Download - Four-Element Receiver for Pulsed 10-μm Heterodyne Doppler Lidar

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Four-element receiver for pulsed 10-mm heterodyneDoppler lidar

Xavier Favreau, Arnaud Delaval, Pierre H. Flamant, Alain Dabas, and Patricia Delville

A four-element photomixer receiver has been tested in a 10-mm heterodyne Doppler lidar. It addressesa reduction of the variance of the power scattered off distributed aerosols targets at ranges as long as 8km. An improvement in performance is expected when the four independent signals recorded on everysingle shot are combined. Two summation techniques of the four signals have been implemented: acoherent summation of signal amplitude and an incoherent summation of intensities. A phasing tech-nique for the four signals is proposed. It is based on a more suitable correlation time with discernibleself-consistent packets ~SCP’s!. The SCP technique has been successfully tested, and the results ob-tained with a coherent summation of the four signals, i.e., variance reduction, carrier-to-noise ratioimprovement, and velocity accuracy improvement, are in agreement with theory. © 2000 OpticalSociety of America

OCIS codes: 280.3640, 040.2840, 030.6140, 030.1670.

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1. Introduction

Environmental monitoring studies call for measure-ments of ~i! density of gaseous species and optical

roperties of airborne particles and ~ii! atmosphericariables such as wind velocity and turbulent param-ters. All these parameters need to be recordedithin a short period of time, if not simultaneously, toccount for atmospheric motion and photochemicaleactions. In this respect, the wind field plays a keyole in transport and dispersion of atmospheric pol-utants.

Differential absorption lidar ~DIAL! and Dopplerlidar techniques are effective tools for atmosphericmonitoring at ranges of several to tens of kilometers.Most of the time, a lidar instrument is dedicated to aspecific application, e.g., DIAL or Doppler. So itwould be necessary to use two lidars or more, depend-ing on the number of atmospheric variables to be

X. Favreau, A. Delaval, P. H. Flamant [email protected]!, and P. Delville are with the Laboratoire de Me-

teorologie Dynamique du Centre National de la RechercheScientifique, Ecole Polytechnique, Palaiseau Cedex F-91128,France. X. Favreau is also affiliated with the Centre d’Etudes duBouchet, Vert le Petit F-91710, France. A. Dabas is with Meteo-France, Centre National de la Recherche Meteorologique, ToulouseF-31000, France.

Received 17 May 1999; revised manuscript received 28 January2000.

0003-6935y00y152441-08$15.00y0© 2000 Optical Society of America

measured, to fulfill measurement objectives ~e.g.,easurement of molecular densities and wind speed!.hus it is highly desirable to combine the capabilitiesf DIAL and Doppler lidar in a multifunctional in-trument.One can use the heterodyne Doppler lidar ~HDL!

echnique for simultaneous range-resolved measure-ents of molecular density and wind velocity in the

oundary layer. The technique has been investi-ated for a 10-mm HDL.1 The required accuracies

for both backscattered power and wind velocity leadto contradictory requirements for signal correlationtime. At a high carrier-to-noise ratio2 ~CNR!, uncer-ainty in the collected power backscattered off aerosolargets is driven by the speckle effect. It depends onhe signal correlation time, which in turn depends onhe duration of the transmitted pulse, the intrapulserequency chirp, and the effects of decorrelation thatre due to wind turbulence, wind shear, andefractive-index turbulence. An average of indepen-ent samples improves the accuracy of the powerstimates. The speckle effect is also detrimental toelocity estimates, even at high CNR; thus it is nec-ssary to accumulate independent samples.3One objective of the present study is to obtain sev-

eral independent samples for every HDL single shotto improve performance when the time for measure-ment is limited. We use a four-element photomixerreceiver in a pulsed 10-mm HDL to conduct simulta-neous measurements of backscattered power andwind velocity on distributed aerosol targets. The

