ORTHOGONAL POLARIMETRIC SAR PROCESSOR BASED ON SIGNAL AND INTERFERENCE SUBSPACE MODELS F. Brigui ∗ , L. Thiron-Lefevre Sondra, SUPELEC, France G. Ginolhac, P. Forster Satie, ENS Cachan, CNRS, UniverSud, France ABSTRACT We develop a new SAR processor based on several orthogo- nal projections. We take into account the scattering properties of the target and the interferences by using subspace models. To detect the target without detecting the interferences, we process images from the orthogonal projection of the recei- ved signal into the target subspace and from the orthogonal projection of the received signal into a part of the interference subspace. We can combine these two images to firstly detect the target and to secondly reduce interference. This new SAR processor is applied to realistic simulated data for FoPen (Fo- liage Penetration) application. Index Terms— SAR Processor, Orthogonal Projection, Subspace Models, Target Detection, Interference Rejection. 1. INTRODUCTION Detection of target in complex environment is a current is- sue in SAR community. In FoPen (Foliage Penetration) appli- cations, a man-made target (MMT) is located in a forest and many scatterers of this environment cause false alarms. To in- crease detection in such environment, SAR processors using the properties of the scattering of the target have been deve- loped [1, 2]. Nevertheless, false alarms still remain as long as their scattering have common properties to that of the target. In this study, we propose a new SAR processor to reduce these false alarms. We first consider the part of the interference scat- tering that is different from the target scattering. Then, we es- timate this part of scattering and process an image in which only the interferences have a response. In order to reduce false alarms, this image is then combine with an image in which the target is detected [1, 2]. Results on simulated data for FoPen application show the interest of this method. The following convention is adopted : italic indicates a scalar quantity, lower case boldface indicates a vector quantity and upper case boldface a matrix. T denotes the transpose opera- tor and † the transpose conjugate. ∗ Thanks to DGA (Direction Générale de l’Armement) for funding this project. 2. PROBLEM STATEMENT 2.1. SAR Configuration and Notations In SAR configuration, we consider that an antenna evolves along a linear trajectory ; at each position u i , i ∈ 1,N  the antenna emits a signal and receives the response from the scene under observation. For more details on SAR configu- ration and process see [3]. The distance between adjacent positions is constant and equal to δu. The emitted signal is a chirp in polarization H (p = H) and V (p = V ) with a frequency bandwidth B, a central frequency f 0 and a dura- tion T e . We denote by z pi ∈ C K (i ∈ 1,N ) the received signal samples at every u i position of the antenna either in horizontal polarization or in vertical polarization and K is the number of time samples. The total received signal z p for one polarization channel is the concatenation of the N vectors z pi (see [1]) : z p ∈ C NK , z p =  z T p1 z T p2 ... z T pN  T (1) The total polarimetric received signal z is then the conca- tenation of z H and z V : z ∈ C 2NK , z =  z T H z T V  T (2) We precise that only the co-polarized channels are consi- dered (H = HH and V = VV ). 2.2. Problem Modeling We consider that the scene under observation contains MMT’s (man-made targets) and interferences. To take into account the physical properties of the target scattering, we assume that a MMT can be modeled by a set of Perfectly Conducting (PC) plates having each one a different orienta- tion described by the angles (α, β). The same idea is applied to describe the scattering of the interference. As for FoPen applications in P-band the false alarms are mainly due to the trunks of trees, the interference is modeled by a dielectric cylinder whose orientation is described by the angles (γ,δ). The orientations (α, β) and (γ,δ) of the target and the inter- ference are unknown. As these latter strongly influence the scattering patterns of the target and the interference, we can