Computation reduction in space time adaptive processing (STAP) of radar signals using orthogonal wavelet decompositions

The STAP of radar signets involves solving a set of linear equations /spl Lambda/w=s. Here /spl Lambda/ is the correlation matrix of noise plus interference signals, w is the weight vector and s is the steering vector. The Weiner solution to estimate the optimum weight vector w/sub 0/ for a given s that minimizes the effect of the interference signal is: w/sub 0/=/spl Lambda//sup -1/s. That is /spl Lambda/ needs to be inverted and such an inversion using the direct approach is computationally expensive. Another solution is to apply the orthogonal similarity transformation to transform the set of linear equations to /spl Lambda//spl tilde/w/spl tilde/=s/spl tilde/ such that /spl Lambda//spl tilde/ is sparse and fast techniques such as the Cholesky algorithm can be applied to solve the transformed linear equations to obtain w/sub 0/. The Karhunen-Loeve orthogonal similarity transformation (KLT) provides the most sparse /spl Lambda//spl tilde/-a diagonal matrix. However, the KLT is computationally as expensive as inverting /spl Lambda/ directly. The wavelet transform (WT) can approximate KLT and is computationally less expensive. Hence, in this paper, we apply the WT to obtain sparse /spl Lambda//spl tilde/. We also discuss wavelet thresholding to further sparsen /spl Lambda//spl tilde/ and thus reduce the computational complexity of solving the transformed set of linear equations. The accuracy of estimates of w/sub 0/ using WT and KLT based approaches is compared in terms of suppressing jamming interference signals using signal-to-interference-noise-ratio (SINR) as the performance measure. The experimental results for four different radar interference signals are provided. The jamming suppression results indicate that the wavelet thresholding approach performs significantly better than the KLT.