Polar Duals of Rotors

Assume K is a rotor in a regular simplex of heihgt 1 in an n-dimensional Euclidean space. Let K~* denote the polar dual of K. Then the volume V(K~*) satisfies the inequality V(K~*)≥(n+1)~nω_n, where ω_n denotes the volume of an n-dimensional unit ball. Equality holds if and only if K is a ball centered at the centroid of the simplex.

Recent Progress in Dual-Polarization Radar Research and Applications in China

Dual-polarization(dual-pol)radar can measure additional parameters that provide more microphysical information of precipitation systems than those provided by conventional Doppler radar.The dual-pol parameters have been successfully utilized to investigate precipitation microphysics and improve radar quantitative precipitation estimation(QPE).The recent progress in dual-pol radar research and applications in China is summarized in four aspects.Firstly,the characteristics of several representative dual-pol radars are reviewed.Various approaches have been developed for radar data quality control,including calibration,attenuation correction,calculation of specific differential phase shift,and identification and removal of non-meteorological echoes.Using dual-pol radar measurements,the microphysical characteristics derived from raindrop size distribution retrieval,hydrometeor classification,and QPE is better understood in China.The limited number of studies in China that have sought to use dual-pol radar data to validate the microphysical parameterization and initialization of numerical models and assimilate dual-pol data into numerical models are summarized.The challenges of applying dual-pol data in numerical models and emerging technologies that may make significant impacts on the field of radar meteorology are discussed.

Dual-Polarized Slot-Coupled Microstrip Antenna with Very High Isolation

A wideband dual-polarized slot-coupled stacked microstrip antenna with very high isolation and low cross-polarization is presented. To improve isolation between two poiarization ports, the stacked patches are excited by an open-ended and a T-shaped microstrip lines both via two H-shaped slots placed in a ＂T＂ configuration. The measured isolation is better than 40.5 dB over the bandwidth from 8.8 to 9.8 GHz with cross-polarization level less than - 28.5 dB. The measured VSWR ≤ 2 bandwidths reach 20.7 96 and 19.196 at the verrical and horizontal polarization ports, respectively. This antenna is suitable to be used as array elements in spacebome synthetic aperture radars （SAR） and active phased array radars.

A New Dual Polarized Aperture-Coupled Printed Array for SAR Applications

This paper presents a new design of dual polarized aperture coupled printed antenna array. The finite difference time domain (FDTD) analysis of an aperture coupled microstrip element is performed, and the effects of antenna parameters on its characteristics are obtained to guide the design of the printed array. Then an 8×2 dual polarized array design in X band is introduced with configuration plots. In order to improve its isolation and cross polarization, an outphase displacement feeding technique is adopted in the feed network. Also, the round bends are used instead of conventional right angle bends so as to achieve better VSWR performance. Experimental results are presented, indicating the validity of the design. This dual polarized array can be applied as a sub array of spaceborne SAR systems.

Measurements of ocean wave and current field using dual polarized X-band radar

A new ocean wave and sea surface current monitoring system with horizontally-(HH) and vertically-(VV) polarized X-band radar was developed.Two experiments into the use of the radar system were carried out at two sites,respectively,for calibration process in Zhangzi Island of the Yellow Sea,and for validation in the Yellow Sea and South China Sea.Ocean wave parameters and sea surface current velocities were retrieved from the dual polarized radar image sequences based on an inverse method.The results obtained from dual-polarized radar data sets acquired in Zhangzi Island are compared with those from an ocean directional buoy.The results show that ocean wave parameters and sea surface current velocities retrieved from radar image sets are in a good agreement with those observed by the buoy.In particular,it has been found that the vertically-polarized radar is better than the horizontally-polarized radar in retrieving ocean wave parameters,especially in detecting the significant wave height below 1.0 m.

Dual-Polarized RIS-Based STBC Transmission with Polarization Coupling Analysis

The rapid development of the reconfigurable intelligent surface(RIS)technology has given rise to a new paradigm of wireless trans-mitters.At present,most research works on RIS-based transmitters focus on single-polarized RISs.In this paper,we propose a dual-polarized RIS-based transmitter,which realizes 4-transmit space-time block coding(STBC)transmission by properly partitioning RIS’s unit cells and utilizing the degree of freedom of polarization.The proposed scheme is evaluated through a prototype system that utilizes a fabricated dual-polarized phase-adjustable RIS.In particular,the polarization coupling phenomenon in each unit cell of the employed dual-polarized RIS is modeled and analyzed.The experimental results are in good agreement with the theoretical modeling and analysis results,and an initial re-search effort is made on characterizing the polarization coupling property in the dual-polarized RIS.

