Bistatic Case Research Articles

Idealized Bistatic RADAR GMTI Detection with Space-Time Processing

In a recent paper by the author a novel approach was utilized for determining upper-bound ground moving target indication (GMTI) radar detection performance with two-dimensional space-time processing. That model utilized an idealized clutter model and other simplifying assumptions to clarify the method. The method is extended here to the general bistatic case. It is shown that the elements of the clutter covariance matrix can be obtained from cross-correlations of the convolutions of (appropriately transformed) transmit and receive aperture functions at different times and locations. A simulation based on this theory was developed that accommodates arbitrary transmitter-receiver geometry. When this general bistatic model is specialized to the monostatic case, it is shown to agree both theoretically and computationally with the earlier results.

Azimuth preprocessing for monostatic and bistatic spotlight synthetic aperture radar maging based on spectral analysis convolution

Dechirping is a technique widely used to reduce sampling rate. It is well suited for the illumination of small scenes. In this paper, we extend this idea to mono/bistatic spotlight synthetic aperture radar (SAR) imaging. An azimuth preprocessor based on the spectral analysis (SPECAN) convolution is presented. The convolution overcomes the Doppler aliasing of echoed signals, while the wavenumber analytic formula keeps unchanged. Since the spatial characteristic of the signal is preserved, the preprocessing is well compatible with conventional focusing approaches, such as chirp scaling algorithm and frequency scaling algorithm The proposed method is validated by simulations in both monostatic and bistatic cases.

Burial depth dependence of the bistatic scattering amplitude for cylinders illuminated by evanescent waves using two–dimensional finite elements.

Prior research examined the dependence on simulated burial depth of the low‐frequency scattering by small targets illuminated by evanescent waves [P. L. Marston, A. L. Espana, C. F. Osterhoudt, and D. B. Thiessen, J. Acoust. Soc. Am. 122, 3034 (2007)]. The backscattering amplitude from targets with localized coupling displayed a spatial decay rate approximately twice that of the evanescent wave. An extended reciprocity relation was proposed which accounts for the more general case of a bistatic observation in the water column above the sea floor. In the bistatic case the spatial decay rate may differ from the case of backscattering. The present research concerns the testing of generalized reciprocity for small circular cylinders using two‐dimensional finite elements. The calculated spatial decay rate for low‐frequency bistatic scattering follows the generalized reciprocity condition when the predicted decay rate (for the specified observation scattering angle) exceeds the spatial decay rate of the incident evanescent wave. This computational result includes agreement with the double decay‐rate case of backscattering. The calculations indicate that bistatic observation can significantly reduce the spatial decay rate of the signal dependence on burial depth. [Work supported by ONR.]

Focusing Bistatic SAR Data Using the Nonlinear Chirp Scaling Algorithm

Bistatic synthetic aperture radar data are more challenging to process than the common monostatic counterparts because the flight geometry is more complicated and the data are usually nonstationary. Whereas time-domain algorithms can handle general bistatic cases, they are very inefficient; therefore, frequency-domain methods are preferred. Several frequency-domain monostatic algorithms have been modified to handle a limited number of bistatic cases, but a general algorithm is sought, which can handle cases such as nonequal platform velocities, nonparallel flight tracks, and high squints. In this paper, we modify the nonlinear chirp scaling (NLCS) algorithm to handle a general case of bistatic data. The key is to use a linear range cell migration correction to reduce the range-azimuth coupling, an NLCS to precondition the data for azimuth compression, and a series expansion to obtain an accurate form of the signal spectrum. The azimuth nonstationarity is handled through the use of invariance regions. Simulations have shown that the modified NLCS algorithm can handle data with more complicated bistatic geometries than the previous algorithms.

Bistatic target detection using a time-reversal operator

Previous work has shown that time-reversal operator (TRO) methods can detect ocean targets using a time-reversal mirror [C. Gaumond, J. Acoust. Soc. Am 119, 976–990 (2006)]. To increase the signal-to-noise ratio, the TRO was measured by transmitting a set of orthogonal beams. The method is extended to a bistatic case where the receiver and transmitter are no longer collocated. Simulated deep ocean convergence zone and up-slope detection at 200 Hz will be discussed. The consequences of array geometry (horizontal and vertical) to beam orthogonality will be addressed. Specifically, under what conditions will a horizontal-receive array have enough aperture to measure a TRO of sufficient rank? It will be shown that the system must be able to both transmit and receive beams that are orthogonal with respect to the waveguide (and not simple free space arguments). [Work supported by the Office of Naval Research.]

