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 雷达学报  2017, Vol. 5 Issue (6): 559-595  DOI: 10.12000/JR16074 0

### 引用本文

Hong Wen. Hybrid-polarity Architecture Based Polarimetric SAR: Principles and Applications (in Chinese and in English)[J]. Journal of Radars, 2017, 5(6): 559-595. DOI: 10.12000/JR16074.

### 文章历史

(微波成像技术国家重点实验室 北京 100190)
(中国科学院电子学研究所 北京 100190)
(中国科学院大学 北京 100049)

Hybrid-polarity Architecture Based Polarimetric SAR: Principles and Applications (in Chinese and in English)
Hong Wen
(National Key Laboratory of Microwave Imaging Technology, Beijing 100190, China)
(Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China)
(University of Chinese Academy of Sciences, Beijing 100049, China)
Foundation Item: The National Natural Science Foundation of China (61431018)
Abstract: The application performance of Synthetic Aperture Radar (SAR) instruments is generally limited in their capability to acquire radar images with both high-resolution and wide swath coverage. The available swath width of Polarimetric SAR (PolSAR) systems is even more restricted. Recently, a new PolSAR architecture called the Hybrid-Polarity (HP) architecture has attracted worldwide attentions. Compared with conventional linearly-polarized PolSARs, HP architecture based PolSARs have significant advantages such as wider swath coverage and lower hardware requirement. In this paper, the principles of the HP architecture, including system designs, system models and calibration methods are first reviewed. Two implementation difficulties of the HP architecture, concerning calibration issue and transmit configuration are illustrated. In order to overcome these problems, an improved version of the HP architecture is proposed. A prototype system based on this improved HP architecture developed for experimental validation is also introduced. In the latter part of this paper, applications suitable for the HP architecture based PolSARs are reviewed. Since the quadrature-polarimetric (quad-pol) data provided by an HP architecture based PolSAR system may be directly transformed into conventional linearly–polarized quad-pol data, this part of review is mainly focused on the corresponding dual-pol applications, i.e. Compact Polarimetry (CP) applications.
Key words: Synthetic Aperture Radar (SAR)    Polarimetric SAR (PolSAR)    Hybrid-polarity architecture    Compact Polarimetry (CP)    Calibration    Classification    Compact PolSAR interferometry
1 引言

2 混合极化架构 2.1 混合双极化架构

 图 1 混合双极化架构的系统框图 (Raney 2007,文献[7]) Fig.1 Block schematic of the HP2 architecture (Raney 2007, Ref.[7])

 $\begin{array}{l} \left[{\begin{array}{*{20}{c}} {{M_{{\rm{RH}}}}}\\ {{M_{{\rm{RV}}}}} \end{array}} \right] = A\left( {r,\theta } \right){{\rm{e}}^{\,{\rm{j}}\phi }}\frac{1}{{\sqrt 2 }} \cdot \left[{\begin{array}{*{20}{c}} 1& {{\delta _2}}\\ {{\delta _1}}& {{f_1}} \end{array}} \right]\\ \quad \quad \quad \quad \quad \cdot \left[{\begin{array}{*{20}{c}} {\cos \varOmega }& {\sin \varOmega }\\ { - \sin \varOmega }& {\cos \varOmega } \end{array}} \right] \cdot \left[{\begin{array}{*{20}{c}} {{S_{{\rm{HH}}}}}& {{S_{{\rm{HV}}}}}\\ {{S_{{\rm{VH}}}}}& {{S_{{\rm{VV}}}}} \end{array}} \right]\\ \quad \quad \quad \quad \quad \cdot \left[{\begin{array}{*{20}{c}} {\cos \varOmega }& {\sin \varOmega }\\ { - \sin \varOmega }& {\cos \varOmega } \end{array}} \right] \\ \quad \quad \quad \quad \quad \cdot \left[{\left[{\begin{array}{*{20}{c}} 1\\ { - {\rm j}} \end{array}} \right] + \delta \left[{\begin{array}{*{20}{c}} 1\\ {\rm j} \end{array}} \right]} \right] + \left[{\begin{array}{*{20}{c}} {{N_1}}\\ {{N_2}} \end{array}} \right] \end{array}$ (1)

 $M=A{{\text{e}}^{\text{j}\phi }}\frac{1}{\sqrt{2}}R{{R}_{F}}S{{R}_{F}}\left[ {{k}_{\text{RHC}}}+\delta {{k}_{\text{LHC}}} \right]+N$ (2)

 ${H_w} = - \sum\limits_{i = 1}^2 {{p_i}{{\log }_2}{p_i}}$ (36)
 $\alpha = \sum\limits_{i = 1}^2 {{p_i}{\alpha _i}} \quad \quad \quad \ \$ (37)

 ${p_i} = \frac{{{\lambda _i}}}{{{\lambda _1} + {\lambda _2}}}\quad \quad \quad \quad \quad \quad \quad \quad$ (38)
 ${{\bf{{u}}}_i} = {{\rm e}^{{\rm j}{\phi _i}}}{\left( {\begin{array}{*{20}{c}} {\cos {\alpha _i}}& {\sin {\alpha _i}{{\rm e}^{{\rm j}{\delta _i}}}} \end{array}} \right)^{\rm T}}$ (39)

${H_w}/\alpha$平面的边界曲线可以通过设${{{C}}_2}$为：

 ${{\bf{{C}}}_2} = \left( {\begin{array}{*{20}{c}} 1& 0 \\ 0& m \end{array}} \right),\;\;\;\;{\rm{or}}\\ {{\bf{{C}}}_2} = \left( {\begin{array}{*{20}{c}} m& 0\\ 0& 1 \end{array}} \right),\;\;\;\;0 \le m \le 1$ (40)

 ${{\bf{{k}}}_{{\rm{CL}}}} = \frac{1}{2}\left( {\begin{array}{*{20}{c}} 1& 1 \\ { - {\rm j}}& {\rm j} \end{array}} \right){{\bf{{k}}}_{{\rm{CC}}}}$ (41)

5.3.4 基于散射模型的方法

 ${{{{C}}}_3} = \frac{{{f\!_v}}}{8}\left( {\begin{array}{*{20}{c}} 3& 0 & 1\\ 0& 2 & 0\\ 1& 0 & 3 \end{array}} \right) + {f\!_d}\left( {\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& 0 & \alpha \\ 0& 0 & 0\\ {{\alpha ^*}}& 0 & 1 \end{array}} \right) \\ \quad \quad \,\,+ {f\!_s}\left( {\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& 0& \beta \\ 0& 0 & 0\\ {{\beta ^*}}& 0 & 1 \end{array}} \right)$ (42)

 $\pi {\rm{/4 \ 模式}} \quad \quad \quad {{\bf{{C}}}_2} = \frac{{{f\!_v}}}{8}\left( {\begin{array}{*{20}{c}} {\rm{2}}& {\rm{1}}\\ {\rm{1}}& {\rm{2}} \end{array}} \right) + {f\!_d}\left( {\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& \alpha \\ { - {\alpha ^*}}& 1 \end{array}} \right) + {f\!_s}\left( {\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& \beta \\ { - {\beta ^*}}& 1 \end{array}} \right) \quad \quad \quad \quad \quad \$ (43)
 ${\rm{CTLR \ 模式}} \quad \quad {{\bf{{C}}}_2} = \frac{{{f\!_v}}}{4}\left( {\begin{array}{*{20}{c}} {\rm{1}}& {\rm{0}}\\ {\rm{0}}& {\rm{1}} \end{array}} \right) + {f\!_d}\left( {\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& {{\rm j}\alpha }\\ { - {\rm j}{\alpha ^*}}& 1 \end{array}} \right) + {f\!_s}\left( {\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& {{\rm j}\beta }\\ { - {\rm j}{\beta ^*}}& 1 \end{array}} \right) \quad \quad \quad \quad$ (44)

 ${{\bf{{J}}}_4} = \left[{\begin{array}{*{20}{c}} {{{\bf{{J}}}_{11}}}& {{{\bf{{J}}}_{12}}}\\ {{\bf{{J}}}_{12}^{*T}}& {{{\bf{{J}}}_{22}}} \end{array}} \right]$ (47)

6.2.1 森林树高反演

 $\gamma \; ({\omega _1},{\omega _2}) = \frac{{\omega _1^{\rm{H}}{{\bf{{J}}}\!_{12}}{\omega _2}}}{{\sqrt {\omega _1^{\rm{H}}{{\bf{{J}}}\!_{11}}{\omega _1}\omega _2^{\rm{H}}{{\bf{{J}}}\!_{22}}{\omega _2}} }}$ (48)

(1) 变换接收天线的极化状态(式(48)中w1,w2)，计算不同极化状态下的复相干，并根据复相干分布拟合直线。

(2) 计算拟合直线与单位圆的两个交点，正确选择其中一个表示地表相位${{\rm e}^{{\rm j}{\phi _0}}}$的交点。

(3) 选择距离地表相位最远的复相干系数表示树高的体散射相干系数${{\rm e}^{{\rm j}{\phi _0}}}{\gamma _v}$。去掉地表相位影响并求得仅由体散射引起的复相干${\gamma _v}$

