Abstract : In our increasingly mobile society we ﬁnd that hands-free operation of communication systems is becoming more and more the norm, whether we talk to other humans or to machine. There are signiﬁcant challenges in enabling high quality speech communication in adverse acoustic environments where the recorded microphone signals are corrupted by background noise, room reverberation, far-end echo signals and competing speech sources. Microphone arrays and more speciﬁcally beamforming methods are enabling technology for hands-free communication that is now viable and cost eﬀective. By oﬀering directional gain to improve the signal-to-noise ratio and taking the spatial correlation of sound ﬁeld into account to dereverberate the desired speech signal and to reduce noise and acoustic echoes, microphone arrays techniques play an important role in hands-free mobile telephony, distant-talker speech recognition, voice controlled systems, hearing aids, or audio monitoring. In this thesis, to tackle time-varying environments with both nonstationary signal characteristics and potentially moving sources, we consider the Generalized Sidelobe Canceller (GSC) which is an eﬃcient implementation of adaptive beamformers. However, one of the main drawback of this well used antenna are the self-cancellation phenomena of the desired signal caused by the signal leakage into the noise reference. To cope with this problem, we propose to take beneﬁt of the ability of the crosstalk-resistant adaptive noise canceller (CTRANC) to deal with crosstalk problem that, in fact, is the same as the signal leakage problem in the GSC. Thus, before describing the new feedback structure for the GSC, we ﬁrst give a complete analysis of the CTRANC and propose new adaptive algorithms in the frequency- domain. In addition, our study establish new results about the convergence properties and the existence of an equilibrium point for this feedback structure. Finally, results show that feedback GSC is an eﬀective solution to solve the leakage problem and to improve the performance.