20 May 2000 y Vol. 39, No. 15 y APPLIED OPTICS 2441

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four-element receiver provides four samples for everysingle shot. We implement a coherent summation ofthe four signals ~summation of amplitudes after

hase adjustment of the four signals! to improve theean CNR and to decrease both the normalized stan-

ard deviation in backscatter power and the fluctu-tions in wind-velocity estimates. The decrease inignal variance is expected to be maximum for fourndependent samples. We address this point in Sec-ion 2, with consideration of the use of a four-elementeceiver in a HDL and a coherent summation tech-ique. In Section 3 we describe the 10-mm HDLperated by the Laboratoire de Meteorologie Dy-amique. In Section 4 we elaborate on the charac-eristics of simultaneous radio-frequency ~rf ! signalselivered by a four-element-receiver HDL. In Sec-ion 5 we present a new technique for phasing theour rf signals. The findings of a field experimentre presented in Section 6. The multifunctional ca-ability of a four-element receiver is addressed.irst, a comparison of coherent summation ~summa-

ion of amplitudes after phase adjustment of the fourignals! and incoherent summation ~summation ofntensities! of the four rf signals is presented. Theomparison addresses an improvement in signalower statistics ~gain in CNR and decrease in theormalized standard deviation of backscattered pow-r!. Then a comparison is made between coherentummation and accumulation of the four rf signalsor wind-velocity estimates.

2. Theory

The coherent summation of rf signals has beenstudied by Fink and Vodopia,4 who showed that themean CNR ~5S# yN# !, where S# and N# are the signal

nd the noise mean powers, respectively, is a per-inent parameter for optimal summation of rf sig-als. Shot-noise-limited detection by the local-scillator power was assumed. Subsequently, twooherent summation methods for radiomobile com-unication,5 referred to as a maximal ratio receiver

MRR!, in which the rf signals are amplified pro-ortionally to their instantaneous CNR beforehasing and summation, and the equal-gain re-eiver ~EGR!, in which the signals are phased beforeummation, were studied. Recently the two coher-nt summation techniques were compared theo-etically.6 It was shown that the maximal ratioeceiver technique results in 20% ~or 0.8-dB! im-rovement in CNR and 3% improvement of theormalized standard deviation for a four-elementeceiver. Because this modest improvement inerformance was obtained at the expense of muchore complexity in signal processing, we decided tose the EGR technique in the research reported inhis paper.

3. Experimental Setup

The EGR technique for coherent summation wastested on a four-element receiver implemented in apulsed 10-mm HDL.7 Figure 1 is a schematic of the10-mm HDL setup for atmospheric measurements.

442 APPLIED OPTICS y Vol. 39, No. 15 y 20 May 2000

The main components are a TEA CO2 laser operatingat 10.6 mm,8 a 17-cm-diameter off-axis telescope, afour-element HgCdTe ~MCT! photomixer cooled at 77

, and a cw CO2 laser used as a local oscillator forheterodyne detection. The frequency shift betweenthe TEA laser and the local oscillator is set at 30 MHz~in the rf domain!. A ZnSe beam splitter is set at theBrewster angle, and a quarter-wave plate separatesthe transmitted laser beam ~linearly polarized! fromthe radiation backscattered off aerosol targets. Theparameters of the 10-mm HDL operated by the Labo-ratoire de Meteorologie Dynamique are summarizedin Table 1. A close view of the four-element photo-mixer is presented in Fig. 2. A circular piece of MCTmaterial ~500-mm diameter! is divided by isolatingstripes ~25-mm width! into four sensing areas. Theharacteristics of the four individual detectors areisted in Table 2. The four MCT detectors are fol-owed by four identical rf electronic chains composedf a low-noise 64 dB rf amplifier, a 25-MHz bandpasslter centered at 30 MHz, and a 250 MHzy8 bitsnalog-to-digital converter. The digital rf signalsre stored in a computer.Figure 3 displays four simultaneous rf signals pro-

ided by the four-element photomixer for a singlehot. The four signals display a high CNR from dis-ributed aerosol targets at ranges between 1.8 and.4 km. The 10-mm HDL looks horizontally into thelanetary boundary layer. The measurements wereecorded at 2:30 pm under clear-sky conditions on 21ebruary 1997. The four rf signals display a well-eveloped speckle effect.9 In the present study we

performed coherent summations on digital rf signals,

Fig. 1. Schematic of the 10-mm HDL operated by the Laboratoirede Meteorologie Dynamique: M’s, mirror; BS, beam splitter; L,lens.

