MIMO radar beampattern optimization with ripple control using sum-of-squares representation

In this paper, we introduce a MIMO radar transmit beam-pattern optimization method in which the peak sidelobe level and the ripple of the focus region can be controlled. Using the sum-of-squares representation of trigonometric polynomials, the beampattern optimization can be done without discretizing the angle domain. The disadvantage of this method is that the desired beampattern has to be a piece-wise trigonometric polynomial or piece-wise constant. Given that the actual beampattern is a trigonometric polynomial, this constraint on the desired beampattern does not incur a loss of performance. It is shown that considerable reduction in computational complexity with equal or smaller approximation error compared to the discretized optimization approach can be achieved when optimizing two-dimensional beampatterns.