This work summarizes the author's research on radar applications of methods resulting from the assumption of signal sparsity. The term sparsity means that a signal under investigation may be modeled with a small number of components taken from a large dictionary. This property makes it possible to employ a new class of mathematical methods, recently made known as Compressive Sensing framework, for recovering the signal from the measured samples. The main feature of sparsity-based methods is that they can recover a signal uniquely from much fewer samples than methods derived from the classical sampling theory. However, this is possible only if me sparse model is adequate and if the model dictionary and measurement process conform to the specific requirements of the mathematical framework. In the present work, the author demonstrates how the mathematical theory of sparse representation and recovery may be applied to practical problems arising in radar signal processing. An overall purpose of radar signal processing is to acquire the knowledge of the radar scene from the received echo of a radio frequency signal which illuminates the investigated area. This is a problem generally belonging to the class of inverse problems, which may be ill-conditioned and ambiguous. The assumption of the sparse model of the received signal is an innovative idea that opens new possibilities of resolving ambiguities. The aim of this work was to demonstrate by means of practical examples that sparse reconstruction methods are capable of solving a series of important problems in different areas of radar signal processing. Also, more detailed research was done on these cases, including the study on sampling requirements as well as simulations of the algorithms used. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter.The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. vThe ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter.The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter. The ideas and methods were verified with the use of live recorded signals wherever possible. In the examples presented in this work, sparsity of the signal model is the key assumption to enable the solution of relevant inverse problems. The application areas described here are closely related to the author's experience with existing radar systems, including those currently under research or development at the Warsaw University of Technology. They cover a wide range of radar types and processing modes, including active and passive radars as well as surveillance and imaging ones. The author proposed applications of sparsity-based methods for active radars with a noise waveform, for classical MTI radars, and for imaging radars, using either die synthetic aperture (SAR) technique with noise illumination, or the inverse synthetic aperture (ISAR) technique with passive illumination from a GSM transmitter.
Praca podsumowuje badania autora na temat radiolokacyjnego zastosowania nowatorskich metod wynikających z założenia o rzadkim modelu sygnału. Pojęcie to oznacza, że dany sygnał może być modelowany jako liniowa kombinacja niewielkiej liczby składowych należących do pewnego, z założenia pojemnego, słownika. Przyjęcie lego założenia otwiera możliwość zastosowania nowej klasy metod matematycznych, znanych od niedawna pod wspólna nazwą "Compressive Sensing" (po polsku ostatnio używa się określenia "oszczędne próbkowanie"), do odtworzenia sygnału ze zmierzonych próbek. Najważniejsza cechą tych metod jest możliwość odtworzenia sygnału ze znacznie mniejszej liczby próbek niż wynikałoby to z założeń metod klasycznych (opartych na twierdzeniu o próbkowaniu). Należy jednak podkreślić, że jest to możliwe tylko pod warunkiem adekwatności modelu rzadkiego oraz spełnienia pewnych wymagań przez słownik oraz przez proces pomiaru, zgodnie z teorią matematyczną oszczędnego próbkowania. W przedstawionej pracy autor pokazuje, w jaki sposób rzadki model