Optimal linear constraints and subspace adaptive filtering

Linearly constrained adaptive filters can remove interference while preserving signals of interest. However, in many applications the interference and signals are distributed throughout a large space. In such cases, fully adaptive filtering is difficult to implement. Instead, data is typically partitioned into subspaces. Then, within each subspace, interference is cancelled. Finally, the resulting subspace signals are recombined. This procedure is used in many fields, such as wideband radar, sonar, communications, and radio astronomy (relevant techniques include subband adaptive beamforming/filtering, adaptive subarrays, frequency jump burst processing, and space-time adaptive processing). The purpose of this paper is to: (1) quantify the performance associated with subspace adaptation, and (2) enumerate techniques to improve its performance. In particular, we formulate a new class of “optimal linear subspace constraints.” The benefits of these techniques are quantified and compared