Abstract: Narrowband assumption is a general underlying assumption when the Minimum Variance Distortionless Response (MVDR) beamformer is applied to broadband signals such as speech.Under the narrowband assumption,the speech covariance matrix is a rank-1 matrix.In practice,however,the rank of the speech covariance matrix is usually greater than one because of the simplified narrowband signal model and unavoidable errors in the estimation process.We propose to reconstruct a rank-1 speech covariance matrix using the relative transfer function which is estimated from the generalized eigenvector of the speech covariance matrix and noise covariance matrix.Compared with the plain MVDR,the low rank approximation based algorithm is shown to be more robust to estimation errors.Experiments are conducted on the REVERB and CHiME-4 datasets,and the output SNRs are on average improved by 0.8 dB and 1.4 dB respectively,and the speech recognition accuracies are also improved.