Mean acquisition time of GNSS peer-to-peernetworks

Nazelie KassabianDepartment of Electronics and Telecommunications

Politecnico di TorinoTurin, Italy

Email: nazelie.kassabian@polito.it

Letizia Lo PrestiDepartment of Electronics and Telecommunications

Politecnico di TorinoTurin, Italy

Email: letizia.lopresti@polito.it

Abstract—The acquisition engine is the most critical block withina Global Navigation Satellite Systems (GNSS) receiver as allsubsequent blocks in the receiver chain depend on it. To thatend, an innovative Peer to Peer (P2P) architecture is studiedin this paper, where special acquisition engines are expected toperform better in terms of Mean Acquisition Time (MAT). Thisis due to peers nearby which share GNSS aiding informationin terms of code delay, Doppler frequency and Carrier-to-NoiseRatio (CNR). It is thus expected to reduce the search spaceover which the Cross-Ambiguity Function (CAF) is evaluatedas well as to initialize the correct integration time a-priori. Theperformance improvement in terms of MAT as a result of theP2P setting is tested against the standard acquisition engine in acomprehensive way. Indeed, the MAT of a standard acquisitionengine is compared to that of a P2P engine with a thoroughinvestigation of several search strategies where the best strategyyielding the optimum MAT is chosen for each acquisition engine.

I. INTRODUCTION

The acquisition engine of a Global Navigation SatelliteSystems (GNSS) receiver is the block that performs a roughestimation of the received signal’s parameters, code delay andDoppler frequency, before moving on to a refined estimationtracking block. As such, the analysis of acquisition enginesis of paramount importance as they can form a bottleneckin the overall GNSS receiver. In fact, the Mean AcquisitionTime (MAT) is a performance metric very often used inthe literature to indicate the efficiency of a GNSS receiver.Almost all literature on the computation of the MAT is eitherfocused on the standard serial search Threshold Crossing(TC) criterion [1], [2], a Maximum (MAX) criterion [3] ora hybrid Maximum Threshold Crossing (MAX/TC) criterion[4]. All these strategies do not show any particular interest inthe potential aidings received by a Peer to Peer (P2P) networkas in [5] where simulations are performed to assess the MATusing a serial search in the context of a P2P setting. TheP2P paradigm consists in exploiting inherent communicationlinks between nodes or peers equipped with GNSS receivers,to share and disseminate valuable GNSS information in thecontext of a cooperative localization.

The innovative aspect of this paper lies in the MATstudy of the afore-mentioned three search strategies in lightof the P2P context coupled with a verification procedure;

a double-dwell time detection in the form of an M over Ndetector. The impact of this detector declaring the signalpresent if M out of N tests are positive is also examinedby comparing it to a single-dwell time detector where theverification process is nonexistent. The use of a verificationprocess is justified according to the penalty time and theoptimum acquisition threshold. Closed form expressions ofthe MAT relative to the MAX and MAX/TC criterion withor without verification procedure are derived and used toperform significant comparisons of a standard acquisitionengine with respect to various versions of a P2P acquisitionengine. In these comparisons, maximum search strategies areadopted for a standard acquisition engine with a typicallylarge search space, whereas a serial search strategy is mostappropriate for the P2P acquisition where the search spaceis reduced significantly. Moreover, the analysis of the MATis carried out under weak and strong signal conditionsand the P2P architecture benefits are demonstrated using acombination of code delay, Doppler frequency aiding andCarrier-to-Noise Ratio (CNR) aiding. The paper is organizedas follows: Section II introduces acquisition systems andcompares cell to system probabilities. Section III analyzesthe MAT of the different search strategies with or withoutverification by deriving closed form solutions and Section IVdevelops a performance comparison between standard andinnovative P2P acquisition engines.

