Phase-only Beam Broadening in Large Transmit Arrays Using Complex- Weight Gradient Descent

摘要

Day recently obtained phase-only element weights for a large transmit array of arbitrary geometry by optimizing complex weights using an objective function that penalized amplitude variation. He used gradient descent modified with a classic SVD technique to create point and sector nulls as desired. Here Day's approach is extended to allow for main-beam broadening as might be needed to illuminate multiple receive beams. This is done by adding a second objective term, one penalizing variation in array-factor amplitude across a grid of beamspace points covering the desired broad main-beam. The tension between the two objective terms turns out to be challenging to manage, and at this preliminary stage of algorithm development, parameter scheduling across a sequence of stages of the optimization is required to obtain good solutions.