Evaluating the Algorithm for Correction of the Bright Band Effects in QPEs with S-, C-and X-Band Dual-Polarized Radars

The bright band, a layer of enhanced radar reflectivity associated with melting ice particles, is a major source of significant overestimation in quantitative precipitation estimation(QPE) based on the Z–R(reflectivity factor–rain rate) relationship.The effects of the bright band on radar-based QPE can be eliminated by vertical profile of reflectivity(VPR) correction. In this study, we applied bright-band correction algorithms to evaluate three different bands(S-, C-and X-band) of dual-polarized radars and to reduce overestimation errors in Z–R relationship–based QPEs. After the reflectivity was corrected by the algorithms using average VPR(AVPR) alone and a combination of average VPR and the vertical profile of the copolar correlation coefficient(AVPR+CC), the QPEs were derived. The bright-band correction and resulting QPEs were evaluated in eight precipitation events by comparing to the uncorrected reflectivity and rain-gauge observations, separately. The overestimation of Z–R relationship–based QPEs associated with the bright band was reduced after correction by the two schemes for which hourly rainfall was less than 5 mm. For the verification metrics of RMSE(root-mean-square error), RMAE(relative mean absolute error) and RMB(relative mean bias) of QPEs, averaged over all eight cases, the AVPR method improved from 2.28,0.94 and 0.78 to 1.55, 0.60 and 0.40, respectively, while the AVPR+CC method improved to 1.44, 0.55 and 0.30, respectively.The QPEs after AVPR+CC correction had less overestimation than those after AVPR correction, and similar conclusions were drawn for all three different bands of dual-polarized radars.

Wideband dual-polarized slot-coupled microstrip array for synthetic aperture radar application

An 8 × 1-element wideband dual-polarized slot-coupled microstrip antenna array with high isolation and low crosspolarization in X-band is presented. The array antenna offers an impedance bandwidth （VSWR≤2） of 23% and 21% for dual polarization ports, respectively. The measured isolation between two polarization ports is better than 35 dB and the measured cross-polarization level below -25 dB in the main beam over the operation frequency band of 9.35 GHz to 9.75 GHz. This array is well suitable for X-band SAR （synthetic aperture radar） antenna apphcation.

Identification and Removal of Non-meteorological Echoes in Dual-polarization Radar Data Based on a Fuzzy Logic Algorithm

A major issue in radar quantitative precipitation estimation is the contamination of radar echoes by non-meteorological targets such as ground clutter,chaff,clear air echoes etc.In this study,a fuzzy logic algorithm for the identification of non-meteorological echoes is developed using optimized membership functions and weights for the dual-polarization radar located at Mount Sobaek.For selected precipitation and non-meteorological events,the characteristics of the precipitation and non-meteorological echo are derived by the probability density functions of five fuzzy parameters as functions of reflectivity values.The membership functions and weights are then determined by these density functions.Finally,the nonmeteorological echoes are identified by combining the membership functions and weights.The performance is qualitatively evaluated by long-term rain accumulation.The detection accuracy of the fuzzy logic algorithm is calculated using the probability of detection（POD）,false alarm rate（FAR）,and clutter–signal ratio（CSR）.In addition,the issues in using filtered dual-polarization data are alleviated.

Broadband printed antennas and dual-polarized microstrip and waveguide slot antenna arrays

In order to meet the urgent needs in wireless communications, microwave image synthetic aperture radars （SAR）, and electronic warfare systems, this dissertation studies several types of broadband dual-polarized planar antenna elements and arrays, and proposes a few of novel designs with experimental verification. The main accomplishments reported in the dissertation are as follows.