(4) 应用查表法(Look-Up Table,LUT)技术最终求得森林的树高以及森林消光系数。

6.2.2 简缩极化干涉SAR目标分解

 $\pi {\rm{/4 \ 模式}} \quad \quad \quad \ {{\bf{{J}}}_2} = \frac{{{f\!_{cv}}}}{8}\left[{\begin{array}{*{20}{c}} {\rm{2}}& {\rm{1}}\\ {\rm{1}}& {\rm{2}} \end{array}} \right] + {f\!_{cd}}\left[{\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& \alpha \\ { - {\alpha ^*}}& 1 \end{array}} \right] + {f\!_{cs}}\left[{\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& \beta \\ { - {\beta ^*}}& 1 \end{array}} \right] \quad \quad \quad \quad \quad \$ (49)
 ${\rm{CTLR \ 模式}} \quad \quad {{\bf{{J}}}_2} = \frac{{{f\!_{cv}}}}{4}\left[{\begin{array}{*{20}{c}} {\rm{1}}& {\rm{0}}\\ {\rm{0}}& {\rm{1}} \end{array}} \right] + {f\!_{cd}}\left[{\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& {\rm j\alpha }\\ { - {\rm j}{\alpha ^*}}& 1 \end{array}} \right] + {f\!_{cs}}\left[{\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& {\rm j\beta }\\ { - {\rm j}{\beta ^*}}& 1 \end{array}} \right] \quad \quad \quad \quad$ (50)

 图 12 仿真数据的Pauli分解图 Fig.12 Simulated dataset Pauli decomposition image
6.3 其他应用

7 结束语

1 Introduction

Synthetic Aperture Radar (SAR) is an active imaging radar, which produces high-resolution microwave images of the earth's surface via signal processing technologies. It has all-day and all-weather imaging capability. Polarimetric SAR (PolSAR) offers additional polarimetric information of the observed scene and has already been successfully applied in a multitude of practical applications[1, 2]. The limitation of current spaceborne SAR systems is mainly the acquisition of radar images with both high-resolution and wide-swath coverage. As for fully, or quadrature polarimetric polarimetric (quad-pol) SAR systems, which could obtain the complete backscattering characterization of scatterers, the available swath width is at least halved compared with conventional SAR systems due to the doubled Pulse Repetition Frequency (PRF) for interleaved transmission of two orthogonal polarizations.

Conventional quad-pol SAR systems operate with Horizontal (H) and Vertical (V) linear polarizations in both transmission and reception. This configuration will give rise to severe range ambiguities in the cross-polarized (HV or VH) measurement channels, which will further limit the swath coverage particularly at larger incidence[3, 4]. Meanwhile, since the like-polarized (HH or VV) returns from natural terrain are generally 6～10 dB higher than the cross-polarized (HV or VH) returns, complex reception strategies are applied in practical radar systems to keep both measured returns within the valid dynamic range of the Analog to Digital Converter (ADC) module[5, 6]. On account of these drawbacks, a new PolSAR architecture called the Hybrid-Polarity (HP) architecture, has been proposed in Refs. [4, 7, 8] in recent years. By transmitting interleaved Right-Handed Circular (RHC) and Left-Handed Circular (LHC) polarized waves and receiving on orthogonal linear polarizations, the range ambiguity performance of the HP architecture based PolSAR system is improved for having no like- or cross-polarized relationship between the transmitting and receiving polarizations[4]. Meanwhile, the mean signal level in either receiving path is also balanced, which implies that no complex reception strategies are more needed. Thereby, PolSAR systems based on the HP architecture will have wider swath coverage and lower hardware requirement than conventional linearly-polarized PolSAR systems[4].

The HP architecture can also support the Circular Transmit Linear Receive (CTLR) mode[7] of Compact Polarimetry (CP), a collection of special dual-polarimetric (dual-pol) modes, which requires the transmission of polarizations with equivalent H and V components, such as RHC and LHC polarizations and the ±45° slant linear polarizations, and retains the relative phase of the received polarizations[9, 10, 11, 12]. CP has attracted wide attentions in the past ten years for having the potential to produce comparable results in many applications as those derived from quad-pol SARs[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61] while maintaining the advantages of dual-pol SARs such as doubled swath width, low power consumption and low system complexity[7, 9].

These advantages make the HP architecture a potential choice for future PolSAR missions. To date, several launched PolSAR missions have adopted the HP architecture: the two mini-Radio-Frequency (mini-RF) radars onboard the Indian Chandrayaan-2-1 moon mission and the American Lunar Reconnaissance Orbiter (LRO)[62], the C-band SAR onboard the Indian remote sensing satellite RISAT-1[63], the L-band SAR onboard the Japanese remote sensing satellite ALOS-2 (experimental mode)[64]. Future SAR missions including the Canadian C-band RADARSAT Constellation Mission (RCM)[12, 65, 66], the American L-band Interferometry SAR (InSAR) system of the Deformation, Ecosystem Structure, and Dynamics of Ice (DESDynI) mission[67, 68]; and the second moon mission of Indian Space Research Organization (ISRO) Chandrayaan-2[69] have also confirmed to adopt the HP architecture.

In this paper, we will first review the basic principles of the HP architecture including system designs, system models, and calibration methods. Two implementation difficulties of the HP architecture will be discussed. The major one is that when operating under the dual-pol mode, the distortions in transmit cannot be calibrated, even if their actual values can be precisely measured with specific calibration methods. The other one is that the transmission in the HP architecture are usually configured as circular polarization. Under this configuration, the dual-pol mode corresponds the CTLR mode. However, beside the CTLR mode, other CP modes with different transmit polarization such as the π/4 mode, which radiates 45° linearly-polarized waves with respect to either H and V orientations, may also produce favorable results in certain applications and deserves consideration. To deal with these two problems, an improved version of the HP architecture will be proposed in this paper. The prototype system developed for experimental validation will also be introduced.

In the next part of this paper, applications suitable for the HP architecture based PolSAR will be illustrated. Since the quad-pol data provided by HP architecture based SAR systems can be directly transformed into conventional linearly-polarized scattering matrix, this part of review will mainly focus on the corresponding dual-pol applications, i.e. CP applications. Four CP information retrieval methodologies, including the covariance matrix expansion method, the Stokes vector based method, the eigenvalue decomposition method, and the scattering model based method will be first introduced. Suitable applications stemmed from these methodologies will be reviewed next. Considering the length of the paper, only investigations on unsupervised classification of land and terrains using CP data and Compact PolSAR interferometry for tree height inversion will be reviewed in detail.

The organization of this paper is given as follows. In Section 2, the system designs and system models of the HP architecture based dual-pol and quad-pol SAR systems are reviewed, respectively. In Section 3, the self-checking property[7] of the HP architecture and calibration techniques are illustrated. Assessment of the transmit distortions, which cannot be calibrated using external calibration methods, are also discussed. In Section 4, an improved version of the HP architecture is proposed. In Section 5, several data processing algorithms including the transformation of HP quad-pol data to linear quad-pol data, and the simulation of CP data with quad-pol data are introduced. Four major CP information retrieval methodologies are also illustrated in this section. In Section 6, investigations on CP applications are reviewed. Conclusions are finally made in Section 7.

2 Hybrid-polarity Architecture 2.1 Hybrid dual-pol architecture

The HP architecture was first proposed in Ref. [7] to support the CTLR mode of CP, which requires the transmission of single circular polarization (either RHC or LHC) and simultaneously receiving on two orthogonal linear polarizations. Since CP is actually a collection of special dual-pol modes, this HP architecture is referred as the Hybrid Dual-Pol (HP2) architecture in this paper. The block schematic of the HP2 architecture is shown in Fig. 1(a). In order to produce circular polarization for transmission, the signal flow generated by the waveform generator is split in two with a power splitter and one of the sub-signal flow is phase shifted 90° afterwards. This part of design is highlighted with a dashed frame in Fig. 1(a). The two sub-signal flows are used to feed the H- and V-elements of a dual-linearly-polarized antenna. The outlined part of the HP2 architecture could be simplified as Fig. 1(b), with ${S_i}$ and ${S_o}$ denoting the input and output ports, respectively, and ${A_t}$ and ${A_r}$ denoting different ports connected to the feeds of the transmitting and receiving antennas, respectively. If the dual-linearly-polarized antenna is used for both transmission and reception, then ${A_{t{\rm{1}}}}{\rm{ = }}{A_{r1}}$ and ${A_{t2}}{\rm{ = }}{A_{r{\rm{2}}}}$.

 Fig.1 Block schematic of the HP2 architecture (Raney 2007, Ref. [7])

As we can see, very few RF hardware is required in the HP2 architecture, which implies fewer losses and fewer sources of potential distortion sources in the radar system. Besides, since neither receive channel is disadvantaged by being cross-polarized, the mean signal level in both channels should be similar. This means also that there will be less chance of having a stronger polarization affect a weaker polarization, i.e. having a strong crosstalk within the radar system[4].