II. ACQUISITION AND PROBABILITIES

A. Acquisition systems

The Acquisition (ACQ) engine is mainly a cross-correlationengine coupled with a decision system. In the cross-correlationengine, the received Signal in Space (SIS) is multiplied bya locally generated signal using an estimated code delay τ̂and Doppler frequency f̂D. The Cross-Ambiguity Function(CAF) is a two-dimensional function and is equal to the cross-correlation function evaluated with a specific combination(τ, fD) which corresponds to a cell. The total number ofcells makes up the search space. P2P networks inherently areequipped with communication and synchronization capabil-ities that consent in highly accurate aiding in terms of bothcode delay and Doppler frequency so as to considerably reduce

978-1-4673-2343-7/12/$31.00 ©2012 IEEE

the search space to just a few cells. In this paper, a serial P2PACQ engine is used and compared to a standard acquisitionengine which uses maximum search strategies. In a serialsearch, it is assumed that the CAF is evaluated or scannedin a starting cell and compared to an ACQ threshold. If thesignal is declared present in the cell, the search process isstopped. If the signal is declared absent in that cell, the searchcontinues by moving to the next cell, evaluating the CAF onthat cell and applying the detection process cell after cell. Formaximum search strategies, the CAF is evaluated in the wholesearch space in parallel and then the decision is made basedon the maximum value of the CAF or the maximum value thatpasses the ACQ threshold. The MAT for all search strategies iscomputed assuming that the search continues indefinitely untilthe signal is declared present in a particular cell. In such asetting, the concept of probability of detection and false alarmis fundamental in evaluating any acquisition time.

B. Cell and system probabilities

Cell and system probabilities are essentially the major corner-stones in the study of the MAT. Indeed, system probabilities,cell probabilities or even both are used in the expression ofthe MAT depending on the search and detection strategy. Cellprobabilities are typically used in a serial search but also in aMAX and MAX/TC search whenever coupled with a double-dwell time detector. While a single-dwell time detector per-forms no verification, a double-dwell time detector performs averification procedure on a single cell where the received SISis believed to be present.

1) Cell probabilities: Two hypotheses are defined over eachcell, H0 where the chosen cell is called an H0 cell and doesnot correspond to the right code delay and Doppler frequencyalignment of the received SIS (Pfa +Pcr = 1) and H1 wherethe chosen cell is called an H1 cell and does correspondto the right alignment (Pd + Pmd = 1). Pfa is the cellfalse alarm probability, Pcr is the cell probability of correctrejection, Pd is the cell probability of detection and Pmd isthe cell missed detection probability. In this paper, coherentintegrations are considered, and the CAF envelope is evaluatedas R = I2 + Q2 (non-normalized summation of the in-phaseand quadrature phase signal at the output of the correlators).The cell and system probabilities expressions can be found in[6]. Moreover, a double-dwell time detector is considered andrepresented by an M over N detector. The detection outcomebeing the result of a Bernoulli process with probabilities Pd

and Pfa, the cell probabilities of detection and false alarm inverification mode can be written as:

Pd,v =N∑

m=M

(N

m

)Pd

m(1 − Pd)N−m (1)

and

Pfa,v =N∑

m=M

(N

m

)Pmfa(1 − Pfa)N−m (2)

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babi

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alar

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fa

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Serial PD

MAX PD

MAX/TC PD

Fig. 1. Cell and system probabilities vs ACQ threshold B for various searchstrategies and a C/N0 equal to 40 dB-Hz

2) System probabilities: System probabilities are used whenassessing the MAT in the context of a MAX or a MAX/TCsearch but also in a serial search whenever coupled witha double-dwell time detector. In this case, two differenthypotheses are defined. Hypothesis H2 applies to the casewhere the Pseudo-Random Noise (PRN) code that is beingtested is actually present in the received signal, and so theprobability rule is P p

FA + PMD + PD = 1 where P pFA

is the system probability of false alarm in presence of thePRN code in question. This probability is also called systemprobability of error PE . Hypothesis H3 on the other hand, isdefined when the PRN code that is being tested is absent inthe received signal, and the system probability rule becomesP aFA + PCR = 1 where P a

FA is the system probability offalse alarm in absence of the PRN code in question. Systemprobabilities summarize the detection situation in an efficientway and as such the system PD is plotted in conjunction withthe MAT in the following figures. In fact, even if the MATfor a serial search depends on cell probabilities Pfa and Pd,it is the system PD that summarizes the behaviour of bothcell probabilities. The behaviour in terms of system PD of allsearch strategies is summarized in Fig. 1 where all curves areplotted vs the ACQ threshold except the pure MAX searchwhich is plotted against the possible maximum value in theCAF. It is intuitive to see that the system PMD and P a

FA donot depend on the search strategy as both entail the searchof all cells in any case. However, PD and P p

FA = PE highlydepend on the search and detection strategy [6] and are derivedin terms of the acquisition threshold B, the number of cells Nc

in the search space, and the two parameters α and σ relating tosignal and noise power. For a serial as well as MAX/TC searchstrategy, where the verification is performed over a single cell,the overall system probabilities are defined as the product ofthe system and cell probabilities, i.e. overall probability ofdetection is PTot