Dual-polarized lens antenna based on multimode metasurfaces

We propose a dual-polarized lens antenna system based on isotropic metasurfaces for 12 GHz applications. The metasurface lens is composed of subwavelength unit cells（0.24λ0） with metallic strips etched on the top and bottom sides of the unit cell, and a cross-slots metallic layer in the middle that serves as the ground. The multimode resonance in the unit cell can realize a large phase shift（covering 0？–360？）, and the total transmission efficiency of the lens is above 80%.The feed antenna at the focal point of the lens is a broadband dual-polarized microstrip antenna. Both the simulated and the measured results demonstrate that the dual-polarized lens antenna system can realize a gain of more than 16.1 dB, and an input port isolation of more than 25.0 dB.

Corner Fed Microstrip Antenna Analysisfor Dual Polarization

This paper investigates a corner fed microstrip patch antenna by means of the cavity model with proposed feed modeling. The input impedance and radiation patterns for a corner feed are calculated. The mutual coupling between two corner feeds is investigated. An improvement in mutual coupling has been found for corner feeds relative to edge feeds, which is helpful for the design of dual polarized antenna arrays in wireless communication and radar applications.

Polarization mode dispersion compensation in a novel dual polarization differential quadrature phase shift keying system

A novel dual polarization differential quadrature phase shift keying （DP-DQPSK） system is proposed, whose receiver is the same as the single polarization DQPSK system, while it does not need polarization de-multiplexing like the conventional polarization division multiplexing QPSK （PDM-QPSK）. Polarization mode dispersion （PMD） is mainly considered and PMD compensation for the DP-DQPSK system is studied. As the feedback signal for PMD compensation, the degree of polarization of the signals is discussed in detail. The results show that PMD tolerance can be improved by 89 ps within 1 dB optical signal noise ratio penalty after PMD compensation for the DP-DQPSK system.

Experimental Research of Dual-Polarization Passive Radar Based on DTTB Signal

The passive radar is a hot research topic. A multi-channel wideband passive radar experimental system is designed and the digital television terrestrial broadcasting (DTTB) signal is chosen to carry out the target detection experiment of civil aviation aircraft. The polarization and spatial filtering methods are used to solve the strong direct path interference suppression problems brought by the receiving system location;combined with the characteristics of DTTB signal, the block length selection interval in the block batch processing method for range-Doppler images calculation is given;the clutter suppression performance is compared through the experimental data receiving from different bistatic polarization channels, the conclusion is different from the monostatic radar and it can guide the passive radar experiment.

Iterative Detection and Decoding Algorithm in Dual Polarized Land Mobile Satellite MIMO Systems

An iterative detection and decoding algorithm with outer code decision feedback is proposed for the dual polarized( DP) land mobile satellite( LMS) MIMO systems using concatenated codes. A feedback structure is added after the outer decoder in the proposed algorithm. The feedback information is exploited to control the detecting list in the MIMO detector and reduce the number of symbols which have to be processed at each iteration. As a result,the computational complexity is reduced. Meanwhile,the successfully decoded outer code words are used to calculate the more reliable initial information for the inner decoder and the system performance can be improved by this step. The simulation results show that the proposed algorithm can reduce the computational complexity compared to the traditional iterative detection and decoding algorithm and achieve better performance.

Compact Interlaced Dual Circularly Polarized Sequentially Rotated Dielectric-Resonator Antenna Array

In this study,a compact 2×2 interlaced sequentially rotated dual-polarized dielectric-resonator antenna array is proposed for 5.8 GHz applications.The array is composed of a novel unit elements that are made of rectangular dielectric resonator(RDR)coupled to an eye slot for generating the orthogonal modes,TEδx 21 and TE1yδ1 to acquire circular polarization(CP)radiation.For the purpose of miniaturization and achieving dual polarized resonance,the array is fed by two interlaced ports and each port excites two radiating elements.The first port feeds horizontal elements to obtain left hand circular polarization(LHCP).The second port feeds vertical elements to obtain right hand circular polarization(RHCP).A quarter-wave length transformer is employed to reduce the attenuation and consequently increase the array gain performance.The 35×35 mm2(0.676λ0×0.676λ0)gains were 8.4 and 8.2 dBi for port 1 and port 2,respectively,with port isolations of−33.51 dB.The design achieves a voltage standing-wave ratio(VSWR)<−10 dB and an axial ratio(AR)<−3 dB bandwidth of 2.48%(5.766 to 5.911 GHz)for LHCP at port 1 and a VSWR<−10 dB and AR<−3 dB bandwidth of 2.28%(5.788 to 5.922 GHz)for RHCP at port 2.The findings of the proposed design validate its use for ISM band applications.

