Maristella Musso1, Gianluca Gera2, Andrea Cattoni1, Carlo S. Regazzoni1. 1Department of ... BIOGRAPHY. Maristella Musso was born in Genoa (Italy) in 1977.
GNSS Multifrequency receivers in urban environment: Theoretical analysis Maristella Musso1, Gianluca Gera2, Andrea Cattoni1, Carlo S. Regazzoni1 1 Department of Biophysical and Electronic Engineering (DIBE) University of Genoa Italy 2 CNIT-DIBE Unit University of Genova
BIOGRAPHY Maristella Musso was born in Genoa (Italy) in 1977. She obtained the Laurea degree in Telecommunications Engineering in January 2003, University of Genoa, with a thesis concerning the study of an integration architecture, based on Software Defined Radio, of satellite positioning systems (GALILEO) and broadband communication systems (S-UMTS). From March 2003 she cooperates with the ISIP40 group, and she is also a Ph.D. student in Information Communication Science and Technology - Science and Space Engineering, her research topics are satellite multimedia communications and advanced positioning systems. She is author and co-author of a book contribution, journal papers and papers presented at international conferences. Gianluca Gera was born in Genoa (Italy) in 1972. He obtained the Laurea degree in electronical engineering in July 1999, University of Genoa, with a thesis concerning the simulation and performance evaluation of high-bitrate transmission systems over HFC networks in remote cable-based video-surveillance applications. From March 1999 he cooperates with the ISIP group. In June 2003, Dr. Gera obtained the Ph.D. in Space Science and Engineering at the University of Genoa, discussing a thesis about signal processing methodologies for interference robust acquisition and tracking in Galileo receivers. Gianluca Gera is author and co-author of more than 20 contributions published on international journals, edited books, international conferences. Andrea Fabio Cattoni was born in Genoa (Italy) in 1979. He obtained the Laurea degree in Telecommunications Engineering in June 2004, University of Genoa, with a thesis concerning feature reduction algorithms for remote sensed hyperspectral images.
From October 2004 he cooperates with ISIP40 group, he worked on Cognitive Radio techniques and location systems. From January 2005 he is a PhD student in Information and Communication Science and Technology – Space Sciences and Engineering, his research topics are: advanced positioning systems and distributed Cognitive Radio technologies. He is author and co-author of some papers presented at international conferences. Carlo Regazzoni was born in Savona (Italy) in 1963. He is Associate Professor in Telecommunications at the Department of Biophysical and Electronic Engineering (DIBE) of the University of Genoa. He obtained the "Laurea" degree and the Ph.D. in Telecommunications and Signal Processing in 1987 and in 1992, respectively. He is responsible of the Signal Processing and Telecommunications Group at DIBE. His main research interests are: video processing and understanding, software radio communications, data fusion and multimodal localization. He was co-editor of several books and Guest editor of four Special Issues on International Journals. He is author or co-author of more than 50 papers in International Scientific Journals. ABSTRACT In this paper, a theoretical approach for the analysis of synchronization performances in GNSS receivers adapted to reduce errors, especially caused by multipath fading, in a urban environment is proposed. In particular, two kinds of bi-frequency receivers based on data fusion methods are analyzed. The performances have been evaluated by comparison of simulated results in a real case and theoretical values based on the dispersion of the S-curve, the characteristic curve output of the DLL. One way to cope with multipath effects is equipping receivers with software modules able to reduce multipath effects.