D,v = PDPd,v and overall probability of erroras PTot

E,v = PEPfa,v . However, the system probabilities areexpressed differently for a pure MAX search strategy wherethe maximum is chosen without comparing it to a threshold.In fact, in this case, the PMD is null (PD + PE = 1), andthe verification process is performed by searching the whole

search space all over again (instead of just a single cell) andverifying that the maximum corresponds to the same cell inconsideration for at least M times:

PTotD,v = PDPD,v = PD

N∑m=M

(N

m

)PmD (1 − PD)N−m (3)

and

PTotE,v = PEPE,v = PE

N∑m=M

(N

m

)PmE (1 − PE)N−m. (4)

III. MAT ANALYSIS USING DIFFERENT SEARCHSTRATEGIES

In this section, the MAT is introduced considering differentsearch strategies, from serial to pure MAX as well as MAX/TCcoupled with a double-dwell time detector, i.e. the M over Ndetector as a verification process. In the literature, a robustprocedure to compute the MAT is mainly based on theprobability generating function (pgf). The whole procedure toderive the MAT is presented for a MAX/TC with single as wellas double-dwell time verification and all search strategies areconfronted amongst themselves. Moreover, MAT curves as afunction of the acquisition threshold are used to justify thepresence or absence of a verification procedure.

A. Serial search

The serial single-dwell time search strategy consists in evalu-ating the CAF in a specific cell and serially moving to the nextcells in some specified direction and order until the H1 cell isfound, i.e. the cell which holds the correct PRN code, Dopplerfrequency and code delay. A double-dwell time detector on theother hand, applies a further verification procedure only onthe cells where it is believed that the signal is present. Thiscell can be both an H0 or an H1 cell. A decision flow graphdiagram has long been adopted in the literature as a procedureto determine the MAT for a serial search [1]. This methoddefines the gain functions that govern the transition from onecell to another, in order derive the system pgf PACQ(z). TheMAT is then given by the flow graph technique describedas:

E[TA] =

∣∣∣∣ ddzPACQ(z)

∣∣∣∣z=1

. (5)

The time needed to test a single cell is denoted as Tc seconds,and is a function of the integration time Ti. Moreover, after afalse acquisition, the system goes through a penalty time Tpin the tracking stage which is usually taken to be the track-ing transient time (around 500 ms) of a successful trackingoperation. In general, two options are considered for settingthe starting cell; uniform probability where the probability tostart from a specific cell is the same for all cells, and worst-case probability which is equivalent to scanning the H1 cellin the last position [2]. A similar analysis is performed fora double-dwell time detector in [3] and the correspondingMAT is found in Table I where Tv is the duration of the

verification procedure. The expressions in Table I are usedto compute the MAT for a range of ACQ thresholds. Thecurves in Fig. 2 are obtained, which yield an interestingcomparison of the performance of a single and double-dwelltime detectors in terms of MAT. In fact, examining a single-dwell time detector, the behavior of both curves relative to auniform and worst-case probability search orders are similar;the MAT decreases with increasing PD, continues decreasingwith decreasing PD and then unexpectedly starts increasing.This is the point where the term TpPfa starts weighing onthe system with respect to Tc (see expression in Table I). Itis worth mentioning that the curves are plotted assuming arange of increasing cell Pfa values, to which corresponds adecreasing acquisition threshold values and consequently anincreasing and a decreasing system PD as can be seen fromFig. 1. In fact, as the acquisition threshold is decreased, ahigher Pfa is expected together with a lower system PD.Consequently, in the absence of a penalty time due to wrongacquisition, a decreasing MAT is expected corresponding toan increasing Pd and a decreasing PD and B. Hence, at timeswhere TpPfa is relatively low with respect to Tc, the MATand PD as well as B are directly proportional. The oppositeis true for relatively high values of TpPfa with respect to Tc,corresponding to PD < 0.1 considered as the inflection pointof the curve relative to the uniform probability search orderwith Tp = 500 ms. In this portion of the plot, the MAT of asingle-dwell time detector and PD are inversely proportional.This inflection point moves to the left as the penalty timeincreases. In this way, depending on the penalty time, the useof a double-dwell time detector can be justified or not over asingle dwell time detector with no verification. In this case,the use of a double-dwell time detector is not justified for theoptimum value of B = Bopt, i.e. the value of B yielding theminimum MAT. In fact, it can be seen that for B = Bopt thecurve with verification results in a slightly higher MAT valuethan that corresponding to a single-dwell time. Conversely,beyond the inflection point, the MAT of a double-dwell timedetector and PD are directly proportional. This is of coursedue to the fact that when adopting a verification process,even if the acquisition threshold is not set correctly, it is lesslikely that the CAF crosses the threshold over a wrong cellfor several consecutive instances, and so the penalty time isavoided more often and does not weigh on the system forhigh Pfa. In fact, looking at Table I, the term TpPfa becomesTpPfaPfa,v , making it harder to be relatively bigger than Tcand TvPfa.

