where A straight forward approach for BSS is to identify the unknown system first and then to apply the inverse of the identified system to the measurement signals in order to restore the signal sources. This approach can lead to problems of instability. Therefore it is desired that the demixing system be estimated based on the observations of mixed signals. The simplest case is the instantaneous mixing in which matrix is a constant matrix with all elements being scalar values. In practical applications such as hands free telephony or mobile communications where multipath propagation is evident, mixing is convolutive, in. | 18 Chapter 2 where s i si stv 1 t. A straight forward approach for BSS is to identify the unknown system first and then to apply the inverse of the identified system to the measurement signals in order to restore the signal sources. This approach can lead to problems of instability. Therefore it is desired that the demixing system be estimated based on the observations of mixed signals. The simplest case is the instantaneous mixing in which matrix H i H is a constant matrix with all elements being scalar values. In practical applications such as hands free telephony or mobile communications where multipath propagation is evident mixing is convolutive in which situation BSS is much more difficult due to the added complexity of the mixing system. The frequency domain approaches are considered to be effective to separate signal sources in convolutive cases but another difficult issue the inherent permutation and scaling ambiguity in each individual frequency bin arises which makes the perfect reconstruction of signal sources almost impossible 10 . Therefore it is worthwhile to develop an effective approach in the time domain for convolutive mixing systems that don t have an exceptionally large amount of variables. Joho and Rahbar 1 proposed a BSS approach based on joint diagonalization of the output signal correlation matrix using gradient and Newton optimization methods. However the approaches in 1 are limited to the instantaneous mixing cases whilst in the time domain. 3. OPTIMIZATION OF INSTANTANEOUS BSS This section gives a brief review of the algorithms proposed in 1 . Assuming that the sources are statistically independent and non-stationary observing the signals over K different time slots we define the following noise free instantaneous BSS problem. In the instantaneous mixing cases both the mixing and demixing matrices are constant that is H i H and W i W. In this case the reconstructed signal vector can be expressed as The instantaneous correlation matrix of
