Set‐membership improved normalised subband adaptive filter algorithms for acoustic echo cancellation

Abstract

In order to improve the performances of recently-presented improved normalized subband adaptive filter (INSAF) and proportionate INSAF algorithms for highly noisy system, this paper proposes their set-membership versions by exploiting the theory of set-membership filtering. Apart from obtaining smaller steady-state error, the proposed algorithms significantly reduce the overall computational complexity. In addition, to further improve the steady-state performance for the algorithms, their smooth variants are developed by using the smoothed absolute subband output errors to update the step sizes. Simulation results in the context of acoustic echo cancellation have demonstrated the superiority of the proposed algorithms.Keywords. Acoustic echo cancellation, improved normalized subband adaptive filter, low signal-noise-ratio, setmembership filtering, sparse system IntroductionIn modern communication network, hands-free telephony and teleconference, the acoustic echo is a common problem that must be eliminated to improve the call quality. In recent decades, therefore, acoustic echo cancellation (AEC) based on adaptive filter has obtained significant attention [1]- [3]. Naturally, AEC is also a system identification problem (i.e., identifying the impulse response of the echo path), but it imposes several characteristics on the adaptive filter. Namely, 1) the input is the speech signal which is nonstationary and highly colored, and 2) the impulse response of the echo path is long and sparse. Owing to its simplicity and ease of implementation, the normalized least mean square (NLMS) algorithm is often used in AEC. However, the NLMS algorithm will suffer from slow convergence when the input signal is colored.To overcome this drawback, the affine projection (AP) family uses K past input signal vectors for updating the filter' coefficients, at each iteration, where K is the projection order [4], [5]. The convergence rate of AP increases as K increases, but meanwhile the steady-state error and computational cost of that become large. To reduce the computational complexity, several AP algorithms with variable projection order [6] as well as fast AP algorithms [7] were opened.

Improved simple set‐membership affine projection algorithm for sparse system modelling: Analysis and implementation

“…Indeed, these algorithms update the adaptive filter coefficients only when the input data brings enough innovation [1, 2]. The SM algorithms have been applied to many problems such as acoustic echo cancellation [3], beamforming [4], wind profile prediction [5], etc. Among the SM algorithms, the SM affine projection (SM‐AP) algorithm [6] is one of the most widely studied.…”

A nonparametric variable step-size subband adaptive filtering algorithm for acoustic echo cancellation

“…Although these algorithms have fast convergence rates and low misalignment, when the input signal is colored, the convergence rate may decay significantly [17] . Therefore, in order to improve the convergence rate of the colored input signal, Lee et al proposed a normalized subband adaptive filtering (NSAF) algorithm [18] , which converts the input signal into subband signal and whitens the subband signal.…”

Torque identification based on LMS adaptive delay inverse system method

“…The frequency domain method is based on the system linear assumption, which cannot identify the load of the nonlinear system. Compared with the frequency domain method, the time domain method does not need to perform Fourier Transform on the acquired signal, and the identification precision is not affected by the signal acquisition method [4][5][6][7][8]. In addition, the time domain method is capable of identifying transient shock loads.…”