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Table 1. Parameters of the 10-mm HDL Operated by the Laboratoire de Meteorologie Dynamiquea

using the EGR technique. The phase-adjustmenttechnique is described in Section 5 below.

4. Multielement Receiver

The efficiency of coherent summation depends on ~i!he presence of uncorrelated rf signals with identicaltatistical distributions and ~ii! the use of an equal-ain receiver. In practice, requirement ~ii! is met byareful design of the four-element receiver ~i.e., withalanced detectors and electronics chains!. Carefulptical alignment of the 10-mm HDL is also impor-ant ~the backscattered power is imaged onto the cir-ular four-element MCT photomixer!. In practice,equirement ~i! is key for improvement of the perfor-ance and needs to be addressed in the design phase

f a multielement receiver.Assuming no optical or electronic leakage ~i.e.,

ross talk! among the four MCT elements, uncorre-ated rf signals are expected to occur because severalpeckle cells ~set by the transverse correlation length!re observed. In a previous study,10 2.6 speckle cells

are predicted for a monostatic diffraction-limitedHDL, even in the absence of refractive-index turbu-

Fig. 2. Geometry of the four-element photomixer. A circularpiece of MCT material ~500-mm diameter! is divided by isolatingstripes ~25 mm! into photosensitive areas.

Subsystem Pa

Transmitter: pulsed TEA CO2 laser ~SAGEM! Operating lineEnergy per puPulse repetitioMode ~beam chIntrapulse chiInterpulse freqPulse duration

Receiver: off-axis Cassegrain telescope ~SigmaOptics!

Primary diamMagnification

Detector: four-element MCT ~SATySAGEM! Overall sizedc quantum yiSensitivity ~D*Operating tem

Electronic chain AmplifierFilter bandpasTransient digi

Local oscillator: cw CO2 laser ~SAGEM! Operating linePowerMode ~beam chFrequency sta

aSee also Fig. 1.

lence ~Cn2 5 0!. In addition, the number of speckle

cells increases with increasing Cn2 values.

The cross-correlation coefficient between twopoints on the HDL telescope primary mirror11 is C~d!5 exp$22 @~dyD!2 1 ~dyr0!5y3#%, where d is the sepa-ation between the two points considered, D is the

primary mirror’s diameter, and r0 is the atmospherictransverse correlation length. We set C~d! 5 0.1 asan upper limit for uncorrelated signals. In the pres-ence of turbulence, the transverse correlation lengthr0 is ~1.09k2RCn

2!23y5, where R is the range, k 52pyl, l is the wavelength, and Cn

2 is the refractive-index structure constant. For Cn

2 5 10213 m22y3

and R 5 2 km, we found that r0 5 4.6 cm and d 5 4.8m. For Cn

2 5 10213 m22y3 and R 5 10 km, r0 5 2.6m and d 5 2.8 cm. These numerical examples showhat, when Cn

2 $ 10213 m22y3, the distances betweenthe receivers @d~1, 2! 5 6.20 cm and d~1, 3! 5 8.75 cm#are greater than the distances that meet the criteriagiven above for decorrelation. A decorrelationamong the various elements is illustrated by the rf

ter Value

velength! 10P20 ~10.6 mm!250 mJ

e 4 Hzteristics! Single mode ~Gaussian shape in the far field!