Bistatic scattering from an anisotropic sea surface: Numerical comparison between the first-order SSA and the TSM models

The first-order small-slope approximation (SSA-1) model is used for numerical predictions of the normalized radar cross section (NRCS) of an anisotropic ocean surface in bistatic configurations for the K u -band radar frequency. The calculations were made by assuming the Elfouhaily et al. surface-height spectrum for fully developed seas. In the forward–backward case, the SSA-1 presents an agreement with the geometric optics limit of the Kirchhoff approximation results in the near-specular directions where it is well known that the last model works well. In the fully bistatic case, SSA-1 numerical results are compared with those of the two-scale model in several configurations as a function of wind speed, wind direction, incident/scattering angles and for co-and cross-polarization states. Good agreement between the two models is noted in the co-and cross-polarization case with a small difference of about 1–2 dB. But in certain configurations, the SSA-1 model tends to overestimate the radar cross section peak behaviour. This irregularity is discussed and interpreted. The main purpose of this paper is to analyse NRCS predictions based on the SSA-1 model in a fully bistatic configuration.

Bistatic SAR – translational invariant processing and experimental results

Bistatic synthetic aperture radar (SAR) uses a separated transmitter and receiver, flying on different platforms, which enables the exploitation of additional information contained in the bistatic reflectivity of targets. The feasibility of the bistatic concept has already been demonstrated although technical problems such as the synchronisation of the oscillators still persist. The processing of bistatic raw data has still not been resolved sufficiently, either. The omega-k (or range migration) processor has proven popular in the monostatic case because of its relatively simple implementation, its close-to-optimum performance and its numerical efficiency, but has not been generalised for the bistatic case. A method to eliminate the deviation of the bistatic range history from the monostatic hyperbolic shape in the omega-k domain making subsequent omega-k processing possible has been recently proposed, and generalisations of the omega-k algorithm to the bistatic case can also be found. Adding to the literature, an omega-k-type processor for the special case of equal-velocity vectors of transmitter and receiver, the so-called ‘spatial invariant’ case, is introduced. This processor is not optimum in the sense of the monostatic omega-k processor but degradation for wide ranges of geometrical parameters proved negligible. During flight testing in November 2003, different spatially invariant flight geometries were tested and high resolution bistatic SAR images were generated successfully.

BISAR MAPPING II TREATMENT, SIMULATION AND EXPERIMENTATION

This second part will be devoted to the development of a bistatic synthetic aperture processing method for radar imaging. Indeed, we establish various process that the received signal must undergo in order to estimate the target reflectivity in the bistatic case. High resolution image is obtained by two treatments on the table image of the bistatic received signal developed in the companion paper. The detail of the image reconstructing by a BISAR will be presented in this paper. The interest of this model is important, because it permits for a defined scenario generation of radar data which can be used in signal processing algorithms for target detection, identification and mapping. We present the simulation results for various scenes. These results are obtained by using two algorithms developed for BISAR imagery. Then we present the experimental results.

Performance of spaceborne bistatic synthetic aperture radar

This paper reports on a model developed for evaluating major system performance of a spaceborne bistatic synthetic aperture radar (SAR) for remote sensing applications. The procedure accounts for formation flying aspects. It is particularly aimed at comparison of monostatic and bistatic cases, and, as a test case, it is applied to study a novel configuration, based on a small satellite equipped with a receiving-only antenna orbiting in tandem with a large, noncooperative transmitting spacecraft, the Italian COSMO-SkyMed mission. Numerical results and plots show the effectiveness of the procedure as a mission design tool and put in evidence key issues and characteristics of the proposed spaceborne bistatic formation.

