Steady-State Performance of an Adaptive Combined MISO Filter Using the Multichannel Affine Projection Algorithm

Abstract

The combination of adaptive filters is an effective approach to improve filtering performance. In this paper, we investigate the performance of an adaptive combined scheme between two adaptive multiple-input single-output (MISO) filters, which can be easily extended to the case of multiple outputs. In order to generalize the analysis, we consider the multichannel affine projection algorithm (APA) to update the coefficients of the MISO filters, which increases the possibility of exploiting the capabilities of the filtering scheme. Using energy conservation relations, we derive a theoretical behavior of the proposed adaptive combination scheme at steady state. Such analysis entails some further theoretical insights with respect to the single channel combination scheme. Simulation results prove both the validity of the theoretical steady-state analysis and the effectiveness of the proposed combined scheme.

Variable-Step-Size Efficient Proportionate Affine Projection Sign Algorithms

“…Observing (9), one can find that µ v is only associated with the small µ rather than μ and µ, which is simpler than the old CSS way [15,17] and means that the proposed CSS method is only needed with one filter to run the whole time in comparison with the conventional combination method (CGCI-M-IPAPSA) [11,18,19]. The modified ( 9) is the step size of the proposed CSS-GCI-M-IPAPSA, which can be viewed as a new variable-step-size (VSS) GCI-M-IPAPSA.…”

“…According to formula (19) and [8], it is clear that the SGCI-M-IPAPSA is an extension of the APSA, which indicates that the cost function of the SGCI-M-IPAPSA is the same as the APSA, and the SGCI-M-IPAPSA has extra operations on the input signal u(k τ ). To ensure the stability of the APSA, ∥ ∆w(k τ ) ∥ 2 2 ≤ µ 2 ≪ 1 from [8].…”