Adaptive Filtering Based on Legendre Polynomials

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.