This paper explains two different methods based on data fusion and in particular on fusion between different frequencies. It is shown that improvement is possible if and when the multipath can be considered independent for two frequencies properly spaced in the frequency domain. A theoretical analysis has been carried on together with computer simulation. The signal channel model has been developed with Galileo in mind to show how data fusion techniques can be applied exploiting the frequency diversity. The receiver modules taken into account are the Equal Gain Combining (EGC) and the Adaptive Gain Combining (AGC). Starting from the statistical model of a classical DLL code-tracking system, a theoretical model for both EGC and AGC is derived. To verify the correctness of the theoretical model, a simulation environment has been set up, with the possibility of varying different parameters. The multipath model is referred to an urban environment. Results are shown both for EGC and AGC receivers. Correct decision probability in the considered cases has confirmed the results in the simulated cases. INTRODUCTION The GPS system modernization phase and the Galileo system development will increase signal availability and hence GNSS system-based applications. This extended evolution of GNSS-based applications will imply the growth of fast and precise navigation systems. In fact GNSS systems are of enormous benefit to myriad military, civil, commercial, and scientific users around the world: in fact different fields of application will benefit of this evolution, like car navigation, automatic position reporting during emergency mobile phone calls, monitoring of Earth crustal deformations. This variety of uses pervades almost every aspect of GNSS activity and provides the stimulus for its future improvement. For all these causes, in the past few years, there has been a growing interest in the research on the development of techniques and methods for improving the signal reception, because to reach the high performances required by this kind of applications it’s necessary to design receivers which allow an accurate estimation of the Time Of Arrival (TOA) of the satellite signal. In fact the computation of the user’s position is based on a trilateration algorithm which employs TOA ranging. Errors and non accurate estimation of TOA have direct effects on the position accuracy. GNSS systems are based on direct-sequence code division multiple access (DS-CDMA) and to estimate the propagation time of the incoming satellite signal (or Signal In Space - SIS) they employ a synchronisation system. It can be divided into two different stages which distinguish different usage moments: • The coarse alignment (or first acquisition stage); • The fine synchronisation (or fine tracking).
The first acquisition stage represents the coarse code synchronisation process. The goal of this stage is to solve code phase errors within a certain bound. The trackingstage aims at resolving the error on time precision. The remaining error after the acquisition-stage is too large to guarantee proper operation. Therefore, a fine-tuning process, “code-tracking”, is needed. This process is a twoway search, meaning that the local replica can be shifted forward and backward. Tracking is continuously performed during data-detection and keeps the timingerror below an acceptable level. Unfortunately, an electromagnetic wave can be reflected by the presence of obstacles such as mountains, buildings, objects or atmospheric disturbances. This factor, better known as “multipath fading”, creates replicas that can be summed up to the direct LOS (Line of Sight) path where multipath fading causes distortions of the received signal. Each path is characterized by a different length, so the spectral components of the received signal are affected by phase and amplitude variations. Another problem, in terms of time, lies in the fact that the received signal suffers a delay spread due to multipath propagation. Multipath fading, in the urban canyon model, heavily affects the received signal so that the Delay Lock Loop (DLL) performances are reduced. Multipath fading, being a dominant source of error in navigation applications, has received considerable interest and is the subject of extensive research. In this paper a theoretical analysis of innovative techniques to reduce the multipath effects on the DLL will be presented. The considered architectures are based on the well known Early-Late scheme, and the chosen discriminator function in this paper is the Early Minus Late Envelope Normalized Function (EMLEN). In particular two bi-frequential receivers which employ the frequency diversity are shown. This paper is structured as follows: after this brief introduction, in the first paragraph the signal model used for the experiments is explained, than a description of the analysed fusion systems and a theoretical analysis are pointed out. Finally the experimental results based on a signal simulator able to model the GNSS system in an urban environment and theoretical values are showed followed by the conclusions. SIGNAL AND CHANNEL MODEL Galileo, the future European navigation system, is still now in the definition, design and development phase. Galileo system, like GPS, will be divided into a space segment, composed by a constellation of MEO (Medium Earth Orbit) satellites, which broadcast navigation information by using the multi-user CDMA technique, and a ground control segment. The World Radio Communication Conference (WRC), Istanbul 2000, assigned to Galileo a frequency plan which includes five sub-bands, four in L band and
