Ramos P., Martin R., Lopez A., Salinas A., Masgrau E.

This paper presents a Filtered-x version of the Stochastic Partial Updates (SPU) LMS algorithm and compares its performance with other algorithms in the context of an Active Noise Control (ANC) system. In order to lessen computational complexity, Partial Updates (PU) adaptive algorithms update only a portion of the coefficients during each period. However, PU algorithms suffer from one drawback: their convergence rate is reduced in proportion to the decimating factor N, defined as the filter length divided by the number of coefficients updated per iteration. The Filtered-x Sequential LMS algorithm with step-size Gain (Gm-FxSeq LMS) proposed in previous works is based on Sequential PU and on the controlled increase -or gain- in the step-size of the adaptive filter. The inherent reduction in convergence rate due to PU is compensated by increasing the step-size. The analysis of the Gm-FxSeq LMS prevents from the use of certain frequencies corresponding to notches which appear in the step-size gain of the adaptive algorithm. The strategy here proposed, Filtered-x Stochastic Partial Updates LMS algorithm with Gain in step-size (Gm-FxSPU LMS), overcomes the limitations imposed by the notches in the gain of the Gm-FxSeq LMS algorithm at the cost of a slight increase in the computational load. The subset of coefficients updated per iteration is sampled at random. Not being so computationally efficient as the Sequential version, the Gm-FxSPU LMS algorithm is, however, operationally less intensive than the conventional FxLMS. The Gm-FxSPU LMS was tested by simulation and was also evaluated in a DSP-based implementation. Even when the number of operations per iteration is significantly reduced due to PU, the affordable increase in step-size compensates the lack of adaptation of most of the coefficients. To sum up, this strategy results in an algorithm with lower computational cost and a performance very close to the conventional FxLMS.