A Second-Order Cone Bounding Algorithm for Robust Minimum Variance Beamforming
A Second-Order Cone Bounding Algorithm for Robust Minimum Variance Beamforming
N. Wong, V. Balakrishnan and T.-S. Ng
In
Switching and Learning in Feedback Systems
European Summer School on Multi-Agent Control, Maynooth, Ireland, September 8-10, 2003, Revised Lectures and Selected Papers,
R. Murray-Smith and R. Shorten, editors, Lectures Notes in Control and
Information Science, Springer, vol 3355, 2005.
Abstract:
We present a geometrical approach for designing robust minimum
variance (RMV) beamformers against steering vector
uncertainties. Conventional techniques enclose the uncertainties with
a convex set; the antenna weights are then designed to minimize the
maximum array output variance over this set. In contrast, we propose
to cover the uncertainty by a second-order cone (SOC). The
optimization problem, with optional robust interference rejection
constraints, then reduces to the minimization of the array output
variance over the intersection of the SOC and a hyperplane. This is
cast into a standard second-order cone programming (SOCP) problem and
solved efficiently. We study the computationally efficient case
wherein the uncertainties are embedded in complex-plane
trapezoids. The idea is then extended to arbitrary uncertainty
geometries. Effectiveness of the proposed approach over other schemes
and its fast convergence in signal power estimation are demonstrated
with numerical examples.
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