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Doctoral report of second year A Doctoral report is due at the end of the first and of the second academic year, before the final year examination and presentation of achievements to the PhD board. This form provides an index and brief description of the items that it should contain. Please leave blank if not relevant and do not change ordering and numbering of sections.
LAST NAME Filippini
NAME Francesca
CURRICULUM Radar and Remote Sensing
DOCTORAL CYCLE XXXII
Current year Second
Supervisor Fabiola Colone
Co-supervisor
PhD Advisory board P. Lombardo, R.Seu, M.Scarpiniti
Double-degree
1. Compliance of activities with doctoral program form of current year
During this year, I attended the 2nd IEEE AES Radar Summer School, which was held in Oklahoma City (OK),
USA and hosted by the organizers of IEEE Radar Conference 2018. Moreover, I attended two seminars
organized by Diet dept., namely ‘Come sbagliare il mio primo colloquio ’ from Dr. Roberto Vaino and the
introductive lesson of the PhD course Digital Calibration of Analog, Mixed-Signal and Radio-Frequency
Systems, from Dr. Pietro Monsurrò.
Moreover, I attended three Video Tutorials offered by IEEE AESS, namely
Bistatic and Multistatic radar – Prof. Hugh Griffith
Fundamental concepts in radar signal processing – Prof. Mark Richards
High level information fusion management and design –Prof. Erik Blasch
The research activities carried out during this year, as planned in the doctoral program form, concerned the
development of advanced processing techniques for Passive Coherent Location (PCL) systems, aiming at
improving their performance.
Sapienza PhD in ICT Doctoral program in Information and Communications Technologies at Sapienza Università di Roma, Rome, Italy
Specifically, the following activities have been carried out:
Threshold region performance of multi carrier ML DOA estimator The capability of estimating the direction of arrival of a target is a very important feature in radar
applications. Assuming the availability of a sensor array, collecting returns on multiple carriers
simultaneously, a theoretical study of the performance of a maximum likelihood estimator has been
carried out. In particular, we were interested in describing its performance in a low SNR scenario,
namely in the threshold region. Preliminary experimental results have also been obtained thanks to
real data set collected by Leonardo Finmeccanica S.p.A.
Long CPI : Range and Doppler migration compensation With the aim of increasing the detection of low RCS targets, or in order to broaden the coverage
area, long coherent processing interval (CPI) could be considered, if proper strategies are applied to
correct the range and Doppler migration effects. Specifically, two Doppler migration compensation
strategies have been considered and extensive analysis have been carried out on both simulated and
real data. This activity has been carried out along with Leonardo Finmeccanica S.p.A.
2. Courses and seminars During this year, I attended the following seminars:
Seminar Duration/Period Exam
Come sbagliare il mio primo colloquio - Roberto Vaino 28/11/2017 No
Seminario introduttivo per il corso Digital Calibration of
Analog, Mixed-Signal and Radio-Frequency Systems - Dr.
Pietro Monsurrò No
IEEE AESS video tutorial on Bistatic and Multistatic Radar -
Prof. Hugh Griffith No
IEEE AESS video tutorial on Fundamental Concepts in Radar
Signal Processing - Prof. Mark Richards No
IEEE AESS video tutorial on High Level Information Fusion
Management and Systems Design - Prof. Erik Blasch No
3. Other activities
During this year I attended the IEEE AES Radar Summer School, which was held in Oklahoma City (OK),
USA and hosted by the organizers of IEEE Radar Conference 2018. Thanks to distinguished lecturers,
experts in the field, this Summer Schoold allowed me to improve my knowledge on radar topics.
Other activities Duration/Period CFU
2nd IEEE AES Radar Summer School April 21-22
Oklahoma City (OK), USA 5+
Moreover, I attended one international conference and one international workshops. They are listed below.