The system model of the HP2 architecture based spaceborne PolSAR system is[70]:

 $\begin{array}{l} \left[{\begin{array}{*{20}{c}} {{M_{{\rm{RH}}}}}\\ {{M_{{\rm{RV}}}}} \end{array}} \right] = A\left( {r, \theta } \right){{\rm{e}}^{\, {\rm{j}}\phi }}\frac{1}{{\sqrt 2 }} \cdot \left[{\begin{array}{*{20}{c}} 1& {{\delta _2}}\\ {{\delta _1}}& {{f_1}} \end{array}} \right]\\ \quad \quad \quad \quad \quad \cdot \left[{\begin{array}{*{20}{c}} {\cos \varOmega }& {\sin \varOmega }\\ { - \sin \varOmega }& {\cos \varOmega } \end{array}} \right] \cdot \left[{\begin{array}{*{20}{c}} {{S_{{\rm{HH}}}}}& {{S_{{\rm{HV}}}}}\\ {{S_{{\rm{VH}}}}}& {{S_{{\rm{VV}}}}} \end{array}} \right]\\ \quad \quad \quad \quad \quad \cdot \left[{\begin{array}{*{20}{c}} {\cos \varOmega }& {\sin \varOmega }\\ { - \sin \varOmega }& {\cos \varOmega } \end{array}} \right] \\ \quad \quad \quad \quad \quad \cdot \left[{\left[{\begin{array}{*{20}{c}} 1\\ { - {\rm j}} \end{array}} \right] + \delta \left[{\begin{array}{*{20}{c}} 1\\ {\rm j} \end{array}} \right]} \right] + \left[{\begin{array}{*{20}{c}} {{N_1}}\\ {{N_2}} \end{array}} \right] \end{array}$ (1)
or

 $M=A{{\text{e}}^{\text{j}\phi }}\frac{1}{\sqrt{2}}R{{R}_{F}}S{{R}_{F}}\left[ {{k}_{\text{RHC}}}+\delta {{k}_{\text{LHC}}} \right]+N$ (2)
where M is the measured scattering matrix, S is the scattering matrix, RF represents the one-way Faraday Rotation (FR) matrix with W being the FR rotation angle, R is the receive distortion matrix, and N is the additive noise term present in each measurement. The subscripts in M stands for RHC polarization transmission and H and V polarization reception. R includes the crosstalk term ${\delta _1}$ and ${\delta _2}$, and the channel imbalance term f1 within reception. kRHC and kLHC are the Jones vectors of RHC and LHC polarization, respectively, and d is the general crosstalk when RHC polarization is transmitted. The real factor A represents the overall gain term, which is the function of range, r, and elevation angle, $\phi$. The complex factor ${{\rm e}^{{\rm j}\phi }}$ represents the round-trip phase delay and system-dependent phase effects on the signal.

The electric field Ei incident on the surface could be further derived as:

 ${{\bf{{{E}}}}_i} ={{R}_F}\left[{{k_{{\rm{RHC}}}} + \delta {k_{{\rm{LHC}}}}} \right] = \left[{\begin{array}{*{20}{c}} {\cos \varOmega }& {\sin \varOmega }\\ { - \sin \varOmega } & {\cos \varOmega } \end{array}} \right] \\ \quad \quad \cdot \left[{\left[{\begin{array}{*{20}{c}} 1\\ { - {\rm j}} \end{array}} \right] + \delta \left[{\begin{array}{*{20}{c}} 1\\ {\rm j} \end{array}} \right]} \right] \\ \quad \, \, = {{\rm e}^{ - {\rm j}\varOmega }}\left[{\left[{\begin{array}{*{20}{c}} 1\\ { - {\rm j}} \end{array}} \right] + \delta {{\rm e}^{\, {\rm j}2\varOmega }}\left[{\begin{array}{*{20}{c}} 1\\ {\rm j} \end{array}} \right]} \right]$ (3)
We can see that if the transmitted circular polarization is perfect, i.e. d=0, then FR can be omitted in the following processing. Even if the transmitted polarization is imperfect, the FR effect upon an HP2 architecture based PolSAR system should be still smaller than those affected on traditional linearly-polarized SAR systems.

Although the distortions in transmission can be simply represented with one single term $\delta$, as in Eq. (1) and Eq. (2), such distortions can also be expressed with conventional transmit distortion matrix T[71]:

 ${\bf{{{T}}}} = \left[{\begin{array}{*{20}{c}} 1 & 0\\ 0 & {{f_2}} \end{array}} \right] \cdot \left[{\begin{array}{*{20}{c}} 1 & {{\delta _4}}\\ {{\delta _3}} & 1 \end{array}} \right]$ (4)
where ${\delta _3}$, ${\delta _4}$, and ${f_2}$ are the crosstalk and channel imbalance terms in transmission, respectively. These distortion terms are connected with the general crosstalk $\delta$ through Eq. (5)[72]:

 ${\bf{{{T}}}} \cdot {k_{\rm RHC}} = \alpha \left[{{\rm k_{RHC}} + \delta {k_{\rm LHC}}} \right]$ (5)
where

 $\alpha = \frac{{\left( {1 + {f_2}} \right) - {\rm j}({\delta _4} - {\delta _3})}}{2}$ (6)

Either expressions of the transmit distortions is applicable. But as we can see in Eq. (1), even if the distortion terms on transmit are explicitly known, the real scattering matrix of the target can still not be obtained through multiplying a corresponding inverse matrix. Therefore, it will be more concise by using the general crosstalk term. But the explicit formulation of the transmit distortions allows us to assess the influences of different distortion sources in detail, respectively. This part of work will be reviewed in Subsection 3.2.

As an alternative to conventional linearly-polarized quad-pol SAR systems, it was suggested in Ref. [7] to use the HP architecture to configure a quad-pol SAR system. The transmitted polarizations would be RHC and LHC, interleaved, and the receive polarizations would be coherent H and V polarizations. This idea was further elaborated in Ref. [4] and Ref. [8].

The block schematic of the Hybrid Quad-Pol (HP4)[8] architecture is shown in Fig. 2(a). The transmit module is similar to the introduced HP2 architecture, with a small modification in the phase shifter. The phase of the signal flow will be shifted between +90° and -90° for RHC and LHC polarization transmission, respectively. This part of design is also outlined in Fig. 2(a) and simplified in Fig. 2(b). If the phase shifter is fixed at either +90° or -90°, the resulting system design is the HP2 architecture. Therefore, the CTLR mode can be regarded as the corresponding dual-pol mode of the HP4 architecture based PolSAR system. In the following text, we will use the phrase “HP architecture” to indicate an HP4 architecture, which can also operate under dual-pol mode.

 Fig.2 Block schematic of the HP4 architecture (Raney 2008, Ref. [8])

The advantages of the HP2 architecture denoted in previous subsection is also inherited by the HP4 architecture. First, there are also no like- or cross-polarized relationship between the transmitted and received polarization. According to the deductions made in Ref. [4], this feature will lead to a better range ambiguity performance, which implies that an HP4 architecture based quad-pol SAR system can have a wider swath coverage, particularly at higher incident angles than conventional linear quad-pol SAR systems.

Moreover, since the mean signal level in both receive channels are similar, conventional complex reception strategies to adjust the receiver gain for different returns[5, 6] are also no longer needed. Therefore, comparing with conventional linearly-polarized PolSAR systems, the system design of the HP4 architecture based PolSAR system is much simpler, which in turn implies a less costly radar and more robust calibration and measurement reliability.

Since there is no need to toggle the gain of receivers between either radar returns, the system model of the HP4 architecture based spaceborne PolSAR system is similar to the standard polarimetric system model concerning the FR effect[73]:

 ${{\mathbf{M}}_{\text{HP4}}}=A{{\text{e}}^{\text{j}\phi }}\mathbf{R}{{\mathbf{R}}_{F}}{{\mathbf{S}}_{\text{HP4}}}{{\mathbf{R}}_{F}}\mathbf{T}+\mathbf{N}$ (7)
where MHP4 is the 2×2 measured matrix and SHP4 is a 2×2 matrix, which composes the elements of a true scattering matrix S by:

 ${{\bf{{{S}}}}_{\rm HP4}} = \left[{\begin{array}{*{20}{c}} {{S_{{\rm{RH}}}}}& {{S_{{\rm{LH}}}}}\\ {{S_{{\rm{RV}}}}}& {{S_{{\rm{LV}}}}} \end{array}} \right] \\ \quad \, \, \quad = \left[{\begin{array}{*{20}{c}} {{S_{{\rm{HH}}}} - {\rm j}{S_{{\rm{HV}}}}}& {{S_{{\rm{HH}}}} + {\rm j}{S_{{\rm{HV}}}}}\\ {{S_{{\rm{VH}}}} - {\rm j}{S_{{\rm{VV}}}}}& {{S_{{\rm{VH}}}} + {\rm j}{S_{{\rm{VV}}}}} \end{array}} \right]$ (8)
The measurement obtained with the HP4 architecture based PolSAR could also be first transformed into linear basis, and then apply the standard polarimetric system model developed for conventional linearly-polarized quad-pol SAR systems for further calibration and data processing algorithms.

3 Calibration and Assessment of Distortions

Since the data derived from HP4 architecture based PolSAR system could be transformed into conventional linear basis, standard algorithms developed for polarimetric calibration could be directly applied on the HP4 architecture based PolSAR systems. The calibration issue left for the HP architecture is the calibration of data obtained through HP2 architecture based PolSAR systems, i.e. the calibration of CP data.

3.1 Calibration of CP data 3.1.1 Self-checking calibration method

Since the mean signal level in both receive path of the HP architecture based PolSAR system is expected to be balanced, the first- and second-order statistics of the return signals should be identical when the H and V backscatter coefficients are equal. In practice, this criterion is achieved when the radar views at an incident angle that is normal to the mean slope of the illuminated terrain. The discrepancies, which do not meet this criterion, can be measured and compensated[7, 74].

This unique calibration strategy of the HP architecture has been adopted by the lunar mini-RF programs[62, 75]. Since there are no Amazon rain forests, nor specially placed radar reflectors available on the Moon, standard calibration techniques used by Earth orbiters were not applicable. During the on-orbit calibration experiment, the spacecraft was rolled to align the mini-RF radar antenna in a nadir-pointing orientation towards the Moon to cooperate the calibration experiment. The V-H gain balance and V-H phase balance were counted to be -2.55 dB±0.25 dB and -138°±2.7°, respectively. These results compare well with the predictions made through an end-to-end system measurement, which were -2.14 dB±0.25 dB and -135.9°±1.5°, correspondingly. The small difference between these two strategies was mainly due to the actual imperfect transmitted circular polarization, which was measured having an Axial Ratio (AR) of 2.46 dB±0.15 dB.

