Chapter 5 Fade and Non-Fade Durations and Phase ... - DESCANSO
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Chapter 5 Fade and Non-Fade Durations and Phase Spreads 5.1
Background m-
It is important to know the length of time an LMSS channelis availableand unavailable without interruptionfor optimally designingcommunicationsystemswhich handle coded messagesover defined bandwidths. Receiversdesignedby communicationengineersmay, for example, be equipped with a digital soft-decisionmodem and a powerfulfoward error correctingcode implementedwith a convolutioncoder and Viterbi decoder. To optimally designsuchreceivers,whichhaveonly two states,good or bad, a knowledgeis requiredof the statisticsassociatedwith durationsof fadeswhichfall below and above definedattenuation thresholds.In order to implementproper designsof demodulatorsfor coded data, it is also important to have knowledgeof the phase fluctuationsduring conditionsof fading arising from multipathand shadowing. Fade duration results at L-Band were derived by the authors from measurementsin central Maryland IGoldhirshand Vogel, 1989] and South-EasternAustralia [Haseet al., 1991]. The formermeasurementcampaignwas implementedemployinga helicopteras the transmitterplatform, and the latter, the JapaneseETS-V ~ogel et al., 1991]. Duringthe latter campaign,phase fluctuationswere also measuredand associatedstatisticsdescribed
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1
5
Exr)erimental Asr)ects
41
[Haseet al., 1991].
5.2
Experimental Aspects
Measurementsperformedin south-easternAustraliaemployedleft-handcircularlypolarized cw transmissionsradiatedfrom the JapaneseETS-V satelliteat a frequencyof 1545.15MHz. The in- and quadrature-phasedetector voltages (noise bandwidth = 1 kHz) as well as the output from a power detector with pre-detectionbandwidth of 200 Hz were recorded at a 1 kHz rate. The receiverantennaconsistedof a crosseddrooping dipole antennahaving a 4 dB gain, an azimuthallyomni-directionalradiationpattern,and a relativelyflat elevation patternover the beamwidth15° to 75° (Table 3.3).
—
Fadedurationresultswerederivedby analyzingthe averageof two consecutive1 millisecond samples. All fade and non-fade durationswere expressedin units of traveleddistance (m) for which the fades were continuouslyexceeded or were less than thresholdsranging from 1 to 8 dB. The ‘distance durations”may be convertedto “time durations”by dividing the formerby the speed (which was nominally25 m/s). The phase data were extractedfrom~he quadraturedetected signalswherethe low frequencycomponents,dueprimarilyto oscillatordrift and Dopplershiftchanges,wererejected by digital filtering. The phase shiftsmeasuredwerethereforecausedby roadsideobstacles. The followingemphasizesthe Australiandata base (elevationto satellite= 510). Fade durationshave also been examinedfor the centralMarylandregion IGoldhirshand Vogel, 1989]and theseresultsshow a slightdependenceon elevationangle. . L
5.3
Cumulative Distributions of Fade Durations
The fade durationswerewith good accuracyobservedto follow the lognormaldistribution
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5.3 CumulativeDistributionsof IikdeDurations
44
Table 5.2: RMS deviationsrelativeto log-normalfit (a = 0.22, c = 1.215) of cumulative distributionsof fade durations(thresholdof 5 dB) for variousruns exhbitingmoderateand extremeshadowing[Equation(5.1)]. ShadowingLevel YoRMS Deviation Distance(km) , Moderate (Run 1) 16.4 33.0 18.0 Moderate (Run 2) 8.1 13.6 2.4 Extreme
nearlycoincidentfor the individualruns. The resultant“best fit” regressionvaluesaregiven by a = 0.22 0 = 1.215
—
. (54) . (55)
As maybe noted from Table5.2, the measuredfade durationsfor the variousrunsshowedan overallrms deviationof lessthan 20% relativeto the thosederivedemployingthe best-fit log normaldistributionshownplotted in Figure5.2. Forengineeringconvenience,the lognormal distributionis plotted on logarithmicscalessince the percentagevaluesare easierto read. The fact that a singleset of valuesof a and ~ may be applied to the “moderate” and ‘extreme” road-typessuggeststhat whenevera fade is encounteredwhichexceeds5 dB, the physicalcharacteristicsof the treeswhichcreatethe fadesare the same. In otherwords,the differentroads are distinguishedby the frequencywith whichtree shadowingis encountered. Once encountered,the shadowingdurationcharacteristicsare similar. Fadedurationstatisticshavealsobeen compiledby Goldhirshand Vogel [1989]in central Marylhd for anglesof 30°, 45°, and 60° for 5 dB and 10 dB thresholds.A slightelevation angle dependencewas discerniblefor the three cases; the smallerthe elevationangle, the largerthe fade durationfor anyfixed percentage.Forexample,the 30° fade durationshowed approximatelytwice that for the 60° case. This is consistentwith the fact that at the lower elevationanglesthereis generallymore persistentshadowing.