one in C band, i.e. E5, E6, E2, E1 and C [1][2][3]. In the succeeding years some modification had been carried to the frequency plan, like the division of the E5 band into two ulterior sub-bands: E5A and E5B, respectively 1176,45MHz and 1207,14MHz. In this paper we’ll focus our attention on an E5 transmission system: the receiver will able to exploit the subdivision of the E5 band into E5A and E5B to provide a better localization accuracy due to the joint use of the information from the E5 subbands. In the present paper the considered signal is composed by a carrier frequency modulated by spread spectrum codes and a QPSK (Quadrature Phase Shift Keying) modulated data signal both on E5A and E5B; then these two QPSK modulated data signal are recombined before high frequency transmission. A two level coding has been taken into account: the primary code is based on Gold sequences with length 16383 cut to 10230 modulated by a secondary code; the resulting code has the length of the longer one. The message has a rate of 125 bps, and it’s QPSK modulated, with the in-phase signal carries the navigation data while the quadrature signal is used as a pilot signal actually without any carried data. From the receiver point of view, the signal sensed by the receiver’s antenna can be modeled as [4]:
r(t) = a ⋅ d (t ) ⋅ s[t −τ ]⋅ cos[ϖ 0 (t −τ ) + φ ] +η(t ) = g(t ) +η(t )
(1)
Where: − − − − −
a represents the LOS attenuation coefficient d and s represent, respectively, the signal and the spreading code τ is the delay of the signal φ is the carrier phase η ( t ) represents the Gaussian noise
Especially in urban environments, the signal is affected by multipath, hence M different paths should have been considered, re-writing the signal as follows: M
r(t) = a0 g(t) + ∑ai gi (t −τ i ) +η(t) i=1
(2)
Where: − ai represents the i-th attenuation coefficient − gi represents the delayed replica of the signal − M is the total number of reflections − τ i is the delay of each path − η ( t ) represents the Gaussian noise The first term of the previous equation represents the LOS component of the signal while the second one is the noise due to replicas and Gaussian noise. Owing to the variability and heaviness of the channel conditions, the error caused by multipath fading strongly limits the performances of the receiver. This phenomenon is of considerable interest. Several advanced signal-processing
techniques have been devised to improve the performances of receivers affected by multipath fading, and multipath mitigation techniques for navigation systems are under of continuous research. From this equation it’s possible to evict that multipath has effects not only on the distortion of the PRN (PseudoRandom Noise) code, which is modulated by the carrier, and of the signal, but also on the phase of the signal itself. METHODS TO REDUCE MULTIPATH Different methods have been proposed to reduce the multipath problems. In particular, there are two ways to cope with multipath effects: using specific antennas and equipping receivers with software modules able to reduce multipath effects. In the field of antennas, an antenna specifically designed to fight against multipath is the choke ring [8]. The major problem of this solution is that, depending on the multipath, the antenna must be set up, so this solution is not suitable for fast-vehicle applications such as those in the field of avionics. The software modules to mitigate multipath errors can be classified in different types on the basis of the used techniques. Typical methods are based on correletors (Narrow Correlator [9], Edge Correlator, Early-Late Slope, Strobe Correlator [10]) or on multipath estimation (Multipath Estimation Technology, Multipath Estimating Delay Lock Loop [11]). Innovative techniques are based on wavelets [12], neural networks [13] or on fusion between different systems or different frequencies [15]; in the last case, to evaluate the behaviour of the fusion system, a theoretical analysis is required. In this paper the previous suggested theoretical analysis of two different methods based on frequency diversity characteristics are presented. In fact it’s possible to fuse the information carried by the signal in the two different bands E5A and E5B to improve the accuracy of the code tracking module. The possible improvement is due to the multipath that can be considered independent for two frequencies properly spaced in the frequency domain. In both proposed methods the used discrimination function is the Early Minus Late Envelope Normalized function (EMLEN) [5]: D(τ ) =
2 2 2 2 I ES (τ ) + QES (τ ) − I LS (τ ) + QLS (τ )
(3)
I (τ ) + Q (τ ) + I (τ ) + Q (τ ) 2 ES
2 ES
2 LS
2 LS
where: − IES and ILS represent the early and late correlation values for the in phase component of the received signal − QES and QLS is the early and late correlation values for the quadrature component of the incoming signal.
The EMLEN function has been chosen, even if it has on high computational cost, because it achieves best performances in the Gaussian environment. From the receiver point of view the discriminator’s output is the feedback signal to control the local code replica. The general DLL architecture can be seen in Figure 1.
R EGC =
1 ⋅ (R1 + R2 ) 2
(4)
where R1 and R2 are the observed variables and REGC the resulting pilot signal. Finally the decision process allow to perform the fine code tracking synchronization shifting the local replica for both the considered bands. ADAPTIVE GAIN COMBINING (AGC) RECEIVER To improve the performances of this kind of data fusion techniques based on signal combining, a receiver able to adapt the combining gains basing on the Signal-to-Noise Ratio (SNR) of the received signal has been implemented, as shown in Figure 3, and simulated.
