loading page

Adaptive Filtering Based on Legendre Polynomials
  • +1
  • Lu Shen ,
  • Yuriy Zakharov ,
  • Long Shi ,
  • Benjamin Henson
Lu Shen
University of York

Corresponding Author:[email protected]

Author Profile
Yuriy Zakharov
Author Profile
Benjamin Henson
Author Profile


In system identification scenarios, classical adaptive filters, such as the recursive least squares (RLS) algorithm, predict the system impulse response. If a tracking delay is acceptable, interpolating estimators capable of providing more accurate estimates of time-varying impulse responses can be used; channel estimation in communications is an example of such applications. The basis expansion model (BEM) approach is known to be efficient for non-adaptive (block) channel estimation in communications. In this paper, we combine the BEM approach with the sliding-window RLS (SRLS) algorithm and propose a new family of adaptive filters. Specifically, we use the Legendre polynomials, thus the name the SRLS-L adaptive filter. The identification performance of the SRLS-L algorithm is evaluated analytically and via simulation. The analysis shows significant improvement in the estimation accuracy compared to the SRLS algorithm and a good match between the theoretical and simulation results. The performance is further investigated in application to the self-interference cancellation in full-duplex underwater acoustic communications, where a high estimation accuracy is required. A field experiment conducted in a lake shows significant improvement in the cancellation performance compared to the classical SRLS algorithm.