The concept of the equi-phase curve is introduced for the cross-polarized channel case. It is proved that the equi-phase curves are a series of half circles on the Poincare sphere, and that all these curves have two common ends. Based on the introduced concept, this letter demonstrates the distribution of the received voltage's phases on the Poincare sphere. In addition, it is shown theoretically that the cross-polarized phase of the off-diagonal elements of a scattering matrix is unstable for most natural targets. Therefore, the cross-polarized phase information cannot be used for extracting target characteristics in polarimetric radar remote sensing.

The combined linear frequency modulation continuous wave (LFMCW) and inverse synthetic aperture radar (ISAR) can be used for imaging long-distance targets because of its long-distance and high resolution imaging abilities. In this paper, we find and study the dechirp distortion phenomenon (DDP) for imaging long-distance targets by a dechirp-on-receive LFMCW radar. If the targets are very far from the radar, the maximum delay-time is not much smaller than a single sweep duration, and the dechirp distortion is triggered since the distance of the target is unknown in a LFMCW-ISAR system. DDP cannot be ignored in long-distance imaging because double images of a target appear in the frequency domain, which reduces resolution and degrades image quality. A novel LFMCW-ISAR signal model is established to analyze DDP and its negative effects on long-distance target imaging. Using the proportionately distributed energy of double images, the authors propose a method to correct dechirp distortion. In addition, the applicable scope of the proposed method is also discussed. Simulation results validate the theoretical analysis and the effectiveness of the proposed method.

The optimization of polarimetric contrast enhancement (OPCE) is a widely used method for maximizing the received power ratio of a desired target versus an undesired target (clutter). In this letter, a new model of the OPCE is proposed based on the Fisher criterion. By introducing the well known two-class problem of linear discriminant analysis (LDA), the proposed model is to enlarge the normalized distance of mean value between the target and the clutter. In addition, a cross-iterative numerical method is proposed for solving the optimization with a quadratic constraint. Experimental results with the polarimetric SAR (POLSAR) data demonstrate the effectiveness of the proposed method.

In this letter, a new terrain type classifier is proposed for polarimetric Synthetic Aperture Radar (Pol-SAR) images. This classifier uses the binary tree structure. The homogenous and inhomogeneous areas are first classified by the support vector machine (SVM) classifier based on the texture features extracted from the span image. Then the homogenous and inhomogeneous areas are, respectively, classified by the traditional Wishart classifier and the SVM classifier based on the texture features. Using a NASA/JPL AIRSAR image, the authors achieve the classification accuracy of up to 98%, demonstrating the effectiveness of the proposed method.

The problem of the super-resolution time delay estimation of the real stationary signals is addressed in this paper. The time delay estimation is first converted into a frequency estimation problem. Then a MUSIC-type algorithm to estimate the subsequent frequency from the single-experiment data is proposed, which not only avoids the mathematical model mismatching but also utilizes the advantages of the subspace-based methods. The mean square errors (MSEs) of the time delay estimate of the MUSIC-type method for varying signal-to-noise (SNR) and separation of two received signal components are shown to illustrate that they approximately coincide with the corresponding Cramer-Rao bound (CRB). Finally, the comparison between the MUSIC-type method and the other conventional methods is presented to show the advantages of the proposed method in this paper.

In this paper, we propose a robust registration method, named Bounded-Variables Least Median of Squares (BVLMS). It overcomes both the misassociations and the ill-conditioning due to the interactions between Bounded-Variables Least Squares (BVLS) and Least Median of Squares (LMS). Simulation results demonstrate the feasibility of this new registration method.

The Sinclair scattering matrix is defined in a fixed radar range. If a radar target extends in the range direction, the reflected signal or the compound scattering matrix will undergo interaction of multiple reflections. Since scattering matrix is subject to target parameters such as shape, size, orientation, material, and radar parameters as frequency, polarization, and incidence angle, it is difficult to specify a representative scattering matrix of a general target. Therefore we choose the simplest target, wire, and its scattering matrix to examine the effect of targets aligned in the range direction with respect to the compound scattering matrix. First, we present a simple formula for the compound scattering matrix of wires with the phase difference due to spacing. Then, we employed the FDTD method to examine the scattering phenomena, changing the spacing in the range direction. The FDTD result reveals that two wires can become sphere (plate) and dihedral corner reflector (diplane) component generators; and that four wires can become a good helix component generator. These phenomena are verified with a laboratory measurement. From the result, the target decomposition should be carefully carried out in terms of range. If a range resolution of a radar is not high enough, the scattering matrix of the desired target may be affected by the targets behind.

