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4.3 Small Scale Path Measurements

4.3 Small Scale Path Measurements multipath structure used to determine small-scale fading effects Classification of Techniques for Wideband Channel Sounding (1) direct pulse (2) spread spectrum sliding correlator (3) swept frequency measurements. T REP. Pulse Gen. f c. BW = 2/ T bb.

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4.3 Small Scale Path Measurements

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  1. 4.3 Small Scale Path Measurements • multipath structure used to determine small-scale fading effects • Classification of Techniques for Wideband Channel Sounding • (1) direct pulse • (2) spread spectrum sliding correlator • (3) swept frequency measurements

  2. TREP Pulse Gen fc BW = 2/Tbb Tx Rx Storage O-Scope Detector Tbb • 4.3.1: Direct RF Pulse System to measure channel impulse response • simple & cheap channel sounding approach - quickly determine PDP • fundamentally a wide-band pulsed bistatic radar • transmit probing pulse, p(t) with time duration = Tbb • receiver uses wideband filter, BW = 2/ Tbb Hz • - envelope detector used to amplify & detect received signal • - results displayed or stored Tbb = minimum resolvable delay between MPCs e.g. let Tbb = 1ns  BW = 2GHz & minimum resolvable delay = 1ns

  3. r(t)= direct pulse measurement yields immediate measure of |r(t)2|, where r(t) is given by set o-scope to averaging mode  system provides local average PDP • main problems: • wide passband filter  subject to interference & noise • o-scope must trigger on 1st arriving signal, if 1st signal blocked or • fades severely  system may not trigger properly • envelope detector doesn’t indicate phase of individual MPCs • - coherent detector would permit phase measurements

  4. Rx Chip Clock = β(Hz) Tx fc Rx Storage O-Scope Detector at fc PN Gen BW2Rc narrowband filter resolution Rc-1 (rms pulse width) wideband filter correlation BW BW2(-) Tx Chip Clock Rc = (Hz) PNGen • 4.3.2 Spread Spectrum (SS) Sliding Correlator Sounding • probe signal is still wideband • possible to detect transmitted signal using narrowband receiver, • preceded by wideband mixer • improved dynamic range compared to pulsed RF system System to Measure SS Channel Response • SS: carrier  PN sequence  spreads signal over large bandwidth • Tc= chip duration • Rc= chip rate = Tc-1

  5. (1) SS signal generated by transmitter using some PN code • (2) received SS signal is filtered & despread using identical PN code • (3) sliding correlator implemented by using slightly slower chipping • rate on receiver – causes periodic maximum correlation • (i) Tx PN Generator clock is slightly faster than Rx clock • (ii) when faster PN generator catches slower PN generator  near • identical alignment & maximal correlation • (iii) when two sequences are not maximally correlated • spread signal mixed with unsynchronized receiver chip sequence • signal is spread into bandwidth  receivers reference PN sequence • narrowband filter following correlator rejects almost all incoming • signal power

  6. Sliding Correlator & SS approach enables receiver to • reject passband interference (advantage over RF pulse sounding) • realize significant processing gain (PG) power spectrum envelope of transmitted signal given by (4.26) S(f) = = null-to-null bandwidth given as: BWnull = 2Rc (4.27) PG = (4.28)

  7. For Sliding Correlator Rbb = -  • Rbb= baseband information rate (Tbb= baseband information period) •  - = frequency offset of transmit & receive PN clocks • (i)when incoming signal is correlated with receiver PN sequence • - signal collapses back into original bandwidth (despread) • - the envelope is detected & displayed • (ii) different incoming multipaths have different delays • - energy in individual paths will pass through correlator at • different times • - multipaths will maximally correlate at different times • (iii) after envelope detection - channel impulse response convolved • with pulse shape of single chip is displayed on o-scope

