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Evaluation of a Registration-Based RangeDependence Compensation Method for a Bistatic STAP Radar Using Simulated, Random Snapshots D. Lapierre - Xavier Neyt* - Jacques G. Verly UniversityFabian of Liège, Department of Electrical Engineering and Computer Science, Sart-Tilman, Building B28, B-4000, Liège, Belgium *Royal Military Academy, Electrical Engineering Department, Avenue de la Renaissance, 30, B-1000, Bruxelles, Belgium {F.Lapierre; Jacques.Verly}@ulg.ac.be,
[email protected]
Abstract— We address the problem of detecting slowmoving targets using space-time adaptive processing (STAP). The construction of the optimum weights at each range implies the estimation of the clutter covariance matrix. This is typically done by straight averaging of snapshots at neighboring ranges. However, in most configurations, the snapshots’ statistics are range-dependent. Straight averaging thus results in poor performance. The proposed compensation method is designed to work on real-life snapshots. The method has been successfully tested on simulated, stochastic snapshots. An evaluation of performance is presented. Index Terms— Radar, bistatic, STAP, nonstationarity, range-dependence.
I. I NTRODUCTION
We consider a space-time adaptive processing (STAP) radar using an array of antenna elements and a coherent train of pulses and operating in a bistatic (BS) configuration, i.e., with physically-separated transmitter and receiver. BS radar systems are currently receiving increasing attention [1], [2]. The data collected by a STAP radar can be viewed as a sequence of vectors, called “snapshots.” Implementing the optimum STAP processor generally involves inverting the covariance matrix (CM) of the snapshots. This matrix is typically estimated by performing a straight averaging of single-sample CMs at neighboring ranges. However, in virtually all BS configurations, the snapshots’ statistics are not stationary with respect to (wrt) range. One of the most visible manifestations of this is the deformation with range of the 2D clutter power spectrum (PS), where the spectral dimensions correspond to spatial and Doppler frequencies. This results in a loss of performance. The lack of stationarity of the snapshots wrt range is referred to as the “range-dependence (RD) problem.” In [3], we proposed registration-based RD compensation methods that compute the CM at a reference range gate by averaging properly-transformed single-sample CMs at a series of neighboring range gates . This transformation, guided by analytical formulas describing the “direction-Doppler (DD) curves,” aims at bringing
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Fig. 1. Example (clutter) power spectra at one range. (a) Expected value of periodogram computed from theoretical covariance matrix. (b) Periodogram computed from one realization of a stochastic snapshot.
into registration with the clutter the clutter ridge at ridge at . We distinguished between “true-parameters (TP)” methods, which assume exact knowledge of the configuration parameters, and “estimated-parameters (EP)” methods, which estimate the parameters from the data. The methods in each class rely on a common “registrationbased compensation (RBC)” module. The EP methods rely on an additional “configuration-parameters estimation (CPE)” module. In [3], we assumed that the CM of the snapshots was known at each range. In contrast, here, we assume that all we have is a single realization of the snapshot at each range. We show how to modify the algorithms of [3] so they continue to perform under the new conditions and we evaluate the performance of the new algorithms. Figure 1 gives a preview of the level of complexity considered in this paper. Figure 1(a) shows the “interference + noise (I+N)” PS at a specific range for a known CM. Figure 1(b) shows the corresponding I+N PS estimated from a single realization of the stochastic snapshot at the same range. The clutter ridge has broken down into an “archipelago of small ridges.” Its appearance is “stochastic,” even for a given configuration and range. II. B ISTATIC RADAR CONFIGURATION The configuration geometry is shown in Fig. 2. The is at the center of an coordinate transmitter
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III. D IRECTION -D OPPLER
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The three important parameters associated with each scatterer are the range , the angular position , and the relative velocity . The related parameters that are more directly measured from the radar returns are the roundtrip delay , the spatial frequency , and the Doppler frequency . For a stationary , we have , , and , where is the carrier wavelength and is the speed of light. For any given configuration and range, all stationary at this range map onto a curve showing the relation between and for any such . This curve is called a “directionDoppler (DD)” curve. DD curves are typically represented in terms of the normalized frequencies and . Figure 3 shows that BS DD curves vary significantly with configuration and range. The variation of these curves with range is one of the most visible manifestations of the RD problem. We call the surface obtained by stacking DD curves for successive values of a DD surface. Figure 4 shows an example DD surface.
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