This paper focuses on different distortion metrics in order to analyze the influence of the imperfect channel state information (CSI) on the improved successive stream selection algorithm that manages the interference in a heterogeneous network. The presented approach initially selects the streams from the user of the pico cell, continuing with the strongest streams among the remaining streams that increase the sum rate and satisfy the constraint that at least one stream is selected from each user. In order to reduce the interference, the channel matrices of the remaining streams are projected orthogonally to the virtual transmit and receive channels of the selected stream. The impact of the quantization distortion on the precoding and postcoding design is examined. The performance of two distortion metrics which are the Chordal distance and the Euclidean distance are compared for different number of quantization bits. The performance evaluations are obtained by considering different locations of small cells with respect to the macro cell.