An HP architecture based PolSAR system can operate under both quad-pol mode and dual-pol mode. Therefore, if such system is stable during the data-taking stage, as is the case for spaceborne SARs, the discrepancies within the system could be directly obtained by operating quad-pol mode at the beginning and/or the end of the data-taking stage[70].

As for spaceborne PolSAR systems operating with low frequency microwaves, the FR effect must also be taken into consideration. Beside the usage of Total Electron Content (TEC) maps[76], FR angles can also be estimated through backscatters from bare surfaces, where the HH-VV phase difference is close to zero[18]. The identification of bare surfaces was made by the conformity coefficient m, which is FR independent:

 $\mu = \frac{{2{\mathop{\rm Im}\nolimits} \left\langle {{M_{{\rm{RH}}}}M_{{\rm{RV}}}^*} \right\rangle }}{{\left\langle {{M_{{\rm{RH}}}}M_{{\rm{RV}}}^*} \right\rangle + \left\langle {{M_{{\rm{RH}}}}M_{{\rm{RV}}}^*} \right\rangle }} \\ \quad \! \cong 2\frac{{{\mathop{\rm Re}\nolimits} \left( {{S_{{\rm{HH}}}}S_{{\rm{VV}}}^*} \right) - {{\left| {{S_{{\rm{HV}}}}} \right|}^2}}}{{{{\left| {{S_{{\rm{HH}}}}} \right|}^2} + 2{{\left| {{S_{{\rm{HV}}}}} \right|}^2} + {{\left| {{S_{{\rm{VV}}}}} \right|}^2}}}$ (9)
As for bare surface scattering, m is positive and conforms one. Meanwhile, the m value for double-bounce scattering is negative and conforms to -1, and the intermediate value (near zero) denotes volume scattering. The threshold between volume and surface is estimated 0.35 and the threshold between volume and double-bounce is estimated -0.2. Utilizing the identified bare surfaces, FR angles can be derived through the following equation:

 ${Ω} \! = \frac{1}{2}\arctan \left(\! {2\frac{{{\mathop{\rm Re}\nolimits} \left\langle {{M_{{\rm{RH}}}}M_{{\rm{RV}}}^*} \right\rangle }}{{\left\langle {{M_{{\rm{RV}}}}M_{{\rm{RV}}}^*} \right\rangle - \left\langle {{M_{{\rm{RH}}}}M_{{\rm{RH}}}^*} \right\rangle }}} \!\right)\!\!\bmod \frac{\pi }{4}$ (10)
3.1.4 Calibrator based calibration method

In Ref.[77], Truong-Loï et al. first proposed a calibrator based calibration method for the CTLR mode. Since the transmit distortions could not be corrected, the transmission of the radar system is considered perfect. Three calibrators, including two dihedrals at 0° and 45° and a trihedral at 0° are utilized to measure and correct the channel imbalance and cross-talk in reception, FR angle and system gain.

In Ref. [78], Chen and Quegan also investigated several calibrator-based calibration strategies for spaceborne low-frequency SAR systems operating with CTLR mode. In their investigation, six different calibration schemes, containing different mixtures of passive and active radar calibrators, were proposed and carefully investigated. First, it was established that calibration strategies involving four calibrators will yield a more accurate estimation of the radar system parameters than those using just three calibrators. However, the augment in cost and complexity in deployment deserves careful consideration. Second, among the three passive calibrators, gridded trihedral is the most preferred against the dihedral and trihedral, because of its much lower Average Polarimetric Noise (APN) and insensitivity to pointing accuracy. The mostly recommended calibration scheme concludes two gridded trihedrals that select for the HH and VV channels, and two active calibrators that select for the HV and VH channels.

In Ref. [79], Chen at al. proposed a general calibration algorithm for all dual-pol SAR systems using only one trihedral and two dihedrals, 0° and 45° in rotation angle. The FR effect is not considered in this method. This method is applicable for all dual-pol modes including the conventional linear dual mode, the CTLR mode, and the p/4 mode of CP. The effectiveness of this algorithm has been verified with a ground-based SAR system with p/4 mode and CTLR mode transmit/receive configurations[34].

3.2 Assessment of the transmit distortions

In previous section, we have discussed one major implementation difficulty of the HP architecture: the transmit distortions in its corresponding dual-pol mode cannot be corrected by simply multiplying a corresponding inverse matrix. Therefore, the influence of such distortions requires careful assessment. In Ref. [71], Guo et al. adopted the Maximum Normalized Error (MNE)[80]for quantitative evaluation. In the case with the HP2 architecture based PolSAR system, MNE is defined as:

 ${\rm{MNE}} = {\left\| {{\bf{{PD}}} - {{\bf{{P}}}_0}} \right\|_2}$ (11)
with

 ${\bf{{P}}} = \left( {\begin{array}{*{20}{c}} {p_h^t} & 0 & {p_v^t} & 0 \\ 0 & {p_h^t} & 0 & {p_v^t} \end{array}} \right)\quad \quad \quad \quad \, \,$ (12)
 ${\bf{{D}}} = {\left[{\left[{\begin{array}{*{20}{c}} {\cos {Ω} } & {\sin {Ω} }\\ { - \sin {Ω} } & {\cos {Ω} } \end{array}} \right] \cdot {{\bf{{X}}}_t}} \right]^{\rm T}} \otimes {\bf{{I}}}$ (13)
 ${{\bf{{P}}}_0} = \left( {\begin{array}{*{20}{c}} 1 & 0 & {\rm j} & 0\\ 0 & 1 & 0 & {\rm j} \end{array}} \right)\quad \quad \quad \quad \quad \quad \, \,$ (14)
where ${\left[{\begin{array}{*{20}{c}} {p_h^t}& {p_v^t} \end{array}} \right]^{\rm T}}$is the Jones vector corresponded to the transmitted polarization, D is a 4×4 matrix representing the system distortion, I is an identity matrix, and P0 is the ideal situation of matrix P, when LHC polarization is transmitted. According to Ref. [80], a -20 dB threshold of MNE is suitable for system quality assessment.

This evaluation campaign can be used to assess the influence of transmit distortions caused by multiple sources, including FR, channel imbalance and crosstalk in transmission, and incident angle. However, in order to assess the influence caused by each distortion source alone, the corresponding MNE changes of each distortion source is simulated, respectively.

According to Eq. (3), when FR is the only distortion in transmit, i.e. the circular polarization transmitted is perfect, the FR angle simply becomes an additional phase term, and can be omitted in the following data processing steps. On the other hand, if the transmit polarization is imperfect, the FR will have an influence on the general crosstalk d, which is already shown in Eq. (3).

3.2.2 Channel imbalance

Assuming that the only existent distortion in transmission is channel imbalance, i.e. ${\delta _3} = {\delta _4} = 0$. Fig. 3 shows the contour lines of MNE due to the interaction of the differential gain factor and the relative phase difference between the H and V channels. To maintain the MNE less than -20 dB, the approximated elliptical boundary could be determined at ±1.2 dB gain and ±8° phase offset.

 Fig.3 MNE evaluation due to channel imbalance
3.2.3 Crosstalk

For the sake of simplicity, the crosstalk is here assumed $\left| {{\delta _3}} \right| = \left| {{\delta _4}} \right|$, and no other distortions exist. Experimental results show that the phase offsets of the crosstalk have no effect on MNE. Therefore, only crosstalk gain is investigated. The result is shown in Fig. 4. As we can see, MNE increases proportionally with crosstalk level on the decibel scale. In order to keep MNE lower than -20 dB, the crosstalk at transmission should be maintained less than -20 dB.

 Fig.4 MNE evaluation due to crosstalk gain
3.2.4 Incident angle

It is admitted that the non-circularity of the transmitted wave also increases with the change of incidence angle[65]. In Ref. [65], Touzi and Charbonneau estimated that the AR of the transmitted polarization with RCM may vary between 1.4 dB (within 50 km at 0° beam scan angle) and 3.0 dB for the most raising beams of the 350 km ScanSAR swath. Such AR variations correspond to an elliptical polarization whose ellipticity varies between 35° and 41°. To evaluate such influence, the transmit Jones vector is set as[81]:

 $\left[{\begin{array}{*{20}{c}} {p_h^t}\\ {p_v^t} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} {\cos \phi }& { - \sin \phi }\\ {\sin \phi }& {\cos \phi } \end{array}} \right] \cdot \left[{\begin{array}{*{20}{c}} {\cos \tau }\\ {{\rm j}\sin \tau } \end{array}} \right]$ (15)
where $\phi \in \left[{ - \pi /2, \pi /2} \right]$is the ellipse orientation and $\left| \tau \right| \in \left[{0, \pi /4} \right]$ is the ellipse aperture, or ellipticity.

In this case, only ellipticity is taken into consideration and the orientation angle is set as $\phi = 0$. The MNE evaluation is shown in Fig. 5. We can see that the value of MNE increases with the bias from the ideal value (45°). To maintain an accuracy better than -20 dB, the bias of the ellipse aperture should be within [-5°, 5°]. While the ellipse aperture drops to 35°, which is the worst case estimated by Touzi and Charbonneau, MNE is approximately -15 dB.

 Fig.5 MNE evaluation due to the change in ellipticity
4 Improved Hybrid-polarity Architecture 4.1 System design

As introduced in previous sections, the HP architecture has one major implementation difficulty within the calibration issue: the transmit distortions can not be calibrated when working under the dual-pol mode, even if the values of transmit distortions can be precisely obtained through various external calibration methods. Therefore, those transmit distortions are always neglected in most HP system related papers. But as is shown in Subsection 3.2, transmit distortions will surely have certain influence on the HP architecture based PolSAR system.

