Towards Quantum Communication from Global Navigation Satellite System

Luca Calderaro,1, 2 Costatino Agnesi,1, 2 Daniele Dequal,3 Francesco Vedovato,1, 2 Matteo Schiavon,1, 2

Alberto Santamato,1 Vincenza Luceri,4 Giuseppe Bianco,3 Giuseppe Vallone,1, 2 and Paolo Villoresi1, 2

1Dipartimento di Ingegneria dell’Informazione, Universita di Padova, via Gradenigo 6B, 35131 Padova, Italy.2Istituto Nazionale di Fisica Nucleare (INFN) - sezione di Padova, Italy

3Matera Laser Ranging Observatory, Agenzia Spaziale Italiana, Matera, Italy4e-GEOS spa, Matera, Italy

(Dated: April 16, 2018)

Satellite-based quantum communication is an invaluable resource for the realization of a quantumnetwork at the global scale. In this regard, the use of satellites well beyond the low Earth orbitsgives the advantage of long communication time with a ground station. However, high-orbit satellitespose a great technological challenge due to the high diffraction losses of the optical channel, and theexperimental investigation of such quantum channels is still lacking. Here, we report on the firstexperimental exchange of single photons from Global Navigation Satellite System at a slant distanceof 20000 kilometers, by exploiting the retroreflector array mounted on GLONASS satellites. We alsoobserved the predicted temporal spread of the reflected pulses due to the geometrical shape of array.Finally, we estimated the requirements needed for an active source on a satellite, aiming towardsquantum communication from GNSS with state-of-the-art technology.

INTRODUCTION

Satellite-based technologies are the enabling tools for awide range of civil, military and scientific applications [1–4], like communications, navigation and timing, remotesensing, meteorology, reconnaissance, search and rescue,space exploration and astronomy. In particular, GlobalNavigation Satellite Systems (GNSS) were developed inthe second half of XX century to provide autonomousgeo-localization by exploiting a network of satellite ex-changing position- and time-information with differentlocations on Earth [5]. The strategic importance of suchinfrastructure led different countries to deploy their ownGNSS constellations, e.g. the American Global Position-ing System (GPS), the Russian GLONASS, the EuropeanGalileo, the Chinese BeiDou, the Japanese QZSS and theIndian INRSS/NAVIC. The very core of these navigationsystems is the capability of safely transmitting informa-tion and data from orbiting satellites to several groundstations on Earth by exploiting radio [2] or optical com-munications [6]. In fact, the protection of such infras-tructure from a malicious adversary is of crucial impor-tance for both civil and military operations, representinga critical issue that is continuously and extensively underdevelopment.

At the same time, space quantum communications(QCs) (see the reviews [7, 8]) represent a promising re-source to guarantee unconditional security for satellite-to-ground [9, 10] and inter-satellite optical links [11, 12],by exploiting quantum information protocols as quan-tum key distribution (QKD) [13, 14]. Despite being arelative new research field born in the 2000s, satelliteQCs developed rapidly from the first experimental stud-ies of photon-exchange [15, 16] from Low-Earth-Orbit(LEO) satellites to the feasibility-test of different photonencodings such polarization [17, 18], time-bin [19], and

continuous-variable [20]. Then, the strong efforts of theChinese Academy of Sciences led to full in-orbit demon-strations of such technologies last year [21–24], culmi-nated in the realization of an intercontinental quantum-secure communication between China and Austria [25].

Due to optical losses, most of the demonstrations ofsatellite QCs were limited, so far, to LEO satellites. How-ever, the high orbital velocity of LEO satellites limitstheir visibility periods from the ground station, and sub-sequently the time available for QCs to just few minutesper passage. Conversely, the use of satellites at higher or-bits can greatly extend the communication time, reach-ing few hours in the case of GNSS. Furthermore, QCscould offer interesting solutions for GNSS security forboth satellite-to-ground and inter-satellite links, offeringnovel and unconditionally secure protocols for the au-thentication, integrity and confidentiality of exchangedsignals. For example, a GNSS inter-satellite network forQC has already been proposed to strengthen the secu-rity of the Galileo architecture [26]. This would allowthe generation of cryptographic keys and the construc-tion of a secure satellite QKD-network, thus preventingthe catastrophic consequences of malicious hijacking ofGNSS satellites.

