Il corso si propone di illustrare il principio di funzionamento dei sistemi radar con particolare riferimento ai radar di sorveglianza. Il radar viene illustrato sia dal punto di vista dell'ingegnere "sistemista" che ha il compito di armonizzare i diversi componenti per il conseguimento della portata richiesta sia da quello dell'analista che ha invece il compito di studiare le strategie di processing ricorrendo all'analisi delle prestazioni e alla simulazione.
The course aims to explain the operating principles of radar systems, with a particular focus on surveillance radar. Radar is presented from both the perspective of the "systems engineer," whose role is to harmonize the various components to achieve the required range, and from the perspective of the analyst, who is responsible for studying processing strategies through performance analysis and simulation.
La verifica delle conoscenze è resa possibile mediante esercizi e attività di laboratorio.
Knowledge assessment is made possible through exercises and laboratory activities.
Il corso intende fornire agli studenti sia le nozioni di base necessarie sia per il progetto di un sistema radar sia per ottimizzare e implementare le moderne strategie di elaborazione del segnale.
The course aims to provide students with both the fundamental knowledge necessary for radar system design and for optimizing and implementing modern signal processing strategies.
La verifica delle capacità è ottenuta tramite progetti da risolvere utilizzando l'ambiente di sviluppo MATLAB in cui si richiede allo studente di applicare le nozioni apprese per l'analisi e l'elaborazione di segnali radar sia acquisiti da dispositivi reali sia riprodotti mediante simulazione.
The assessment of skills is achieved through projects that need to be solved using the MATLAB development environment. Students are required to apply the knowledge acquired for the analysis and processing of radar signals, both acquired from real devices and reproduced through simulation.
Lo studente potrà acquisire e sviluppare la sensibilità relativa al progetto di sistemi radar sia studiando il dimensionamento di massima dello stesso sia realizzando algoritmi di elaborazione e verificando la loro efficacia su dati sperimentali.
Students will have the opportunity to acquire and develop sensitivity related to radar system design by studying design methods and by developing processing algorithms, verifying their effectiveness with experimental data.
Lo studente potrà valutare la sua capacità di portare avanti in autonomia la gestione di un progetto durante le attività di esercitazione.
The student will be able to assess their ability to independently manage a project during the exercise activities.
Si ritengono propedeutici gli insegnamenti di analisi matematica, algebra, fondamenti di telecomunicazioni, teoria dei segnali e DSP.
Courses in mathematical analysis, algebra, fundamentals of telecommunications, signal theory, and DSP are suggested as prerequisites.
Le lezioni sono tenute mediante lucidi che coprono l’intero contenuto del corso. L’attività di laboratorio è documentata mediante il testo dei progetti da risolvere e la disponibilità di una traccia di soluzione in termini di codice MATLAB. Le esercitazioni sono anch’esse presentate tramite lucidi e rese disponibili sulla piattaforma teams insieme alle lezioni.
The lectures are conducted using slides that cover the entire course content. The laboratory activities are documented through project to be solved, along with the availability of a solution outline in terms of MATLAB code. Exercises are also presented through slides and made available on the Teams platform alongside the lectures.
Stima della densità spettrale di potenza: Stimatori non parametrici: Metodi indiretti e diretti. Il periodogramma: analisi delle proprietà di correttezza e consistenza. Metodi di Bartlett, Welch e Blackmann-Tuckey.
Metodi di predizione e filtraggio: Modello di un sistema dinamico a variabili di stato Il filtro di Kalman scalare: Equazione di stato e equazione di misura. Calcolo del guadagno di Kalman. Prestazioni del filtro. Condizioni di funzionamento a regime del filtro di Kalman. Modelli di sistemi vettoriali. Il filtro di Kalman vettoriale. Esempio dell’applicazione del filtro di Kalman al tracking di un bersaglio.
Outline of the radar system:
Overview of radar systems. Range and angle resolution. The Doppler effect. Block diagram of non-coherent and coherent radars. Signal analysis using complex representation. Intermediate frequency filter sizing. Filter adapted to an RF pulse and its simplified realization. Equivalent noise bandwidth of the RF pulse-adapted filter and straddle loss. "Colored" noise-adapted filter. Radar equation.
Pulse compression: LFM waveform and its use for improved range resolution. Spectrum of the LFM signal. Pulse compression using an adapted filter. Compression gain. Use of windows to reduce sidelobes and associated losses in terms of range resolution and gain. Laboratory: simulation of the LFM waveform, spectrum analysis, and implementation of the processing chain (adapted filter and windows for sidelobe reduction).
Radar clutter: Clutter in a radar system. Classification of clutter sources. Calculating clutter power from surface clutter in pulse-limited and beam-limited systems. Reflectivity: frequency and grazing angle dependence. Probability models for surface clutter: Weibull and K distributions. Illustration of clutter measurements and empirical models (GTRI). Volumetric clutter. Signal-to-clutter ratio. Models for the power spectral density of clutter.
