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Many space-time adaptive signal processing algorithms rely on the estimates of the bases of signal and noise subspaces. Traditionally, these bases' estimates are formed using singular vectors of the data matrix or eigenvectors of the sample covariance matrix. These estimates are not very accurate and their use in subspace-based algorithms yield high errors. We present bases' estimates that are optimal to first order term in the noise matrix. The use of the first order optimal bases leads to significant improvement in the outcomes of subspace-based signal processing algorithms.