Here, we experimentally demonstrate the feasibility ofQC between a GNSS terminal and a ground station, overa channel length of about 20000 km by using current tech-nology. We report on the first exchange of few photonsper pulse between two different satellites of GLONASSconstellation and the Space Geodesy Centre of the ItalianSpace Agency in Matera, Italy, by exploiting the passiveretro-reflectors mounted on the satellites. By estimat-ing the actual losses of such a channel, we can evaluatethe characteristics of both a dedicated quantum payloadand a receiving ground station, hence attesting the fea-sibility of QC from GNSS in terms of achievable signal-

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FIG. 1. Illustrative representation (to scale) of the typical distance (≈ 20000 km) between GLONASS terminals and theMLRO ground station in Italy. GNSS constellations are well above the LEO satellites (maximum altitude about 2000 km).In the right panel it is shown the setup used to experimentally study the optical channel (see the main text). In particular,the communication protocol starts with the SLR start signal at t = 0 ms. The 100-MHz pulses are sent to the satellite fromt = 0 ms to t = 100 ms, opening the shutter placed in the transmission path. At t = 100 ms a second SLR pulse is sent to thesatellite and after 5 ms the receiving shutter open the receiving path till t = 180 ms. Image of Glonass-K satellite taken fromRussian SpaceWeb.

to-noise ratio and detection rate. Our work extends thelimit of long-distance free-space single-photon exchange,which was demonstrated so far with a channel lengthof about 7000 km by exploiting a Medium-Earth-Orbit(MEO) satellite [27].

THE OPTICAL SETUP

The feasibility of QC from GNSS orbits was studied ex-perimentally using some of such satellite equipped withan array of corner-cube retroreflectos (CCRs). A weaksource in GNSS orbit is emulated by exploiting the two-way scheme already tested with LEO [17] and MEO satel-lites [27]. Our scheme takes advantages of Satellite LaserRanging (SLR) technique, in which bright laser pulsessent to CCRs are used to accurately measure the dis-tance of such satellites for geodynamics purposes [28].

The experiment presented here was performed at theItalian Space Agency’s Matera Laser Ranging Observa-tory (MLRO) by using the setup sketched in Figure 1.The observatory is a SLR station equipped with a mode-locking Nd:YVO4 laser oscillator (ML-laser), operatingat 1064 nm with 100 MHz repetition rate and paced by anatomic clock. The SLR pulses (wavelenght, 532 nm; en-ergy, ∼100 mJ; repetition rate, 10 Hz) are obtained by se-lecting one seed pulse every 107 with a pulse-picker (PP),which is then amplified and up-converted via a second-harmonic-generation (SHG) stage. The SLR pulses aresent to the targeted satellites equipped with CCRs [28] byusing the 1.5-m diffraction-limited Cassegrain telescopeof MLRO [29]. Then, after the reflection by the orbit-ing terminals the pulses are collected by a fast analogmicro-channel plate detector (Hamamatsu R5916U-50)placed after a 50:50 polarizing beam-splitter (PBS) usedto separate the transmitted beam from the received one.A dedicated time-tagger with sub-picosecond accuracy

recorded the start and stop signals generated by the PPand the detector respectively. The single-shot measure-ment of the satellite distance is then estimated from thetime-difference of these two signals, i.e. the round-trip-time, with an error below 20 ps.

A setup dedicated to the feasibility study of QC fromGNSS was implemented in parallel to the SLR system.The same laser oscillator is used to produce a 100-MHzpulse-train with wavelength λ = 532 nm, ∼1 nJ of energyand 55 ps of pulse duration at full-width-half-maximum(FWHM) by exploiting a 50 mm long periodically poledlithium niobate (PPLN) non linear crystal from HC Pho-tonics. This beam, synchronized with the SLR pulse-train, is combined with the outgoing SLR pulses by us-ing a 50:50 beam splitter (BS) and the two light beamsare sent to the targeted GNSS satellites. The receiv-ing apparatus of the 100-MHz beam is comprised of a50:50 BS to separate the outgoing and ingoing beam, a3 nm FWHM spectral filter (F) with transmission bandcentered at 532 nm, a focusing lens (L) and a siliconsingle photon avalanche detector (SPAD), provided byMicro-Photon-Devices (MPD, Italy), with ∼50% quan-tum efficiency, ∼400 Hz dark count rate and 40 ps ofjitter. The time of arrival of the returning photons (tag)is recorded with 1 ps resolution by the time-to-digitalconverter QuTAG from QUTOOLS.

