This concept covers systolic array architectures for QR decomposition via Givens rotations, applied to recursive least squares (RLS) adaptive filtering. The core principle is that a sequence of orthogonal rotation matrices can triangularize an exponentially-weighted data matrix without ever explicitly forming the orthogonal matrix Q, so that only the resulting upper-triangular factor R and updated vector U are propagated recursively as new data rows arrive. This belongs to the domain of adaptive signal processing and VLSI array processor design, where the algebraic QR-update recursion of RLS is mapped onto a pipelined systolic array of boundary (rotation-generating) and internal (rotation-applying) processing cells, with linear-independence conditions on the data columns and pipelining/cutset timing analysis determining array throughput.
This concept covers systolic array architectures for QR decomposition via Givens rotations, applied to recursive least squares (RLS) adaptive filtering. The core principle is that a sequence of ortho…