Doppler radar: Target motion and Doppler frequency. Overview of Continuous Wave (CW) radar. Radar Moving Target Indication (MTI): two or more pulse cancellers and implementation of customized digital filters. Clutter improvement factor. Blind velocity problem and staggered PRF technique. Pulse Doppler radar. Data matrix. Range/Doppler plane analysis using FFT. Use of windows to reduce artifacts from sidelobes. Spectral resolution, peak and SNR losses, straddle loss, and zero padding. FFT as a bank of adapted filters. I/Q branch imbalance in the coherent demodulator. Digital I/Q. Laboratory: implementation of the processing chain on real I/Q data.
Elements of Decision Theory: Neyman-Pearson criterion. Decision based on a single pulse: ROC curves and their use in the maximum sizing of a radar system. Albersheim's empirical formula. Integration of M pulses in the Coherent Processing Interval (CPI). Coherent (perfectly known and known except for a constant phase) and non-coherent integration. Optimal strategy for coherent integration and ROC calculations. Optimal strategy for non-coherent integration and ROC calculations. Empirical formulas. RCS fluctuations and Swerling models I, II, III, IV. ROC curves and Shnidman's formula. Binary integration. Laboratory: implementation of the radar equation and calculation of the maximum detection range from system specifications.
CFAR Techniques: Sensitivity of decision performance to RCS variability. CFAR structure on white noise. Estimation window. CA-CFAR calculation of ROC for SW0 target and SNR loss. Masking due to extended target: guard window and its sizing. Introduction to GO-CFAR, OS-CFAR, Trimmed-Mean CFAR strategies. Clutter map CFAR. Laboratory: Illustration of CFAR strategy operation in the presence of multiple and extended targets.
Statistical Approach to Estimation Problems: Sample estimation, sample mean, and sample variance. Biased estimators and consistent estimators. Maximum Likelihood Estimation (MLE): Definition of likelihood for an unknown deterministic parameter. Maximum Likelihood (ML) estimator for a vector of unknown parameters. Joint estimator of mean and variance of Gaussian variables. Performance verification of an estimator through simulation. Search for optimal estimators: Minimum Mean Squared Error (MSE) criterion. Unattainable estimators. Unbiased estimators with minimum variance. Cramer-Rao theorem. Fisher information and CRLB for the case of mean estimator and variance estimator of a Gaussian variable. Cramer-Rao theorem for a vector of unknown parameters.
Bayesian Estimators: Cost function, average cost or Bayesian risk. Quadratic cost and derivation of the MMSE estimator: properties. Absolute cost and derivation of the MMAE estimator. Hit-Miss cost and derivation of the MAP estimator. Posterior probability density and finding its mode.
Linear Estimators: Optimal linear estimator according to the Minimum Mean Squared Error (LMMSE) criterion. LMMSE estimator for multiple observations. The orthogonality principle and its application in finding the LMMSE estimator. Causal Wiener filter and linear one-step or multi-step predictor. Whitening problem.
Parametric Models of Random Processes: AR(P) models. Difference equation for the autocorrelation function. Power spectral density in complex form. Yule-Walker equations. Whitening filter in the case of AWGN noise. Calculation of roots of the spectral density in complex form and selection of the minimum-phase filter of the AR model signal added to noise. ARMA(P,Q) models: finite difference equation for the autocorrelation function. MA(Q) models: transfer function of the model filter, zero-only model. FIR-type impulse response and determination of the autocorrelation function. Estimators of the autocorrelation function of a process. Criteria for choosing the order of an AR model. Partial autocorrelation coefficient and Levinson-Durbin method. Choosing the order of an MA model.
Power Spectral Density Estimation: Non-parametric estimators: Indirect and direct methods. The periodogram: analysis of correctness and consistency properties. Bartlett, Welch, and Blackman-Tukey methods.
Prediction and Filtering Methods: Model of a dynamic system with state variables. Scalar Kalman filter: State equation and measurement equation. Calculation of the Kalman gain. Filter performance. Steady-state operation conditions of the Kalman filter. Vector systems models. Vector Kalman filter. Example of Kalman filter application for tracking a target.
[1] M.A. Richards, J.A. Scheer, W.A Holm, Principles of Modern Radar, Vol. 1 basic principles, Scitech publishing, 2010.
[2] M. A. Richards, Fundamentals of Radar Signal Processing, McGrawHill Education, 2014.
[3] S.M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall, 1993.
[1] M.A. Richards, J.A. Scheer, W.A Holm, Principles of Modern Radar, Vol. 1 basic principles, Scitech publishing, 2010.
[2] M. A. Richards, Fundamentals of Radar Signal Processing, McGrawHill Education, 2014.
[3] S.M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall, 1993.
Lo studente non frequentante può seguire la struttura delle lezioni consultando il registro reso disponibile online dal docente e richiedendo i lucidi presentati o scaricandoli da Microsoft Teams creato appositamente per il corso. Lo stesso vale per le esercitazioni e le attività di laboratorio.
Non-attending students can follow the course structure by consulting the attendance register made available online by the instructor and by downloading the ìpresented slides from the Microsoft Teams page created for the course. The same applies to exercises and laboratory activities.
Prova orale (può richiedere l'uso dell'ambiente MATLAB).
Oral examination (may require the use of the MATLAB environment).