Conference / Workshop Duration/Period
IEEE Radar Conference 2018 April 23-27 2018 - Oklahoma City (OK),
USA
2nd GTTI Radar and Remote Sensing Workshop
2018 May 28-29 2018 - Pavia, Italy
4. Research activities
As declared in the Second Year Doctoral Program Form, the main activities that have been be carried
out during the second year of my PhD are briefly summarized in the following. Specifically, they have been
focused on two different topics:
Threshold region performance of multi carrier ML DOA estimator
Long CPI : Range and Doppler migration compensation
Threshold region performance of multi carrier ML DOA estimator
Direction of arrival (DoA) estimation of narrow-band signals is a key problem in sensor array signal with
a variety of application fields, such as radar, sonar, mobile communications, etc. The conspicuous interest
attracted by this issue is testified by the amount of research literature dedicated to the topic.
A variety of advanced estimation methods has been proposed and their performances have been extensively
studied. However, the majority of studies published over the years addressed the problem of characterizing
the performance of DoA estimators under asymptotic assumptions, where asymptotic generally refers to
either a high number of samples or high signal-to-noise ratio (SNR) regime. Nevertheless, in many practical
applications, such conditions are unlikely to be continuously guaranteed. This is the case of passive location
systems, where the object of the location task could be an emitting source or a target that backscatters a
signal of opportunity, as in passive radar or passive sonar systems. The passive nature of such systems
intrinsically limits the possibility to fully control the performance for any target of interest. Specifically, the
DoA estimation accuracy largely depends on the power level and the transmission rate of either the emitting
source, in one-way propagation systems, or the illuminator of opportunity, in two-way propagation systems.
These parameters cannot be directly controlled by the system designer. Therefore it is not unlikely that the
aforementioned systems operate in the low SNR regime where accurate angular localization might represent
a challenging task. This is especially true when a limited number of receiving sensors is employed in order
to limit the system complexity.
As it is well known, at low SNR values, the estimation accuracy of a nonlinear DoA estimator rapidly
deviates from its asymptotic performance, experiencing the so-called threshold effect. This effect is
qualitatively shown in Fig. 1, where the mean square error (MSE) is reported versus the SNR: three regimes
can be identified, referred to as no information region (as SNR→0), threshold region and asymptotic region
(as SNR→∞). The Cramér-Rao lower bound (CRB), in dashed red, correctly describes the estimator
performance in the asymptotic region, but it is not able to predict the estimator performance for low SNR
values. In fact, while the CRB essentially depends on the local errors around the true value, the threshold
effect is due to outliers, namely global estimation errors that occur due to an actual estimate outside the
mainlobe. This issue has been addressed in the open literature by several authors. A number of lower bounds
has been proposed, accounting for the global errors contribution to the overall MSE, see e.g. the Barankin
bound , the Bayesian CRB, the Ziv-Zakai bound. An accurate approach to predict the threshold behavior of
a maximum likelihood (ML) DoA estimator for an array of sensors, receiving narrow-band signals from far-
field emitters, is to consider that the MSE is split into two parts, one coming from local errors obtained when
the estimates are close to the true value, and the other due to outliers.
We deal with the case of a multiple frequency (MF) ML DoA estimator that exploits a non-uniform linear
array receiving multiple signals simultaneously emitted at different carrier frequencies. We have referred to
DoA estimation based on the non-coherent exploitation of signals received at multiple carriers as a mean to
mitigate the problem of angular ambiguities in arrays composed by a limited number of antenna elements.
This idea is well known in radar applications and it is based on recognizing the change in the array grating
lobe pattern that results from the change of frequency.
Specifically, the purpose was to provide a reliable performance characterization of the MF ML estimator
in the threshold region, exploiting some recent results from the theory of indefinite quadratic forms in
Gaussian random variables to evaluate the probability of outliers for the considered estimator. With
reference to the source signal, two different models are considered, namely the deterministic and the
stochastic, also often referred to as conditional model assumption (CMA) and unconditional model
assumption (UMA), respectively. The theoretical derivations of the aforementioned expressions have been
reported in a recently submitted journal paper and they will not be reported here for simplicity.