Ultra-broadband polarization splitter based on graphene layer-filled dual-core photonic crystal fiber

An ultra-broadband polarization splitter based on graphene layer-filled dual-core photonic crystal fiber （GDC-PCF） that can work in a wavelength range from 1120 nm to 1730 nm is proposed in this paper. Through optimizing fiber configuration, the polarization splitter has an extinction ratio of-56.3 dB at 1.55 μm with a fiber length of 4.8 mm. Compared with the photonic crystal fiber reported splitters, to our knowledge, the GDC-PCF splitter with the extinction ratio below-20 dB has a super wide bandwidth of 610 nm. Due to the excellent splitting characteristics, the GDC-PCF will be used in coherent optical communication systems in a wavelength range from infrared to mid-infraed.

A Low Profile Four-Way Directional Antenna with Dual Polarization

This paper presents a low profile dual polarized directional antenna composed of loop and dipole arrays mounted on a ground plane with each loops and dipoles being fed independently. Each loop antenna is paired with a reflector while each dipole antenna is paired with a director and a reflector. The proposed antenna is intended for an indoor base station (BS) with resonance frequency of 2.4 GHz and capable of producing four orthogonal directional pattern with downward elevation angle equals to 30°;and half power bandwidth (HPBW) less than 80°;in both vertical and horizontal polarization. The reflection characteristics of the loop and dipole arrays are less than -10 dB and the mutual coupling between the vertical and horizontal polarization elements is nearly less than -20 dB. In later progress, the dipole antenna was substituted with printed dipole antenna to achieve a better performance. Both the calculated and measured results demonstrated that the desired radiation patterns were achieved, and the measured results agreed well with the calculated ones. Consequently, a low profile antenna with a thickness of 0.16 λ (20 mm) having the expected radiation pattern is successfully designed.

An Efficient CSI Feedback Scheme for Dual-Polarized MIMO Systems Using Layered Multi-Paths Information

Massive MIMO is one of the enabling technologies for beyond 4G and 5G systems due to its ability to provide beamforming gain and reduce interference Dual-polarized antenna is widely adopted to accommodate a large number of antenna elements in limited space. However,current CSI(channel state information)feedback schemes developed in LTE for conventional MIMO systems are not efficient enough for massive MIMO systems since the overhead increases almost linearly with the number of antenna. Moreover,the codebook for massive MIMO will be huge and difficult to design with the LTE methodology. This paper proposes a novel CSI feedback scheme named layered Multi-paths Information based CSI Feedback(LMPIF),which can achieve higher spectrum efficiency for dual-polarized antenna system with low feedback overhead. The MIMO channel is decomposed into long term components(multipath directions and amplitudes)and short term components(multipath phases). The relationship between the two components and the optimal precoder is derived in closed form. To reduce the overhead,different granularities in feedback time have been applied for the long term components and short term componentsLink and system level simulation results prove that LMPIF can improve performance considerably with low CSI feedback overhead.

Diversity–Multiplexing Tradeoff and Outage Performance for 2&times;2 Dual-Polarized Uncorrelated Rice MIMO Channels

In this paper, diversity-multiplexing tradeoff (DMT) curve for 2×2 Dual-Polarized uncorrelated Rice MIMO channels is studied. Exact expressions for statistic information of mutual information exponent are derived. Impacts of channel parameters such as signal to noise ratio (SNR), k-factor and cross polarization discrimination (XPD) on mutual information exponent are analyzed. Compared to conventional single-polarized (SP) Rice MIMO systems, a qualitatively different behavior is observed for DP Rice systems. The work in this paper, allows identifying quantitatively for which channels (k-factor) and SNR levels the use of dual polarization becomes beneficial. Gamma or lognormal distribution are used to describe mutual information component, and a theoretical formulation for finite-SNR DMT curve in 2×2 DP uncorrelated Rice channels is presented for the first time, which is valid in low and medium SNRs when multiplexing gain is larger than 0.75.