We implemented a communication protocol to sepa-rate the transmitting and receiving phases by using twomechanical shutters. Since the round trip time of pho-tons reflected by GNSS satellites is around 130 ms, thetotal period of the communication protocol is 200 ms. Inthe first half, the transmitting (receiving) shutter is open(close) and the 100-MHz pulses are transmitted. Vice-versa, in the second half the the receiving (transmitting)shutter is open (close) and the 100-MHz pulses comingfrom the satellite can be detected.

Due to optical diffraction, atmospheric absorption, and

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the finite sizes of the cross-section and active area ofthe CCR-array, the beams are attenuated by several or-ders of magnitude after being retro-reflected. As a re-sult the reflected pulses of the 100-MHz train have alow mean number of photons µsat at the satellite reflec-tion, thus emulating an active weak source placed on aGNSS terminal orbiting 20000 km away from the MLROground station. In the following sections a detailed es-timation of the channels losses and of µsat is providedby measuring the detection rate of the returning pho-tons, attesting the faithfulness of our implementation.The targeted GNSS satellites are two different terminalsof the GLONASS constellation, namely Glonass-134 andGlonass-131 (Space Vehicle Number: 802 and 747, re-spectively).

MODEL OF THE CHANNEL LOSSES

In our experiment, the mean photon number per pulseµsat emitted by the simulated source at the satellite isnot known a priori. We can estimate it a posteriori asµsat = Rdet/(νtxtdowntrx), by experimentally evaluatingthe detection rate Rdet, and by knowing the down-linktransmittance tdown, the transmittance of the receivingapparatus trx and the repetition rate νtx = 100 MHz ofthe source. Losses are expressed in dB as l = −10 log10 t,where t is the transmittance. The receiver losses arepromptly estimated taking into account the reflectionand transmission losses through all the optical elements(8.8 dB) and the detector quantum efficiency (3 dB).

The down-link channel losses can be evaluated as theproduct of the atmospheric transmission ta and the geo-metrical transmission due to diffraction tdiff . We followtwo independent approaches for estimating the transmis-sion due to diffraction and compares the results for thevalidation of the model. The targeted GNSS satellites arepart of different generations, GLONASS-K1 for Glonass-134 and GLONASS-M for Glonass-131, both equippedwith a planar array of CCRs, with circular and rectan-gular shape respectively [30]. Their CCRs are character-ized by the absence of coating on the reflecting faces, suchthat the light is back reflected by total internal reflection(TIR). This implies a far field diffraction pattern (FFDP)which is quite different from the simple Airy disk given bya circular aperture [31]. The FFDP of a TIR corner cubehas a central Airy-like disk, with 26.4% reduced centralintensity peak from the circular aperture with equivalentarea, surrounded by six lobes placed on the vertices ofa hexagon. The lobes are displaced from the center ofthe FFDP by θd ≈ 1.4λ/DCCR, with DCCR = 26 mmthe CCR diameter [32], corresponding to a displacementθd ≈ 29 µrad. Since the velocity aberration of GNSSsatellite is around 26 µrad [28], the MLRO telescope isreceiving the lateral lobes of the FFDP. In particular, thelateral lobes have an intensity which is ≈ 30% of the cen-

tral peak. Since the central intensity peak I0 of a circularaperture of area A depends on the power P0 incident onit via I0 = P0A/(λ

2R2), with R the distance from theaperture, the transmission due to diffraction can be eval-uated by

tdiff = 0.264 · 0.3ACCRAtel

λ2R2, (1)

where ACCR and Atel are the areas of the CCR and theground telescope, respectively [31].

An alternative approach is given in [27] in which theFFDP is approximated as a top-hat pattern with solidangle Ω, so that the diffraction transmittance is evaluatedas Atel/(ΩR

2). Since the solid angle can be estimated bythe array cross-section Σ [28, 33], we have that

tdiff =Σ

4πρARRA

Atel

R2, (2)

being ρ = 0.93 the reflectivity of the uncoated CCR andARRA the array effective area.

