We consider a sensor array located in an enclosure, where arbitrary transfer functions (TFs) relate the source signal and the sensors. The array is used for enhancing a signal contaminated by interference. Constrained minimum power adaptive beamforming, which has been suggested by Frost (1972) and, in particular, the generalized sidelobe canceler (GSC) version, which has been developed by Griffiths and Jim (1982), are the most widely used beamforming techniques. These methods rely on the assumption that the received signals are simple delayed versions of the source signal. The good interference suppression attained under this assumption is severely impaired in complicated acoustic environments, where arbitrary TFs may be encountered. In this paper, we consider the arbitrary TF case. We propose a GSC solution, which is adapted to the general TF case. We derive a suboptimal algorithm that can be implemented by estimating the TFs ratios, instead of estimating the TFs. The TF ratios are estimated by exploiting the nonstationarity characteristics of the desired signal. The algorithm is applied to the problem of speech enhancement in a reverberating room. The discussion is supported by an experimental study using speech and noise signals recorded in an actual room acoustics environment.