B. MAX search

The pure maximum or MAX search strategy is based onthe evaluation of the whole search space and picking thecell which holds the maximum value of the CAF withoutcomparing it to a threshold. This strategy is particularly usefulin a P2P environment where an indication of the presence ofa particular SIS by nearby peers is most likely to be true. Inthis case, there is no need to compare the maximum CAF

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Fig. 2. MAT vs ACQ threshold indicating the range of the ACQ thresholdfor which a verification procedure is justified.

TABLE IMAT OF SERIAL SEARCH STRATEGIES

Strategy MAT

SerialTc

Pd+

(Nc − 1)

Pd(Tc + TpPfa)

Worst-case

SerialTc

Pd+

(Nc − 1

2

)(2− Pd

Pd

)(Tc + TpPfa

)Uniform

SerialTc + TvPd

PdPd,v+

(Nc − 1

2

)·

uniform with

verification(2− PdPd,v

PdPd,v

)(Tc + TvPfa + TpPfaPfav)

value against a threshold. To derive an expression of theMAT, a similar approach as presented for the serial searchcan be followed, drawing a flow graph diagram and derivingthe corresponding pgf [3] to deduce the MAT with (5). Thisis a fairly simple procedure for a single-dwell time detector,whereas the situation gets more complex for a double-dwelltime detector. In fact, as previously mentioned in SectionII-B2, the verification process for a MAX approach consists incomputing the whole search space at least N times, instead ofjust a single cell. Assuming that Ts is the time spent to evaluatethe whole CAF, the MATs for a MAX approach are reportedin Table II where PMD,v = 1 − PD(1 − PD,v). As expected,the double-dwell time detector expression is simplified to thatof the single-dwell detector when PD,v and PE,v are replacedby 1 and Tv = 0 for a single-dwell time detector.

C. MAX/TC search

Unlike the MAX search, the MAX/TC search picks thecell relative to the maximum of the CAF and comparesits value to the acquisition threshold. In this case, the flowgraph diagram includes an additional gain function HM (z)representing the case of an immediate missed detection asseen in Fig. 3. The gain functions here are HD(z) =

Collect N

samplesHFA(z) HP(z)

HD(z)

ACQ

HM(z) Σ

+

+

Fig. 3. MAX/TC single-dwell time acquisition flow graph.

Collect N

samplesHFA1(z) HP(z)HFAV(z)

HNFAV(z)HD1(z)

HDV(z)

ACQ

HMV(z)

HM1(z) Σ

+

+

+

Fig. 4. MAX/TC double-dwell time acquisition flow graph.

PDzTs , H0(z) = HFA(z)Hp(z) = PE z

(Ts+Tp), HM (z) =PMDz

Ts and H0M (z) = HM (z) + HFA(z)Hp(z) witha pgf of PACQ(z) = HD(z)/(1 − H0M (z)). As in theserial search, the verification procedure is applied whenthe SIS is declared present, such that the acquisition flowgraph for the double-dwell time detector is represented inFig. 4. In this case, the gain functions are written asHD(z) = HD1(z)HDV (z) = PDPd,vz

(Ts+Tv) , HM (z) =HD1(z)HMV (z) = PD(1 − Pd,v)z(Ts+Tv), and H0M (z) =HM1(z) + HFA1(z)[HNFAV (z) + HFAV (z)Hp(z)] =PMDz

Ts +PE(1−Pfa,v)z(Ts+Tv)+PEPfa,vz(Ts+Tv+Tp) and

the pgf is equal to PACQ(z) = HD(z)/([1 − H0M (z)][1 −HM (z)]). The MAT for the single-dwell time detector asreported in Table II is obtained after substituting its pgf into(5). In a similar way, the MAT of a double-dwell time detectoris obtained:

T̄A =Pd,v

PDPMD,v[TsPMD + PE(Ts + Tv + TpPfa,v)]

+ (Ts + Tv)

(Pd,v

PMD,v+PDPd,v(1 − Pd,v)

P 2MD,v

)(6)

Fig. 5 shows the MAT curves vs ACQ threshold relative toall three considered search strategies with a single-dwell timedetector. In summary, for the minimum MAT values of eachstrategy, the MAX/TC together with the MAX strategy is themost performant strategy. The MAT values relative to bothmaximum search strategies are less than those of the serialsearch by almost two orders of magnitude and so maximum

TABLE IIMAT OF MAX AND MAX/TC SEARCH STRATEGIES

MAXTs

PD+

(1− PD

PD

)Tp

MAX/TC Ts + TsPMD

PD+ (Ts + Tp)

PE

PD

MAX withPD,v

PMD,v

[Ts + Tv

PMD,v+

1− PD

PD(Ts + Tv + TpPE,v)

]verification

MAX/TC with (6)verification

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Fig. 5. Performance comparison of all three search strategies using a standardACQ engine and a single-dwell time detector with a C/N0 = 40 dB-Hz anda Ti = 1 ms.

search strategies will be used in the next section as theoptimum search strategy for a standard ACQ engine.

IV. PERFORMANCE COMPARISON OF STANDARD AND P2PACQUISITION ENGINES

In this section, standard and special P2P acquisition enginesare confronted in terms of MAT. To guarantee a fair com-parison, a MAX or MAX/TC approach is selected for thestandard ACQ engine whereas a serial search is opted forthe P2P ACQ engine such that the best possible search isadopted for each case. In fact, a serial search is usually thebest choice for a P2P architecture where the search spaceis reduced to a few cells over which the CAF is computed.This is done by providing code delay and Doppler frequencyaiding with a certain accuracy, depending on the topology andsynchronization of the network [7]. Moreover, an innovativeacquisition approach, particularly favorable for weak signalconditions, is explored in a P2P setting where the coherentintegration time is set on the basis of the estimated C/N0

value made available by the P2P network [7].

A. Standard MAX search vs P2P serial search

For a time and frequency synchronized network to less thana µs and less than a tenth of Hertz, the P2P architecture

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Fig. 6. MAT and system PD performance of a P2P engine using a serialsearch with a C/N0 = 40 dB-Hz and a Ti = 1 ms.

offers an aiding which can reduce the search space to a fewchips and most likely a single Doppler step. The number ofthese candidate cells depends on the code delay and Dopplerfrequency step used in the acquisition engine. The code delaystep is usually half a chip whereas the Doppler frequencystep is set empirically to ∆f = 2/(3Ti). The MAT of a P2Pnetwork is computed using the same system probabilities asthose computed for a standard ACQ engine. This is becausealthough only L candidate cells are scanned in the P2P case,the remaining cells are nontheless existent and associated witha certain cell Pfa and Pd. The only difference in the MAT isthe scanning time, and to account for that, Nc is replaced byL the number of P2P candidate cells in the serial case, andTs is replaced by the corresponding P2P reduced search spacescanning time for the MAX and MAX/TC case. Assuming aC/N0 equal to 40 dB-Hz, Fig. 7 compares the performance ofa standard ACQ engine (shown individually in Fig. 6) using aMAX search to that of a P2P ACQ engine using a serial search.The plot also shows on the right vertical axis, the system PD

for each search strategy. First and foremost, the optimum MATof a P2P serial search is one order of magnitude lower thanthat of a standard MAX search (0.17 ms compared to 17.5ms). Moreover, the MAT curve of the MAX search growsexponentially with decreasing maximum CAF value comparedto the decreasing MAT of the P2P serial search with decreasingacquisition threshold as shown in Fig. 6. In fact, when themaximum value of the CAF is not so high, the MAT of a MAXsearch increases drastically together with a decreasing systemPD. This suggests that the MAX search is not a controllableenvironment and can yield very bad results. Similarly, Fig. 8compares the performance of a standard ACQ engine usinga MAX/TC search to that of a P2P serial search engine.The superior performance conveyed by the P2P architectureis demonstrated in this figure as well.