In clear sky conditions, the losses due to atmospherictransmission for the used λ is la ≈ 0.4 dB [28] and con-sidering a satellite slant distance R ≈ 20000 km, thepredicted down-link channel losses are ldown ≈ 62 dB,from both models Eqs. 1 and 2 to estimate the diffrac-tion losses. This assessment of the channel losses allowus to experimentally estimate µsat by measuring the de-tection rate, as presented in the following section.

DETECTION OF SINGLE PHOTONS FROMGNSS TERMINALS

In this section, we present the results obtained with thetwo satellites above described. We provide here a detailedanalysis of the data obtained from Glonass-134. The caseof Glonass-131, in which we used also a single-photonphotomultiplier (PMT) in parallel to the SPAD to com-pare their performances, is described in the Supplemen-tary Material (SM). In a single passage of Glonass-134,we had two distinct acquisitions separated by almost onehour corresponding to the maximum and minimum dis-tance of the satellite from MLRO. In particular, the firstacquisition lasted about 2 minutes, with mean slant dis-tance of about 20200 km, whereas the second one lastedabout 5 minutes, with mean slant distance of 19500 km.

In Fig. 2 we show the signal detection rate fromGlonass-134 for the second acquisition (the results forthe first acquisition are analogue). The detection ratewas estimated in the following way. We divided the wholeacquisition in time intervals Ik of duration τ = 5 s. Foreach interval we made the histogram (see Figure 3) ofthe time difference between the tagged detection tmeas

and the expected time of arrival of the photon tref , es-timated from the SLR acquisition performed in parallel

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FIG. 2. Detection rate from Glonass-134 at 19500 km slantdistance. Each point is calculated integrating over an acqui-sition time window Ik of τ = 5 s.

[17, 27]. Then, we chose a time window w = 400 ps, cen-tered around tref , and estimated the number of photondetections Ndet as the difference of the total and back-ground counts within w, which was chosen much largerthan the detector jitter (≈ 40 ps) since the retroreflectedpulses are temporally spreaded by the CCR array. Thebackground was uniformly distributed within the 10 nsperiod between two sent pulses (see Figure 3), thereforewe estimated its rate counting the detections over a timewindow which is at least 1 ns away from tref . Finally, thesignal detection rate was obtained via Rdet = Ndet/(τδ)where δ = 0.3 is the duty cycle of the communicationprotocol. Then, we discarded the time windows Ik withRdet < 30 Hz, to filter out acquisition with low signal-to-noise ratio (SNR). Such selected time windows gave theintegrated histogram shown in Fig. 3.

At the end of such analysis, we obtained a mean de-tection frequency Rdet ≈ 58 Hz, a SNR of 0.53 and meannumber of photons at the satellite µsat ≈ 14.5 for thesecond acquisition of Glonass-134. In the same way weanalyzed the first acquisition of the same passage, ob-taining a mean detection frequency Rdet ≈ 59 Hz, a SNRof 0.41 and a mean number of photons at the satelliteµsat ≈ 16.1. In this case we used a signal time window wof 600 ps due to the larger temporal spread. The resultsare summarized in Tab. I, along with the acquisition ofGlonass-131 detailed in the SM.

It is worth noticing that, with our apparatus, it is pos-sible to resolve the temporal distribution of the returningpulse given by the particular design of the CCR array,hence revealing the “signature” of Glonass-134 that isequipped with a holed circular CCR array [32]. If the in-cident angle on the array is not zero, the pulses reflectedby the CCRs closer to the ground station have a smaller

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tmeas − tref (ns)

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FIG. 3. Histogram of residuals between the measured and theexpected time of arrival of the photons, from Glonass-134 ata slant distance of 19500 km. Here, we consider acquisitiontime windows Ik with detection rate Rs > 30 Hz. Each binis 100 ps wide.

round trip time with respect to the further CCRs, re-sulting in a temporal spread of the pulse. We simulatedthe temporal shape of the pulse for incident angles 5 degand 9 deg, corresponding to the incident angles of the twoacquisitions, and compare them with the actual data inFig. 4. From the simulation, the corresponding temporalpeak-to-peak distance is 250 ps and 430 ps for the two ac-quisitions respectively in agreement with the experimen-tal estimation. The simulation is performed supposingthat the single CCR does not change the temporal shapeof the pulse but introduces a temporal offset dependingon its position in the array and on the incident angleof the beam. Using a pulse with 100 ps of FWHM andsumming up the contributions of all CCRs we obtainedthe shapes depicted in the figure. It is worth noticingthat the continuous lines shown in Fig. 4 are obtained bysuch a-priori model (adding the measured background)and not by fitting the data.