. -
46
S.3 Cumulative Distributionsof Fade Durations
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Fade Duration(m) Figure5.2: Best fit log-normaldistribution(5.1) depictingfade durationsfor a 5 dB threshold. The distribution encompassesroad types which exhibit “moderate” and ‘extreme” shadowing.The distributionis plotted on logarithmicscalesfor convenience.
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5.4 CumulativeDistributionsof Non-Ikde Durations
46
Table 5.3: Non-fade durationregressionvaluesof ~ and ~ satisfyingthe power expression (5.6) at a 5 dB thresholdfor road-typesexhibiting‘moderate” and ‘extreme” shadowingat a path elevationangleof 51°. ?
5.4
p ~ % rms Deviation Distance (km) ShadowingLevel 33.0 Moderate(Run 1) 20.54 0.58 33.3 8.1 Moderate(Run 2) 20.54 0.58 20.5 2.4 Extreme 11.71 0.8371 9.3
Cumulative Distributions of Non-Fade Durations
A ‘non-fade duration” event of distancedurationdd is definedas the distanceover which the fade levelsarepersistentlysmallerthana prescribedfade threshold.A non-fadeduration analysiswas performedby the authorsemployingthe same data set as describedabove for the “fade duration” case. The measureddata werenoted to fit the power expression P(NFD > dd IA < A,) = /3(dd)-7
(56) .
where P(NFD > dd I A < A~) is the percentageprobability that a continuousnon-fade distance NFD exceeds the duration distance dd (m) given the condition that the fade is smallerthan the thresholdA~. The valuesof the parameters@ and ~ in the formulation (5.6) are listedin Table 5.3 for road typesexhibiting‘moderate” and ‘extreme” shadowing assuminga 5 dB fade threshold.As noted, a singlebest fit powercurvehas been derivedfor the two “moderate” runs. In Figure5.3 are plotted the best fit curves(5.6) for the indicated parametervaluesgiven in Table 5.3. L
Employingan analogousexpressionto (5.2), the joint absoluteprobability of exceeding a non-fadedurationdistancedd for which the fade is smallerthan A~ is given by, P(NFD > dd, A < Aq) = P(NFD > dd I A < ~) P(A Aq) from (5.3).