In Subsection 3.2, the transmit distortions are evaluated by MNE, which is a generic metric defined to measure the polarization purity of a PolSAR system. On the other hand, the transmit distortions can also be quantified by their outcomes, which is the distortion of transmitted polarizations. Under this point of view, AR is used to quantify transmit distortions. As for a perfect circularly polarized wave AR=0 dB, and AR=+∞ is for a linearly-polarized wave. It is reported that the transmitted polarization in the two Lunar Mini-RF radars have an AR on the order of 2.5 dB[62]. Besides, it is expected that AR may vary between 1.4 dB and 3 dB in the worst case of the upcoming RCM radar system[65], and the radar system of the second moon mission of ISRO is designed to have an AR of less than 2 dB[69]. According to our research, AR and MNE values are not one to one related. But AR should be less than 1.8 dB to fulfill the aforementioned ${\rm{MNE}} \le - 20 \; {\rm{ dB}}$ criterion.

In order to overcome this flaw, internal calibration techniques should be built in the HP architecture based PolSAR systems. But conventional internal calibration loops may greatly increase the RF hardware required in the radar system, which implies an augment in cost and potential distortion sources. Alternatively, we have just modified the transmit module of the HP architecture. The block schematic of the resulting improved HP architecture is shown in Fig. 6(a). The modified transmit module is also outlined and simplified in Fig. 6(b). Comparing with the system designs shown in Fig. 1(b) and Fig. 2(b), the original ±90° phase shifter is replaced by two high-accuracy variable attenuator and 360° -covering phase shifter, denoted by “A” and “P”, respectively.

 Fig.6 Block schematic of the improved HP architecture

With these improvements, a pre-distortion technique can be used to correct the transmit distortions. First, the attenuator and phase shifter are tuned so that the two transmit path have balanced power level and wanted phase difference (for example +90° or -90° for circular polarizations). Next, the transmit distortions are measured with calibration methods introduced in previous section. Then, we can further tune the attenuator and phase shift to compensate those distortions. Thereby, the transmit distortions can be mitigated to an acceptable level.

With the two high-accuracy tunable attenuator and phase shifter, the PolSAR system based on the improved HP architecture can also generate arbitrary transmit polarizations. Original HP architecture based PolSAR systems usually operate with circularly-polarized transmissions with the consideration of mitigated FR effect and having no rotational selectivity upon the observation. But other transmit configurations also deserve further researches and applications. For example, Ref. [29] founded that with p/4 mode data, better decomposition results can be derived than those derived from CTLR mode data utilizing model-based decomposition algorithms[29]. Similar algorithms can also be applied to p/4 mode compact PolSAR interferometry (PolInSAR) data and produce promising target decomposition results[31].

Similar to the original HP architecture, the improved HP architecture can also support quad-pol mode. By switching the attenuator and the phase shifter, the improved HP architecture can produce interleaved orthogonal polarization pairs. Although arbitrary transmit polarization pairs can be generated, but in order to retain the advantage of having a wider swath coverage, the adopted transmit polarization pairs should differ from the receive polarization basis, i.e. H and V polarizations.

4.2 System model

The system model introduced in Subsection 2.1 and Subsection 2.2 also suits for the improved HP architecture based PolSAR system. When operating under dual-pol mode, the Jones vector of the transmitted polarization with general transmit distortion term d in Eq. (1) and Eq. (2) should be adjusted accordingly. For example, if traditional H and V transmission, or the aforementioned slant linear polarization are utilized in transmission, those term should be adjusted as[79]:

 ${\rm{H \ transmission}} \quad \quad \quad \quad \left[{\begin{array}{*{20}{c}} {{T_H}}\\ {{T_V}} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} 1\\ \delta \end{array}} \right]$ (16)
 ${\rm{V \ transmission}} \quad \quad \quad \quad \left[{\begin{array}{*{20}{c}} {{T_H}}\\ {{T_V}} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} \delta \\ 1 \end{array}} \right]$ (17)
 $\quad \;\pi /4 \; {\rm{linear \; polarization \; transmission}}\\ \quad \quad \quad \quad \ \left[{\begin{array}{*{20}{c}} {{T_H}}\\ {{T_V}} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} 1\\ 1 \end{array}} \right] + \delta \left[{\begin{array}{*{20}{c}} 1\\ { - 1} \end{array}} \right] \quad \quad \quad \quad \quad \quad$ (18)

As for the quad-pol mode, the 2×2 matrix SHPA in Eq. (7) should be adjusted according to the utilized transmit and receive polarization pairs.

4.3 Prototype system

As is shown in Fig. 7, our research team has already built a prototype system consisting the transmit and receive modules of the proposed improved HP architecture. A Vector Network Analyzer (VNA) is utilized to measure the magnitude and phase characteristics of the prototype system. Besides, we have also developed a program to control the attenuators, phase shifter and switches within the prototype system and communicate VNA through network. The pre-distortion related functions are also built in the program. It is estimated that the AR of the circular polarized wave transmitted by an ideal dual-linearly polarized antenna can be maintained within 1 dB with the pre-distortion technique.

 Fig.7 Prototype system of the improved HP architecture measured by a VNA

Another issue to be discussed is the usage of different antennas. In original HP architecture, it is suggested to utilize one dual-linearly polarized antenna for both transmit and receive. But we can also use two orthogonal single polarized antennas to replace one dual-linearly-polarized antenna. If different antennas are used for transmitting and receiving, then up to four single polarized antennas are required. In this research program, we have adopted this antenna configuration including four single polarized antennas. This configuration has the advantage of lower cost and better isolation, but suffers from parallax problem due to the boresight separation between two different antennas. Whether this trade is favorable still requires further verification.

Utilizing this prototype system, we will first validate the expected pre-distortion feature. Next, we will implement further experiments on different CP modes and assess actual influence of the transmit distortions on different radar observations. As for the analysis of data obtained from the improved HP architecture based PolSAR system, the unified data analysis framework for general compact and quad-pol SARs developed by Sabry and Vachon[82] can be applied.

5 Data Processing Methodologies

According to basic radar polarimetry theories[81], any quad-pol data can be directly transformed into other polarimetric data with different transmit/receive configuration, including dual-pol mode data. Therefore, quad-pol data derived from the HP architecture based PolSAR system can be directly transformed into conventional linear quad-pol data. Thereby, analyzing tools developed for conventional PolSAR can be similarly applied to HP architecture based quad-pol SARs.

On the other hand, the corresponding dual-pol modes, i.e. CP modes, of the HP architecture based PolSAR was newly introduced in the past ten years. Corresponding data processing methodologies and applicable applications still deserves to be reviewed. In the following two sections, data processing methodologies and the applications based on both CTLR mode and p/4 data are introduced, since those data could be derived from the proposed improved HP architecture.

5.1 CP data simulation

To date, only RISAT-1 and ALOS-2 are capable of providing CP data. ALOS-2 has acquired CP data with experimental mode, and those data are still not made public for the research community. Therefore, most CP researches are still based on simulated CP data, which is the dual-pol data directly transformed from corresponding quad-pol data. As is illustrated above, any quad-pol data can be used to transform other polarimetric data, including dual-pol data. An example of transmitting linear quad-pol data to CTLR mode data is shown in the Appendix of Ref. [7]. This formulation utilized the covariance matrix C3 of conventional linear quad-pol data. Similarly, one can use the coherency matrix T3 of conventional linear quad-pol data to simulate CP data[83]. In Ref. [11], the scattering vectors and covariance matrices of all three CP modes composed by the elements of the 2×2 Sinclair matrix are also shown. This transformation process could also be carried out in the newest PolSAR Pro 5.0 software[84].

It is important to note that though the transformed CP data is called as “simulated CP data”, but since the quad-pol data used for transformation is real, the generated CP data is real. Moreover, this transformation also makes the comparison between CP and quad-pol repeatable, since same data is used in either cases.

5.2 Fundamental data products

The fundamental data products of the CP data include the 2×2 covariance matrix C2 and the Stokes vector (SV) ${\bf{{g}}}{\rm{ = [}}\begin{array}{*{20}{c}} {{g_0}}& {{g_1}}& {{g_2}}& {{g_3}} \end{array}{{\rm{]}}^{\rm T}}$:

 ${{\bf{{C}}}_2}{\rm{ = }}\left\langle {{{\bf{{k}}}_{{\rm{CP}}}} \cdot {\bf{{k}}}_{\rm CP}^{*{\rm T}}} \right\rangle = \frac{1}{2}\left[{\begin{array}{*{20}{c}} {{g_0} + {g_1}}& {{g_2} - {\rm j}{g_3}}\\ {{g_2} + {\rm j}{g_3}}& {{g_0} - {g_1}} \end{array}} \right]$ (19)
where the $\left\langle \cdot \right\rangle$ function represents spatial averaging, kCP is the scattering vector of different CP modes, and *T stands for conjugate transpose. According to the investigations using the Monte Carlo simulation[38, 40, 71], the spatial averaging performed in Eq. (19) must be at least 49 looks (a 7×7 boxcar filter, or other filters with equivalent number of looks) to obtain reliable polarimetric child parameter estimation. These data products could be further processed by the following methodologies.

