On the evaluation of multichannel blind system identification from the viewpoint of system equalization

The normalized projection misalignment (NPM), which is a measure of blind system identification (BSI), is studied in the context of multichannel speech dereverberation. The NPM errors are convolved with the multichannel equalization filters, and the angle between vectors obtained from channel-wise NPM errors convolving with equalization filters is computed. The mean squared error (MSE), which is a measure of system equalization, is computed both channel-wise and in total. The NPM is compared with the total MSE. Statistical results show that the angle is always close to p for 2-channel systems, and the channels-wise MSE is higher the total MSE, because the channel-wise equalized errors cancel each other substantially when they sum up; though the difference between NPM and MSE is large, the peaks and valleys of them agree with each other well among different systems; the NPM results among different systems vary in a large range.