On an RLS-like LMS adaptive filter

Abstract

A unified and generalized framework for a recursive least squares (RLS)-like least mean square (LMS) algorithm is proposed, which adopts the cost function of the RLS to minimize the mean square error. This paper aims to explore, in a systematic way, the corresponding ideas scattered and multiple-time re-invented in the literature, and introduces a unified approach in the same spirit as in [1], which relates LMS with the Kalman filter. The proposed alternative to the RLS is favored when the matrix inversion lemma is not useful, such as the case of multivariate or multichannel data where the input is not a vector. Furthermore, all the derivations are conducted in the quaternion domain and are hence generalizable to complexand real-valued models. The resulting algorithm has a neat form and a similar complexity to the RLS. Through experiments, the method is shown to exhibit performance close to or even better than the RLS algorithm. Other aspects, such as the choice of descent directions and variable stepsizes, are also discussed to support the analysis.

A Sparse Conjugate Gradient Adaptive Filter

“…In adaptive filtering, however, the sample-by-sample update of R n and b n causes a loss of the search direction conjugacy, which in turn results in loss of convergence. Thus, some modifications are necessary to relax the standard conjugacy constraint, e.g., see [34], [35], [36], [37]. The authors of [37] To develop CG algorithms for (1), first recognize that solving R n h = b n indirectly minimizes the quadratic function:…”

“…Thus, some modifications are necessary to relax the standard conjugacy constraint, e.g., see [34], [35], [36], [37]. The authors of [37] To develop CG algorithms for (1), first recognize that solving R n h = b n indirectly minimizes the quadratic function:…”

“…The above are summarized in Algorithm 1, which is essentially the memory-normalized LMS (m-NLMS) 1 proposed in [37].…”

“…A more recent class of adaptive filters is the conjugate gradient (CG) method [33], [34], [35], [36], [37], [38]. The CG adaptive filter can be viewed as an alternative algorithm which inherits the virtues of LMS and RLS, while mitigating some of their drawbacks -it has a faster convergence rate and is less sensitive to signal correlation than LMS, while being numerically more stable than the conventional RLS [37]. Surprisingly, given its effectiveness, CG has yet to receive considerable attention in the adaptive filtering literature.…”

Unconstraint 2-Level Cost Optimization Coding for Signal Processing

“…For the estimation of signal, in [7] an impulse response of channel effect is used, where a correlation logic is developed for a correlative approach for transmit and receive antenna. An approach of integrated LMS filter [8] is used for the optimization of interference estimation in a time frequency domain. The estimation performance under highly varying interference units for time dependent channel effect.…”