>1.2 MHzy jitter >1.0 MHz

>2.5 ms17 cm73Circular, 500 mm-diameter>0.65>8 3 1010 cm Hz1y2 W21

ture 77 K ~8-h-Dewar, liquid nitrogen!64 dB

nter frequency! 25 MHz ~30 MHz!~Tektronics! 250 MHz-sampling frequency, 8 bits

velength! 10P20 ~10.6 mm!1 W

teristics! Single mode ~TEM00!Better than 0.20 MHzyms

Table 2. Characteristics of the Four Individual HgCdTe Detectors ThatMake Up the Four-Element Receivera

Characteristic

Detector Number

1 2 3 4

Quantum yield ~unit! 0.66 0.67 0.62 0.66Detectivity D* ~cm

Hz1y2 W21 3 106!8.3 8.5 7.7 8.6

Inverse resistance ~kV! 31.9 39.6 34.5 41.7Series resistance ~V! 9 12 10 10

aSee also Fig. 2. The quantum yield is measured for no local-oscillator power. The inverse resistance is given for 110-mVinverse polarization. The series resistance is indicated for nolocal-oscillator power on the detectors.

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signals displayed in Fig. 3. It can be seen that thepeaks and fading segments of the four rf signals areuncorrelated. The correlation coefficient betweenany two signals ~si and sj! is Cij 5 ~sisj!y=si

2sj2 . The

xperimental values for moderate Cn2 conditions in

the planetary boundary layer are listed in Table 3.The correlation coefficient is an average of ten suc-cessive signal samples, at a point that is equivalent to0.040 ms or a spatial resolution of 6 m, and 200 shotsr a time resolution of 50 s. A processing window of.04 ms is long enough for accurate detection ~thearrier frequency is 30 MHz! and short enough not toverage over the speckle effect. The 12 correlationoefficients are all smaller than 0.10, matching theriteria used for uncorrelated rf signals. These cor-elation coefficients account for a possible leakagemong the four MCT detectors.These results were confirmed with the inverse rel-

tive root variance ~IRRV! technique12 on return sig-nals from a hard target located 1.65 km away. The10-mm HDL was operated in direct detection.13 Theesults show that M 5 3–4 for each of the four rfignals ~we derived the statistical properties by using00 shots!.

Fig. 3. Simultaneous rf signals delivered by a four-element re-ceiver from 1.8 to 2.4 km. The HDL schematic is displayed in Fig.1; the HDL parameters are listed in Table 1.

Table 3. Correlation Coefficients between Two Simultaneous rf Signals~si, sj! Delivered by the Four-Element Photomixera

DetectorNumber

Detector Number

1 2 3 4

1 – 20.067 20.046 20.0422 20.067 – 0.094 0.0433 20.046 0.094 – 0.0714 0.042 0.042 0.071 –

aSee Fig. 2. The rf signals are averaged on 10 signal samples~equivalent to a 6-m spatial resolution! and 200 shots ~50 s!.


5. Self-Consistent Packets Technique

Coherent summations were performed with the EGRtechnique at the digital level after phase adjustmentof the four simultaneous rf signals. The phasingoperations were conducted during a time periodshorter than the signal correlation time ~tc!.14 Apractical value of tc can be derived from experimentalconsiderations. We considered two approaches:the IRRV technique12 ~tc! and the self-consistentpackets ~SCP’s! technique ~^t&!.

The IRRV technique addresses a statistically rele-vant parameter on a large data set ~here, the variousHDL shots!. We found tc 5 0.60 ms at ranges be-tween 1.8 and 2.4 km for a total of 800 samples ~or200 lidar shots!, as presented in Fig. 3. The signalprocessing was performed with a 3-ms range gate.

We propose a new technique based on the observa-tion of SCP’s determined by the duration of timebetween two successive minima, as presented in Fig.4. We proceed as follows: Several tc values are cal-culated for every rf signal at a certain range ~e.g.,ight values in Fig. 4!. A histogram built on 200hots ~i.e., 800 independent samples! is shown in Fig.. The mean SCP time duration is ^t& 5 0.49 ms,hich is shorter than the value derived with the

Fig. 4. SCP’s observed on a single rf signal ~see Fig. 3, top!. TheSCP time duration is set between two successive minima.

