Comparison of optimum and linear prediction techniques for clutter cancellation S. Barbarossa E. D'Addio Prof. G. Galati Indexing terms: Radar and radionavigation, Filters and filtering, Signal processing, Detection Abstract: Two techniques for the adaptive cancel- lation of clutter in pulse radars are considered. The first, based on the maximisation of the signal/ interference improvement, leads to an eigenvector problem; simpler suboptimal structures according to a straightforward model with a minimum number of parameters are considered. The second, based on the linear prediction of the interference, leads to a whitening (or prediction error) filter. The basic performance of both techniques is evaluated in a typical radar environment of two clutter sources. 1 Introduction The detection problem of an a priori known signal in a background of coloured Gaussian noise (clutter) is exten- sively treated in the literature [1]. The solution of this problem depends on the optimality criterion selected. Two criteria are normally considered [2]: (i) maximisation of the so-called 'improvement factor' [3,4] (ii) minimisation of the residual clutter power. The first approach leads to an eigenvector problem [3] while the latter leads to a linear prediction problem [5]. Both the methods involve a FIR (finite impulse response) filter for the clutter rejection. The two techniques and their possible implementation in typical radar environments will be analysed in the following. In many radar environments [6] the main interference is due to a limited number of clutter sources (i.e. land, land plus rain, sea and rain) whose power is much greater than the target signal. Assuming the clutter to be a zero- mean Gaussian random process, it is completely charac- terised by its covariance matrix: M = E{c*c T ) (1) where c represents the vector containing the N clutter's samples received by the radar system. A commonly accepted model for the clutter spectrum is Barlow's one, Paper 5267F(E15), first received 11th November 1985 and in revised form 23rd September 1986 Sergio Barbarossa is with the Info-Corn Department, University of Rome 'La Sapienza', Via Eudossiana 18,00184 Roma, Italy Egidio D'Addio is with the Radar Department, Selenia SpA, Via Tibur- tina km 12.4, 00131 Roma, Italy Prof. Gaspare Galati is with the Department of Electronic Engineering, 'Tor Vergata' University of Rome, Via Orazio Raimondor s.n.c, 00173 Roma, Italy IEE PROCEEDINGS, Vol. 134, Pt. F, No. 3, JUNE 1987 which corresponds to a Gaussian shape for the power spectral density. The (i, fc)th element of the matrix M of one power-normalised clutter source is i, k) = exp {j2nf c (k - i) (2) where p is the 'correlation coefficient' at lag T (the pulse repetition interval of the radar) and f c is the mean Doppler frequency of the clutter. The normalised covariance matrix of L independent clutter sources is (3) where Q n is the power ratio of the nth source to the Lth one (Q L = 1), and M n is a matrix whose elements are M n (i, k) = exp {j2nf m (k - i) The figure commonly used to assess the performance of any linear filter for clutter rejection is the improvement factor (IF), defined as follows [4, 7]: IF = (SIR) 0 (SIR), (4) where (SIR)j and (SIR) 0 denote the signal/interference power ratios at the input and output of the filter, respec- tively. For a given FIR filter having coefficients W the expression for IF, when the Doppler frequency of the signal is a random variable, uniformly distributed in the (0, 1/T) interval, is IF = W H W W H M W (5) where the index H stands for conjugate transpose. The partial IF, i.e. the IF on the single (nth) clutter source, is defined as IF = W H W W H M-W 2 Optimal filtering techniques With reference to the above-mentioned optimisation cri- teria, for the clutter rejection, consider the maximisation of the IF in eqn. 5. The maximisation can be obtained by minimising the quadratic form W H • M • W with the constraint W H • W = constant [3]. As a consequence, the vector W is given by the eigen- vector E min associated with the minimum eigenvalue of M. = E m (6) 277