  8. minimal delay between resolvable MPCs =2Tc • if 2 MPCs are < 2Tc apart  can’t be resolved 2Tc 1.5Tc Time Resolution of MPCs (width of excess delay bin) given by  = 2Tc = 2/Rc (4.29) • Sliding Correlation Process provides equivalent time measurements • updated each time 2 sequences are maximally correlated • Time Between Maximal Correlations is given by • T = Tc l (4.30) • Tc = chip period= Rc-1 •  = /- , slide factor (dimensionless) • l = 2n-1, chip sequence length (n bit m-sequence, ) Time Between Updates= 2T

  9. actual propagation time = (4.33) • incoming signal is mixed on receiver with slower PN sequence • information transfer rate to o-scope = - • - relative rate of 2 PN sequences • signal essentially down-converted (collapsed) to low frequency, • narrow band signal • - narrowband signal allows narrow band processing • - eliminates passband noise & interference • PG realized using narrowband filter with BW = 2(-) • equivalent time measurements refer to relative times of MPCs as • they are displayed on o-scope • using sliding correlator, observed time scale on o-scope relates to • actual propagation time scale

  10. PNseq =Tcl (4.34) • Time Dilation effect due to relative information transfer rate in sliding • correlator • Tc of 4.30 is observed time, not actual propagation time • actual propagation delays are expanded by sliding correlator • must ensure that PNseq > longest multipath delay PN sequence periodgiven by estimated maximum unambiguous range of incoming MPCs is given by PNseq· 3108m/s

  11. SS technique can reject passband noise – improving coverage range • for given transmit power • Sliding Correlator eliminates explicit Tx-Rx PN code • synchronization • However, measurements are not real-time, but derived as PN codes • slide by each other - may require excessive time to measure PDP

  12. Vector Network Analyzer with Swept Frequency Oscillator Rx Tx X(w) port 1 Y(w) port 2 S-Parameter Test-Set S21(w)  H(w) = Y(w)/X(w) IFT h(t) = F-1[H(w)] Frequency Domain Channel Sounding System • 4.3.3 Frequency Domain Channel Sounding • vector network analyzer controls synthesized frequency sweeper • S-parameter test-set monitors channel frequency response • sweeper scans specified frequency band (centered on a carrier) • - steps through discrete frequencies • - number & spacing of discrete components affects resolution of • impulse response measurement

  13. For each frequency step the S-parameter test-set • transmits known signal on port 1 • monitorsreceived signal on port 2 • Network Analyzer processes signal levels to determine complex • response of the channel over the measured frequency give as • S21(w) H(w) • - S21(w) = transmissivity • - transmissivity response is frequency domain representation of • channel impulse response • - IFT used to convert back to time domain • Works well for short ranges if carefully calibrated & synchronized

  14. 4.4 Multipath Channel Parameters • Power Delay Profile (PDP) is measured using techniques discussed • in section 4.3 • several parameters are derived from PDP given in(4.18) • represented as plots of relative received poweras a function of • excess delay with respect to fixed time delay reference • average small-scale PDP found by averaging many samples of • instantaneous PDP measured over local area

  15. Small Scale Sampling mustavoid large scale averaging bias in resulting small-scale statistics • Spatial Separations of samples  ¼ , depending on • (i) time resolutionof probing pulse • (ii) type of multipath channels (indoor, outdoor,…) • e.g. at 2.4GHz   = 125mm and ¼   31mm  1.25 inches • Receiver Movement Ranges: range at which measurements will be • consistent • Indoor channels, 450MHz-6GHz range •  sample over receiver movement < 2m • Outdoor channels •  sample over receiver movement < 6m

  16. -85 -90 -95 -100 -105 -110 -115 Received Signal Level (dBm per 40ns) 0 10 20 30 40 50 60 70 80 90 100 Excess Delay Time(us) Plots show typical PDP from outdoor & indoor channels determined from many closely sampled instantaneous profiles • 1. Outdoor: 900MHz Cellular System worst-case in San Francisco • Display Threshold = -111.5 dBm per 40ns • RMS delay spread = 22.85us

  17. 10 0 -10 -20 -30 Normalized Receive Power (dB) -50 0 50 150 250 350 450 Excess Delay Time(ns) • 2. Indoor: Grocercy Store at 4GHz • 39.4m path, • 18dB attenuation • 2mV/div, • 100ns/div • 51.7ns RMS • 43.0 dB loss

