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)