4.3 Small Scale Path Measurements
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Transcript of 4.3 Small Scale Path Measurements
04/19/23
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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
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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
BW = 2/TbbTbb
TREP
Detector StorageO-Scope
RxTx
PulseGen
fc
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set o-scope to averaging mode system provides local average PDP
r(t)= )(
2
1 1
0i
N
i
iji tpe
direct pulse measurement yields immediate measure of |r(t)2|, where r(t) is given by
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
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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
SS: carrier PN sequence spreads signal over large bandwidth• Tc = chip duration• Rc = chip rate = Tc
-1
Tx
PN Gen
Tx Chip ClockRc = (Hz)
fc RxPNGen
Rx Chip Clock = β(Hz)
correlation BWBW2(-)
resolution Rc-1
(rms pulse width)BW2R
cwideband filter
Detectorat fc
StorageO-Scope
narrowband filter
System to Measure SS Channel Response
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(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
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Sliding Correlator & SS approach enables receiver to • reject passband interference (advantage over RF pulse sounding)• realize significant processing gain (PG)
PG = (4.28) in
out
c
bb
bb
c
NS
NS
T
T
R
R
)/(
)/(22
(4.27)
null-to-null bandwidth given as:
BWnull = 2Rc
power spectrum envelope of transmitted signal given by
(4.26)
2
)(
)(sin
cc
cc
Tff
Tff
S(f) = = cc Tff 2Sa
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(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
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
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Time Resolution of MPCs (width of excess delay bin) given by
= 2Tc = 2/Rc (4.29)
• if 2 MPCs are < 2Tc apart can’t be resolved
• minimal delay between resolvable MPCs = 2Tc
2Tc 1.5Tc
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
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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
TimeObserved
actual propagation time = (4.33)
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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
(4.34)PNseq = TclPN sequence period given by
estimated maximum unambiguous range of incoming MPCs is given by
PNseq · 3108m/s
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• 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
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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
Frequency Domain Channel Sounding System
RxTx
IFT
Vector Network Analyzer with Swept Frequency Oscillator
S-Parameter Test-Set
h(t) = F-1[H(w)]
S21(w) H(w) = Y(w)/X(w)
Y(w)port 2
X(w) port 1
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For each frequency step the S-parameter test-set • transmits known signal on port 1
• monitors received 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
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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 power as 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
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Spatial Separations of samples ¼ , depending on
(i) time resolution of 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
Small Scale Sampling must avoid large scale averaging bias in resulting small-scale statistics
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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
0 10 20 30 40 50 60 70 80 90 100
-85-90-95
-100-105-110-115
Excess Delay Time (us)
Rec
eive
d S
igna
l Lev
el
(dB
m p
er 4
0ns)
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2. Indoor: Grocercy Store at 4GHz • 39.4m path, • 18dB attenuation• 2mV/div, • 100ns/div• 51.7ns RMS• 43.0 dB loss
Excess Delay Time (ns)
Nor
mal
ized
Rec
eive
P
ower
(dB
)
-50 0 50 150 250 350 450
10
0
-10
-20
-30
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18.5m LOS Distance LOS Channel Response
3. UWB Impulse Radio – Outdoor-Indutrial , Warren, MIfc = 4.4GHz, B-41dBm = 2GHz (3.1GHz-5.1 GHz)
mV
DC
mV
DC
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Power Delay Profile used to determine multipath channel parameters• consecutive impulse response measurements 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
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
Time-invariant Multipath PDP, P() derived from average of many snapshots of |hb(t,)|2 over local area
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= mean excess delay
X = excess delay spread (X dB ) or maximum excess delay
= rms delay spread
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()
