Subspace invariance: the RO-FST and TQR-SVD adaptive subspace tracking algorithms

Subspace decomposition and tracking are quintessential ingredients in high-resolution adaptive array processing. MUSIC, minimum norm, and eigenbeamforming (projection nulling) are examples. Unfortunately, high computational complexity limits the use of subspace tracking in real-time systems. Adaptive algorithms with lower complexities have been proposed to address this limitation. The authors compare two such algorithms: TQR-SVD and fast subspace tracking (FST). Both have lower complexity than traditional approaches, with FST´s complexity being lower than TQR-SVD´s by a factor of r (the dimension of the dominant subspace). The authors show that a simplified version of FST (called RO-FST-refinement only-FST) produces the same subspace estimates as the TQR-SVD algorithm