  18. 18.5m LOS Distance LOS Channel Response 15.4m LOS Distance NLOS Channel Response 3. UWB Impulse Radio – Outdoor-Indutrial , Warren, MI fc = 4.4GHz, B-41dBm = 2GHz (3.1GHz-5.1 GHz) mVDC mVDC

  19. 4.4.1 Time Dispersion Parameters • Parameters that grossly quantify multipath channels are used to • develop general guidelines for wireless systems design • compare different multipath channels • Power Delay Profile used to determine multipath channel parameters • consecutive impulse responsemeasurements collected & averaged • over a local area • averaged measurements based on temporal or spatial averages • typically many measurements made at many local areas • enough to determine statistical range of multipath channel • parameters for mobile system over large scale areas Time-invariant Multipath PDP,P() derived from average of many snapshots of |hb(t,)|2over local area

  20. = mean excess delay X = excess delay spread (X dB ) or maximum excess delay = rms delay spread   •  and are defined from single PDP • typical values for  are us for outdoor & ns for indoor channel Multipath channel parameters determined fromPDP • commonly used to quantify time dispersive properties of wideband • multipath channels Delays are measured relative to 1st detectable signal received at 0 =0 Eqns 4-35 thru 4-37 rely on relative amplitudes of MPCs within P() – not on absolute power level of P()

  21. (4.35) = mean excess delay= 1st moment of PDP  = (4.36) where (4.37)  = rms delay spreadsquare root of 2nd central moment of PDP • X= maximum excess delay (X dB) of the power delay profile • time delay during which multipath energy falls to X db below • maximum (typically X = 10dB)

  22. ,   2, Delay measures, depend on selection of noise threshold • noise threshold used in processing P() to differentiate between • received MPCs and thermal noise • if threshold set too low  noise will be processed as multipath • low threshold gives rise to artificially high delay measures • e.g. maximum excess delay X - 0 • 0 = 1st arriving signal • X = maximum delay at which multipath component is within XdB • of strongest arriving multipath signal • also called excess delay spread • always relevant to threshold relating multipath noise floor to • maximum received multipath component

  23. X = maximum excess delay  = rms delay spread 10 0 -10 -20 -30  = 46.40 ns = mean excess delay  X < 10dB = 84 ns -50 0 50 100 150 200 250 300 350 400 450 Normal Receive Power (dB)  = 45.05 ns noise threshold = -20dB Excess Delay (ns) • indoor power delay profile • maximum excess delay (X) for MPCs within 10dB of maximum • maximum excess delay defines temporal extent of multipath • that is above a threshold

  24. Mobile RF channel • PDP & spectral response (magnitude of frequency response) are • related by Fourier transform • possible to obtain equivalent channel description in frequency • domain using frequency response characteristics • Coherence Bandwidth, Bc • analagous to delay spread parameters • used to characterize channel in the frequency domain •  and Bc are inversely proportional, exact relationship depends on • multipath structure

  25. P() 0dB -10dB 0 1us  mean excess delay: rms delay spread: e.g. 4.4 (a ) Compute RMS delay spread for P() (b) if BPSK used – what is Rb_max without equalizer (within Bc) for BPSK, normalized rms delay spread: d = if Ts 5us  Rs 200ksps and Rb 200kbps

  26. Fading 100% 90% Signal Level Bc f • 4.4.2 Coherence Bandwidth,Bc • Delay Spread is caused by reflected & scattered propagation paths • Bc is a defined relation derived from (rms delay spread) • statistical measure of frequency range over which channel is • considered flat • channel passes all spectral components with approximately equal • gain & linear phase • e.g. frequency range over which 2 frequency components have • strong potential for amplitude correlation • Consider 2 sinusoids with frequency f1 and f2and fs = f2 – f1 • - if fs > Bc signals are affected by channel very differently • - if fs < Bc signals are affected by channel nearly the same