Huynen has already provided a method to decompose a Mueller matrix in order to retrieve detailed target information in a polarimetric radar system. However, this decomposition sometimes fails in the presence of small error or noise in the elements of a Mueller matrix. This paper attempts to improve Huynen's decomposition method. First, we give the definition of stable decomposition and present an example, showing a problem of Huynen's approach. Then two methods are proposed to carry out stable decompositions, based on the nonlinear least square method and the Newton's method. Stability means the decomposition is not sensitive to noise. The proposed methods overcomes the problems on the unstable decomposition of Mueller matrix, and provides correct information of a target.

In this paper, a new method is proposed for supervised classification of ground cover types by using polarimetric synthetic aperture radar (SAR) data. The concept of similarity parameter between two scattering matrices is introduced for characterizing target scattering mechanism. Four similarity parameters of each pixel in image are used for classification. They are the similarity parameters between a pixel and a plane, a dihedral, a helix and a wire. The total received power of each pixel is also used since the similarity parameter is independent of the spans of target scattering matrices. The supervised classification is carried out based on the principal component analysis. This analysis is applied to each data set in image in the feature space for getting the corresponding feature transform vector. The inner product of two vectors is used as a distance measure in classification. The classification result of the new scheme is shown and it is compared to the results of principal component analysis with other decomposition coefficients, to demonstrate the effectiveness of the similarity parameters.

The optimization of polarimetric contract enhancement (OPCE) is one of the important problems in radar polarimetry since it provides a substantial benefit for target enhancement. Considering different scattering mechanisms between the desired targets and the undesired targets, Yang et al. extended the OPCE model to the generalized OPCE (GOPCE) problem. Based on a modified GOPCE model and the linear discriminant analysis, a ship detector is proposed in this paper to improve the detection performance for polarimetric Synthetic Aperture Radar (SAR) imagery. In the proposed method, we modify the combination form of the three polarimetric parameters (i.e., the plane scattering similarity parameter, the diplane scattering similarity parameter and the Cloude entropy), then use an optimization function resembling the classical Fisher criterion to optimize the optimal polarization states corresponding to the radar received power and the fusion vector corresponding to the polarimetric parameters. The principle of the optimization detailed in this paper lies in maximizing the difference between the desired targets and sea clutter, and minimizing the clutter variance at the same time. RADARSAT-2 polarimetric SAR data acquired over Tanggu Port (Tianjin, China) on June 23, 2011 are used for validation. The experimental results show that the proposed method improves the contrast of the targets and sea clutter and meanwhile reduces the clutter variance. In comparison to another GOPCE based ship detector and the classical polarimetric whitening filter (PWF), the proposed method shows a better performance for weak targets. In addition, we also use the RADARSAT-2 data acquired over San-Francisco on April 9, 2008 to further demonstrate the improvement of this method for target contrast.

A new unsupervised classification method is proposed for polarimetric SAR images to keep the spatial coherence of pixels and edges of different kinds of targets simultaneously. We consider the label scale variability of images by combining Inhomogeneous Markov Random Field (MRF) and Bayes' theorem. After minimizing an energy function using an expansion algorithm based on Graph Cuts, we can obtain classification results that are discontinuity preserving. Using a NASA/JPL AIRSAR image, we demonstrate the effectiveness of the proposed method.

In this letter, a new formula is proposed for calculating the polarization entropy, based on the least square method. There is no need to calculate the eigenvalues of a covariance matrix as well as to use logarithms of values. So the time for computing the polarization entropy is reduced. Using polarimetric SAR data, the authors validate the effectiveness of the new formula.

For the completely polarized wave case, this paper presents the explicit formulae of the characteristic polarization states in the co-polarized radar channel, from which one can obtain the CO-POL Max, the CO-POL Saddle and the CO-POL Nulls in the Stokes vector form. Then the problem on the polarimetric contrast optimization is discussed, and the explicit formula of the optimal polarization state for contrast enhancement is presented in the Stokes vector form for the first time. To verify these formulae, we give some numerical examples. The results are completely identical with other authors', which shows the validity of the presented method.

In this paper, the expectation maximization (EM) algorithm is used for unsupervised classification of polarimetric synthetic aperture radar (SAR) images. The EM algorithm provides an estimate of the parameters of the underlying probability distribution functions (pdf's) for each class. The feature vector is 9-dimensional, consisting of the six magnitudes and three angles of the elements of a coherency matrix. Each of the elements of the feature vector is assigned a specific parametric pdf. In this work, all the features are supposed to be statistically independent. Then we present a two-stage unsupervised clustering procedure. The EM algorithm is first run for a few iterations to obtain an initial partition of, for example, four clusters. A randomly selected sample of, for example, 2% pixels of the polarimetric SAR image may be used for unsupervised training. In the second stage, the EM algorithm may be run again to reclassify the first stage clusters into smaller sub-clusters. Each cluster from the first stage will be processed separately in the second stage. This approach makes further classification possible as shown in the results. The training cost is also reduced as the number of feature vector in a specific cluster is much smaller than the whole image.

