STATE-SPACE ARCHITECTURE OF THE PARTITIONED-BLOCK-BASED ACOUSTIC ECHO CONTROLLER Fabian Kuech, Edwin Mabande Fraunhofer IIS Am Wolfsmantel 33 D-91058 Erlangen, Germany fabian.kuech@iis.fraunhofer.de Gerald Enzner Institute of Communication Acoustics Ruhr-Universit¨ at Bochum D-44780 Bochum, Germany gerald.enzner@rub.de ABSTRACT Acoustic echo cancellation has traditionally employed basi- cally all variants known from deterministic adaptive filter design, such as least mean-square (LMS), recursive least-squares (RLS), and frequency-domain adaptive filters (FDAF). More recently, a stochas- tic adaptive filter design based on the concept of acoustic state-space modeling of the echo path has been introduced to accommodate for an ever sought unification of adaptive filtering and adaptation con- trol. The corresponding Kalman filter theory has been formulated for single-channel, multi-channel, and nonlinear echo cancellation problems. This paper closes an important gap by formulating the state-space model and the corresponding adaptive algorithm for the partitioned-block filtering structure which is especially relevant in practice. This structure allows for the use of significantly longer filter lengths in comparison to previous work, and for the flexible design and implementation of acoustic echo cancellers for widely differing acoustic conditions. Index Terms— acoustic echo control, adaptive filtering 1. INTRODUCTION AND RELATION TO PRIOR WORK Acoustic echo represents a well-known distraction in hands-free voice communication systems. Due to acoustic coupling between the loudspeaker and the microphone of a telecommunication termi- nal, the far-end talker receives a delayed version of his own voice that will eventually inhibit fluent conversation. The general setup of the acoustic echo problem is illustrated in Fig. 1. The far-end signal x(n) is played back by the near-end loudspeaker. The microphone signal y(n) then picks up the echo d(n) together with the near-end signal s(n), including background noise and local speech. The adaptive acoustic echo canceler (AEC) regenerates and subtracts an estimate of the echo from the microphone signal. A variety of adaptive filter structures and methods to control the adaptation in adverse environments have been proposed for this purpose [1, 2, 3]. Typically, due to time-varying acoustics and echo-path undermodel- ing, the AEC is not always able to sufficiently remove the echo and, thus, a residual echo suppressor (RES) is introduced after the AEC AEC RES d(n) s(n) x(n) y(n) e(n) ˆ d(n) z(n) Fig. 1. Setup of the acoustic echo cancellation problem. to attenuate remaining echo components [4, 5, 6, 7]. In modern communication systems such as Voice-over-IP ser- vices or high-quality video conferencing systems, sampling rates of 16 kHz and higher are used. This implies a significant increase in computational complexity for the AEC. Moreover, the convergence speed of time-domain adaptive filters is usually not sufficient in case of high sampling rates and long echo paths. Besides subband adap- tive filters [8, 9], frequency-domain adaptive filters using block pro- cessing are well-known solutions to address both of these issues [10, 11, 12, 13]. However, the required length of the frequency transform becomes relatively large for long echo paths, leading to potential algorithmic noise, e.g., when implementing the AEC with fixed point arithmetic in embedded devices. In this case, approaches based on partitioned-block filtering [14, 15, 16, 17, 18] are more suit- able, as they allow for flexible designs, e.g., a separate choice of the transformation length and the time span covered by the AEC, and the filter length is not bounded to powers of two as typically used in fast fourier transform implementations. Moreover, a reduction of the transformation length also reduces the algorithmic delay caused by post-processing stages such as the RES. By using a partitioned block structure, approximations of the RES filter to reduce the delay as, e.g., proposed in [19], can be avoided. The step-size parameter to control the adaptation of the filter co- efficients is generally a critical component of the AEC. An overview of popular methods is found, e.g., in [1, 2, 3]. The alternative ap- proach in [6] relies on an acoustic state-space model of the echo path to deduce a robust and efficient frequency-domain adaptive fil- ter with inherent step-size control, however, not considering block partitioning. This approach has analogously been applied to multi- channel as well as nonlinear adaptive filtering problems [20, 21]. In this paper, we extend the approach in [6] to the partitioned-block fil- tering structure, which is of practical importance for the application of AECs for widely varying acoustic conditions. In our paper, Sec. 2 revises partitioned-block adaptive filtering based on state-space modeling in analogy with [6]. Sec. 3 shows that the corresponding exact Kalman filter in the block-frequency- domain can be simplified into a diagonalized version. This light approximation leads to a variant of the known multi-delay adaptive filter [14], but providing inherent adaptive step-size control. While the resulting step-size turns out to be similar to the one in [15], we propose a different estimator for the required system distance, again in analogy with the non-partitioned algorithm in [6]. In Sec. 4, a so far unique relation between the step-size parameters of all parti- tions and the optimum RES filter is derived in order to efficiently obtain the RES coefficients. Simulation results in Sec. 5 confirm the suitability of the proposed architecture for acoustic echo control. 2014 IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP) 978-1-4799-2893-4/14/$31.00 ©2014 IEEE 1309