Modeling the clutter re ection suppression algorithm in synthetic-aperture radar is considered in the article. The proposed algorithm allows one to increase the signal detection e ciency with closely located sources of clutter due to the use of a priori data of static objects of the infrastructure. Y =
The forming problem of the optimal algorithm for signal detection in the radar with synthesized aperture (SAR) under the presence of the clutter re ections from the local objects and the design of the e ciency estimation method of such detection are the main problems in the development air and satellite observational platforms for remote earth and water surfaces sensing system.
Devoted to the problems of signal processing within the SAR papers [1{3] pay great attention to research of the detection algorithms under clutter impact caused by the re ection from the underlying surface and noises. A SAR antenna pattern in some practical situations (along with the valid signal re ected from the multiple-unit target) has powerful clutter signals produced by the re ections from the clutter objects. Therefore, in these cases the processing algorithm should be formed accounting both the distribution target character and the clutter presence. Determination of the main principles of algorithm construction and the analysis methods present the content of this paper. Suppose the side-looking radar moves along the linear path. The range resolution cell has the target and clutter signals formed by the separate re ectors, which are distant at dit(i = 1; n) and dic(i = 1; N ) from the coordinate origin with the t step, and n and N are the numbers of the target and clutter re ectors respectively (Fig. 1). Under the discrete time processing, the vector of the observed data is presented in the following form:
X(dtn;k) =www exp( j 4R0 dtnrk) www (
RTC1 is the processing weight function, = Y T
Y; RTC =
TQT TT + RC1; RC =
CQC CT + RN;
QT = diag( T21 ; : : : ; T2n );
are the correlation matrices of vector (
QC = diag( C21 ; : : : ; C2N );
RN =
N2E where * is a complex conjugation, T is a transpose sign, E is the identity matrix with the noise dispersion N2 = 1. Using Woodbury formula for the determination of the optimal weight function the equation of the su cient statistics derives as where
= ZP Z T;
P = (E + QT TTRC1 T) 1QT; RC1 = RN1
RN1 C(E + QC CTRN1 C) 1QC CTRN1; Z = Y TRC1 T = Y TX (dit)
liY TX (dlc); N X l=1 n li = X ltXT(dtc)X (dic)
t=1 where lt is the matrix (11) element.
The schematic structure with the optimal algorithm (10) is shown on Fig. 2. The main functional operation in (13) is
Y TX (di) =
XM exp( j 4 k=1
R0 ditrk) that presents the chirp demodulation and the discrete Fourier transform (DFT) estimated for the spatial frequencies 2di= R0 that corresponding to all elements of target (clutters). 3
The relative gain of the optimal processing in comparison with the traditional one in SAR does not allow one to estimate the absolute values of the detection characteristics with multiple-unit sources of signals and clutters. On the other hand, the exact calculation of these characteristics is connected with the signi cant calculation di culties caused in the determination and integration of distributed statistics (10). Therefore, the e ciency estimation of the considered algorithm uses the method based on the Cherno bound [3], according to which the detection and false alarm probabilities are counted the formulas PD = exp[ ( (s) + (1
s)( _ (s) + 0:5(1 erfc[(1 s)p (s)]; s)2)(s))] (16) (8) (9) (10) (11) (12) (13) (14) (15) where (17) (18)
erfc[sp (s)]; (s) = ln
: : : 1 1 and _ (s) and (s) are the rst and second derivatives of (18), s = 0 : : : 1 is the dummy argument, is the number of independent tests (for SAR is the nlook, e.g. the number of used frequencies with multi frequency probing or the number of non-coherent summed synthesized images for partly coherent SAR working mode), P (Y =(T + C)); P (Y =C) are the probability densities of the observed vector under presence or absence of the target signal.
According to the case presented in the paper, formula (18) has the following form: (s) = 0:5 ln(det(RT) s + det(RC) (1 s) +0:5s ln(RT) + 0:5(1 s) ln(det(RC)): (19)
Using formulas (16){(19), the performance and detection characteristics are calculated. The perfomance curves shown in Fig. 3|5 are calculated for the case when there is only one target and one clutter, T2 = C2 = N2 = 1, and the number of observation periods is M = 1300.
In the graphs, the performance curves are also shown for the no-clutter case and for processing that does not use the algorithm presented in the article.
Detection characteristics of a multi-element target (n = 5) against a background of multiple-element clutter (N = 5) for N2 = 1; C2 = f0:1; 1; 0:1; 0:7; 0:5g, M = 100; = 2 for di erent target-clutter location cases (Fig. 6) are shown in Fig. 7.
From the presented curves it follows that with a greater spatial separation of the target and clutters the algorithm signi cantly increases the detection probability of the target.
Clutter re ection suppression algorithm in SAR presented in the article signi cantly improves the detection e ciency of the signals re ected from targets, which are locatered closely with clutter objects, even in cases where the clutters overlap targets.