S.4 CumulativeDistributionsof Non-EkdeDurations
47
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-
5
S.5
CumulativeDistributionsof Phase Fluctuations
48
Cumulative Distributions of Phase Fluctuations
Phaseswere obtained from measuredI and Q componentsafter variationsdue to Doppler and oscillatordrifts wereeliminatedusinga high passfilter [Haseet al., 1991]. Conditional cumulativephasedistributionswerederivedfor eachof the road-typesdescribedabove. The conditionsfor these distributionswere that the fades exceed attenuationthresholdslevels rangingbetween2-8 dB. The ‘best fit” phasefluctuationdistributionswerefound with good accuracyto follow a fifth order polynomialover a percentageexceedancerangeof 1% to 90% havingthe form p(~ > #tilA > A~) = ~ ai-l~i-l
. (58)
i=l
where(5.8) may be read as the probabilitythat the phase # (degrees)exceedsthe threshold level d. given a fade A(dB) exceedsthe thresholdlevel A~. In Table 5.4 is given a listing of the values of the polynomial coefficientsa; at the thresholdfade level of 5 dB for the “extreme” and ‘moderate” road types (Figure 5.1). The correspondingphase fluctuation distributionsare given in Figure5.4. We note that over the range5% to 95% in Figure5.4, the phasesarewithin +15° relative to the average for both the ‘moderate” and ‘extreme” cases. The indicated “best fit” polynomials agreed (in phase) with the individualmeasureddistributionsto within 15% rmso For the ‘moderate” runs, cumulativedistributionsof phasesover the probability range 1% to 90% werefound to be minimallydependenton fade thresholdsof 2 to 8 dB. We define the ‘phase spread” as the maximumphase difference(at equal probability) between the “ individualdistributionsfor the differentfade thresholds.A phasespreadof lessthan 5° was noted for the ‘moderate” case over the rangeof distributionshavingfade thresholds2 to 8 dB. Forthe ‘extreme” case, an approximate20° phasespread(or less) wasnoted within the 1% and 99% levelsover the fade thresholdlevelof 2 to 8 dB. Based on the above results,it would appear the influenceof phase fluctuationson demodulation techniquesat the elevation angle considered (e.g., 51°) is minimal and that LMSS channelcharacteristicscan be estimatedwithout consideringphase. At lowerelevation angles,greatermultipathmaybe prevalentincreasingthe phasefluctuationspread. Loo
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5.5 CumulativeDistributionsof Phase Fluctuations
49
Table5.4: Listingof polynomialcoefficientscharacterizingphasefluctuationdistributionsof the form (5.8) for road types exhibiting “moderate” and ‘extreme” shadowingand a 5 dB fade threshold
I
I Wad Type a. al Moderate 56.51 –6.516 Extreme 54.23 –4.242
PolynomialCoefficients ad as as as –7.325 X 10-2 2.380 X 10-2 2.059 X 10-4 –3.985 X 10-5 –1.0897 X 10-2 6.425 X 10-3 2.082 X 10-5 –4.258 X 10-6
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(private communication)reported large phase fluctuationsfor elevationanglesbetween5° and 20° whichhave a significantimpact on digitalcommunications.
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5.5 Cumulative Distributions of Phase Fluctuations
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Chapter 5 Fade and Non-Fade Durations and Phase Spreads 5.1
Background m-
It is important to know the length of time an LMSS channelis availableand unavailable without interruptionfor optimally designingcommunicationsystemswhich handle coded messagesover defined bandwidths. Receiversdesignedby communicationengineersmay, for example, be equipped with a digital soft-decisionmodem and a powerfulfoward error correctingcode implementedwith a convolutioncoder and Viterbi decoder. To optimally designsuchreceivers,whichhaveonly two states,good or bad, a knowledgeis requiredof the statisticsassociatedwith durationsof fadeswhichfall below and above definedattenuation thresholds.In order to implementproper designsof demodulatorsfor coded data, it is also important to have knowledgeof the phase fluctuationsduring conditionsof fading arising from multipathand shadowing. Fade duration results at L-Band were derived by the authors from measurementsin central Maryland IGoldhirshand Vogel, 1989] and South-EasternAustralia [Haseet al., 1991]. The formermeasurementcampaignwas implementedemployinga helicopteras the transmitterplatform, and the latter, the JapaneseETS-V ~ogel et al., 1991]. Duringthe latter campaign,phase fluctuationswere also measuredand associatedstatisticsdescribed
L
r-
L
1
5
Exr)erimental Asr)ects
41
[Haseet al., 1991].
5.2
Experimental Aspects
Measurementsperformedin south-easternAustraliaemployedleft-handcircularlypolarized cw transmissionsradiatedfrom the JapaneseETS-V satelliteat a frequencyof 1545.15MHz. The in- and quadrature-phasedetector voltages (noise bandwidth = 1 kHz) as well as the output from a power detector with pre-detectionbandwidth of 200 Hz were recorded at a 1 kHz rate. The receiverantennaconsistedof a crosseddrooping dipole antennahaving a 4 dB gain, an azimuthallyomni-directionalradiationpattern,and a relativelyflat elevation patternover the beamwidth15° to 75° (Table 3.3).