Acoustical imaging of underwater objects using the bistatic ramp response signals

The T-matrix methods have been successfully employed for underwater acoustical imaging techniques and the inverse analysis of acoustic scattering problems. Most inverse techniques use the backscattering signals in the acoustical far field to retrieve the shape and size information of an underwater object, such as the ramp response technique. This paper addresses a modified ramp response technique, which could be used to reconstruct the 3D image of an object for the bistatic case. This technique shows that the bistatic ramp response is proportional to the profile function of an underwater object based on the small bistatic angle assumption. The numerical examples demonstrate that the bistatic ramp response technique is still valid to obtain an excellent profile function even for the bistatic case with a fairly big bistatic angle. This bistatic ramp response technique allows us to reconstruct the 3D image of an underwater object with only one receiver.

Acoustical imaging of underwater objects using the bistatic ramp response signals

Underwater acoustical imaging techniques and the inverse analysis of acoustic scatteringproblems have now found many important engineering applications. Most of the inversetechniques use the backscattering signals in the acoustical far field to retrieve the shapeand size information of an underwater object, such as the ramp response technique.This paper addresses a modified ramp response technique, which could be usedto reconstruct the 3D image of an object for the bistatic case. This techniqueshows that the bistatic ramp response is proportional to the profile function of anunderwater object based on the small bistatic angle assumption. The numericalexamples demonstrate that the bistatic ramp response technique is still validto obtain an excellent profile function even for the bistatic case with a fairlylarge bistatic angle. The numerical results also suggest that, if the object is of amore slender shape, then its bistatic ramp response will be closer to the exactprofile function for a larger bistatic angle. Finally, a 3D image of a spheroid witha/b = 5 has been reconstructed using the bistatic ramp response signals in three incident directions.This bistatic ramp response technique allows us to reconstruct the 3D image of anunderwater object with only one receiver.

Monostatic and bistatic scattering from a density contrast surface

Chu’s formalism for the impulse response of a point source to a density contrast isovelocity wedge [J. Acoust. Soc. Am. 86, 1883–1896 (1989)] is of significant practical importance, since it facilitates the extension of wedge diffraction boundary scattering models to rough penetrable surfaces. The method is used here to study scattering from an experimental surface described by Li et al. [J. Acoust. Soc. Am. 96, 3715–3720 (1994)]. The geometry contains both interior and exterior wedges, and allows the diffracted scattering component to be studied independently of the reflected component. For density contrast values which emulate rigid boundary conditions, the formalism correctly models the experimental results, and duplicates predictions of the Biot–Tolstoy solution for a rigid wedge [J. Acoust. Soc. Am. 29, 381–391 (1957)]. The formalism is then used to investigate an assumption commonly made in boundary scattering work, i.e., that scattering levels can be effectively estimated by scaling the predictions of a rigid surface scattering model by the reflectivity of the surface. The results suggest that the assymption is most valid for monostatic (backscattering) configurations, and less good for bistatic cases, with increasing differences occurring between interior and exterior wedge geometries. [Work supported by ONR.]

Small-Slope Approximation Method: A Further Study of Vector Wave Scattering FROM Two-Dimensional Surfaces and Comparison with Experimental Data

This paper deals with the calculation of the scattering cross-section of polarized electromagnetic plane waves from 2-D metallic and dielectric randomly rough surfaces. The scattering cross- section of object is calculated by the Local Small Slope Approximation (SSA), the scattering cross-section is then compared with experimental data. In this paper, second order terms of the SSA method have been numerically implemented in order to obtain accurate results for a large range of slope. In this paper, we consider scattered and incident wave vectors in arbitrary directions, metallic and dielectric materials with complexpermittivity. Surfaces are considered with Gaussian probability density functions for surface heights and Gaussian or non-Gaussian correlation functions. The coherent and incoherent components of the electromagnetic intensity for cross- and co-polarization are calculated in the bistatic case and we give several comparisons of the theory with measured data.

High‐frequency bistatic cross sections of the ocean surface

An analysis leading to the first and second‐order bistatic cross sections of the ocean surface in the context of high‐frequency ground wave radar operation is presented. Initially, a pulsed dipole source is introduced into the previously derived electric field expressions for the bistatic reception of vertically polarized radiation scattered from rough surfaces that do not vary with time. To make application to the ocean, a time‐varying surface is introduced via a three‐dimensional Fourier series with two spatial variables and one temporal variable. The surface randomness is accounted for by allowing the Fourier coefficients to be zero‐mean Gaussian random variables. Fourier transformation of the autocorrelations of the resulting fields gives the appropriate power spectral densities. The latter are used in the bistatic radar range equation to produce the cross sections. The features of the bistatic case are seen to reduce to the well‐known monostatic results when the appropriate geometry is introduced. Illustrative comparisons of monostatic and bistatic reception are presented.

