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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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Values for Tc

0

10

20

30

0 1 2 3 4 5

fm (KHz)

Tc

Tc1

Tc2

Tc3

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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