تجزیه و تحلیل عملکرد از دو ساختار تخمین ماتریس کواریانس در درهم ریختگی ترکیبی نرمال

In this work we present a thorough performance analysis of two algorithms for estimating Toeplitz covariance matrices, the structured sample covariance matrix estimator (SCME) and the structured normalised SCME (NSCME), which are employed by adaptive radar detectors against Gaussian and compound-Gaussian clutter. Performance predictions are checked with real-life sea clutter data.

Adaptive radar detection against Gaussian noise has been largely investigated in the past [4] and [7]. The same detection problem against a background of correlated compound-Gaussian clutter has been investigated only recently [1] and [5]. Different adaptive detection algorithms have been proposed to operate against Gaussian and compound-Gaussian clutter; most of them make use of secondary data from adjacent range cells to estimate the clutter covariance matrix, but the estimation algorithms are different. In a previous paper [6], the performance of the sample covariance matrix estimator (SCME) [7] and the normalised SCME (NSCME) [1] against compound-Gaussian clutter have been investigated. These two estimators furnish estimates that are positive-definite and Hermitian, but not Toeplitz. When the actual covariance matrix is Hermitian–Toeplitz, performance improvement can be obtained by incorporating this constraint into the detector formulation, as shown in [4] and [5]. In this paper we expand on [6] to consider the case of clutter covariance matrices which have the Toeplitz structure. To this purpose we proceed as follows. In Section 2, brief descriptions are provided for the clutter model as well as the covariance estimators. In Section 3, the expression for the mean square error (mse) of the structured SCME is derived and compared to that of the structured NSCME obtained by Monte Carlo simulation. We also checked our performance prediction with real-life sea clutter data. Some concluding remarks are given in Section 4.

In this work we have investigated the performance of two clutter covariance matrix estimators which take into account the Toeplitz structure when the clutter is compound-Gaussian distributed. The results reported here (and those not reported for lack of space) suggest the following conclusions. The structured SCME is unbiased. The mse depends on m and on the shape of the speckle covariance sequence. It decreases with m and increases with ρτ and ρX. It decreases with ν and K; when ρτ≅1 the mse cannot be reduced beyond a given value increasing m or K, save for ν→∞. The structured NSCME is biased but asymptotically unbiased and consistent. The bias is quite insensitive to K and decreases with m, approaching to zero when m goes to infinity. The bias depends on ρX and is maximum for ρX≅0.9. The mse depends on ρX, and is maximum at ρX≅0.9. The error variance decreases with m and with the ratio K/m, while the mse decreases with K/m. For any given m and K, the structured NSCME outperforms the structured SCME for all values of ν and ρτ.