Fig. 2 shows the Probability of Outliers versus the SNR under (a) CMA and (b) UMA for three different
case studies. Fig. 3 reports the results for the same case studies in terms of MSE under CMA. The curves
represent the derived expressions while the results of Monte Carlo simulations are reported in dots.
Fig. 1 Qualitate behavior of the MSE versus the SNR for nonlinear DoA estimation.
Three different operative regions are distinguished.
(a) (b)
Fig. 2 Probability of outlier under (a) CMA and (b) UMA for a three-element array 𝑑 = [0 2 6.8] 𝜆1 and :
- case A: three snapshots (𝑀 = 3) from one frequency channel (𝑁 = 1)
- case B: one snapshot (𝑀 = 1) from each of three frequency channels (𝑁 = 3) with wavelengths 𝜆1, 𝜆2, 𝜆3
- case C: three snapshots (𝑀 = 3) from each of three frequency channels (𝑁 = 3) with wavelengths 𝜆1, 𝜆2, 𝜆3
Fig. 3 Mean square error versus SNR under CMA for case studies A, B and C
The figures show the capability of modelling the estimator performance quite well. The capability to
predict jointly the threshold and asymptotic performance of the MF ML DoA estimator via the expressions
derived enables a fair comparison between different array configurations without resorting to time-
consuming Monte Carlo simulations. In addition, the benefits of the multi-carrier approach can be easily
characterized based on the developed tool. Finally, the results derived in this work could also be used to
carry out a robust design optimization of the sensor array layout.
Long CPI : Range and Doppler migration compensation
Long coherent integration times can be considered for the evaluation of the bistatic range-Doppler map,
if the range and Doppler walk effects are effectively corrected. By assuming a linear variation in both the
range and the Doppler domains, we can compensate for those effect according to a cascade of two processing
stages, namely the Range Migration Compensation (RMC) stage, followed by the Doppler Migration
Compensation (DMC).
With reference to the range migration, which represents the first limit when extending the coherent
processing interval, our research group has recently proposed and investigated effective strategies to
compensate for its effect. During the last months, we addressed the problem of the Doppler migration
compensation. Specifically, we considered two different approaches, say approach A and approach B,
sketched in Fig. 4. For both approaches, a closed form expression for the false alarm probability has been
obtained in order to set a proper threshold for the detection stage.
The results of the DMC approaches on a simulated target is reported in Fig. 5. An extensive analysis has
been carried out on both simulated and real data showing that both approaches effectively compensate the
target Doppler migration and that, in both cases, it is possible to control the false alarm probability. This
activity has been carried out in cooperation with Leonardo S.p.A. and the results of the extensive analysis
will be reported in a paper in preparation.
(a) (b)
Fig. 4 Main processing steps for Doppler migration compensation, according to : (a) approach A (b) approach B
5. Software
The research activities have been the developed in Matlab witch is a proprietary product of
MathWorks.
6. Periods abroad 7. List and description of applications/patents
8. Prizes and awards
June 2018: 2018 Premium Award for Best Paper in IET Radar, Sonar & Navigation for paper F. Filippini, F. Colone, D. Cristallini and G. Bournaka, "Experimental Results of Polarimetric
Detection Schemes for DVB-T Based Passive Radar", in IET RSN, vol. 11, no. 6, pp. 883-891, 2017.
April 2018: 2nd Best Student Paper Award at 2018 IEEE Radar Conference for paper F. Filippini, T. Martelli, F. Colone and R. Cardinali, "Target DoA estimation in passive radar using
non-uniform linear arrays and multiple frequency channels," 2018 IEEE Radar Conference (RadarConf18) ,
Oklahoma City, OK, USA, 2018, pp. 1290-1295.
(a)
(b) (c)
Fig. 5 Results on a simulated target with initial position [-18Km,0,0], using Tint = 2s, when the range-
velocity map is evaluated according to
(a) conventional CAF (b) RMC + DMC (approach A) (c) RMC + DMC (approach B)