5.3 CP information retrieval methodologies 5.3.1 Covariance matrix expansion method

According to Ref. [11], the covariance matrix C2 of the three main CP modes can all be expressed as a sum of three terms: one only contains elements which have dependency with SHH and SVV, one contains |SHH|2 elements, and another term is consist of only co-polarization correlations. Based on the reciprocity assumption, i.e. SVH=SHV, and the reflection symmetry assumption, i.e. $\left\langle {{S_{{\rm{HH}}}}S_{{\rm{HV}}}^*} \right\rangle =$$\left\langle {{S_{{\rm{VV}}}}S_{{\rm{HV}}}^*} \right\rangle = 0$, unknowns in C2 can be simplified into only five scalars, i.e. |SHH|2, |SHV|2, |SVV|2, and the real and imaginary part of $\left( {{S_{{\rm{HH}}}} \cdot S_{{\rm{VV}}}^*} \right)$. If one further constraint of these five scalars could be found, then C2 can be further expanded into a conventional 3×3 covariance matrix C3 . The expanded covariance matrix is also called as pseudo quad-pol data. The constraint assumed in Ref. [9] is:

 $\frac{{\left\langle {{{\left| {{S_{{\rm{HV}}}}} \right|}^2}} \right\rangle }}{{\left\langle {{{\left| {{S_{{\rm{HH}}}}} \right|}^2}} \right\rangle + \left\langle {{{\left| {{S_{{\rm{VV}}}}} \right|}^2}} \right\rangle }} = \frac{{1 - \left| \rho \right|}}{4}$ (20)
where

 $\rho \equiv \frac{{\left\langle {{S_{{\rm{HH}}}} \cdot S_{{\rm{VV}}}^*} \right\rangle }}{{\sqrt {\left\langle {{{\left| {{S_{{\rm{HH}}}}} \right|}^2}} \right\rangle \cdot \left\langle {{{\left| {{S_{{\rm{VV}}}}} \right|}^2}} \right\rangle } }}$ (21)

This constraint is further developed by Nord et al.[11] as:

 $\frac{{\left\langle {{{\left| {{S_{{\rm{HV}}}}} \right|}^2}} \right\rangle }}{{\left\langle {{{\left| {{S_{{\rm{HH}}}}} \right|}^2}} \right\rangle + \left\langle {{{\left| {{S_{{\rm{VV}}}}} \right|}^2}} \right\rangle }} = \frac{{1 - \left| \rho \right|}}{N}$ (22)
where

 $N = \frac{{{{\left| {{S_{{\rm{HH}}}} - {S_{{\rm{VV}}}}} \right|}^2}}}{{{{\left| {{S_{{\rm{HV}}}}} \right|}^2}}}$ (23)

Utilizing these constraints, the value of |SHV|2 can be derived though an iterative solving process. Thus, other unknowns of the pseudo quad-pol data could be calculated. There are also some other reconstruction algorithms, which are either based on the scattering decomposition models[48, 85] or the eigenvalues of the C2, or Degree of Polarization (DoP)[86, 87]. Detailed assessment and comparisons of these approaches could be found in Ref. [87].

This kind of retrieval method has the advantage that, once the pseudo quad-pol data is obtained, all analysis tools developed for quad-pol SARs could be directly applied. However, the objective in many applications of PolSARs is to ascertain the scattering properties of the scene, rather than to presume them at the outset, and to realize image classification over an unconstrained variety of scene characteristics. Therefore, the application of this methodology is in fact restricted.

5.3.2 Stokes vector based method

Polarimetric information contained in CP data could also directly extracted from SV, from which various child parameters containing different polarimetric features could be generated[7, 62, 88]:

The aforementioned DoP:

 $m = \frac{{\sqrt {g_1^2 + g_2^2 + g_3^2} }}{{{g_0}}}$ (24)

The degree of linear polarization mL:

 ${m_L} = \frac{{\sqrt {g_1^2 + g_2^2} }}{{{g_0}}}$ (25)

The linear polarization ratio ${\mu_L}$:

 ${\mu _L} = \frac{{{g_0} - {g_1}}}{{{g_0} + {g_1}}}$ (26)

The degree of circular polarization mC:

 ${m_C} = \frac{{{g_3}}}{{{g_0}}}$ (27)

The Circular Polarization Ratio (CPR) ${\mu_C}$:

 ${\mu _C} = \frac{{{g_0} - {g_3}}}{{{g_0} + {g_3}}}$ (28)

The relative phase between the two linear E-vectors of the backscattered field:

 $\delta = {\tan ^{ - 1}}\left[{\frac{{{g_3}}}{{{g_2}}}} \right], \;\;\;\; - {180^ \circ } < \delta \le - {180^ \circ }$ (29)

Besides these six child parameters, other two very important parameters derived from SV are: the target parameter ${\alpha _s}$, derived from compact Random Volume over Ground (RVoG) scattering model[83], and the Poincar ellipticity parameter $\chi$[89, 90].

In Ref. [83], the compact RVoG scattering model is formed as:

 ${\bf{{g}}} = {g_0}\left( {1 - m} \right)\left( {\begin{array}{*{20}{c}} 1\\ 0\\ 0\\ 0 \end{array}} \right) + {g_0}m\left( {\begin{array}{*{20}{c}} 1\\ {\sin 2{\alpha _s}\cos \phi }\\ { \pm \sin 2{\alpha _s}\sin \phi }\\ { \mp \cos 2{\alpha _s}} \end{array}} \right)$ (30)
where the upper and lower signs are for LHC and RHC transmission, respectively. The corresponding target parameters are:

 ${\alpha _s} = \frac{1}{2}{\tan ^{ - 1}}\left( {\frac{{\sqrt {g_1^2 + g_2^2} }}{{ \mp {g_3}}}} \right)$ (31)
 $\phi = \arg \left( {{g_1} \pm {\rm j}{g_2}} \right)\quad \quad \quad \quad$ (32)
As we can see, in the compact RVoG scattering model, SV is decomposed into two separated terms, one denoting random volume, and the other denoting polarized surface or ground component.

According to the well-known Born and Wolf wave decomposition[81], SV could also be decomposed into a completely polarized and a completely depolarized wave component, in which the polarized term could be further written as a function of the polarization ellipse parameters, i.e. the orientation angle y and the ellipticity angle c:

 ${\bf{{g}}} = {g_0}\left( {1 - m} \right)\left( {\begin{array}{*{20}{c}} 1\\ 0\\ 0\\ 0 \end{array}} \right) + m{g_0}\left( {\begin{array}{*{20}{c}} 1\\ {\cos 2\psi \sin 2\chi }\\ { \pm \sin 2\psi \cos 2\chi }\\ { \mp \sin 2\chi } \end{array}} \right)$ (33)

Comparing the decomposition models in Eq. (30) and Eq. (33), we can conclude that $\phi = \psi$, and ${\alpha _s}$ is surely related to the ellipticity $\chi$ through:

 $\cos 2{\alpha _s} = \sin 2{c}$ (34)
These two parameters and the aforementioned relative phase d are usually utilized as an indicator of surface and double-bounce scatterers. But as the dependence of the orientation angle is undesirable, as and c are usually more prefered in decomposition and classification algorithms.

5.3.3 Eigenvalue decomposition based method

Similar to the famous H/alpha decomposition algorithm, C2 could also be directly decomposed with the eigenvalue decomposition[40, 83, 91]:

 ${{\bf{{C}}}_2} \!=\! \left[{{{\bf{{U}}}_2}} \right]\left(\!\! {\begin{array}{*{20}{c}} {{\lambda _1}}\!\!& \!\!0\\ 0 \!\!& \!\!{{\lambda _2}} \end{array}} \!\!\right){\left[{{{\bf{{U}}}_2}} \right]^{ - 1}}, \;\;{{\bf{{U}}}_2} \!=\! \left(\!\! {\begin{array}{*{20}{c}} {{{\bf{{u}}}_1}}& {{{\bf{{u}}}_2}} \end{array}} \!\!\right)$ (35)
where ${\lambda _i}$ and ${{{u}}_i}$ are the eigenvalues and the unitary eigenvectors of ${{\bf{{C}}}_2}$, respectively. The wave entropy ${H\!_w}$ and the scattering angle $\alpha$ can be further obtained as:

 ${H_w} = - \sum\limits_{i = 1}^2 {{p_i}{{\log }_2}{p_i}}$ (36)
 $\alpha = \sum\limits_{i = 1}^2 {{p_i}{\alpha _i}} \quad \quad \quad$ (37)
with

 ${p_i} = \frac{{{\lambda _i}}}{{{\lambda _1} + {\lambda _2}}}\quad \quad \quad \quad \quad \quad \quad \quad$ (38)
 ${{\bf{{u}}}_i} = {{\rm e}^{{\rm j}{\phi _i}}}{\left( {\begin{array}{*{20}{c}} {\cos {\alpha _i}}& {\sin {\alpha _i}{{\rm e}^{{\rm j}{\delta _i}}}} \end{array}} \right)^{\rm T}}$ (39)

The boundary curves of the derived ${H_w}/\alpha$ plane can be derived through setting ${{{C}}_2}$ as:

 ${{\bf{{C}}}_2} = \left( {\begin{array}{*{20}{c}} 1& 0 \\ 0& m \end{array}} \right), \;\;\;\;{\rm{or}}\\ {{\bf{{C}}}_2} = \left( {\begin{array}{*{20}{c}} m& 0\\ 0& 1 \end{array}} \right), \;\;\;\;0 \le m \le 1$ (40)
Optimal boundaries between different Polarimetric Scattering Mechanisms (PSMs) were fully investigated in Ref. [40] for various sensor data, including various spaceborne and airborne platforms.

It is established that this method is only applicable to CP data under the dual circular polarization (DCP, or CC) mode, which transmits circular polarization, and receives in orthogonal circular polarizations[10]. But since the scattering vectors of the CTLR mode and CC mode are linearly related through the following equation[91]:

 ${{\bf{{k}}}_{{\rm{CL}}}} = \frac{1}{2}\left( {\begin{array}{*{20}{c}} 1& 1 \\ { - {\rm j}}& {\rm j} \end{array}} \right){{\bf{{k}}}_{{\rm{CC}}}}$ (41)
where kCL and kCC are the scattering vectors of the CL and CC mode, respectively. Thereby, CTLR mode data can be directly transformed to CC mode data, and thus apply this method.

