A computational method for the LU decomposition of rectangularmatrices and its implications to the realization of 2-D digital filters

The realization of 2-D digital filters based on the lower-upper triangular decomposition of the coefficient matrix is investigated. A numerical method based on the QA decomposition, which has some important characteristics, is proposed for reaching the LU structure. The coefficients in the final LU structure have values favorable to fixed-point arithmetic implementation. Furthermore, the QR structure can be used for the realization and possesses good numerical characteristics in terms of the approximate decomposition scheme. The symmetry in the impulse response coefficient matrix of an octagonally symmetric 2-D FIR filter is utilized to reduce the computational effort spent in the decomposition and the total number of multipliers in the final realization structure     

Analysis and applications of backscattered frequency correlationfunction

The application of the radar backscatter frequency correlation for classification and inversion of physical parameters of terrestrial targets is investigated. Traditionally, in radar remote sensing, the backscattering coefficients and the backscatter phase difference statistics of a distributed target are considered for estimating the biophysical parameters of interest. Because of the complex nature of random media scattering problems, however, target classification and parameter inversion algorithms are very convoluted. One obvious way of enhancing the success and accuracy of an inversion algorithm is to expand the dimension of the input vector space. Depending on the radar parameters, such as footprint (pixel) size, incidence angle, and the target attributes (physical parameters), the backscatter signal decorrelates as function of frequency. In this paper, analytical and experimental procedures are developed to establish a relationship between the complex frequency correlation function (FCF) of the backscatter and the radar and target attributes. Specifically, two classes of distributed targets are considered: 1) rough surfaces and 2) random media. Analytical expressions for the frequency correlation function are derived and it is shown that the effect of radar parameters can be expressed explicitly and thus removed from the measured correlation functions. The University of Michigan wideband polarimetric scatterometer systems are used to verify the theoretical models and inversion algorithms developed in this study     

An ultrafast wide-band millimeter-wave (MMW) polarimetric radar for remote sensing applications

With the advent of high-frequency radio frequency (RF) circuits and components technology, millimeter-wave (MMW) radars are being proposed for a large number of military and civilian applications. Accurate and high-resolution characterization of the polarimetric radar backscatter responses of both clutter and man-made targets at MMW frequencies is essential for the development of radar systems and optimal detection and tracking algorithms. Toward this end, a new design is developed for ultrafast, wide-band, polarimetric, instrumentation radars that operate at 35 and 95 GHz. With this new design, the complete scattering matrix of a target (magnitude and phase) can be measured over a bandwidth of 500 MHz in less than 2 /spl mu/s. In this paper, the design concepts and procedures for the construction and calibration of these radars are described. In addition, the signal processing algorithm and data-acquisition procedure used with the new radars are presented. To demonstrate the accuracy and applicability of the new radars, backscatter measurements of certain points and distributed targets are compared with their analytical radar cross section (RCS) and previously measured /spl sigma//spl deg/ values, respectively, and good agreements are shown. These systems, which can be mounted on a precision gimbal assembly that facilitates their application as high-resolution imaging radar systems, are used to determine the MMW two-way propagation loss of a corn field for different plant moisture conditions.     

Semi-empirical model for radar backscatter from snow at 35 and 95GHz

Radar backscatter experiments were conducted at 35 and 95 GHz to measure the response of snow-covered ground to snow depth, liquid water content, and ice crystal size. The measurements included observations over a wide angular range extending between normal incidence and 60° for all linear polarization combinations. A numerical radiative transfer model was developed and adapted to fit the experimental observations. Next, the radiative transfer model was exercised over a wide range of conditions and the generated data were used to develop relatively simple semi-empirical expressions that relate the backscattering coefficient (for each linear polarization) to incidence angle, snow depth, crystal size, and liquid water content     

Millimeter-wave measurements of foliage attenuation and ground reflectivity of tree stands at nadir incidence

In this paper, the phenomenology of wave propagation through foliage and forest ground reflectivity is investigated for assessing the feasibility of foliage-covered target detection at millimeter-wave frequencies. An experimental procedure for simultaneous measurements of foliage attenuation and ground reflectivity is outlined. This measurement procedure is implemented for two different tree stands, one mostly coniferous and the other deciduous, using a nadir-looking, high-resolution, 35-GHz radar positioned above the tree canopy. Statistics of the two-way attenuation and ground reflectivity for these two well-characterized stands are derived. Strong spatial and angular fluctuations in the two-way foliage attenuation coefficient are observed. The mean, standard deviation, and median of the measured two-way attenuation factor at Stand 1 (mostly coniferous trees with 0.140 trees/m/sup 2/ stocking density and 45.45 Kg/m/sup 2/ green biomass) are -25.4, -18.3, and -48.2 dB, respectively, while the mean, standard deviation, and median of the measured two-way attenuation factor at Stand 2 (deciduous trees with 0.1055 trees/m/sup 2/ stocking density and 30.90 Kg/m/sup 2/ green biomass) are -15.4, -12.7, and -33.6 dB, respectively. The mean attenuation rates of Stand 1 and Stand 2, derived from the measured two-way attenuation factor, are 0.40 and 0.24 Np/m, respectively. Only a small percentage of the data had two-way foliage attenuation values exceeding 70 dB. The mean, standard deviation, and median of the power reflectivity of the forest floor at Stand 1 are -14.2, -11.0, and -21.1 dB, respectively, while for Stand 2, the same statistical measures are -16.0, -14.3, and -22.2 dB, respectively. The results demonstrate the potential for using MMW nadir-looking radars for the detection of targets underneath foliage-cover.     