As shown in the work by Otsubo et al. [34], GLONASSflat CCRs array exhibits particular temporal distributiondetermining higher error in the laser ranging measure-ment, in which the mean number of photons at the re-ceiver is usually much greater than one. The authors of[34] observed the “signature” of the GLONASS satellitesby integrating one year of data acquisition. On the con-trary, our result shows that using single photons detec-tors and high repetition source the temporal distributionof the pulse can be measured, even with low mean num-ber of photon at the satellite and short data integrationtime. A more accurate measurement could be done usinga mean number of photons at the receiver about one, but

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FIG. 4. Histogram of residuals between measured and ex-pected time of arrival of the photons for Glonass-134 at 20200km (top) and 19500 km (bottom). The incident angle of thebeam on the array is about 9 deg and 5 deg, respectively. Herewe integrate on time windows Ik with high detection rate tohighlight the temporal spread of the back reflected impulse.Based on our model, the temporal peak to peak distance isabout 430 ps and 250 ps for incident angles of 9 deg and 5 deg,respectively (continuous lines).

this is beyond the scope of this work. We note that thismeasurement could even be used to increase the accu-racy in the determination of the orientation of the arrayand hence the attitude of the satellite, which is of criticalimportance for the processing of GNSS data [35, 36].

TOWARDS QUANTUM COMMUNICATIONFROM GNSS

Based on these results, we can estimate the perfor-mance of a transmitter and receiver needed for the real-ization of quantum communication from GNSS satellites.For practical quantum communication we target a SNRlarger then 100 and a detection rate larger than 10 kHz.

At the receiver, the background affecting the SNR canbe significantly reduced with respect to present experi-ment in a dedicated QC application. In our work, thebackground was estimated by using the detections dis-tribution on the 200 ms period, which is shown in Fig 5for the passage of Glonass-134 at 19500 km. The bluebars corresponds to the counts in which we expect thetransmitted photons to arrive at the detector. This timewindow starts one RTT from the first transmitted qubitand ends when the receiving shutter is closed. A largepart of these counts are due to noise. The intrinsic darkcount rate of the detector amounts to Nrx = 700 Hz.They are estimated in the first 100 ms of the period,when the receiving shutter is closed. This noise could be

almost halved, reaching the intrinsic dark count rate ofthe detector, by optimizing the optical isolation of thedetector from the room light. Another source of noise isthe fluorescence that occurs when the upgoing SLR pulsepasses through the optical elements in common with ouroptical path. The intensity of the fluorescence light re-duces exponentially in time with half-life that dependson the material. A remaining tail is included in the blueregion and amounts to Nfluo = 195 Hz. This noise can beeliminated, since this pulse is useless for the protocol andcan just be avoided. The remaining, and predominant,detections are due to satellite albedo and background ofthe field of view. This noise is uniformly distributed intime in the blue region and amounts at Nalb = 1.9 kHz.We can reduce it by an order of magnitude using a band-pass filter of 0.3 nm instead of 3 nm. Moreover, a ded-icated receiver may avoid the use of signal losses due tobeam splitters. Indeed the satellite tracking may be doneusing a different wavelength. With respect to our setup,this would enhance four times the signal, although cor-respondingly augmenting Nalb. Adopting these solutionsat the receiver we expect a SNR and a detection rateraised of a factor 10 and 4, respectively.

Regarding the transmitter, we consider an activesource on the satellite with a mean photon number perpulse close to 1. Compared to the current result, thisinvolves a signal reduction of about a factor 15. How-ever, the down-link coupling efficiency can be greatly en-hanced by using an appropriate telescope. We consider adown-going beam with 10 µrad of semi angular aperture,shrinking the beam spot on ground and using a pointahead to compensate for velocity aberration as recentlydemonstrated in [23]. This would reduce the diffractionlosses of 20 dB with respect to the channel losses esti-mated above. The temporal spread due to the reflectorarray would not be present, allowing for a narrower tem-poral filter w that could be chosen considering only thejitter of the detector (≈ 40 ps). Moreover, with 40 ps jit-ter, the repetition rate could be increased to more than1 GHz, thus enhancing the detection rate. With theseexpedients, the expected SNR and detection rate are ofthe order of 100 and 10 kHz, respectively.

