “01100010” 6 Internet & Mobile Communications - 2009 Signal transmission 7 Internet & Mobile Communications - 2009 Signal transmission –  b coded with 8 bits : “01100010” an = 1   π n  3π n   6π n   7π n   cos − cos + cos − cos          4   4   4   π n   4  bn = 1   3π n   π n  7π n   6π n   sin − sin + sin − sin          4   4   4   π n   4  c= 3 4 the frequency spectrum associated to a given periodic function is the comb spectrum. Each ray of the comb corresponds to the amplitude of each harmonic. 8 Internet & Mobile Communications - 2009 Signal transmission 9 Internet & Mobile Communications - 2009 Data signal characterisation –  –  –  Spectral support of the signal is the set of frequencies it uses Spectral support at n dB Bandwidth is the width of the support ^ 2 x( f ) Max Max/2 F 0 c f LB à 3 dB 10 Internet & Mobile Communications - 2009 Maximum data rate of a channel   Shannon’s law –  Shows the existence of a fundamental limit of the transmission rate beyond which it is not possibe to transmit without error C = B . log2 (1 + PS/PN) C maximum theoritical capacity of the channel (bit/s)   B bandwidth of the channel (Hz)   PS/PN signal to noise ratio (Power of the signal over the power of the noise)   S/N = 10 . log10 (PS/PN) S/N in dB   11 Internet & Mobile Communications - 2009 Maximum data rate of a channel   Example: –  Bandwidth= 3KHz, Noise= 30 dB What is the maximum capacity on that channel ? Solution: 10 log10(S/N) = 30 dB <=> S/N = 103 Capacity = 3000. log2 (1+S/N) = 30000 bit/s 12 Internet & Mobile Communications - 2009 Maximum data rate of a channel   Nyquist’s theorem –  On a noiseless channel the maximum data rate is limited Maximum data rate = 2 B Log2 V (bit/s) With V number of discrete values of the signal –  Example : Bandwidth= 3KHz, Noise= 30 dB What is the maximum capacity on that channel for a binary signal ? … when the valence is 8 ? 13 Internet & Mobile Communications - 2009 Signal propagation ranges   Transmission range –  –    Detection range –  –    communication possible low error rate detection of the signal possible no communication possible Interference range –  –  signal may not be detected signal adds to the background noise sender transmission distance detection interference 14 Internet & Mobile Communications - 2009 Signal Propagation               15   Propagation in free space always like light (straight line) Receiving power proportional to 1/d² (d = distance between sender and receiver) Receiving power additionally influenced by fading (frequency dependent) shadowing reflection at large obstacles scattering scattering at small obstacles diffraction diffraction at edges Internet & Mobile Communications - 2009 reflection Example in the real world 16 Internet & Mobile Communications - 2009 Multi path Propagation signal transmitted Signal received       Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction Time dispersion: signal is dispersed over time  interference with “neighbor” symbols, Inter Symbol Interference (ISI) The signal reaches a receiver directly and phase shifted  distorted signal depending on the phases of the different parts 17 Internet & Mobile Communications - 2009 Effects of mobility   Channel characteristics change over time and location –  –  –  signal paths change different delay variations of different signal parts different phases of signal parts    quick changes in the power received (rapid fading)   Additional changes in –  –    puissance distance to sender obstacles further away long term fading  slow changes in the average power received (long term fading) short term fading 18 Internet & Mobile Communications - 2009 t Effects of mobility   Doppler-Fizeau effect -  The Doppler effect, named after Christian Doppler, is the change in frequency and wavelength of a wave that is perceived by an observer moving relative to the source of the waves. 19 Internet & Mobile Communications - 2009 Antennas: isotropic radiator     Radiation and reception of electromagnetic waves, coupling of wires to space for radio transmission Isotropic radiator: equal radiation in all directions (three dimensional) only a theoretical reference antenna y z z y x x     ideal isotropic radiator Real antennas always have directive effects (vertically and/or horizontally) Radiation pattern: measurement of radiation around an antenna 20 Internet & Mobile Communications - 2009
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