5.3.4 Scattering model based method

In the famous Freeman-Durden decomposition, quad-pol SAR data can be decomposed into three canonical scattering components utilizing three physically based scattering models[92]:

 \begin{aligned} {C_3} = \frac{{f\!_v}}{8}\left( {\begin{array}{*{20}{c}} 3 & 0 & 1\\ 0 & 2 & 0\\ 1 & 0 & 3 \end{array}} \right) + f{\!_d}\left( {\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& 0 & \alpha \\ 0 & 0 & 0\\ {{\alpha ^*}}& 0 & 1 \end{array}} \right) + f{\!_s}\left( {\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}} & 0 & \beta \\ 0 & 0 & 0\\ {{\beta ^*}}& 0 & 1 \end{array}} \right) \end{aligned} (42)
where ${f\!_v}$, ${f\!_d}$, and ${f\!_s}$ represents the contribution of volume, double-bounce, and surface components, respectively, $\left| \alpha \right| \ge 1$ represents the conjugative value between HH and VV terms of the double-bounce component, and $\left| \beta \right| < 1$ is the conjugative value between HH and VV terms of the surface component.

Similarly, the $2 \times 2$ covariance matrix ${{\bf{{C}}}_2}$ could also be formed as the sum of these three scattering components[93, 94]:

 $\pi {\rm{/4 \ mode}} \quad \quad \quad {{\bf{{C}}}_2} = \frac{{{f\!_v}}}{8}\left( {\begin{array}{*{20}{c}} {\rm{2}}& {\rm{1}}\\ {\rm{1}}& {\rm{2}} \end{array}} \right) + {f\!_d}\left( {\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& \alpha \\ { - {\alpha ^*}}& 1 \end{array}} \right) + {f\!_s}\left( {\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& \beta \\ { - {\beta ^*}}& 1 \end{array}} \right) \quad \quad \quad \quad \quad \$ (43)
 ${\rm{CTLR \ mode}} \quad \quad {{\bf{{C}}}_2} = \frac{{{f\!_v}}}{4}\left( {\begin{array}{*{20}{c}} {\rm{1}}& {\rm{0}}\\ {\rm{0}}& {\rm{1}} \end{array}} \right) + {f\!_d}\left( {\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& {{\rm j}\alpha }\\ { - {\rm j}{\alpha ^*}}& 1 \end{array}} \right) + {f\!_s}\left( {\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& {{\rm j}\beta }\\ { - {\rm j}{\beta ^*}}& 1 \end{array}} \right) \quad \quad \quad \quad$ (44)

For both modes, there are up to 5 unknowns (or 10 real unknowns) in ${{\bf{{C}}}_2}$, namely: ${f\!_v}$, ${f\!_d}$, ${f\!_s}$, $\alpha$ and $\beta$, and only 4 knowns, i.e. the four elements of C2. Therefore, similar to the pseudo quad-pol reconstruction method, at least one further constraint of the unknowns must be set to solve the system of equations. In Ref. [93] and Ref. [94], Liu et al. and Guo et al. both followed the assumption made in Ref. [92], i.e. if surface scatter is considered as dominant, the parameter $\alpha$ is fixed with $\alpha {\rm{ = }} - 1$, and if double-bounce scatter is considered as dominant, the parameter $\beta$ is fixed with $\beta$=+1. However, the judgement of surface or double-bounce scatter dominance differs in these two papers. Liu et al. utilized the aforementioned $\delta$ parameter, i.e. the relative phase between the two linear E-vectors of the backscattered field to decide the dominant scattering, while Guo et al. utilized the sign of ${\mathop{\rm Re}\nolimits} \left( {{S_{{\rm{HH}}}}S_{{\rm{VV}}}^*} \right)$.

6 Compact Polarimetry Applications 6.1 Unsupervised classification of terrains

One of the most important applications in radar polarimetry is arguably terrain and land-use classification and surveillance. The advantage of wide swath coverage of CP will surely enhance this ability of spaceborne PolSAR systems and provide time series or stacks of coherent radar images in a shorter time interval. But as the polarimetric information received through CP are naturally incomplete, our research goal of CP data processing is to strive for quantitative backscatter classification of the same finesse as those derived from quad-pol SAR systems.

6.1.1 Stokes vector based classification algorithms

Utilizing the m and d parameter shown in previous section, Charbonneau et al. first demonstrated a decomposition strategy of double-bounce, volumetric and surface scattering based on the decomposition of total power (g0) with trigonometric functions[12]. The derived powers of each scattering category are:

 $\left[{\begin{array}{*{20}{c}} {{P_D}}\\ {{P_V}}\\ {{P_S}} \end{array}} \right]{\rm{ = }}\left[{\begin{array}{*{20}{c}} {\frac{1}{2}{g_0}m\left( {1 \pm \sin \delta } \right)}\\ {{g_0}\left( {1 - m} \right)}\\ {\frac{1}{2}{g_0}m\left( {1 \mp \sin \delta } \right)} \end{array}} \right]$ (45)
where D, V, S stand for the double-bounce, volumetric and surface scattering, respectively, and the upper and lower signs correspond to the transmit settings. These derived powers of each main PSM classes can either be used to form the color basis of the PolSAR image, or be used to classify the pixels within the image into the three PSM categories. Note that the color basis should be in amplitude form, i.e. the extraction of powers. A very straightforward classification scheme is to determine the category of each pixel by the dominant backscattering power of each PSMs[36].

Similarly, the powers of each scattering category derived from m-c or m-as parameters based decomposition algorithms are:

 $\left[{\begin{array}{*{20}{c}} {{P_D}}\\ {{P_V}}\\ {{P_S}} \end{array}} \right]{\rm{ = }}\left[{\begin{array}{*{20}{c}} {\frac{1}{2}{g_0}m\left( {1 + \sin 2\chi } \right)}\\ {{g_0}\left( {1 - m} \right)}\\ {\frac{1}{2}{g_0}m\left( {1 - \sin 2\chi } \right)} \end{array}} \right] \\ \quad \quad \quad \!\!\quad = \left[{\begin{array}{*{20}{c}} {\frac{1}{2}{g_0}m\left( {1 + \sin 2{\alpha _s}} \right)}\\ {{g_0}\left( {1 - m} \right)}\\ {\frac{1}{2}{g_0}m\left( {1 - \sin 2{\alpha _s}} \right)} \end{array}} \right]$ (46)
Since the definitions of c and as parameters are adaptive to the transmit settings, Eq. (46) always holds for either transmission of the CTLR mode.

A demonstration of the classification results derived from these algorithms is given in Fig. 8. The utilized dataset is the well-known four-look NASA/JPL AIRSAR L-band dataset over San Francisco. Corresponding CTLR mode data with LHC transmission is transformed through PolSAR Pro 5.0 software developed by the European Space Agency (ESA). Since the dataset is already four-look, the spatial averaging process is implemented with a 5×5 boxcar filter. As we can see, the two classification map are almost identical, and the volume category is obvious overestimated in either classification map. According to Cloude et al.[83], this might be a common feature of CP, due to higher scattering entropy (than quad-pol SAR) in forest environments.

 Fig.8 Classification maps with different decomposition algorithms
6.1.2 Compact H-alpha classification algorithm

Another unsupervised classification strategy is to utilize the CP information derived from the aforementioned eigenvalue decomposition, or the compact H/alpha decomposition. The optimum boundaries between the PSMs are suggested as[40]:

The boundary between low-entropy zones and medium-entropy zones is set as H=0.65, and the boundary between medium-entropy zones and high-entropy zones is set as H=0.96.

In low-entropy zones, the boundary between multiple and dipole scattering types is a=42°, and the boundary between dipole and surface scattering types is a=48°.

In medium-entropy zones, the boundary between multiple and vegetation scattering types is about a=40°, and the boundary between vegetation and surface scattering types is a=51°.

In high-entropy zones, nearly all the PSMs are vegetation scattering. The boundary between multiple and vegetation scattering types is a=34.5°, and the boundary between vegetation and surface scattering types is a=51°.

The classification results of the same dataset used in previous subsection is demonstrated in Fig. 9.

 Fig.9 Compact H/alpha classification results
6.1.3 Wishart classifier based classification algorithms

Due to the indispensable spatial averaging process, the classification results presented in previous two subsections can hardly guarantee the details and texture features of the image. In order to improve those classification results, statistical property of the CTLR mode data could be further utilized. One main statistical property of such data is that its scattering vectors do obey the multivariate complex Gaussian distribution, just like the scattering vectors of quad-pol SAR data[39]. Therefore, we could also implement the famous Wishart classifier on the CTLR mode data.

In Refs. [33, 39] and Ref. [38], the Wishart classifier is combined with the compact H/alpha decomposition algorithm and the Stokes parameter based decomposition algorithms. In Fig. 10, we have presented the classification results of the former scheme with the H/alpha plane boundaries suggested by Zhang et al.[40]. We can see that the details and texture features of the image are surely well preserved.

 Fig.10 The classification maps of the compact H/alpha/Wishart algorithm with the same color labels as in Fig. 9(a)

As for the latter classification scheme, we have added two steps of refining process, i.e. excluding pixels with no clear defined PSMs and cluster merging process utilizing span (the total power), to ensure the reliability of the initial Wishart classes[38]. The classification results are shown in Fig. 11.

