# Motion Compensation for Long Integration Times and DoA Processing in Passive Radars
## 1 Introduction  
Passive radars (PRs) encompass all those techniques used for the detection and estimation of target parameters making use of Illuminators of Opportunity (IoO) instead of a dedicated transmitter [1]. PR are not subject to electromagnetic emissions legislation and do not cause an environmental impact or electromagnetic compatibility problems. These systems involve reduced cost, portability potential, a lack of electromagnetic spectrum allocation, and robustness against interception and jamming. However, the absence of the dedicated transmitter is also the origin of the challenges to be solved due to the use of signals not designed for detection purposes, and of uncontrolled transmitters whose locations, transmitted powers, and coverages have been designed to meet the quality of service requirements imposed by the radio services they belong to. Broadcasting systems such as FM [2], digital audio broadcasting (DAB) [3], digital video broadcasting terrestrial and satellite (DVB-T and DVB-S, respectively) [4; 5; 6; 7] are IoOs of great interest that are under study due to their different, and, in many cases, complementary characteristics, related to IoO availability, radiated power, bandwidth, and their impact in PR coverages and resolutions. PRs have proven their capabilities in air, land, and maritime traffic monitoring and imaging (inverse synthetic-aperture radar, ISAR) [8; 9; 10; 11; 12; 13]. Over the last few years, the exploitation of satellite IoOs in PRs has been under intense investigation. One of its main advantages is based on the large number and diversity of available constellations. Different waveforms, frequencies, bandwidths, and radar geometries can be exploited for improving PR performance. Satellite systems provide high availability, global coverage, and near total invulnerability to natural disasters or physical attacks. However, these types of systems also have a number of drawbacks such as reduced signal power at ground level due to the large distance to the transmitter, and the requirement of high gain antennas, which can compromise the detection capabilities due to the inverse relationship between antenna gain and beamwidth. As a result, asignificant reduction in PR coverage is expected by employing satellite IoOs compared to using ground-transmitted signals such as FM, DAB, or DVB-T [14]. In spite of these drawbacks, the exploitation of DVB-S signals' potential benefits is relevant, and many studies can be found in the radar literature. DVB-S satellites are located in a geosynchronous equatorial orbit (GEO) providing an almost static radar geometry. As a result, radar signal processing is simplified, thus avoiding the need for transmitter motion compensation. The transmitted waveform corresponds to a B1-type signal, whose ambiguity function (AF) is a thumbtack that spreads throughout the delay-Doppler plane but at range bins far away from the expected detection coverages. DVB-S based on PR systems have been considered for the detection of maritime targets [15], drones [16; 17; 18], ground vehicles [7; 19; 20; 21], inverse synthetic aperture radar (ISAR) imaging [22], and forward scatter for aerial target detection [23]. The theoretical integration gain associated with coherent processing is calculated as the product of the integration time \(T_{int}\) and the signal bandwidth (\(BW\)). Wide \(BWs\) can give rise to Doppler spread effects in targets' contributions because of the different Doppler shifts associated with different carrier frequencies; long \(T_{int}\) values can generate target Doppler and range migration [24]. These effects produce integration gain losses that limit the detection and localization performances. Focus-before-detection (FBD) methods are able to perform long-time coherent integration for weak targets without prior knowledge of the target motion parameters.