CONCLUSIONS

This work demonstrates the first exchange of few pho-tons per pulse (µsat ' 10) along a channel length of 20000km, from Glonass-134 and Glonass-131 to MLRO, reach-ing a SNR about 0.5 and a detection rate around 60 Hz.We evaluated the requirements needed for a transmittermounted on a GNSS satellite and a ground receiver forthe realization of QC between the two terminal. Our find-ings demonstrate that QC from GNSS satellite is feasiblewith current state-of-the-art technology.

Extending QC to GNSS is of primary importance for

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Satellite passage Slant distance (km) Detector Rdet (Hz) SNR µsat ldown (dB) lrec (dB)

Glonass-134 19500 SPAD 58 0.53 15 62.1 11.8

20200 SPAD 59 0.41 16 62.5 11.8

Glonass-131 20250 SPAD 27 0.43 15 62.6 14.8

PMT 6 0.21 16 62.6 21.8

TABLE I. Summary of the results. Mean signal detection rate Rdet, mean photon number at the satellite µsat, mean down-linklosses ldown.

FIG. 5. Stacked histogram of detection rate with respect tostart signal for the second acquisition of Glonass-134. Thishistogram shows the duty cycle of the communication proto-col. Orange bars show the detection rate when the receivingshutter is closed. Blue and Green bars shows detections whenthe receiving shutter is open. In particular the Blue bars aredetections that occurs a RTT after the start signal.

secure communications at the global scale, as discussedabove, but it is also a resource for fundamental tests ofphysics in space. Indeed, QC from satellite opens thepossibility of testing the foundations of quantum me-chanics in the space scenario, as envisaged in theoret-ical studies [37] and mission proposals [38–40], and al-ready realized in actual implementations [21, 22, 41] atthe LEO distance. A channel length of over 20000 kmcould enable the design of new experiments that test thevalidity of quantum mechanics at higher orbits and per-mit the use of satellites following highly elliptical orbits.Such orbital characteristics might be of key importanceto observe gravity-induced effects on quantum interfer-ence, [42–44], that could shed light on the interplay be-tween general relativity and quantum mechanics, thusvalidating physical theories and placing bounds on phe-nomenological models. Concluding, our results pave theway for new applications of quantum technologies andfundamental experiments of physics exploiting QC fromhigh-orbit satellites, which may be implemented on next-generation GNSS constellation.

We would like to thank Francesco Schiavone, GiuseppeNicoletti, and the MRLO technical operators for thecollaboration and support. We acknowledge the Inter-national Laser Ranging Service (ILRS) for the satellitedata. L.C. and F.V. acknowledge the Center of Studiesand Activities for Space (CISAS) “Giuseppe Colombo”for financial support. Our research was partially fundedby the Moonlight-2 project of INFN.

SUPPLEMENTARY MATERIAL

Analysis of photons coming from Glonass-131.In the passage of Glonass-131, we used a slightly differ-ent receiver setup with respect to the one in Figure 1.Instead of using a single receiving detector, we placed aSPAD and a PMT detector (detection efficiency, 10%;active diameter, 22 mm; H7360-02, Hamamatsu Photon-ics), coupled both to the down-going link with an addi-tional 50:50 beam splitter. In this way we could comparethe performances of the two detectors. Using the sameanalysis described in the main text, we obtained the sig-nal detection rate presented in Fig. 6. We noted a goodcorrelation between the signal detection rate of the twodetectors, although the PMT shows a much lower rate,since its quantum efficiency if five times lower than theone of SPAD. We then discarded the time windows withlow signal detection rate, obtaining two comparable val-ues for µsat for the two detectors. The results are sum-marized in Tab. I. We noted that MPD has about fivetimes the signal rate of the PMT, as expected for thehigher quantum efficiency. Also the SNR of the MPD istwo times the SNR of the PMT, since the jitter on thetime of arrival of the photons is lower.

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FIG. 6. Signal detection rate for Glonass-131. The blue solidline refers to the MPD detector, while the red one refers tothe PMT.

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