  27. Bc bandwidth related to frequency correlation function (FRC) estimated relationship between Bc &  larger delay spreads  smaller coherence bandwidth • spectral analysis &simulation required to determine exact impact of • multipath fading on particular signal • accurate multipath channel models are used in designing specific modems

  28. Pr() 0dB -10dB -20dB -30dB X = maximum excess delay  = rms delay spread  = mean excess delay 0 1 2 3 4 5  (us)  = (100)5 + (10-1)1 + (10-1)2 + (10-2)(0) = 4.38 us (100) + (10-1) + (10-1) + (10-2)  2 = (100)52 + (10-1)12 + (10-1)22 + (10-2)(0)2 = 21.07 us2 (100) + (10-1) + (10-1) + (10-2) = 1.37 us = e.g. 4.4: determine Bc= (5·1.37us)-1 = 146kHz (for FRC > 0.5) • AMPS requires 30kHz bandwidth  equalizer not required • GSM requires 200kHz bandwidth  equalizer required

  29. Coherence Time, TC • characterizes time varying nature of channel’s frequency dispersion • time domain dual of BD and is inversely proportional to BD • statistical measure of interval when channel impulse response is invariant - quantifies similarity of channel response at different times - time interval when 2 signals have strong potential for amplitude correlation 4.4.3 Doppler Spread and Coherence Time • Doppler Spectrum = received signal spectrum with range of fc fd • fc= transmitted sinusoid wave • fd = Doppler shift - function of relative velocity & angle of incidence • Doppler Spread, BD = measure of spectral broadening at receiver • implies motion  Doppler spectrum  0 • if baseband signal bandwidth, BS>> BD BD is negligible

  30. One measure of TCis given in terms of maximum Doppler shift • assumes angle of incidence between Tx and Rx= 0 > TC • fm = v/ is maximum Doppler shift (4.40)a TC (i) If magnitude of baseband signal bandwidth < coherence time • channel varies during baseband signal transmission • results in distortion at the receiver

  31. TC (4.40b) (ii) if TC is defined as interval when time correlation function > 0.5 then e.g. assume v = 100m/s

  32. TC (4.40c) (iii) in Digital communications TC is often defined as geometric mean of 4.40a & 4.40b • 4.40a = time duration when Rayleigh fading signal can have wide • fluctuations • 4.40b - often too restrictive • Definition of TC implies if 2 signals arrive at t1 & t2 with ts = t2-t1 • if ts> TC both are affected differently by channel • if ts< TC both are affected approximately the same

  33. e.g. v = 60mph (27.8 m/s) and fc= 900MHz • Determine distortion due to motion • (i) determine TC from one of the equations • (ii) determine maximum symbol rate, RS for no distortion • RS > • conservative value obtained from 4.40b  TC = 2.2ms (454 Hz)-1 • if RS≥ 454 symbols/sec  signal won’t distort from motion • value from 4.44c  TC = 6.77ms (150 Hz)-1 • if RS > 150 symbols/sec  signal won’t distort from motion • any signal could still distort from multipath delay spread

  34. TC = 565us • number of samples over 10m = NX = 10/ x = 708 samples • time required to make measurements = x/v = 0.2s • Doppler Spread:BD = fm = v/ = 316Hz • e.g. 4.5: require that consecutive samples are highly correlated in time • fc= 1900 MHz   = 0.158m • v = 50m/s • x = 10m is travel distance evaluated • Determine proper spatial sampling interval to make small-scale • propagation measurements • for high correlation in time, ensure sample interval = TC/2 • - using conservative TC  - temporal sampling interval  282 us - spatial sampling interval: x = vTC/2 = 1.41cm

  35. if frequency correlation > 90% then Bc≈ if time correlation> 50% then TC Small-Scale time/frequency dispersive nature of RF channel • i. propagation effects (scattering, reflections) described by • delay spread (e.g. ) • Bc = coherence bandwidth (spectral components affected the same) • ii. effects from motion of transceiver or objects described by • Doppler spread, BD  fm • Coherence time, TC (temporal components affected the same)

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