Fast system identification using prominent subspace LMS

In this paper, we propose prominent subspace least-mean-square (PS-LMS) algorithms for fast identification of time-varying system. It is shown that the dimensionality of system identification can be dramatically reduced if the unknown system is sparse in the sense that its parameter set has a skewed statistical distribution when expressed in a proper basis. In such cases, the system identification can be effectively carried out in a prominent subspace without introducing significant modeling error. A PS-LMS algorithm, that exploits this property, is proposed first. The proposed algorithm can significantly improve the convergence speed of the traditional LMS algorithm if the unknown systems are sparse and have long impulse responses in the time-domain. To reduce the modeling error of PS-LMS introduced by dimension reduction, an enhanced PS-LMS (PS-LMS+) algorithm is further proposed. It is shown that PS-LMS+ is able to reduce the modeling error of PS-LMS while preserving its fast convergence property. Finally, experiments were conducted to compare the performances of PS-LMS and PS-LMS+ with those of conventional LMS, recursive least squares (RLS), proportional normalized LMS (PNLMS), improved PNLMS (IPNLMS) and μ-law PNLMS (MPNLMS) algorithms on systems of different levels of sparseness in transform domain, and the results confirm the superiority of the proposed algorithms for sparse systems.