 Fig.11 Classification results of the m/chi/Wishart algorithm
6.2 Compact PolSAR interferometry

Compact PolInSAR is also one of the research hotspot within CP technologies. Compact PolInSAR system can measure two target scattering vectors of each resolution element in the scene from two slightly different look angle in a single-pass or repeated-pass interferometric configuration. The compact polarimetric scattering vectors measured at ends 1 and 2 of the baseline, can be expressed as ${{\bf{{k}}}_{cp1}}$, and ${{\bf{{k}}}_{cp2}}$. A four-element complex scattering target vector ${{\bf{{k}}}_4}$ can be formed by stacking the ${{\bf{{k}}}_{cp1}}$, and ${{\bf{{k}}}_{cp2}}$, i.e. ${{\bf{{k}}}_4} = {\left[{{{\bf{{k}}}_{cp1}}\:{{\bf{{k}}}_{cp2}}} \right]^{\rm T}}$. The complete polarimetric and interferometric information of two CP acquisitions are therefore represented by a 4×4 matrix

 ${{\bf{{J}}}_4} = \left[{\begin{array}{*{20}{c}} {{{\bf{{J}}}_{11}}}& {{{\bf{{J}}}_{12}}}\\ {{\bf{{J}}}_{12}^{*T}}& {{{\bf{{J}}}_{22}}} \end{array}} \right]$ (47)
where matrices J11 and J22 are the compact covariance matrices and J12 is the compact cross-covariance matric representative of compact PolInSAR configuration.

There are two main directions to process compact PolInSAR data. One is to reconstruct the quad PolInSAR data from the compact PolInSAR[24, 25], similar to the covariance matrix expansion method introduced in Subsection 5.3.1. Another important and more typical one is to process compact PolSAR dataset directly. Once pseudo-quad-pol data is reconstructed, conventional PolInSAR methodologies can be applied. Therefore, we will only review the two typical compact PolInSAR applications stemmed from the latter research direction in this subsection.

6.2.1 Forest height estimation

One typical application of compact PolInSAR technique is the estimation of forest heights. All methods of forest heights inversion are based on the RVoG model, which is modeled as the combination of a ground contribution and a volume only contribution. The inversion consists of fitting a line through the coherences, computing the topographical phase which is the intersection of fitting line with the unit circular and computing the volume only coherence which provides the vegetation height. The key step is therefore to fit line and find the correct volume only coherence. No matter which methods, their theory basis all are the complex coherence of compact PolInSAR data, which can be expressed as

 $\gamma \; ({\omega _1}, {\omega _2}) = \frac{{\omega _1^{\rm{H}}{{\bf{{J}}}_{12}}{\omega _2}}}{{\sqrt {\omega _1^{\rm{H}}{{\bf{{J}}}_{11}}{\omega _1}\omega _2^{\rm{H}}{{\bf{{J}}}_{22}}{\omega _2}} }}$ (48)
where w1, w2 represent polarimetric projection vectors.

In Refs. [21, 22], the compact polarimetric coherence locus associated with all the polarization states of the receiving antenna (a two-parameter space) were computed. Based on the coherence locus, a straight line was fitted, and then the three-stage inversion method was applied to estimate the tree heights. Detailed steps are listed as following:

(1) Synthesize many interferometric coherence values by varying the polarization of the receive antennas (varying w1, w2 of Eq. (48)) and identify the fitting line.

(2) Identify the two intersection points between the fitting line and the circle. Choose between the two the one that is associated with the topographical phase ${{\rm e}^{{\rm j}{\phi _0}}}$.

(3) Select the interferometric coherence that is furthest from the ground coherence as ${{\rm e}^{{\rm j}{\phi _0}}}{\gamma _v}$. Remove the topographical phase and obtain the volume only coherence ${\gamma _v}$.

(4) Apply the Look-Up Table (LUT) technique to find the tree height and the attenuation.

The tree heights inversion procedure in Ref. [26] is different from those in Refs. [21, 22]. In Ref. [26], the compact polarimetric coherence locus was not computed, instead, only several coherences were computed to fit the straight line. The coherence used to fit the straight line included two receiving channel coherences, unconstrained optimal coherences and maximum phase separation coherences. The maximum phase separation coherences were used to estimate the topographical phase and initial volume decorrelation. Then volume decorrelation estimation was updated with coherence boundary extraction method. After obtaining the ground phase and the accurate volume only coherence, LUT technique was used to find the tree heights and the attenuations.

6.2.2 Compact PolInSAR target decomposition

In Refs. [28, 30] a target decomposition method utilizing compact PolInSAR data is proposed. The Freeman-Durden decomposition technique was applied to the compact PolInSAR data[25]. The complex cross-correlation matrix of compact PolInSAR was decomposed into three 2×2 scattering matrices corresponding to the surface, double-bounce, and volume scattering.

 $\pi {\rm{/4 \ mode}} \quad \quad \quad {{\bf{{J}}}_2} = \frac{{{f\!_{cv}}}}{8}\left[{\begin{array}{*{20}{c}} {\rm{2}}& {\rm{1}}\\ {\rm{1}}& {\rm{2}} \end{array}} \right] + {f\!_{cd}}\left[{\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& \alpha \\ { - {\alpha ^*}}& 1 \end{array}} \right] + {f\!_{cs}}\left[{\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& \beta \\ { - {\beta ^*}}& 1 \end{array}} \right] \quad \quad \quad \quad \quad \$ (49)
 ${\rm{CTLR \ mode}} \quad \quad {{\bf{{J}}}_2} = \frac{{{f\!_{cv}}}}{4}\left[{\begin{array}{*{20}{c}} {\rm{1}}& {\rm{0}}\\ {\rm{0}}& {\rm{1}} \end{array}} \right] + {f\!_{cd}}\left[{\begin{array}{*{20}{c}} {{{\left| \alpha \right|}^2}}& {{\rm j}\alpha }\\ { - {\rm j}{\alpha ^*}}& 1 \end{array}} \right] + {f\!_{cs}}\left[{\begin{array}{*{20}{c}} {{{\left| \beta \right|}^2}}& {{\rm j}\beta }\\ { - {\rm j}{\beta ^*}}& 1 \end{array}} \right] \quad \quad \quad \quad$ (50)
Note that fcv, fcs, and fcd are complex unknowns containing amplitude and phase center heights information.

The algorithm was validated with simulated data derived from PolSARProSim program. One simulated L-band PolInSAR forest dataset was generated corresponding to 10 m forest heights. Fig. 12(a) is the Pauli image of the simulated scenario: here we analyzed an image transect indicated by the red line. We transformed the simulated quad-pol data to compact- pol data, and then constructed the compact-pol cross-correlation observable matrix J2. Decomposing results are shown in Fig. 12(c). The phrase ODD, DBL, and VOL stands for odd-bounce scattering, double-bounce scaffering, and volume scaffering, respectively, and VC and HC stands for circular polarization in transmission and receiving in linear (vertical or horizontal) polarization. According to the compact PolInSAR target decomposition, the amplitude and phase of each scattering mechanism were obtained. In addition, the decomposition results quite agreed with fully PolInSAR decomposition[95], which demonstrated that the compact PolInSAR also has the potential for target decomposition.

 Fig.12 Simulated dataset Pauli decomposition image
6.3 Other applications

Beside the two main applications introduced in previous subsections, other wide-swath-bene-fitted applications, such as soil moisture estimation[17, 18, 19, 20], iceberg[43, 44, 45], oil-spill[46, 47, 48, 49, 50, 51, 52, 53] and ship detection[42, 45, 52, 53, 54, 55, crop classification[56, 57, 58, 59, 60, 61] and sea ice surveillance[12, 13, 14, 85, 86] have also been carefully investigated in the latest researches. According to their investigations, comparable data processing results could be obtained with CP data comparing with those derived from quad-pol SAR data.

7 Conclusion

In this paper, we have fully reviewed the principles and applications of the HP architecture based PolSAR. As we can see, the HP architecture is actually a PolSAR system design scheme, which firstly emphasis the synthesis of transmit polarizations with two separated signal channels. Thereby, any polarization can be generated theoretically, including the circular polarizations and the slant linear polarizations required in compact polarimetry. In other words, this feature makes an HP architecture based PolSAR system possible to operate under different CP modes, which can produce classification results superior than conventional linear dual-pol modes. Moreover, if the adopted transmit polarizations have equal H and V components, as is the case with all CP modes, the HP architecture based PolSAR system will have a unique self-calibration feature. Secondly, this design scheme also emphasis that the transmitted polarization should differ from the receiving polarization basis. Thus, the range ambiguity performance of the HP architecture based PolSAR system can be improved and the swath coverage of the HP architecture based PolSAR system can be further broadened, particularly at higher incident angles, when operating under quad-pol mode. Last but not least, this design scheme actually requires very few RF hardware, which implies a less costly and more robust PolSAR system. Besides, shorter repetition intervals, in which coherent radar images are obtained, can also be reached by HP architecture based PolSAR systems due to the advantage of wider swath coverage.

Meanwhile, this paper has also pointed out the implementation difficulties of the HP architecture, i.e. the transmit distortions cannot be calibrated when the HP architecture based PolSAR system works under the dual-pol mode. Besides, the polarization adopted for transmission is also always circular. Since PolSAR data acquired with other transmit polarization may also produce favorable results in certain applications, this configuration is also regarded as one problem. In order to overcome these problems, we have proposed an improved version of the HP architecture. With the improved HP architecture, a pre-distortion technique can be applied to correct the transmit distortions. Comparing with radar systems with extra internal calibration loops, the proposed improved version requires less RF hardware. Besides, instead of just transmitting circular polarizations, a PolSAR system based on the improved HP architecture can operate with arbitrary transmit polarization configurations. This feature implies that the improved HP architecture can also support the π/4 mode and other quad-pol modes with different orthogonal transmit polarization pairs. At last, we have illustrated a prototype system based on the improved HP architecture. Associated experimental verifications are still in progress.