Joint domain space-time adaptive processing with small training data sets

The classical problem of optimum detection of a complex signal of unknown amplitude in colored Gaussian noise is revisited. The focus, however, is on adaptive system designs with limited training data sets and low computational optimization complexity. In this context, the target vector is equipped with a carefully selected orthogonal auxiliary vector for disturbance suppression with one complex space-time degree of freedom. Direct generalization leads to adaptive generation of a sequence of conditionally optimized weighted auxiliary vectors that are orthogonal to each other and to the target vector of interest. This approach appears here for the first time. Adaptive disturbance suppression with any desired number of complex degrees of freedom below the data dimension is therefore possible. It is shown that processing with multiple auxiliary vectors falls under well known flocking-matrix processing principles. The proposed blocking matrix, however, is data dependent, adaptively generated, and no data eigen analysis is involved. While the issues treated refer to general adaptive detection procedures, the presentation is given in the context of joint space-time adaptive processing for array radars.