Space-borne radar platforms are becoming increasingly prevalent in current and planned missions by NASA and partner organizations (e.g. the European Space Agency [ESA]) for a number of microwave remote sensing applications in the terrestrial and space domains. Examples of such missions include the Mars Express, Mars Reconnaissance Orbiter (MRO), BIOMASS, JUICE, Global Precipitation Measurement system, CloudSat, and Cassini. Depending upon the specific application, certain frequency ranges are typically deemed more optimal than others. In applications wherein the radar signal must achieve deep penetration through layers such as ice, vegetation, and top-soil, low-frequency radar systems (typically sub-500MHz) such as those of the MRO, Mars Express, JUICE, and BIOMASS are typically favored over higher-frequency alternatives like those used in CloudSat and Cassini due to lower signal loss associated with conductive ground layers. Despite this advantage of low-frequency signals, when using such signals to perform terrestrial and Martian remote sensing operations from space, the ionosphere will distort propagating electromagnetic (EM) fields, with these distortive effects exacerbating as the frequency reduces. Without adaptive, robust distortion prediction and mitigation techniques, the ionosphere will continue posing a barrier to current and future NASA/ESA remote sensing missions seeking to probe deep into ice, vegetation, and ground layers. Furthermore, despite the presence of external data sources such as the Global Positioning System to perform ionospheric mapping, it may be desired to map the ionosphere in real-time using the same low-frequency radar to capture instantaneous snapshots of the ionosphere's properties during the radar's flight path to provide more accurate information to bias mitigation algorithms. Therefore, the development of robust, low-frequency ionospheric mapping techniques represents an equally important and complementary pursuit to developing bias correction techniques. Similar issues will assume relevance when sounding extraterrestrial sub-surface environments containing media exhibiting exotic EM properties, potentially hindering the success of underground water and hydrocarbon detection without proper mitigation measures. However, these efforts all hinge upon accurate modeling of the environments EM characteristics to better understand the signal-environment interaction and its dependence upon the specific radar system used, which is the central theme of my proposed research. I will first extend and unify a number of isolated models concerning EM wave propagation in complex media into a comprehensive model that more accurately predicts the received EM fields at the radar platform. I will then implement this model in numerical EM codes to study how the ionosphere and complex sub-surface topologies can be expected to distort low-frequency EM waves propagating through these environments. Numerical results and conclusions on signal distortions incurred, as well as on the performance limits of current ionospheric mapping and sub-surface sounding techniques, as a function of center operating frequency, signal bandwidth, antenna geometry, and environmental topology, are expected to be the final outcomes of this research, which are expected to markedly aid NASA/ESA mission-related trade and performance studies while stimulating development of comprehensive, robust low-frequency ionospheric mapping and environmental distortion mitigation techniques.