# Motion Compensation for Long Integration Times and DoA Processing in Passive Radars
## 1 Introduction
One of the best well-known methods to solve this type of problem is the Radon Fourier transform (RFT), which achieves high integration times of the target whose range migration is significant, by parametric signal modelling and projecting echoes into a low-dimension parameter space. On the other hand, there is also the generalized Radon-Fourier transform method (GRFT), which provides a general method for high coherent integration times [25; 26]. However, these methods do not solve the Doppler migration problem. To solve this problem, the modified Radon Fourier transform (MRFT) for long-time coherent integration is presented in [27; 28], which searches the Doppler rate during the integration of pulses. The MRFT integrates the target echo energy by searching for the range, Doppler, and Doppler rate of the target. This algorithm is able to correct both range and Doppler migration problems and significantly improve the signal-to-noise ratio (SNR) of the signal echo. In [29] classical compensation methods are compared such as the use of Keystone transform (KT), which is used in a multitude of applications such as SAR (synthetic aperture radar), or the envelope alignment based on envelope correlation for range compensation and the Chirp-Fourier transform (CFT) in Doppler compensation. The CFT is also proposed in [16; 27]. According to the paper [30], for high integration times, it is proposed to make use of long-time integration Fourier transform (LIFT) to obtain high coherent processing gain. After clutter cancellation, the LIFT is proposed to achieve azimuth compensation. In addition, the Doppler shift is defined as the relative acceleration, which must be calculated before applying for Doppler compensation. If the estimation of this parameter is not precise, a residual white dispersion will be obtained. The presented solution in this work allows for an improvement in detection and tracking capabilities for non-collaborative targets with unknown dynamic implementing target motion compensation in both Doppler and bistatic range domains. The signal processing scheme is based on a multistage range-Doppler migration compensation architecture that combines detection, tracking, and feature-extraction techniques to provide automatic adaptation to each target dynamic in the bistatic scenario of interest. The main steps are as follows:  
1. First detection and tracking performances are used to characterized the targets movements during the acquisition time to define a set of discrete possible target bistatic accelerations. 2. Doppler migration compensation is performed using a filter bank generating a set of Range-Doppler Maps (RDMs) for each single element of the surveillance array and each considered target bistatic acceleration. As the integration gain is expected to be increased, the detector and tracker are again performed. The bistatic tracker results for each acceleration are combined to obtain an improved target trajectory declaration. 3. For each target trajectory, the acceleration and velocity information are extracted to perform the Doppler and range compensation at a single radiation element level. 4. The final signal-to-interference ratio (SIR) values will outperform those achieved without target motion compensation techniques, allowing for detection capabilities improvement and range and azimuth-tracking-accuracy enhancement. The proposed radar signal processing scheme has been validated using data acquired by the PR demonstrator IDEPAR (Improved DEtection techniques for PAssive Radars), developed in the University of Alcala for DVB-T and DVB-S exploitation [31; 32; 33], in a bistatic semiurban scenario with a collaborative terrestrial target. This controlled scenario allows one to perform a detailed study of the detection improvement in the different processing stages. The results confirm the PR performance improvement even when long-time integration time is considered.