Probing signal waveforms play a central role in the signal processing performance of a MIMO radar. In practice, for a given desired beam pattern, we need to design a probing signal waveform whose beam pattern closely matches the desired one and whose auto-correlation and cross-correlation sidelobes are kept low. The latter properties are important to mitigate undesirable interference caused by multiple targets or scatterers. In this paper, we present an efficient optimization method to design a

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... constant modulus probing signal which can synthesize a desired beam pattern while maximally suppressing both the auto-correlation and cross-correlation sidelobes at/between given spacial angles. We formulate this problem as an unconstrained minimization of a fourth order trigonometric polynomial and propose an efficient quasi-Newton iterative algorithm to solve it. Besides, we give an analysis of the local minima of the fourth order trigonometric polynomial and prove that any local minima is a 1/2-approximation of its global optimal solution. Numerical examples show that the proposed approach compares favorably with the existing approach.