Beampattern optimization by minimization of quartic polynomial

Beampattern synthesis is a common problem in array signal processing. Recently, methods for beampattern optimization using multiple simultaneously transmitted waveforms have been published in the context of MIMO radar. In this paper, we formulate the beampattern optimization problem as minimization of a multivariate quartic polynomial. The advantage of this approach is that iterative line searches are not needed and that the low-rank case can be solved directly without finding the minima of the full-rank system. The method does not guarantee convergence to the global minimum, but numerical examples provided demonstrate that results comparable to the other approaches are achieved.