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24 October 1997 Recursive one-sided algorithm for subspace projection beamforming
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A recursive algorithm is described which performs approximate numerical rank estimation and subspace-projection of the least squares weight vector. Although it appears to work well in practice, being based upon a one-sided rank-revealing QR factorization, it lacks a formal guarantee to reveal the rank and it is more approximate than URV or Chan's rank-revealing QR factorization. However, it may be implemented very simply, requires little additional computation and, being based upon QR, it is able to exploit the established and numerically sound architecture of the Gentleman-Kung QRD-based RLS algorithm. It is implemented by redefining the cells in the array and performing additional updates so that the R matrix which is stored at any time approximates that which would be obtained for the QR factorization of the projected data matrix. Thus, the projected least-squares residual is output directly from the array and the projected weight vector is readily extracted if required.
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Mark A.G. Smith and Ian K. Proudler "Recursive one-sided algorithm for subspace projection beamforming", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997);

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