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ0 is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.

Bistatic reflection of electromagnetic waves from random rough surfaces: Application to the sea surface and snowy-covered

The scattering of waves by random rough surfaces has important applications in remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ 0 is dependent upon (at least) radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a random rough surface is analyzed using the Kirchhoff approximation (stationary phase, scalar approximation), the small perturbation model and the two-scale model. The first major new consideration in this paper is the polarimetric signature calculation as a function of the transmitter location and receiver location for a bistatic radio- link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, the study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various of the surface height rms and correlation length both normalized to the incident wave number (denoted by σ and L , respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross-section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.

Reconstruction of multilayered lossy dielectrics from one-sided plane wave impulse reflection responses: the bistatic case

Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media.

Seafloor scattering: Modeling and analysis of classification clues

Possibilities of scattering data inversion for various seabed properties are analyzed using recently developed models of acoustic bottom interaction. Different scattering mechanisms are considered giving the main contributions to total bottom scattering which are due to different types of medium irregularities: volume inhomogeneities of the sediment medium and roughness of its surface and internal interfaces. High-frequency model of scattering corresponds to sufficiently strong absorption and small penetration into the sediment such that the influence of seabed stratification is negligible. At lower frequencies, a layered seabed scattering model considers also refraction and interference effects due to sediment stratification as well as effects of elastic scattering and reflection from the basement supporting both compressional and shear waves. Frequency-angular dependencies of the scattering strength for both monostatic and bistatic cases are calculated and analyzed for various seabed types. Distinctive features are discussed which can be used as classification clues for determination of various parameters of the seafloor. Additional clues are revealed from an analysis of the spatial correlation function of the scattered field that can be used for distinguishing and/or separating the volume and roughness components of scattering.

Models of volume and roughness scattering in stratified seabeds

At high frequencies, two mechanisms of seabed scattering are usually taken into account which are due to roughness of the seabed surface (sediment–water interface) and volume inhomogeneities of near-surface sediment. The mean parameters of bottom medium are usually considered as independent from spatial coordinates. This corresponds to the assumption that sound penetration into the sediment is sufficiently small because of strong absorption. In this paper, more general models are considered where seabeds are assumed as statistically stratified (plane-layered on the average) with the mean parameters taken as various functions of depth. In particular, they can be step functions corresponding to different types of sediments in different layers. Another type of stratification corresponds to continuous depth-dependences and involve gradients of mean parameters. Effects of stratification are shown to be important at lower frequences due to scattering from internal interfaces and volume inhomogeneities of deep layers as well as the influence of regular refraction and reflection within seabed medium. As numerical examples, angular dependencies of the scattering strength in both monostatic and bistatic cases at different frequencies are calculated for seabeds of various types. Comparison with available data is presented and discussed. [Work supported by ONR.]

Effects of cross correlation between different types of medium perturbations on seabed scattering

Sound scattering from the seabed can be generally attributed to two major mechanisms connected with seabed roughness and volume inhomogeneities. Each of these two mechanisms in turn can contain different components. For unconsolidated (fluid) sediments, volume inhomogeneities are due to spatial fluctuations of two different parameters, the density and compressibility, or the density and compressional wave speed, with respect to their mean values. For elastic bottoms, one more fluctuating parameter, shear wave speed, is to be considered. The roughness component can be attributed to the water–sediment interface and to various internal interfaces in the seabed medium as well. In this paper, the effects of cross correlations between the roughness of different interfaces and between the volume fluctuations of different parameters, as well as possible volume–roughness correlations, are examined using a first-order perturbation model. Expressions for the bottom scattering cross section involve corresponding cross-correlation and cross-spectral matrices of seabed medium perturbations. Frequency-angular dependencies of the scattering strength in monostatic and bistatic cases are analyzed for various types of seabed stratification and correlated irregularities. Comparisons are presented for the cases of strongly correlated, anticorrelated, and partially correlated perturbations. Examples are given where the cross-correlation effects are important and should be taken into account in development of methods for inversions of seabed properties. [Work supported by ONR.]