A Nonorthogonal Joint Block Diagonalization Algorithm Avoiding Degenerate Solutions

Abstract

The joint block diagonalization algorithm is instrumental to the convolution blind signal separation. However, the nonorthogonal joint block diagonalization algorithm based on a Weighted least-squares (WLS) criterion sometimes converges to the degenerate or trivial solution. It is simple to avoid the trivial solution by adding some constraint on the de-mixing matrix. But the degenerate solution is hard to be excluded. This paper probes the phenomenon of the degenerate solution. By adding a new penalty function to the WLS criterion, an efficient algorithm which can avoid the degenerate solution is developed. Through the theoretical derivation and numerical simulation, we can make the conclusion that the proposed algorithm is more robust and not sensitive to the square or non-square mixing matrix.