Figure 1 General DLL architecture As visible the discriminator is an error function that depends on the correlation function. The S-curve is a characteristic signature of the tracking code block, that relates the discriminator output and the shift of the local replica [6], and its shape looks different according to the chosen discriminator function. Due to this fact the theoretical analysis in the follow is based on the S-curve. In the following two paragraphs these two methods [15] are briefly described. EQUAL GAIN COMBINING RECEIVER The first analyzed receiver is the Equal Gain Combining one, which performs a division of the received signal into the two sub-bands, hence the two IF demodulated signals are correlated with the PRN local replica, as shown in Figure 2.
Figure 3 AGC proposed receiver The receiver, called Adaptive Gain Combining (AGC) receiver, performs an estimation of the SNR, for each code epoch and for each path; to increase the accuracy of the evaluation, in each epoch an average with the previous evaluation is computed. More is the number of available measurements, more is the accuracy of the SRN estimation. This information is used to fuse the two signals with a weighted average, whose weight are proportional to the estimated SNRs and normalized respect to the sum of the two SNRs. The considered fusion technique can be written as:
RADAPT = w1 ⋅ R1 + w2 ⋅ R2
Figure 2 EGC proposed receiver The correlations with the Early and Late replicas are then processed by the EMLEN blocks, whose outputs, which represent the information extracted by E5A and E5B bands, are fused in a unique pilot signal; the used fusion technique is the computation of the arithmetic average for the prevision information:
(8)
where R1 and R2 are the observed variables, RADAPT the resulting pilot signal and w1 and w2 the weighting coefficients. These coefficients w1 and w2 are obtained by estimating variances on the two different paths. Precisely w1 and w2 are defined as:
w1 =ˆ
σˆ r2
2
σˆ + σˆ 2 r1
2 r2
and w2 = ˆ
σˆ r2 1
σˆ + σˆ r2 2 r1
2
(9)
where σˆ r2 and σˆ r2 are respectively the estimation of the 1 2 variances on the first (about the E5A frequency) and on the second path (about the E5B frequency) obtained by the average of the measure of the variances made every epoch. THEORICAL MODEL To evaluate the performances of the proposed methods it’s possible to define a theoretical framework for the receiver. A statistical model of a classical DLL code tracking system can be found in [7]; starting from this formulation it’s possible to derive the theoretical model for S-curve both EGC and AGC receivers. In fact for each branch of the receiver it’s possible to extract the probability density function of discriminator output and than these outputs can be combined. The chosen discriminator function, see (3), evaluates the difference between the correlation of the received signal with early and late local replica. The presence of an additive band pass Gaussian noise n has been considered and, thanks to the equivalent base band model, its effects on the two signal components can be modelled as [7]: I XS (τ ) = I X (τ ) + ni for the in phase component QXS (τ ) = QX (τ ) + nq
for the in quadrature component
and σ 2 = σ i2 = σ q2 where E {n} = 0 ⇒ ⎪⎧ E {ni } = 0 ⎨ ⎪⎩ E {nq } = 0 for X=E or X=L. Some approximations of the square roots of the function (3) allow to extract two random variables [7] both for the numerator and for the denominator:
•
X N (τ ) =ˆ RE (τ ) − RL (τ )
•
X D (τ ) =ˆ RE (τ ) + RL (τ )
Both can be described as linear combinations of Gaussian pdfs, hence the final obtained pdfs are Gaussian too. A random variable d, obtained from the ratio of the previously shown r.v., can be defined as [7]:
d (τ ) =ˆ
X N (τ ) X D (τ )
if τ is fixed, d(τ ) characterizes the variation of S-curve function respect to its ideal case, when the presence of noise disturbs the functioning of the system. Being: − z = d (τ ) : the “dispersion” of S-curve for a τ delay as input to the discriminator function − x = X N (τ ) : the random variable of the discriminator function numerator
y = X D (τ ) :
−
the random variable of the discriminator function denominator − x = mN (τ ) : the expected value of the discriminator function numerator y = m D (τ ) : the expected value of the discriminator function denominator It can be shown [7] that the pdf of z =ˆ x is: y
−
p z (z ) =
k −c kb π e e + 2a a a
b 2 − 4 ac 4a
⎛ b ⎞ erf ⎜ ⎟ ⎝2 a ⎠
(10)
where: k =ˆ
1 4πσ
2
a =ˆ
z2 +1 4σ 2
b =ˆ
(
− xz + y 2σ 2
)
c =ˆ
(x
2
+y
4σ
2
2
)
Obviously, the previous formulas are valid when the correlation values are non zero. This pdf is the basis of the following analysis. In fact the ECG and the AGC receivers can be analysed with the aid their pdfs. These can be obtained for the two different paths pdfs, called pE 5 A ( z ) and pE 5 B ( z ) respectively. For major clearness the previous two schemes can be summed in Figure 4. The difference is given only by the values of the two weights.
