A Fast Blocking Matrix Generating Algorithm for Generalized Sidelobe Canceller Beamformer in High Speed Rail Like Scenario

A fast algorithm to generate the Blocking Matrix for Generalized Sidelobe Canceller (GSC) beamforming is proposed in this paper. The proposed algorithm uses a Simplified Zero Placement Algorithm (SZPA) to directly generate the column vectors of the Blocking Matrix using the polynomial method. The constrained signal incoming angles are converted to spatial frequency and designated as zero locations in the
Z
domain. Independent vectors that span the whole left null space of the constraint matrix is then built using a simple shift operation. The algorithm also supports the derivative constraints used for robust beamforming. Compared to the conventional methods based on Singular Value Decomposition (SVD), the SZPA algorithm can generate Blocking Matrix more than 9 times faster for scenarios with 15 constraints and will be even more advantageous for more constraints. The Blocking Matrix generated by the SZPA and SVD methods is then implemented in the same GSC architecture for performance evaluation. The numerical simulation confirms that the same overall optimum state performance and learning speed can be achieved. By reducing the calculation time of blocking matrix from 1.541ms of SVD method to 0.168ms, the proposed SZPA algorithm is fast and insensitive to the number of constraints as the required calculation time incremental for each additional constraint with SZPA is only around 1/16 of SVD method. This makes it suitable for scenarios like train to infrastructure communication in High Speed Rail (HSR) where there are multiple constraints and frequent constraints update is required.