Solving the Max-Min SNR Optimization Problem of Array Antenna Signal Processing – An Iterative Approach using Convex Optimization Steps

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Authors
  1. Yasotharan, A.
Corporate Authors
Defence R&D Canada - Ottawa, Ottawa ONT (CAN)
Abstract
The Max-Min SNR optimization problem was formulated in the author¡¯s previous report ¡®DRDC Ottawa TM 2011-202¡¯, in the context of using an array antenna to protect a GPS receiver from interferences. There, it was proposed to choose the array combining weights to maximize the minimum SNR of the satellites. Towards solving this problem, a convex Min-Max Eigenvalue problem was stated, and it was shown that: 1) the min-max eigenvalue is an upper bound on the Max-Min SNR, 2) if the min-max eigenvalue is simple, the upper bound is tight and the corresponding eigenvector solves the Max-Min SNR problem. A combinatorial search was proposed for the case when the min-max eigenvalue is multiple. Recently, the author discovered that Sidiropoulos, Davidson, and Luo, writing in a communications context (physical-layer multicasting), had formulated two problems that are equivalent to the Max-Min SNR problem and proposed to solve them via Semidefinite Relaxation (SDR). This method sometimes finds optimum solutions, but in general gives suboptimum solutions. In this report, we derive another solution method and show by simulations that it can outperform the SDR method. We formulate an auxiliary optimization problem which is equivalent to the Max-Min SNR problem and solve the auxiliary problem by an iterative process which uses convex optimization. We mathematically prove some convergence properties of the iterative process and show by simulations that by repeating the process several t

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Report Number
DRDC-OTTAWA-TM-012-120 — Technical Memorandum
Date of publication
01 Dec 2012
Number of Pages
52
DSTKIM No
CA037823
CANDIS No
537594
Format(s):
Electronic Document(PDF)

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