• commonly used to quantify time dispersive properties of wideband multipath channels
are defined from single PDP• and
• typical values for are us for outdoor & ns for indoor channel
Multipath channel parameters determined from PDP
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kk
kkk
kk
kkk
P
P
)(
)(
2
2
(4.35)
= mean excess delay = 1st moment of PDP
= rms delay spread square root of 2nd central moment of PDP
kk
kkk
kk
kkk
P
P
)(
)( 2
2
22
2
where (4.37)
22 (4.36) =
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)
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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
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
, 2,
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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
X = maximum excess delay = rms delay spread
= mean excess delay
= 45.05 ns
= 46.40 ns
X < 10dB = 84 ns
noise threshold = -20dB
Excess Delay (ns)
Nor
mal
Rec
eive
P
ower
(dB
)
10
0
-10
-20
-30-50 0 50 100 150 200 250 300 350 400 450
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Environment Frequency max Notes Urban 910 MHz 1300ns avg
600 ns std-dev 3500nsNYC
Urban 892 MHz 10-25us - SF Suburban 910 MHz 200-310ns - Avg Typical Suburban 910 MHz 1960-2110ns - Avg Extreme Indoor 1500 MHz 10-50ns
median = 25ns- office bldg
Indoor 850 MHz - 270ns office bldg Indoor 1900 MHz 70-94ns avg 1470ns 3 SF bldgs
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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
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e.g. 4.4
(a ) Compute RMS delay spread for P()P()0dB
-10dB0 1us mean excess delay: us
2
1
)11(
)11()01(
rms delay spread:
us5.025.05.05.0 222
222
2
2
1
)11(
)11()01(us
(b) if BPSK used – what is Rb_max without equalizer (within Bc)
if Ts 5us Rs 200ksps and Rb 200kbps
ss
TT
1.0
1.0 for BPSK, normalized rms delay spread: d =
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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 f2 and fs = f2 – f1
- if fs > Bc signals are affected by channel very differently
- if fs < Bc signals are affected by channel nearly the same
Bc
Signal Level f
100%90%
Fading
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Bc bandwidth related to frequency correlation function (FRC)
Bc FRC(50 )-1 FRC > 0.9(5 )-1 FRC > 0.5
• spectral analysis & simulation required to determine exact impact of multipath fading on particular signal• accurate multipath channel models are used in designing specific modems
estimated relationship between Bc &
FRC Bc
2us > 0.9 10KHz2us > 0.5 100KHz
20ns > 0.9 1MHz20ns > 0.5 10Mhz
larger delay spreads smaller coherence bandwidth
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e.g. 4.4: determine X = maximum excess delay = rms delay spread = mean excess delay
0 1 2 3 4 5 (us)
Pr()0dB
-10dB
-20dB
-30dB
= (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)
= 22 = 1.37 us
Bc = (5·1.37us)-1 = 146kHz (for FRC > 0.5)
•AMPS requires 30kHz bandwidth equalizer not required•GSM requires 200kHz bandwidth equalizer required
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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
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
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> TC SB
1
• channel varies during baseband signal transmission• results in distortion at the receiver
If magnitude of baseband signal bandwidth < coherence time
• fm = v/ is maximum Doppler shift
TC
vfm
1 (4.40)a(i)
One measure of TC is given in terms of maximum Doppler shift
• assumes angle of incidence between Tx and Rx = 0
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(ii) if TC is defined as interval when time correlation function > 0.5 then
(4.40b)TC mf16
9
v BS BS-1 fm TC
100m/s1GHz 1ns 0.3m
333Hz 537us10m/s 33.3Hz 5.37ms
100m/s10KHz 0.1ms 30000m
0.0033Hz 53.7 s10m/s 0.0003Hz 537s
e.g. assume v = 100m/s
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• 4.40a = time duration when Rayleigh fading signal can have wide fluctuations
• 4.40b - often too restrictive
(iii) in Digital communications TC is often defined as geometric mean of 4.40a & 4.40b
(4.40c)TC mm ff
423.0
16
92
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
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• 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
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 >CT
1
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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 = 565usTC
mf16
9
- temporal sampling interval 282 us - spatial sampling interval: x = vTC/2 = 1.41cm
• 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
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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)
Small-Scale time/frequency dispersive nature of RF channel
if frequency correlation > 90% then Bc ≈50
1
if time correlation > 50% then TC mf16
9