Adaptive Polynomial Filters and their Application to Nonlinear Acoustic Echo Cancellation

Bibliography 184 viii Contents 1 1 Introduction Linear adaptive filtering plays an important role in statistical signal processing and respective theoretical and practical results are well established [23]. In practice, however, nonlinear adaptive filtering often becomes desirable if the considered systems exhibit non-linear behaviour. Acoustic echo cancellation represents an important example for such situations. Acoustic echoes arise from acoustic coupling between the receive path and the transmit path of telecommunication systems. Such feedback occurs, e.g., with hands-free telecom-munication terminals or mobile phones. The general setup of the echo cancellation problem is illustrated in Fig. 1.1. The received signal of the far-end subscriber is output at PSfrag replacements AEC acoustic echo estimate of echo at near-end ¡ receive path (from far-end) ¢ transmit path (to far-end) Figure 1.1: General setup of the acoustic echo cancellation problem. the near-end loudspeaker. In case of hands-free communication systems, the loudspeaker signal is reflected at the enclosure and picked up by the microphone. In mobile phones, the loudspeaker and the microphone are mounted very closely. Thus, the signal leakage via their shell and the acoustic propagation path along the head of the user have to be taken into account, too. Due to this acoustic feedback, the loudspeaker signal reaches the transmit path of the telecommunication device and the far-end subscriber notices a delayed version of his own speech. This echo signal represents a very distracting disturbance for the far-end subscriber and can even inhibit interactive, full-duplex communication. The most common method to cope with these echoes is to place an acoustic echo canceller (AEC) in parallel to the propagation path of the echo signal. In the AEC, a digital replica of the echo signal is estimated which is then subtracted from the observed microphone signal. The AEC is usually realized on a digital signal processor (DSP) which 2