# Hybrid Dual-Polarization Synthetic Aperture Radar
## Appendix A Quadrature Polarimetry  
Consider a SAR that uses orthogonal linear polarizations (such as H and V) on interleaved sequential transmissions, and then receives two orthogonal linear polarizations (such as H and V) after each transmission [26]. The resulting data may be organized into a \(4\times 4\) matrix. If those data are retained for subsequent operations, such a SAR is termed fully polarimetric. However, it is customary to reduce that array to a \(3\times 3\) matrix, by taking advantage of symmetries that are true in almost all known situations [63]. This form is known as quadrature polarimetry (QP). The simpler form is preferred, as its data files are significantly smaller, hence more efficiently incorporated into classification algorithms.  
Since its introduction in the mid-1980s, quad-pol has been acknowledged as the \"Rolls-Royce\" of synthetic aperture radar (SAR) polarimetric imaging modes. In theory, that reputation is well-deserved, because the data collected by a QP SAR are necessary and sufficient to recover a complete characterization of the observed scene's polarimetric properties. The main advantage enjoyed by a quad-pol system is that the resulting Stokes parameter matrix can be obtained (either \(4\times 4\) or \(3\times 3\)), thus capturing the complete polarization signature of the scene with an array of real numbers. Algebraic operations on those data can search over alternative transmit polarizations to select the one that best discriminates a scene's feature of interest, or to provide a graphic illustration of the variation of a target's response over all possible transmit polarizations. The result of such a search is expressed as a polarimetric signature [36]. With that in mind when considering polarimetric options, it is tempting to presume that quad-pol architecture should always be the favored choice.  
Quadrature polarization for a space-based SAR comes at a significant cost, whose technical consequences are manifest in the radar system, which then imposes undesirable limitations on the resulting data products [64]. In particular, quad-pol requires that the radar's pulse-repetition frequency must be doubled, which implies that the imaged swath can be no more than half the width of a singly polarized or dual-polarized SAR. The average data rate should be comparable to that of a dual-polarimetric radar, although the data volume per pixel is doubled. The nearest range ambiguities (in conventional linearly polarized QP systems) are always cross-polarized with respect to the backscatter from the imaged swath. That is unfortunate, because range ambiguities--which are an unwanted nuisance--may be stronger than the desired signal, hence suppressing (or avoiding) them requires extra measures. For adequate signal-to-ambiguity data quality, it follows that the span of useful incident angles available from a conventional linearly-polarized QP SAR must be substantially smaller than for non-quad-pol systems. A QP radar requires twice the (average) transmitted power relative to that of its CP counterpart. Smaller swath width, limited choice in incidence, and twice the data volume per pixel are the most significant disadvantages for users.