Figure 4 Fusion schemes Therefore
s fus = nE 5 A ⋅ s E 5 A + nE 5 B ⋅ s E 5 B
(11)
Where n E 5 A + nE 5 B = 1 Thanks to the frequency diversity the two variables can be considered independent. Considering
u = nE 5 A ⋅ s E 5 A and
v = nE 5 B ⋅ s E 5 B the pdf of the
s fus signal is:
ps fus ( s fus ) = pU (u ) * pV (v) Where
(12)
⎛s ⎞ ⎛s ⎞ psE 5 A ⎜⎜ E 5 A ⎟⎟ psE 5 B ⎜⎜ E 5 B ⎟⎟ ⎝ nE 5 A ⎠ and p (v) = ⎝ nE 5 B ⎠ pU (u ) = V nE 5 A nE 5 B
In Figure 5 all these two effects are shown.
Therefore
⎛ 1 ⎛ s ⎞⎞ ⎛ 1 ⎛ s ⎞⎞ ⋅ psE5 A ⎜⎜ E5 A ⎟⎟⎟⎟ * ⎜⎜ ⋅ psE 5B ⎜⎜ E5B ⎟⎟⎟⎟ (13) ps fus (s fus ) = ⎜⎜ n n n ⎝ E 5 A ⎠ ⎠ ⎝ E 5B ⎝ nE5B ⎠⎠ ⎝ E5 A Due to the fact that pU (u ) and pV (v) can be evaluated by (10) a theoretical pdf for the analysed fusion system has be obtained by the numerical convolution of the pdf on the considered frequency. As already said the difference of the two receivers is the n1 and n2 values. In the EGC case the weights are set to ½ for all the analysis; on the contrary in the AGC case the two weights are varied each epoch on the base of the an estimation of the noise and therefore an estimation of the less corrupted frequency. RESULTS In general the pdf functions allow one to compute the “dispersion” that the noise makes on the S-curve and therefore the correct decision percentage of the analysed system. In this paragraph some theoretical results has been compared with simulated ones. In order to analyze the systems in a first phase a simulation environment [12] has been set up. This is able to vary different set of parameters: i.e. the carrier to noise ratio and the signal carrier frequency. For this purpose the transmission system has been simulated by using MATLAB™ SIMULINK™ 6.0 environment. It has been necessary the insertion of the multipath propagation caused by the presence of obstacle, such as mountain, buildings or object that create, by reflection, replicas that can summarized with the direct LOS signal. This has been modeled as a tapped delay line with Rayleigh distribution. In these cases the considered multipath is always characterized by a Doppler Spread of 100Hz, typical value for land mobile and aeronautical environment More in particular, in the follow, a multipath channel characterized by 28 replicas with a spacing of 1/8 Tc (chip time) has been considered. One of the most important characteristics of the pdf curve is that the width of the dispersion depends closely on the inserted noise. In presence of only additive noise the model shows, as expected, that the dispersion is when C/N increase. In presence of multipath two principal effects are visible: • the dispersion is more spread than the ideal case and meanly different varying the operating frequency • a translation from the ideal centre caused by replicas that modify the correlation form.