B. Standard MAX search vs CNR aided P2P serialsearch

A new P2P acquisition approach is analyzed herein, based onthe C/N0 aiding information shared by nearby peers. This

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Fig. 7. Performance of a P2P ACQ engine using a serial search comparedto a standard ACQ engine using a MAX search with a C/N0 = 40 dB-Hzand a Ti = 1 ms.

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Fig. 8. Performance of a P2P ACQ engine using a serial search compared toa standard ACQ engine using a MAX/TC search with a C/N0 = 40 dB-Hzand a Ti = 1 ms.

approach consists in setting the integration time as a functionof the weighted P2P CNR, the acquisition metric SNRc, non-coherent accumulations L, and the receiver bandwidth Bwith the aim of decreasing the MAT [7]. Using the equationreported in [7], the coherent integration time with no non-coherent accumulations can be obtained. In fact, Ti = 25 msfor a C/N0 = 20 dB-Hz, an acquisition metric of 4 dB, anIF bandwidth B of 1.023 MHz and a sampling frequency of2.046 MHz. In order to assess the impact of the integrationtime setting according to the CNR, it is worth checking theMAT performance in weak signal conditions.For a CNR of 20 dB-Hz and a typical Ti = 1 ms, the MATof both strategies, standard MAX/TC and a P2P serial ACQengine, significantly increases with a highly unreliable systemPD of the order of 10−5. Using this motivation, for the sameC/N0 = 20 dB-Hz, Fig. 9 shows the extent by which the CNRaided P2P acquisition is more performant in terms of MATthan the usual P2P engine with no integration time setting. Itis worth noting how this figure summarizes the relationshipbetween the system PD and the MAT. Indeed, as the systemPD relative to the usual P2P acquisition is much lower thanthat of the CNR aided P2P acquisition, its corresponding MATis higher by an order of magnitude. Both curves show the same

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T [s

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P2P Serial MATP2P Serial C/N

0 aided MAT

Serial PD

Serial C/N0 aided P

D

Fig. 9. Performance of a P2P serial ACQ engine in both cases: Ti = 1 msand an integration time set according to the P2P C/N0 aiding, i.e. Ti = 25ms with a C/N0 = 20 dB-Hz.

decreasing trend, which can be interpreted, following the sameline of thought presented in Section III-A, i.e. the fact thatTpPfa is relatively small with respect to Tc.

V. CONCLUSION

The MAT of a serial, MAX and MAX/TC search strategieswith or without verification have been analyzed in this paper,and closed form expressions have been derived using the ac-quisition flow graph technique. The performance improvementcontributed by a P2P network in terms of MAT is thoroughlyinvestigated by exploring two types of aiding, code delayand Doppler frequency aiding from one side and CNR fromanother. It is shown that together with the aiding availableto reduce the search space, exploiting the CNR aiding toset an appropriate integration time, further reduces the MATespecially in weak signal conditions.

REFERENCES

[1] J. K. Holmes, Spread Spectrum Systems For GNSS And Wireless Com-munications. Artech House, Boston, London, 2007.

[2] A. Polydoros and C. Weber, “A unified approach to serial search spread-spectrum code acquisition - part i: General theory,” IEEE Transactionson communications, vol. 32, no. 5, pp. 542–549, May,1984.

[3] J. H. J. Iinatti, “On the threshold setting principles in code acquisitionof DS-SS signals,” IEEE journal on selected areas in communications,vol. 18, no. 1, pp. 62–72, January,2000.

[4] G. Corazza, “On the MAX-TC criterion for code acquisition and its ap-plication to DS-SSMA systems,” IEEE Transactions on communications,vol. 44, no. 9, pp. 1173–1182, September,1996.

[5] N. Kassabian and L. Lo Presti, “Technique for MAT analysis andperformance assessment of P2P acquisition engines,” in The Position andNavigation System (PLANS) conference, Myrtle Beach, South California,US, April 2012.

[6] D. Borio, L. Camoriano, and L. Lo Presti, “Impact of GPS acquisition ondecision probabilities,” IEEE Transactions on Aerospace and Electronicsystems, vol. 44, no. 3, July, 2008.

[7] D. Margaria, N. Kassabian, L. Lo Presti, and J. Samson, “A New Peer-to-Peer Aided Acquisition Approach Exploiting C/N0 aiding,” in 5th ESAWorkshop on Satellite Navigation Technologies, ESTEC, Noordwijk, TheNetherlands, 8-10 December 2010.