sygnału i matematyczna teoria oszczędnego próbkowania mogą być użyte w zagadnieniach praktycznie występujących w radiolokacji. Ogólnym celem przetwarzania sygnałów radiolokacyjnych jest uzyskanie wiedzy o oświetlanej scenie poprzez badanie sygnału radiowego od tej sceny odbitego. Jest to problem z dziedziny zagadnień odwrotnych (inverse problems), i jako taki może być źle uwarunkowany i nie mieć jednoznacznego rozwiązania. Ograniczenie swobody szukanego rozwiązania poprzez przyjęcie rzadkiego modelu otwiera nowe możliwości usunięcia niejednoznaczności wyniku. Autor zaproponował w pracy wykorzystanie metod opartych na rzadkiej reprezentacji sygnału do modelowania silnych ech w celu usunięcia ich wpływu na proces detekcji cech słabych, zwanego efektem maskowania. Ma to zastosowanie w aktywnych radarach z oświetleniem szumowym i w radarach pasywnych. Autor badał kilka algorytmów w aspekcie modelowania ech złożonych, wskazał przyczyny niepowodzenia algorytmu kolejnego usuwania składowych i zaproponował w zamian algorytm modelowania łącznego ograniczonej liczby składowych. Kolejne zaproponowane przez autora rozwiązanie przeznaczone jest dla szumowego radaru z syntetyczną aperturą (SAR). Pozwala ono zmniejszyć znacznie liczbę pobieranych próbek w wymiarze przestrzennym a zatem i łączny czas akwizycji sygnału. Zastosowanie rzadkiego modelu sygnału pozwoliło rozwikłać niejednoznaczność odtworzenia obrazu sceny radarowej powstałą wskutek zmniejszenia częstości próbkowania poniżej granicy Nyquista. Rozwiązanie zostało przebadane w symulacjach i w eksperymentach z wykorzystaniem zarejestrowanych rzeczywistych sygnałów. W zastosowaniu do klasycznych radarów MTI, autor zaproponował zastosowanie rzadkiego modelu sygnału w dziedzinie częstotliwości w celu zwiększenia zdolności pomiaru prędkości kilku obiektów znajdujących się w tej samej odległości od radaru. Następne zaproponowane przez autora rozwiązanie dotyczy estymacji wysokości w radarze pasywnym. Na przykładzie radaru pasywnego pracującego z wykorzystaniem nadajnika telewizji cyfrowej DVB-T autor pokazał, że metody oszczędnego próbkowania pozwalają na rozdzielenie ech obiektu propagujących z i bez odbicia od ziemi. Dysponując pomiarami opóźnienia ech wzdłuż różnych dróg propagacji można określić wysokość obiektu. Jest to istotna innowacja wobec faktu, że określenie wysokości poprzez pomiar kąta przyjścia sygnału jest bardzo trudne przy typowych rozmiarach anten dla pasma telewizji cyfrowej. Przy pracy radaru pasywnego z wykorzystaniem niewielkiej liczby nadajników uzyskanie niezależnego pomiaru wysokości obiektu znacząco poprawia jakość lokalizacji obiektu w przestrzeni trójwymiarowej. Rozpatrując zagadnienie obrazowania obiektów ruchomych w radarze pasywnym wykorzystującym nadajnik GSM, autor zaproponował metodę uzyskiwania wyraźnego obrazu w technice ISAR (odwrotnej syntetycznej apertury), korzystając z faktu, że ruchomy obiekt przy obrazowaniu ISAR może być uważany za zbiór niewielu punktów odbijających, poruszających się w jednolity sposób. Zastosowanie tej metody pozwoliło z rzeczywistych, zarejestrowanych sygnałów uzyskać obraz ISAR jadącego pojazdu. Klasyczne metody oparte na filtracji dopasowanej w tej samej sytuacji zawiodły, gdyż cały obserwowany obiekt był mniejszy niż rozmiar komórki rozdzielczości odległościowej, który wynika z szerokości pasma sygnału. W opisanych przez autora przykładach zastosowań rzadkość modelu jest kluczowym założeniem przy rozwiązywaniu postawionych zagadnień odwrotnych. Przykłady dotyczą obszarów zastosowań ściśle związanych z długoletnim doświadczeniem autora w projektowaniu i konstruowaniu urządzeń radarowych, w tym eksperymentalnych urządzeń aktualnie opracowywanych w Politechnice Warszawskiej. Zastosowania przedstawione w pracy obejmują szerokie spektrum różnych typów radarów i sposobów ich wykorzystania, włączając w to radary pasywne i aktywne czy też radary przeznaczone do wykrywania obiektów lub tworzenia ich obrazów.