Fig. 5. Histogram of SCP time duration ~see Figs. 3 and 4!. Thehistogram is built on 200 shots or 800 independent samples. Themean value is ^t& 5 0.49 ms. The correlation time derived by theIRRV method, 0.60 ms, is shown for comparison. PDF,probability-density function.

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IRRV technique ~tc 5 0.60 ms!. The difference canbe explained by underlying assumptions of the IRRVmethod, i.e., no atmospheric fluctuations and no vari-ations of instrumental parameters. Additional fluc-tuations may increase the variance ~sih

! of the rfelectrical current ~ih!, which in turn increases thecorrelation time according to ~^P&2ysP

2! > @1 1 ~Tytc!

2#1y2, where P is the backscattered-power estimatend T is the duration of the processing range gate.Two advantages of the SCP technique can be

ointed out: First, the IRRV technique relies on lim-ting assumptions.12,16 The SCP technique, how-

ever, is based on observational evidence; it isconducted shot by shot and accounts for fluctuationsin pulse length and energy. In addition, the SCPtechnique provides a statistical distribution ~histo-ram! of the correlation times, whereas the IRRVechnique provides only single average value ~tc! for aiven data set.Reliable phase adjustment of the four rf signals

elies on there being a constant phase over the pro-essing gate. In practice, we process the rf signalsn a range gate shorter than ^t&: We use T > ^t&y3;

i.e., a range gate of 0.16 ms. Phasing of the four rfsignals is made two by two: elements 1 and 2 andthen elements 3 and 4 are phased and summed; thensums ~1 1 2! and ~3 1 4! are phased and summed, by

maximization of the total power. The accuracy ofhasing depends on the number of samples. We

Fig. 6. CNR ~dB! on an aerosol distributed target in the planetaryboundary layer as a function of range: coherent summation ~fromEGR technique! and incoherent summation. The signals accountfor four instantaneous rf signals delivered by the four-elementreceiver and N 5 100 shots.

Table 4. Comparison of CNR Obtained with the F

Method of Signal Processing

Mean of four rf signalsIncoherent summation, four simultaneous signalsCoherent summation, four successive signalsCoherent summation, four simultaneous signals

sed a 250-MHz sampling frequency ~or 0.004-msime bin! to increase the number of signal samples.

The accuracy in phasing varies from py4 to py5.The effects on coherent summation are presented inSection 6.

6. Results

A comparison of actual lidar data taken by a 10-mmHDL ~see Section 3! was made. Backscattered

ower ~or CNR! off distributed aerosol targets andhe wind-velocity estimates along the line of sightradial velocity! were compared.

A. Power Measurements

Figure 6 displays the CNR as a function of range fora coherent summation ~EGR technique! and an inco-herent summation of the four rf signals, averaged on100 shots. The measurements were taken in theplanetary boundary layer for clear-sky conditions at3:00 pm on 23 May 1997. HDL measurements arereliable beyond 0.5–1 km. The near range signal ishampered by a strong parasitic signal. The noisepower is calculated at 11 km on a large number ofsignal samples, so the statistical uncertainty is neg-ligible. The noise powers are identical for coherentand incoherent summations.

The theory predicts that the CNR after phasingand a coherent summation of N rf signals ~CNRN! willbe theoretically slightly less than N*CNR1 ~see Sec-tion 2!, where CNR1 stands for a single element andCNRN 5 CNR1 for an incoherent summation. Also,over four successive shots, the coherent summationdoes not improve the CNR because of shot-to-shotfrequency fluctuations ~which are due to transmitterinterpulse frequency jitter and wind-velocity fluctu-ations!.

