Persymmetric structure has been utilized in space-time adaptive processing for heterogeneous environment, which leads to some detection methods based on persymmetric structure, such as persymmetric adaptive matched filter (PS-AMF). However, when the sample support is extremely limited, these methods still suffer the serious degradation in detection performance due to the large error in estimating covariance matrix. In this paper, an asymptotically optimal convex linear combination between transformed sample covariance matrix and identity matrix is considered herein to improve PS-AMF. The asymptotically optimal convex linear combination is conducive to diminishing the estimate error in estimating the transformed covariance matrix by weighting the transformed sample covariance matrix and identity matrix. Furthermore, the asymptotically optimal convex linear combination is improved by the reutilization of the convex linear combination, and the corresponding coefficients are derived. Then, the detection performance of the proposed method is approximately analyzed. At last, numerical simulations show that the proposed method performs well, compared with its counterparts, when the sample support is extremely limited.

中文翻译：

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基于渐近最优凸线性组合的非对称检测

过对称结构已被应用于异构环境的时空自适应处理中，从而产生了一些基于过对称结构的检测方法，例如过对称自适应匹配滤波器（PS-AMF）。然而，当样本支持极其有限时，由于估计协方差矩阵的误差较大，这些方法仍然会严重降低检测性能。本文考虑变换样本协方差矩阵和单位矩阵之间的渐近最优凸线性组合来改进PS-AMF。渐进最优凸线性组合通过对变换样本协方差矩阵和单位矩阵进行加权，有利于减小变换协方差矩阵估计时的估计误差。进一步利用凸线性组合对渐近最优凸线性组合进行改进，并推导出相应的系数。然后，对所提出方法的检测性能进行了近似分析。最后，数值模拟表明，当样本支持极其有限时，与同类方法相比，所提出的方法表现良好。