Figure 5 Different multipath effect on the two frequencies In the considered case the multipath on the two frequency is independent EGC RECEIVER In [15] simulated results have shown the possibility to improve the synchronization with an EGC data fusion method. This fact is visible in Figure 6 in which a comparison between different S-curves has plotted in case of multipath presence and C/N0=34dB-Hz. The hypothesis has been done that multipath is more strong on a band, in this case on the E5A band. Therefore an improvement of the S-curve, especially related to the E5A frequency is shown.
Figure 6 Comparison between S-curve of EGC method and ideal case in multipath environment (C/N0 = 34 dB-Hz) By applying (12) and (13) an analysis of correct decision probability (Pd) improvement on the E5A signal strengthened by the other observation on the E5B band can be carried out. The Pd has been calculated by an integration of the pdf numerically obtained by (13) between the thresholds –0,5 and 0,5. These values have been chosen because are generally used in a classical DLL receiver.
As already said in this case n1 and n2 are set to the same value, i.e.
n1 = n2 =
1 2
In Table 1 the correct decision probability is shown in the three considered cases: E5A single frequency, E5B single frequency and EGC receiver. Even if the considered case is characterized by a heavy multipath and a low carrier to noise ratio as expected the improvement on the E5A band is significant respect to the reduction of the E5B correct decision.
E5A Single Frequency E5B Single Frequency Equal Gain Combining (EGC)
Correct Decision Probability 43.5 53.2 51.3
Table 1 Correct Decision Probability Comparison in case of C/N0=34 dB-Hz Similar results can be obtained with different carrier to noise ratios. In Table 2 and Table 3 the correct decision probability in case of C/N0=37 dB-Hz and 40 dB-Hz has shown. Receiver type E5A Single Frequency E5B Single Frequency Equal Gain Combining (EGC)
Correct Decision Probability 48.5 60.1 56.1
Table 2 Correct Decision Probability Comparison in case of C/N0=37 dB-Hz Receiver type E5A Single Frequency E5B Single Frequency Equal Gain Combining (EGC)
Correct Decision Probability 55 65.6 60.3
Table 3 Correct Decision Probability Comparison in case of C/N0=40 dB-Hz AGC RECEIVER In this case through the estimator of the signal-to-noise ratios it is possible that the receiver configures itself in optimal way to look for the weights, in order to guarantee a good trade off between the code tracking on both frequencies. This fact is clearly visible in the following figure (Figure 7). The AGC fusion system has been simulated for ten different epochs, in an already described channel. The multipath is time-varying and characterised by a Doppler Spread of 100Hz. In this case the S-curve of the AGC fusion system is more and more similar to the ideal.
Figure 7 AGC receiver: resulting S-curve for 10 different epochs The analysis of the correct decision probability has been made, as in the previous case, from (13). Due to the fact that the weights are derived from channel estimation, the following figures are obtained from a mean of 200 correct decision probability values. In fact 200 different sequences of 10 weights extracted from the considered channel have been used to implement the theoretical pdf (13). As visible in all the figures the performances improve during the time. Each simulation cycle is an epoch of pseudo noise code. In Figure 8 the percentage in case of C/N0=34 dB-Hz is shown. This case is principally influenced by the AWGN channel. Therefore the advantage due to the weights values obtained from a multipath influence and consequently of are not very evident. However a performance improvement is present. P (C/N = 34 dB-Hz) d
o
52 51.8 Percentage
Receiver type
51.6 51.4 51.2 51
2
4
6 cycle
8
10
Figure 8 Correct decision probability percentage with C/N0=34 dB-Hz The previous considerations are clearer with an analysis of the data in different carrier to noise ratio situation.