—
Fadedurationresultswerederivedby analyzingthe averageof two consecutive1 millisecond samples. All fade and non-fade durationswere expressedin units of traveleddistance (m) for which the fades were continuouslyexceeded or were less than thresholdsranging from 1 to 8 dB. The ‘distance durations”may be convertedto “time durations”by dividing the formerby the speed (which was nominally25 m/s). The phase data were extractedfrom~he quadraturedetected signalswherethe low frequencycomponents,dueprimarilyto oscillatordrift and Dopplershiftchanges,wererejected by digital filtering. The phase shiftsmeasuredwerethereforecausedby roadsideobstacles. The followingemphasizesthe Australiandata base (elevationto satellite= 510). Fade durationshave also been examinedfor the centralMarylandregion IGoldhirshand Vogel, 1989]and theseresultsshow a slightdependenceon elevationangle. . L
5.3
Cumulative Distributions of Fade Durations
The fade durationswerewith good accuracyobservedto follow the lognormaldistribution
(51) ●
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5.3 CumulativeDistributionsof IikdeDurations
44
Table 5.2: RMS deviationsrelativeto log-normalfit (a = 0.22, c = 1.215) of cumulative distributionsof fade durations(thresholdof 5 dB) for variousruns exhbitingmoderateand extremeshadowing[Equation(5.1)]. ShadowingLevel YoRMS Deviation Distance(km) , Moderate (Run 1) 16.4 33.0 18.0 Moderate (Run 2) 8.1 13.6 2.4 Extreme
nearlycoincidentfor the individualruns. The resultant“best fit” regressionvaluesaregiven by a = 0.22 0 = 1.215
—
. (54) . (55)
As maybe noted from Table5.2, the measuredfade durationsfor the variousrunsshowedan overallrms deviationof lessthan 20% relativeto the thosederivedemployingthe best-fit log normaldistributionshownplotted in Figure5.2. Forengineeringconvenience,the lognormal distributionis plotted on logarithmicscalessince the percentagevaluesare easierto read. The fact that a singleset of valuesof a and ~ may be applied to the “moderate” and ‘extreme” road-typessuggeststhat whenevera fade is encounteredwhichexceeds5 dB, the physicalcharacteristicsof the treeswhichcreatethe fadesare the same. In otherwords,the differentroads are distinguishedby the frequencywith whichtree shadowingis encountered. Once encountered,the shadowingdurationcharacteristicsare similar. Fadedurationstatisticshavealsobeen compiledby Goldhirshand Vogel [1989]in central Marylhd for anglesof 30°, 45°, and 60° for 5 dB and 10 dB thresholds.A slightelevation angle dependencewas discerniblefor the three cases; the smallerthe elevationangle, the largerthe fade durationfor anyfixed percentage.Forexample,the 30° fade durationshowed approximatelytwice that for the 60° case. This is consistentwith the fact that at the lower elevationanglesthereis generallymore persistentshadowing.
. -
46
S.3 Cumulative Distributionsof Fade Durations
-----
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Fade Duration(m) Figure5.2: Best fit log-normaldistribution(5.1) depictingfade durationsfor a 5 dB threshold. The distribution encompassesroad types which exhibit “moderate” and ‘extreme” shadowing.The distributionis plotted on logarithmicscalesfor convenience.
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.
5.4 CumulativeDistributionsof Non-Ikde Durations
46
Table 5.3: Non-fade durationregressionvaluesof ~ and ~ satisfyingthe power expression (5.6) at a 5 dB thresholdfor road-typesexhibiting‘moderate” and ‘extreme” shadowingat a path elevationangleof 51°. ?
