ESPTR (English) Signal Processing in Telecommunications and Radar Channel properties
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1 ESPTR (English) Signal Processing in Telecommunications and Radar Channel properties Jacek Misiurewicz Institute of Electronic Systems Warsaw University of Technology Warsaw, Poland
2 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Communications channel Channel (usually) everything between modulator and demodulator: (mainly) the transmission medium (space between antennas, or the connecting cable) (plus:) antennas, amplifiers, cables, waveguides, couplers, optics... Channel properties: Channel bandwidth Channel noise Channel capacity Bandpass channel & equivalent baseband channel
3 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Channel model: noise Model: linear system + added noise; AWGN model Thermal noise (mainly receiver) with white PSD e.g. for room temp. and 10 khz channel ū 2 n = 4k B T R [ V 2 /Hz ] P = k B T f = J/K 300 K 10 4 Hz = W = 134dBm rule: P = log( f )[dbm] Interfering signals (know nothing, assume white (??) not always true!) Outer space Atmospheric ( static ) Man-made (EMC problems computer, broken shaver motor...) impulse noise Other transmissions (unintentional and ECM) (radar only) clutter
4 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Channel model: linear Transmission properties Physical parts characteristics Cable (etc) losses and reflections (standing wave effect) Directional antenna gain G and effective aperture S e f f : S e f f = Gλ2 4π or G = S e f f 4π λ 2 Propagation characteristics, including propagation losses P 1 4πR 2 (one way) note that this is POWER voltage (or field strength) drops as 1/R Multipath propagation self-interference Multipath description: Time domain: impulse response Frequency domain: transfer function (phase is important!) Non-LTI effects: Doppler effect Impulse noise saturating the receiver
5 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Multipath (l2=distance vs. h=tower height), 7GHz, curves for [ ]*lambda/2, flat earth geometry
6 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Effects in baseband Echo (ghosts on TV) Nonuniform frequency characteristics Fading in subchannels Fading at some locations (e.g. when you drive and listen to FM) Fading in some regions with radar (a plane undetected at some range/height combinations) Echo interpretation in telecommunications: inter-symbol interference (ISI): energy from a symbol leaks to the next one Fought with: guard interval waste of time! equalization of channel (note: workload, stability, dynamics...) advanced detectors (ML sequence detector)
7 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Frequency dependence of multipath See the blackboard example: different λ, different interference the same expressed as frequency characteristics of channel
8 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Radar fading Plot points = detections. Note lighter and darker regions.
9 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Rayleigh fading Many paths to a moving receiver (or from a moving transmitter) destructive and constructive interference. Model: multitude of paths, with random amplitude and phase 360deg) summing to complex gaussian distribution. Effect: Rayleigh distribution of received amplitude When moving: Rayleigh distributed changes in amplitude.
10 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Channel capacity With AWGN ( C = Blog S ) N (otherwise: integrate over whole B, with S/N as a function of f, d f )
11 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Doppler effect Transmitted signal: a band-limited envelope x T (t) carrier of frequency F c X T (t) = x T (t) cos(2π jf c t) The received signal at r 0 + vt distance is delayed by t d = r c = r 0+vt c. factor Received carrier Received envelope (r 0 ) phase change delay (v) Doppler shift stretch (dilation) X R (t) = A 0 X T (t t d ) = A 0 x T (t t d ) cos(2π jf c (t t d )) + ξ(t) After the demodulation (baseband received signal): x R (t) = A 0 x T (t t d ) e 2π jf ct d or, putting t d = r 0+vt c Doppler frequency F c v c ; ( A 0 x T (1 v c )t r 0 c ) e 2π jf c r 0 c e 2π jf c vt c stretch factor 1 v c
12 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3, Titan calling (Doppler) (whole story IEEE Spectrum, October Huyghens-Cassini mission to Titan (moon of Saturn). Huyghens - lander Cassini - orbiter, retrasnmitting data to Earth Doppler effect on carrier frequency Doppler effect on data rate & sync (usually neglected, but not for spacecraft...) ( solution: make Cassini orbit perpendicular to the line-of-sight Landing: 14 January 2005
13 ESPTR 2008 Revision : 0.0 LATEXed on April 3, 2014 (image: 12 huygens/posterd H.jpg)
14 ESPTR 2008 Revision : 0.0 LAT E Xed on April 3,
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