P (C/N = 37 dB-Hz) d
o
CONCLUSIONS AND FUTURE WORKS
58
Percentage
57.5 57 56.5 56 55.5
2
4
6 cycle
8
10
Figure 9 Correct decision probability percentage with C/N0=37 dB-Hz As expected in all the shown cases (Figure 9, Figure 10 and Figure 11) a performances improvement with the cycles increase is present. Moreover better results can be reached with high carrier to noise ratios. However a comparison between the percentage improvements shows that the AGC receiver is better adapted to the multipath presence. In fact in ten cycles the increment of correct decision probability is more than 2% in case of C/N0=43dB-Hz, i.e. in the case in which the major source of error is the multipath. P (C/N = 40 dB-Hz) d
o
63
ACKNOWLEDGEMENTS
62.5 Percentage
In this paper a theoretical model able to analyse the correct decision probability in the DLL block has been developed and used as basis to verify the performances of two GNSS systems to reduce multipath effects. A comparison between theoretical and real performances of bi-frequency receivers has been shown, by using a signal simulator able to model the GNSS system in an urban environment. More in particular this simulator has modelled multicarrier navigation systems, such as Galileo, in a channel characterised by additive gaussian noise and time varying multipath fading. Correct decision probability in the considered cases has confirmed the results obtained in the simulated cases. In particular in an AGC receiver it has been proved an improvement more significant in channel characterised by the presence of multipath as main source of noise. For future works, more experiments involving different types of multipath should be carried out. Furthermore, to have a more general model, different sources of interferences could be inserted both in the theoretical model and in the simulated system. In this manner the model could be useful further to recognize the performances of new receiver techniques, but also different type of interferences.
62
Authors wish to thank Mr. Marco D’Addezio for his valuable contribution to the collection of the paper results.
61.5 61
Reference 60.5 60
2
4
6 cycle
8
10
Figure 10 Correct decision probability percentage with C/N0=40 dB-Hz
[1] European Commission, “Galileo-Mission High Level
[2]
[3] P (C/N = 43 dB-Hz) d
o
65.5
Percentage
65
[4]
64.5 64
[5]
63.5 63 62.5
2
4
6 cycle
8
10
Figure 11 Correct decision probability percentage with C/N0=43 dB-Hz
[6]
[7]
Definition”, Doc. EMRF 5/5/2 (Pt.2), ESA, April 2001 Guenter W. Hein and Bernd Eissfellen “Galileo designe options for the european GNSS – 2”, Galileo -NavTech seminar, ION GPS 2001 G.W. Hein, J. Godet, J.L. Isseler, J.C. Martin, R.L. Rodriguez, T. Pratt, “Status of Galileo frequency and signal design”, European Commission, September 2002 Parkinson W., J.J. Spilker Jr ’Global Position System: Theory and Applications’ – volume 1, Editor Axelrad – Enge, 1996 Elliot D. Kaplan (Editor), ‘Understanding GPS: Principles and Applications’, Artech House Telecommunications Library, 1996. P. Misra, P, Enge, “Global Positioning System: Signals, Measurements, and Performance” GangaJamuna Press. Massachusetts, 2004. M. Musso, G. Gera, C.S. Regazzoni "Theoretical Analysis of S-curve for GNSS System", ION GNSS
2004 conference, Long Beach, California, 21-24 September 2004 [8] A. Brown, “Multipath Rejection Through Spatial Processing”, ION GPS-00, Salt Lake City, UT, September 2000. [9] Van Dierendonck, A.J., ‘Theory and Performance of Narrow Correlator Spacing in a GPS Receiver’, Navigation: Journal of The Institute of Navigation, vol.39, No.3, Fall 1992. [10] A. Cichra, R. Kaufmann, M. Sust, “Comparison of global navigation satellite system receiver multipath mitigation techniques”, GNSS-03 conference, 22-25 April 2003, Graz Austria [11] B. R. Townsend, P. C. Fenton, K. J. Van Dierendonck, “Ll Carrier Phase Multipath Error Reduction Using MEDLL Technology”, ION GPS-95, Palm Springs, CA, September 1995 [12] Yujie Zhang, Chris Bartone, “Real-time Multipath Mitigation with WaveSmoothTM Technique using Wavelets” ION GNSS 2004, 21-24 September. 2004, Long Beach, CA [13] G. Gera, M. Musso, S. Piva, C. S. Regazzoni, "Neural Networks algorithms for Improving Delay Lock Loops Performances for Navigation Satellite Systems in urban environment", GNSS-03 conference, 22-25 April 2003, Graz Austria [14] F.M. Gardner, J.D. Baker, “Simulation techniques“, Wileyn New York, 1997 [15] M. Musso, G. Gera, C. Regazzoni, “Data Fusion Techniques for Multi-frequency Navigation Receivers” ENC-GNSS 2005 Conference, 19-22 July 2005 Munich Germany