5.4
p ~ % rms Deviation Distance (km) ShadowingLevel 33.0 Moderate(Run 1) 20.54 0.58 33.3 8.1 Moderate(Run 2) 20.54 0.58 20.5 2.4 Extreme 11.71 0.8371 9.3
Cumulative Distributions of Non-Fade Durations
A ‘non-fade duration” event of distancedurationdd is definedas the distanceover which the fade levelsarepersistentlysmallerthana prescribedfade threshold.A non-fadeduration analysiswas performedby the authorsemployingthe same data set as describedabove for the “fade duration” case. The measureddata werenoted to fit the power expression P(NFD > dd IA < A,) = /3(dd)-7
(56) .
where P(NFD > dd I A < A~) is the percentageprobability that a continuousnon-fade distance NFD exceeds the duration distance dd (m) given the condition that the fade is smallerthan the thresholdA~. The valuesof the parameters@ and ~ in the formulation (5.6) are listedin Table 5.3 for road typesexhibiting‘moderate” and ‘extreme” shadowing assuminga 5 dB fade threshold.As noted, a singlebest fit powercurvehas been derivedfor the two “moderate” runs. In Figure5.3 are plotted the best fit curves(5.6) for the indicated parametervaluesgiven in Table 5.3. L
Employingan analogousexpressionto (5.2), the joint absoluteprobability of exceeding a non-fadedurationdistancedd for which the fade is smallerthan A~ is given by, P(NFD > dd, A < Aq) = P(NFD > dd I A < ~) P(A Aq) from (5.3).
S.4 CumulativeDistributionsof Non-EkdeDurations
47
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-
5
S.5
CumulativeDistributionsof Phase Fluctuations
48
Cumulative Distributions of Phase Fluctuations
Phaseswere obtained from measuredI and Q componentsafter variationsdue to Doppler and oscillatordrifts wereeliminatedusinga high passfilter [Haseet al., 1991]. Conditional cumulativephasedistributionswerederivedfor eachof the road-typesdescribedabove. The conditionsfor these distributionswere that the fades exceed attenuationthresholdslevels rangingbetween2-8 dB. The ‘best fit” phasefluctuationdistributionswerefound with good accuracyto follow a fifth order polynomialover a percentageexceedancerangeof 1% to 90% havingthe form p(~ > #tilA > A~) = ~ ai-l~i-l
. (58)
i=l
where(5.8) may be read as the probabilitythat the phase # (degrees)exceedsthe threshold level d. given a fade A(dB) exceedsthe thresholdlevel A~. In Table 5.4 is given a listing of the values of the polynomial coefficientsa; at the thresholdfade level of 5 dB for the “extreme” and ‘moderate” road types (Figure 5.1). The correspondingphase fluctuation distributionsare given in Figure5.4. We note that over the range5% to 95% in Figure5.4, the phasesarewithin +15° relative to the average for both the ‘moderate” and ‘extreme” cases. The indicated “best fit” polynomials agreed (in phase) with the individualmeasureddistributionsto within 15% rmso For the ‘moderate” runs, cumulativedistributionsof phasesover the probability range 1% to 90% werefound to be minimallydependenton fade thresholdsof 2 to 8 dB. We define the ‘phase spread” as the maximumphase difference(at equal probability) between the “ individualdistributionsfor the differentfade thresholds.A phasespreadof lessthan 5° was noted for the ‘moderate” case over the rangeof distributionshavingfade thresholds2 to 8 dB. Forthe ‘extreme” case, an approximate20° phasespread(or less) wasnoted within the 1% and 99% levelsover the fade thresholdlevelof 2 to 8 dB. Based on the above results,it would appear the influenceof phase fluctuationson demodulation techniquesat the elevation angle considered (e.g., 51°) is minimal and that LMSS channelcharacteristicscan be estimatedwithout consideringphase. At lowerelevation angles,greatermultipathmaybe prevalentincreasingthe phasefluctuationspread. Loo
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5.5 CumulativeDistributionsof Phase Fluctuations
49
Table5.4: Listingof polynomialcoefficientscharacterizingphasefluctuationdistributionsof the form (5.8) for road types exhibiting “moderate” and ‘extreme” shadowingand a 5 dB fade threshold
I
I Wad Type a. al Moderate 56.51 –6.516 Extreme 54.23 –4.242
PolynomialCoefficients ad as as as –7.325 X 10-2 2.380 X 10-2 2.059 X 10-4 –3.985 X 10-5 –1.0897 X 10-2 6.425 X 10-3 2.082 X 10-5 –4.258 X 10-6
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(private communication)reported large phase fluctuationsfor elevationanglesbetween5° and 20° whichhave a significantimpact on digitalcommunications.
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5.5 Cumulative Distributions of Phase Fluctuations
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