In Table 4 we present a direct comparison made at, 4, and 6 km of the mean CNR for an averageingle-element contribution, the CNR for incoherentummation of four simultaneous signals, the CNR foroherent summation of four successive shots, and theNR for coherent summation of four simultaneousignals ~one shot!.The experimental results show that, in agreementith theory, the CNR does not improve with an in-

oherent summation compared with the CNR for aingle channel. The experimental improvement inNR in favor of coherent summation compared withsingle channel or incoherent summation is less thanhat is predicted by theory ~3 rather than 4.2 dB!.his difference can be explained by the limited accu-

ifferent Summation Techniques at Three Ranges

CNR ~dB!

m Range 4-km Range 6-km Range

17.9 9.3 2.317.9 9.3 2.418.4 10.0 2.720.8 12.2 5.0

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racy of the SCP phasing technique ~see Section 5! andhe slight residual correlation ~,0.1! of the four-

element receiver.The CNR for coherent summation of four succes-

sive shots is slightly better than for a single channel~gain of >0.5 dB!. This result may be due to a slightfrequency correlation between successive lidar shots.

The results show that a coherent summation iseffective with a gain of >3 dB for samples recordedsimultaneously in one shot but is less effective with again of >0.5 dB for successive shots. Thus themethod of signal processing that provides significantCNR improvement is the coherent summation of si-multaneous samples recorded in one shot.

The statistical properties of the normalized back-scattered power py^p& ~where p } uihu2 and ih is the rfsignal; see Section 5! are presented in Fig. 7. Thefigure shows one rf signal ~top!, an incoherent sum-mation of four instantaneous rf signals ~middle!, anda coherent summation ~EGR technique! over four in-stantaneous signals ~bottom!. The power estimateis calculated on a 300-m range gate from 1.8 to 2.1km. The CNR for a single-element receiver is 17.9dB ~Table 4!, and the power fluctuations are due tothe speckle effect. The theoretical chi-squared dis-tribution16,17 is displayed for the normalized stan-dard deviation derived from the experimental data.In Table 5 we list the normalized standard deviationfor one rf signal, incoherent summation of four in-stantaneous rf signals, and a coherent summation

Fig. 7. Histograms of normalized backscattered power and nor-malized standard deviation ~sp

0! on a 300-m range gate from 1.8 to.1 km: top, one rf signal; middle, incoherent summation of fournstantaneous rf signals delivered by the four-element receiversingle shot!; bottom, coherent summation of four instantaneousignals from the EGR technique ~see Section 5!. The theoreticalrobability-density function ~chi-squared distribution! is displayeds solid curves for sp

0 derived from experimental data.


~EGR technique! over four instantaneous signals.sing the incoherent summation or the coherent

ummation of four simultaneous signals, we decreasehe normalized standard deviation sp

0 5 spy^p& by afactor of 1.5 ~instead of nearly 2, as expected fromtheory; see Section 2! with respect to that for one rfignal.Table 5 also shows that there is no difference be-

ween the normalized standard deviations obtainedrom coherent and incoherent summations for theame four rf signals. This finding is in agreementith theory,1 which predicts the same gain for the

two techniques. The departures from theory arethus due mainly to residual correlation among thefour rf signals.

B. Velocity Estimates

The estimates of velocity from 3 to 3.6 km displayedin Fig. 8 ~top! were made for the rf signals shown atthe bottom. A pulse-pair frequency estimator18 isused for signal processing. The search bandwidth is612.5 MHz, corresponding to 666 m s21 at 10.6 mm.