This paper presents a new form of gap waveguide technology - the half-height-pin gap waveguide. The gap waveguide technology is a new transmission line technology introduced recently, which makes use of the stopband of wave propagation created by a pair of parallel plates, one PEC (perfect electric conductor) and one PMC (perfect magnetic conductor), with an air gap in between less than a quarter of the wavelength at operation frequency. Applying this PEC/PMC gap plate structure to ridged waveguides, rectangular hollow waveguides and microstrip lines, we can have the ridged gap waveguides, groove gap waveguides and inverted gap waveguide microstrip lines, respectively, without requiring a conductive or galvanic contact between the upper PEC and the lower PMC plates. This contactless property of the gap waveguide technology relaxes significantly the manufacturing requirements for devices and antennas at millimeter wave frequencies. PMC material does not exist in nature, and an artificial PMC boundary can be made by such as periodic pin array with the pin length about a quarter wavelength. However, the quarter-wavelength pins, referred to as the full-height pins, are often too long for manufacturing. In order to overcome this difficulty, a new half-height-pin gap waveguide is introduced. The working principles and Q factors for the half-height-pin gap waveguides are described, analyzed and verified with measurements in this paper. It is concluded that half-height-pin gap waveguides have similar Q factors and operation bandwidth to the full-height-pin gap waveguides. As an example of the applications, a high gain planar array antenna at V band by using the half-height-pin gap waveguide has been designed and is presented in the paper with a good reflection coefficient and high aperture efficiency.

Phase synchronization is a crucial problem in Bistatic Synthetic Aperture Radar (BiSAR). As phase synchronization error and Doppler phase have nearly the same form, Doppler Centroid (DC) cannot be estimated with traditional method in BiSAR. A DC estimation method is proposed through phase-interferometry of Dual-channel direct signal. Through phase interferometry, phase synchronization error can be counteracted while Doppler phase is reserved and DC can be estimated from the reserved phase.

This paper proposes two numerical methods to solve the optimal problem of contrast enhancement in the cross-pol and co-pol channels. For the cross-pol channel case, the contrast (power ratio) is expressed in a homogeneous form, which leads the polarimetric contrast optimization to a distinctive eigenvalue problem. For the co-pol channel case, this paper proposes a cross iterative method for optimization, based on the formula used in the matched-pol channel. Both these numerical methods can be proved as convergent algorithms, and they are effective for obtaining the optimum polarization state. Besides, one of the proposed methods is applied to solve the optimal problem of contrast enhancement for the time-independent targets case. To verify the proposed methods, this paper provides two numerical examples. The results of calculation are completely identical with other authors', showing the validity of the proposed methods.

The periodicity of a target scattering matrix is studied when the target is rotated about the sight line of a monostatic radar. Except for the periodicity and invariance of the scattering matrix diag(a,a), it is proved that only helixes have the quasi-invariance, and that only N-targets have the quasi-periodicity, demonstrating that a target with some angle rotation symmetry also has the scattering matrix form diag(a,a). From this result, we conclude that it is impossible to extract the shape characteristics of a complex target from its scattering matrix or its Kennaugh matrix.

In this paper, a new method is proposed for unsupervised speckle level estimation in synthetic aperture radar (SAR) images. It is assumed that fully developed speckle intensity has a Gamma distribution. Based on this assumption, estimation of the equivalent number of looks (ENL) is transformed into noise variance estimation in the logarithmic SAR image domain. In order to improve estimation accuracy, texture analysis is also applied to exclude areas where speckle is not fully developed (e.g., urban areas). Finally, the noise variance is estimated by a 2-dimensional autoregressive (AR) model. The effectiveness of the proposed method is verified with several SAR images from different SAR systems and simulated images.

Classification of terrain is one of the most important applications of Polarimetric Synthetic Aperture Radar (POLSAR) image analysis. This paper presents a simple method to classify terrain by the use of the correlation coefficients in the circular polarization basis together with the total power of the scattering matrix in the X-band. The reflection symmetry condition that the co-polarized and the cross-polarized correlations are close to zero for natural distributed scatterers is utilized to extract characteristic parameters of small forests or cluster of trees, and oriented urban building blocks with respect to the direction of the radar illumination. Both of these kinds of scatterers are difficult to identify in high resolution POLSAR images of complex urban areas. The indices employed here are the correlation coefficient, a modified coefficient normalized by the reflection symmetric conditional case, and the total power. It is shown that forest areas and oriented building blocks are easily detected and identified. The terrain classification yielded by these combinations is very accurate as confirmed by photographic ground truth images.