Spectrally constrained channel shortening using least-squares optimisation

Channel shortening by least-squares (LS) optimisation is an attractive technique for its simplicity and computational efficiency. However, the method does not have suitable control over the frequency response of the shortened channel. As a result, the deep spectral nulls may inhibit some subcarriers to carry data bits and thereby reduce bit rate in multicarrier communication systems. Channel shortening is also proposed as a potential dereverberation technique in some recent research results. Again, shortening by LS optimisation leads to severe spectral distortion in the dereverberated speech signal. In this paper, we propose a spectrally constrained iterative LS minimisation algorithm that enforces spectral flatness in the shortening filter and thereby removes nulls without sacrificing the shortening performance. We also propose an optimal step-size for the iterative LS technique, which yields the fastest convergence rate for the gradient descent algorithm. The effectiveness of the proposed algorithm is tested for asymmetric digital subscriber line channels and speech dereverberation problems. The simulation results show that it outperforms the conventional techniques, resulting more subcarriers to carry bits when applied to communication channels and better quality of the speech signal when acoustic channels are considered.