A Systematic Procedure For Implementing The Blocking Matrix In Decomposed Form

The Generalized Sidelobe Canceller (GSC) is an important beam- forming structure for implementing adaptive linearly constrained beamformers. A significant feature of the GSC is that it effi- ciently eliminates the constraints such that the weights can be updated unconstrainedly in a reduce-dimensional space. The elimination of constraints is achieved by specifying a blocking matrix whose columns form a basis orthogonal to the constraints. For a given linearly-constrained minimization problem, the specification of the blocking matrix is not unique. However, the com- putational complexity of GSC depends entirely on the detailed composition of the blocking matrix. This paper presents a systematic procedure to construct the blocking matrix with effective implementation structure.