he two velocity estimates in Fig. 8 ~top! stand for 1nly a single rf signal and 2 a coherent summation ofhe four instantaneous rf signals. An improvementn performance is clearly shown, in particular at 3.3–.4 km, which corresponds to the largest velocity er-or for a single rf signal. Even at a high CNR, largerrors in wind-velocity estimates are observed for sig-als captured by a single-element receiver because ofhe speckle effect. At the same time, the use of theoherent summation of four instantaneous rf signalsecreases the amount of signal fading ~which corre-ponds to an increase in the signal-to-noise ratio; seeubsection 6.A! and thus provides more-reliableind-velocity estimates on a single-shot basis.Histograms of radial velocity estimates for a single-

lement receiver ~top! at a high CNR regime ~CNR ofpproximately 10 dB!, an accumulation3 of four in-

stantaneous rf signals ~middle! and a coherent sum-ation ~EGR technique! for the same rf signals

bottom! are presented in Fig. 9. The histogramsre built on 100 lidar shots. The signals are pro-essed with a 60-m range gate. In each case, aaussian probability distribution with the experi-ental standard deviation is displayed for compari-

on. The performances for an accumulation and aoherent summation of four instantaneous rf signalsre the same for mean radial velocity estimates ~v# 51.5 ms21!. It is apparent that there is no bias

Deviation Obtained for Three Signal Processing Techniques

Method of Signal ProcessingNormalized Standard

Deviation

One rf signal 0.69Incoherent summation of

four simultaneous signals0.46

Coherent summation of foursimultaneous signals

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owing to a coherent summation. These mean radialvelocities differ slightly from that obtained with asingle-element receiver ~v# 5 21.7 m s21!. This dif-ference is negligible compared with that in the windestimate fluctuations ~2.0 ms21!. There is also a de-crease by a factor of 1.3 in the wind estimates fluc-tuation in favor of both the accumulation and thecoherent summation techniques ~sv 5 1.5 ms21! com-pared with that obtained with a single-element re-ceiver ~sv 5 2.0 ms21!.

7. Discussion

An accumulation of several independent samples isexpected to improve the performance of a 10.6-mmheterodyne Doppler lidar with respect to a reductionin variance of the return signal power from distrib-uted aerosols targets. Independent signal samplescan be obtained in several ways: by successive lidarshots at the expense of time sampling ~or resolution!,by simultaneous realizations with a multi-elementreceiver, as presented in this paper, and by consider-ing a multimode laser transmitter as discussed byDrobinski et al.19 We have described implementa-ion of a four-element receiver in a 10-mm HDL. Theest conducted on distributed aerosol targets showedhat the coherent technique is effective in improvingerformance on a single-shot basis. Even in weak-efractive-index turbulence conditions, the four HDLf signals are uncorrelated, which results in an effec-ive coherent summation. A new phasing technique

Fig. 8. Velocity estimates and rf signal from 3 to 3.6 km. Top,velocity estimates from the pulse-pair frequency estimator for 1,one rf signal and 4, four rf signals after phasing and coherentsummation ~EGR technique!. The search bandwidth is 612.5

Hz ~or 666 m s21!. Bottom, 1, amplitude of one rf signal and 4,coherent summation of four rf signals after phasing.

based on the so-called self-consistent packet was pro-posed and validated. It resulted in a 3-dB gain inCNR compared with that for an incoherent summa-tion. The normalized standard deviation of thepower estimates decreased by a factor 1.5 with re-spect to the same measurements made with a singleelement. A coherent summation also improved themeasurement of wind velocity in terms of estimatesof wind fluctuation.

This study was conducted at the Laboratoire deMeteorologie Dynamique, Ecole Polytechnique, Pal-aiseau Cedex, France. The authors thank ClaudeLoth, Francois Nicolas, and Jacques Pelon for fruitfuldiscussions and Christophe Boitel and Bernard Ro-mand for technical support. This research was sup-ported by the French Delegation Generale pour’Armement and Centre National d’Etudes Spatiales.

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Fig. 9. Histogram of velocity estimates from the pulse-pair fre-quency estimator: top, single lidar signal; middle, accumulationtechnique3; bottom, coherent summations ~EGR technique! after

hasing. The velocity estimates are conducted on four instanta-eous rf signals ~single shot! delivered by the four-element re-eiver. The Gaussian distributions are displayed as solid curvesith the standard deviation derived from experimental data.


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