Experimental characterization of the effective propagation constantof dense random media

A new technique for measuring the effective propagation constant of dense random media is presented. This technique involves two major steps: (1) measurement of the mean bistatic scattered field of a cluster of the random medium confined in a spherical boundary and (2) characterization of the complex permittivity for a homogeneous dielectric sphere having identical radius and bistatic scattered field as those of the spherical cluster of the random medium. Using this measurement technique, not only the effective propagation constant of complex dense random media for which an analytical solution does not exist can be characterized, but it can also be used to establish the validity region of the existing models. The sensitivity analyses of the proposed algorithm show that the imaginary part of the effective propagation constant can be measured very accurately. It is also shown that the effective complex permittivity of media with very low dielectric contrast or volume fractions can be characterized accurately. Measurements of the effective propagation constant of different dense random media comprised of homogeneous spherical particles of different packing densities are reported and compared with the existing analytical models     

95-GHz scattering by terrain at near-grazing incidence

This study, consisting of three complimentary topics, examines the millimeter-wave backscattering behavior of terrain at incidence angles extending between 70 and 90°, corresponding to grazing angles of 20° to 0°. The first topic addresses the character of the statistical variability of the radar backscattering cross section per unit area σ_A. Based on an evaluation of an extensive data set acquired at 95 GHz, it was determined that the Rayleigh fading model (which predicts that σ_A is exponentially distributed) provides an excellent fit to the measured data for various types of terrain covers, including bare surfaces, grasses, trees, dry snow, and wet snow. The second topic relates to the angular variability and dynamic range of the backscattering coefficient σ⁰, particularly near grazing incidence. We provide a summary of data reported to date for each of several types of terrain covers. The last topic focuses on bare surfaces. A semi-empirical model for σ⁰ is presented for vertical (VV), horizontal (HH), and cross (HV) polarizations. The model parameters include the incidence angle &thetas;, the surface relative dielectric constant ϵ, and the surface roughness ks, where k=2π/λ and s is the surface root mean square (RMS) height     

Measurement and modeling of the millimeter-wave backscatterresponse of soil surfaces

The millimeter-wave (MMW) backscatter response of bare-soil was examined by conducting experimental measurements at 35 and 94 GHz using a truck-mounted polarimetric scatterometer and by developing appropriate models to relate the backscattering coefficient to the soil's surface and volume properties. The experimental measurements were conducted for three soil surfaces with different roughnesses under both dry and wet conditions. The experimental measurements indicate that in general the backscattering coefficient is comprised of a surface scattering component σ^s and a volume scattering component σ ^v. For wet soil conditions, the backscatter is dominated by surface scattering, while for dry conditions both surface and volume scattering are significant, particularly at 94 GHz. Because theoretical surface scattering models were found incapable of predicting the measured backscatter, a semiempirical surface scattering model was developed that relates the surface scattering component of the total backscatter to the roughness parameter ks, where k=2π/λ and s is the rms height, and the dielectric constant of the soil surface. Volume scattering was modeled using radiative transfer theory with the packed soil particles acting as the host material and the air voids as the scattering particles. The combined contribution of surface and volume scattering was found to provide good agreement between the model calculations and the experimental observations     

A calibration technique for polarimetric coherent-on-receive radarsystems

A new technique for calibrating a coherent-on-receive polarimetric radar system is proposed. A coherent-on-receive polarimetric radar is capable of measuring the Mueller matrix of point or distributed targets directly by transmitting at least four independent polarizations and measuring the vertical and horizontal components of the backscatter signal simultaneously. The technique requires the use of two calibration targets, a target with known scattering matrix (such as a metallic sphere or a trihedral corner reflector) and any depolarizing target (for which knowledge of its scattering matrix is not required) to determine the system distortion parameters. The system distortion parameters, which include the channel imbalances, the cross-talk factors of both the transmit and the receive antennas, and the phase shifts and amplitude variations of the transmitter polarizers, are determined by measuring the calibration targets for four different transmit polarizations. The validity of the new calibration technique is examined by measuring the scattering matrices of spheres and cylinders as test targets using a coherent-on-receive radar operating at 34.5 GHz. Excellent agreement between the theoretical and the measured scattering matrices for the test targets are obtained